Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [70,6,Mod(1,70)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(70, 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("70.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 70 = 2 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 70.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: | \(11.2268673869\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 70.1 |
$q$-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 | ||||||||
\(3\) | −17.0000 | −1.09055 | −0.545275 | − | 0.838257i | \(-0.683575\pi\) | ||||
−0.545275 | + | 0.838257i | \(0.683575\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | −68.0000 | −0.771136 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | 46.0000 | 0.189300 | ||||||||
\(10\) | 100.000 | 0.316228 | ||||||||
\(11\) | −715.000 | −1.78166 | −0.890829 | − | 0.454339i | \(-0.849876\pi\) | ||||
−0.890829 | + | 0.454339i | \(0.849876\pi\) | |||||||
\(12\) | −272.000 | −0.545275 | ||||||||
\(13\) | 331.000 | 0.543212 | 0.271606 | − | 0.962408i | \(-0.412445\pi\) | ||||
0.271606 | + | 0.962408i | \(0.412445\pi\) | |||||||
\(14\) | −196.000 | −0.267261 | ||||||||
\(15\) | −425.000 | −0.487709 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −1699.00 | −1.42584 | −0.712920 | − | 0.701245i | \(-0.752628\pi\) | ||||
−0.712920 | + | 0.701245i | \(0.752628\pi\) | |||||||
\(18\) | 184.000 | 0.133856 | ||||||||
\(19\) | −1718.00 | −1.09179 | −0.545895 | − | 0.837854i | \(-0.683810\pi\) | ||||
−0.545895 | + | 0.837854i | \(0.683810\pi\) | |||||||
\(20\) | 400.000 | 0.223607 | ||||||||
\(21\) | 833.000 | 0.412189 | ||||||||
\(22\) | −2860.00 | −1.25982 | ||||||||
\(23\) | −3950.00 | −1.55696 | −0.778480 | − | 0.627669i | \(-0.784009\pi\) | ||||
−0.778480 | + | 0.627669i | \(0.784009\pi\) | |||||||
\(24\) | −1088.00 | −0.385568 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 1324.00 | 0.384109 | ||||||||
\(27\) | 3349.00 | 0.884109 | ||||||||
\(28\) | −784.000 | −0.188982 | ||||||||
\(29\) | 4579.00 | 1.01106 | 0.505529 | − | 0.862810i | \(-0.331298\pi\) | ||||
0.505529 | + | 0.862810i | \(0.331298\pi\) | |||||||
\(30\) | −1700.00 | −0.344862 | ||||||||
\(31\) | 6756.00 | 1.26266 | 0.631329 | − | 0.775516i | \(-0.282510\pi\) | ||||
0.631329 | + | 0.775516i | \(0.282510\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | 12155.0 | 1.94299 | ||||||||
\(34\) | −6796.00 | −1.00822 | ||||||||
\(35\) | −1225.00 | −0.169031 | ||||||||
\(36\) | 736.000 | 0.0946502 | ||||||||
\(37\) | −16518.0 | −1.98360 | −0.991798 | − | 0.127816i | \(-0.959203\pi\) | ||||
−0.991798 | + | 0.127816i | \(0.959203\pi\) | |||||||
\(38\) | −6872.00 | −0.772012 | ||||||||
\(39\) | −5627.00 | −0.592400 | ||||||||
\(40\) | 1600.00 | 0.158114 | ||||||||
\(41\) | 18876.0 | 1.75368 | 0.876840 | − | 0.480782i | \(-0.159647\pi\) | ||||
0.876840 | + | 0.480782i | \(0.159647\pi\) | |||||||
\(42\) | 3332.00 | 0.291462 | ||||||||
\(43\) | 2258.00 | 0.186231 | 0.0931157 | − | 0.995655i | \(-0.470317\pi\) | ||||
0.0931157 | + | 0.995655i | \(0.470317\pi\) | |||||||
\(44\) | −11440.0 | −0.890829 | ||||||||
\(45\) | 1150.00 | 0.0846577 | ||||||||
\(46\) | −15800.0 | −1.10094 | ||||||||
\(47\) | −537.000 | −0.0354593 | −0.0177296 | − | 0.999843i | \(-0.505644\pi\) | ||||
−0.0177296 | + | 0.999843i | \(0.505644\pi\) | |||||||
\(48\) | −4352.00 | −0.272638 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 2500.00 | 0.141421 | ||||||||
\(51\) | 28883.0 | 1.55495 | ||||||||
\(52\) | 5296.00 | 0.271606 | ||||||||
\(53\) | −10984.0 | −0.537119 | −0.268560 | − | 0.963263i | \(-0.586548\pi\) | ||||
−0.268560 | + | 0.963263i | \(0.586548\pi\) | |||||||
\(54\) | 13396.0 | 0.625159 | ||||||||
\(55\) | −17875.0 | −0.796782 | ||||||||
\(56\) | −3136.00 | −0.133631 | ||||||||
\(57\) | 29206.0 | 1.19065 | ||||||||
\(58\) | 18316.0 | 0.714925 | ||||||||
\(59\) | −25956.0 | −0.970751 | −0.485375 | − | 0.874306i | \(-0.661317\pi\) | ||||
−0.485375 | + | 0.874306i | \(0.661317\pi\) | |||||||
\(60\) | −6800.00 | −0.243855 | ||||||||
\(61\) | 39188.0 | 1.34843 | 0.674215 | − | 0.738535i | \(-0.264482\pi\) | ||||
0.674215 | + | 0.738535i | \(0.264482\pi\) | |||||||
\(62\) | 27024.0 | 0.892833 | ||||||||
\(63\) | −2254.00 | −0.0715488 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 8275.00 | 0.242932 | ||||||||
\(66\) | 48620.0 | 1.37390 | ||||||||
\(67\) | 4416.00 | 0.120183 | 0.0600914 | − | 0.998193i | \(-0.480861\pi\) | ||||
0.0600914 | + | 0.998193i | \(0.480861\pi\) | |||||||
\(68\) | −27184.0 | −0.712920 | ||||||||
\(69\) | 67150.0 | 1.69794 | ||||||||
\(70\) | −4900.00 | −0.119523 | ||||||||
\(71\) | −31880.0 | −0.750538 | −0.375269 | − | 0.926916i | \(-0.622450\pi\) | ||||
−0.375269 | + | 0.926916i | \(0.622450\pi\) | |||||||
\(72\) | 2944.00 | 0.0669278 | ||||||||
\(73\) | −5018.00 | −0.110211 | −0.0551053 | − | 0.998481i | \(-0.517549\pi\) | ||||
−0.0551053 | + | 0.998481i | \(0.517549\pi\) | |||||||
\(74\) | −66072.0 | −1.40261 | ||||||||
\(75\) | −10625.0 | −0.218110 | ||||||||
\(76\) | −27488.0 | −0.545895 | ||||||||
\(77\) | 35035.0 | 0.673403 | ||||||||
\(78\) | −22508.0 | −0.418890 | ||||||||
\(79\) | −27977.0 | −0.504352 | −0.252176 | − | 0.967681i | \(-0.581146\pi\) | ||||
−0.252176 | + | 0.967681i | \(0.581146\pi\) | |||||||
\(80\) | 6400.00 | 0.111803 | ||||||||
\(81\) | −68111.0 | −1.15347 | ||||||||
\(82\) | 75504.0 | 1.24004 | ||||||||
\(83\) | 37644.0 | 0.599792 | 0.299896 | − | 0.953972i | \(-0.403048\pi\) | ||||
0.299896 | + | 0.953972i | \(0.403048\pi\) | |||||||
\(84\) | 13328.0 | 0.206095 | ||||||||
\(85\) | −42475.0 | −0.637655 | ||||||||
\(86\) | 9032.00 | 0.131685 | ||||||||
\(87\) | −77843.0 | −1.10261 | ||||||||
\(88\) | −45760.0 | −0.629911 | ||||||||
\(89\) | −17216.0 | −0.230387 | −0.115193 | − | 0.993343i | \(-0.536749\pi\) | ||||
−0.115193 | + | 0.993343i | \(0.536749\pi\) | |||||||
\(90\) | 4600.00 | 0.0598620 | ||||||||
\(91\) | −16219.0 | −0.205315 | ||||||||
\(92\) | −63200.0 | −0.778480 | ||||||||
\(93\) | −114852. | −1.37699 | ||||||||
\(94\) | −2148.00 | −0.0250735 | ||||||||
\(95\) | −42950.0 | −0.488263 | ||||||||
\(96\) | −17408.0 | −0.192784 | ||||||||
\(97\) | −63175.0 | −0.681736 | −0.340868 | − | 0.940111i | \(-0.610721\pi\) | ||||
−0.340868 | + | 0.940111i | \(0.610721\pi\) | |||||||
\(98\) | 9604.00 | 0.101015 | ||||||||
\(99\) | −32890.0 | −0.337269 | ||||||||
\(100\) | 10000.0 | 0.100000 | ||||||||
\(101\) | −29250.0 | −0.285314 | −0.142657 | − | 0.989772i | \(-0.545565\pi\) | ||||
−0.142657 | + | 0.989772i | \(0.545565\pi\) | |||||||
\(102\) | 115532. | 1.09952 | ||||||||
\(103\) | −149189. | −1.38562 | −0.692809 | − | 0.721121i | \(-0.743627\pi\) | ||||
−0.692809 | + | 0.721121i | \(0.743627\pi\) | |||||||
\(104\) | 21184.0 | 0.192055 | ||||||||
\(105\) | 20825.0 | 0.184337 | ||||||||
\(106\) | −43936.0 | −0.379801 | ||||||||
\(107\) | 83742.0 | 0.707105 | 0.353552 | − | 0.935415i | \(-0.384974\pi\) | ||||
0.353552 | + | 0.935415i | \(0.384974\pi\) | |||||||
\(108\) | 53584.0 | 0.442054 | ||||||||
\(109\) | 105377. | 0.849532 | 0.424766 | − | 0.905303i | \(-0.360356\pi\) | ||||
0.424766 | + | 0.905303i | \(0.360356\pi\) | |||||||
\(110\) | −71500.0 | −0.563410 | ||||||||
\(111\) | 280806. | 2.16321 | ||||||||
\(112\) | −12544.0 | −0.0944911 | ||||||||
\(113\) | −122754. | −0.904356 | −0.452178 | − | 0.891928i | \(-0.649353\pi\) | ||||
−0.452178 | + | 0.891928i | \(0.649353\pi\) | |||||||
\(114\) | 116824. | 0.841918 | ||||||||
\(115\) | −98750.0 | −0.696294 | ||||||||
\(116\) | 73264.0 | 0.505529 | ||||||||
\(117\) | 15226.0 | 0.102830 | ||||||||
\(118\) | −103824. | −0.686424 | ||||||||
\(119\) | 83251.0 | 0.538917 | ||||||||
\(120\) | −27200.0 | −0.172431 | ||||||||
\(121\) | 350174. | 2.17431 | ||||||||
\(122\) | 156752. | 0.953484 | ||||||||
\(123\) | −320892. | −1.91248 | ||||||||
\(124\) | 108096. | 0.631329 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | −9016.00 | −0.0505927 | ||||||||
\(127\) | −219196. | −1.20593 | −0.602967 | − | 0.797766i | \(-0.706015\pi\) | ||||
−0.602967 | + | 0.797766i | \(0.706015\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | −38386.0 | −0.203095 | ||||||||
\(130\) | 33100.0 | 0.171779 | ||||||||
\(131\) | −96682.0 | −0.492229 | −0.246115 | − | 0.969241i | \(-0.579154\pi\) | ||||
−0.246115 | + | 0.969241i | \(0.579154\pi\) | |||||||
\(132\) | 194480. | 0.971494 | ||||||||
\(133\) | 84182.0 | 0.412658 | ||||||||
\(134\) | 17664.0 | 0.0849820 | ||||||||
\(135\) | 83725.0 | 0.395385 | ||||||||
\(136\) | −108736. | −0.504111 | ||||||||
\(137\) | 187288. | 0.852528 | 0.426264 | − | 0.904599i | \(-0.359830\pi\) | ||||
0.426264 | + | 0.904599i | \(0.359830\pi\) | |||||||
\(138\) | 268600. | 1.20063 | ||||||||
\(139\) | 176894. | 0.776562 | 0.388281 | − | 0.921541i | \(-0.373069\pi\) | ||||
0.388281 | + | 0.921541i | \(0.373069\pi\) | |||||||
\(140\) | −19600.0 | −0.0845154 | ||||||||
\(141\) | 9129.00 | 0.0386701 | ||||||||
\(142\) | −127520. | −0.530710 | ||||||||
\(143\) | −236665. | −0.967819 | ||||||||
\(144\) | 11776.0 | 0.0473251 | ||||||||
\(145\) | 114475. | 0.452158 | ||||||||
\(146\) | −20072.0 | −0.0779307 | ||||||||
\(147\) | −40817.0 | −0.155793 | ||||||||
\(148\) | −264288. | −0.991798 | ||||||||
\(149\) | −199078. | −0.734611 | −0.367306 | − | 0.930100i | \(-0.619720\pi\) | ||||
−0.367306 | + | 0.930100i | \(0.619720\pi\) | |||||||
\(150\) | −42500.0 | −0.154227 | ||||||||
\(151\) | 471583. | 1.68312 | 0.841561 | − | 0.540162i | \(-0.181637\pi\) | ||||
0.841561 | + | 0.540162i | \(0.181637\pi\) | |||||||
\(152\) | −109952. | −0.386006 | ||||||||
\(153\) | −78154.0 | −0.269912 | ||||||||
\(154\) | 140140. | 0.476168 | ||||||||
\(155\) | 168900. | 0.564677 | ||||||||
\(156\) | −90032.0 | −0.296200 | ||||||||
\(157\) | −72054.0 | −0.233297 | −0.116648 | − | 0.993173i | \(-0.537215\pi\) | ||||
−0.116648 | + | 0.993173i | \(0.537215\pi\) | |||||||
\(158\) | −111908. | −0.356630 | ||||||||
\(159\) | 186728. | 0.585756 | ||||||||
\(160\) | 25600.0 | 0.0790569 | ||||||||
\(161\) | 193550. | 0.588476 | ||||||||
\(162\) | −272444. | −0.815623 | ||||||||
\(163\) | 385334. | 1.13597 | 0.567987 | − | 0.823038i | \(-0.307722\pi\) | ||||
0.567987 | + | 0.823038i | \(0.307722\pi\) | |||||||
\(164\) | 302016. | 0.876840 | ||||||||
\(165\) | 303875. | 0.868931 | ||||||||
\(166\) | 150576. | 0.424117 | ||||||||
\(167\) | −542957. | −1.50652 | −0.753259 | − | 0.657724i | \(-0.771519\pi\) | ||||
−0.753259 | + | 0.657724i | \(0.771519\pi\) | |||||||
\(168\) | 53312.0 | 0.145731 | ||||||||
\(169\) | −261732. | −0.704920 | ||||||||
\(170\) | −169900. | −0.450890 | ||||||||
\(171\) | −79028.0 | −0.206676 | ||||||||
\(172\) | 36128.0 | 0.0931157 | ||||||||
\(173\) | 370953. | 0.942331 | 0.471166 | − | 0.882045i | \(-0.343833\pi\) | ||||
0.471166 | + | 0.882045i | \(0.343833\pi\) | |||||||
\(174\) | −311372. | −0.779662 | ||||||||
\(175\) | −30625.0 | −0.0755929 | ||||||||
\(176\) | −183040. | −0.445414 | ||||||||
\(177\) | 441252. | 1.05865 | ||||||||
\(178\) | −68864.0 | −0.162908 | ||||||||
\(179\) | −754172. | −1.75929 | −0.879646 | − | 0.475629i | \(-0.842220\pi\) | ||||
−0.879646 | + | 0.475629i | \(0.842220\pi\) | |||||||
\(180\) | 18400.0 | 0.0423289 | ||||||||
\(181\) | 303840. | 0.689364 | 0.344682 | − | 0.938720i | \(-0.387987\pi\) | ||||
0.344682 | + | 0.938720i | \(0.387987\pi\) | |||||||
\(182\) | −64876.0 | −0.145180 | ||||||||
\(183\) | −666196. | −1.47053 | ||||||||
\(184\) | −252800. | −0.550469 | ||||||||
\(185\) | −412950. | −0.887091 | ||||||||
\(186\) | −459408. | −0.973680 | ||||||||
\(187\) | 1.21478e6 | 2.54036 | ||||||||
\(188\) | −8592.00 | −0.0177296 | ||||||||
\(189\) | −164101. | −0.334162 | ||||||||
\(190\) | −171800. | −0.345254 | ||||||||
\(191\) | −186271. | −0.369455 | −0.184728 | − | 0.982790i | \(-0.559140\pi\) | ||||
−0.184728 | + | 0.982790i | \(0.559140\pi\) | |||||||
\(192\) | −69632.0 | −0.136319 | ||||||||
\(193\) | 92504.0 | 0.178759 | 0.0893794 | − | 0.995998i | \(-0.471512\pi\) | ||||
0.0893794 | + | 0.995998i | \(0.471512\pi\) | |||||||
\(194\) | −252700. | −0.482060 | ||||||||
\(195\) | −140675. | −0.264930 | ||||||||
\(196\) | 38416.0 | 0.0714286 | ||||||||
\(197\) | −736368. | −1.35185 | −0.675926 | − | 0.736969i | \(-0.736256\pi\) | ||||
−0.675926 | + | 0.736969i | \(0.736256\pi\) | |||||||
\(198\) | −131560. | −0.238485 | ||||||||
\(199\) | −481620. | −0.862128 | −0.431064 | − | 0.902321i | \(-0.641862\pi\) | ||||
−0.431064 | + | 0.902321i | \(0.641862\pi\) | |||||||
\(200\) | 40000.0 | 0.0707107 | ||||||||
\(201\) | −75072.0 | −0.131065 | ||||||||
\(202\) | −117000. | −0.201747 | ||||||||
\(203\) | −224371. | −0.382144 | ||||||||
\(204\) | 462128. | 0.777476 | ||||||||
\(205\) | 471900. | 0.784269 | ||||||||
\(206\) | −596756. | −0.979780 | ||||||||
\(207\) | −181700. | −0.294733 | ||||||||
\(208\) | 84736.0 | 0.135803 | ||||||||
\(209\) | 1.22837e6 | 1.94520 | ||||||||
\(210\) | 83300.0 | 0.130346 | ||||||||
\(211\) | 189531. | 0.293072 | 0.146536 | − | 0.989205i | \(-0.453188\pi\) | ||||
0.146536 | + | 0.989205i | \(0.453188\pi\) | |||||||
\(212\) | −175744. | −0.268560 | ||||||||
\(213\) | 541960. | 0.818499 | ||||||||
\(214\) | 334968. | 0.499999 | ||||||||
\(215\) | 56450.0 | 0.0832852 | ||||||||
\(216\) | 214336. | 0.312580 | ||||||||
\(217\) | −331044. | −0.477240 | ||||||||
\(218\) | 421508. | 0.600710 | ||||||||
\(219\) | 85306.0 | 0.120190 | ||||||||
\(220\) | −286000. | −0.398391 | ||||||||
\(221\) | −562369. | −0.774534 | ||||||||
\(222\) | 1.12322e6 | 1.52962 | ||||||||
\(223\) | −22597.0 | −0.0304291 | −0.0152145 | − | 0.999884i | \(-0.504843\pi\) | ||||
−0.0152145 | + | 0.999884i | \(0.504843\pi\) | |||||||
\(224\) | −50176.0 | −0.0668153 | ||||||||
\(225\) | 28750.0 | 0.0378601 | ||||||||
\(226\) | −491016. | −0.639476 | ||||||||
\(227\) | −998117. | −1.28563 | −0.642816 | − | 0.766020i | \(-0.722234\pi\) | ||||
−0.642816 | + | 0.766020i | \(0.722234\pi\) | |||||||
\(228\) | 467296. | 0.595326 | ||||||||
\(229\) | −854644. | −1.07695 | −0.538476 | − | 0.842641i | \(-0.681000\pi\) | ||||
−0.538476 | + | 0.842641i | \(0.681000\pi\) | |||||||
\(230\) | −395000. | −0.492354 | ||||||||
\(231\) | −595595. | −0.734380 | ||||||||
\(232\) | 293056. | 0.357463 | ||||||||
\(233\) | 1.25818e6 | 1.51829 | 0.759144 | − | 0.650922i | \(-0.225618\pi\) | ||||
0.759144 | + | 0.650922i | \(0.225618\pi\) | |||||||
\(234\) | 60904.0 | 0.0727120 | ||||||||
\(235\) | −13425.0 | −0.0158579 | ||||||||
\(236\) | −415296. | −0.485375 | ||||||||
\(237\) | 475609. | 0.550021 | ||||||||
\(238\) | 333004. | 0.381072 | ||||||||
\(239\) | −706581. | −0.800142 | −0.400071 | − | 0.916484i | \(-0.631015\pi\) | ||||
−0.400071 | + | 0.916484i | \(0.631015\pi\) | |||||||
\(240\) | −108800. | −0.121927 | ||||||||
\(241\) | 616330. | 0.683551 | 0.341775 | − | 0.939782i | \(-0.388972\pi\) | ||||
0.341775 | + | 0.939782i | \(0.388972\pi\) | |||||||
\(242\) | 1.40070e6 | 1.53747 | ||||||||
\(243\) | 344080. | 0.373804 | ||||||||
\(244\) | 627008. | 0.674215 | ||||||||
\(245\) | 60025.0 | 0.0638877 | ||||||||
\(246\) | −1.28357e6 | −1.35233 | ||||||||
\(247\) | −568658. | −0.593074 | ||||||||
\(248\) | 432384. | 0.446417 | ||||||||
\(249\) | −639948. | −0.654103 | ||||||||
\(250\) | 62500.0 | 0.0632456 | ||||||||
\(251\) | 190842. | 0.191201 | 0.0956004 | − | 0.995420i | \(-0.469523\pi\) | ||||
0.0956004 | + | 0.995420i | \(0.469523\pi\) | |||||||
\(252\) | −36064.0 | −0.0357744 | ||||||||
\(253\) | 2.82425e6 | 2.77397 | ||||||||
\(254\) | −876784. | −0.852724 | ||||||||
\(255\) | 722075. | 0.695395 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −1.13094e6 | −1.06809 | −0.534045 | − | 0.845456i | \(-0.679329\pi\) | ||||
−0.534045 | + | 0.845456i | \(0.679329\pi\) | |||||||
\(258\) | −153544. | −0.143610 | ||||||||
\(259\) | 809382. | 0.749729 | ||||||||
\(260\) | 132400. | 0.121466 | ||||||||
\(261\) | 210634. | 0.191394 | ||||||||
\(262\) | −386728. | −0.348059 | ||||||||
\(263\) | −1.67377e6 | −1.49213 | −0.746065 | − | 0.665874i | \(-0.768059\pi\) | ||||
−0.746065 | + | 0.665874i | \(0.768059\pi\) | |||||||
\(264\) | 777920. | 0.686950 | ||||||||
\(265\) | −274600. | −0.240207 | ||||||||
\(266\) | 336728. | 0.291793 | ||||||||
\(267\) | 292672. | 0.251248 | ||||||||
\(268\) | 70656.0 | 0.0600914 | ||||||||
\(269\) | −630942. | −0.531629 | −0.265815 | − | 0.964024i | \(-0.585641\pi\) | ||||
−0.265815 | + | 0.964024i | \(0.585641\pi\) | |||||||
\(270\) | 334900. | 0.279580 | ||||||||
\(271\) | −372476. | −0.308088 | −0.154044 | − | 0.988064i | \(-0.549230\pi\) | ||||
−0.154044 | + | 0.988064i | \(0.549230\pi\) | |||||||
\(272\) | −434944. | −0.356460 | ||||||||
\(273\) | 275723. | 0.223906 | ||||||||
\(274\) | 749152. | 0.602828 | ||||||||
\(275\) | −446875. | −0.356332 | ||||||||
\(276\) | 1.07440e6 | 0.848972 | ||||||||
\(277\) | 867010. | 0.678930 | 0.339465 | − | 0.940619i | \(-0.389754\pi\) | ||||
0.339465 | + | 0.940619i | \(0.389754\pi\) | |||||||
\(278\) | 707576. | 0.549112 | ||||||||
\(279\) | 310776. | 0.239021 | ||||||||
\(280\) | −78400.0 | −0.0597614 | ||||||||
\(281\) | −1.94498e6 | −1.46943 | −0.734716 | − | 0.678375i | \(-0.762685\pi\) | ||||
−0.734716 | + | 0.678375i | \(0.762685\pi\) | |||||||
\(282\) | 36516.0 | 0.0273439 | ||||||||
\(283\) | 1.18501e6 | 0.879543 | 0.439771 | − | 0.898110i | \(-0.355059\pi\) | ||||
0.439771 | + | 0.898110i | \(0.355059\pi\) | |||||||
\(284\) | −510080. | −0.375269 | ||||||||
\(285\) | 730150. | 0.532476 | ||||||||
\(286\) | −946660. | −0.684351 | ||||||||
\(287\) | −924924. | −0.662829 | ||||||||
\(288\) | 47104.0 | 0.0334639 | ||||||||
\(289\) | 1.46674e6 | 1.03302 | ||||||||
\(290\) | 457900. | 0.319724 | ||||||||
\(291\) | 1.07398e6 | 0.743467 | ||||||||
\(292\) | −80288.0 | −0.0551053 | ||||||||
\(293\) | 33669.0 | 0.0229119 | 0.0114560 | − | 0.999934i | \(-0.496353\pi\) | ||||
0.0114560 | + | 0.999934i | \(0.496353\pi\) | |||||||
\(294\) | −163268. | −0.110162 | ||||||||
\(295\) | −648900. | −0.434133 | ||||||||
\(296\) | −1.05715e6 | −0.701307 | ||||||||
\(297\) | −2.39454e6 | −1.57518 | ||||||||
\(298\) | −796312. | −0.519449 | ||||||||
\(299\) | −1.30745e6 | −0.845760 | ||||||||
\(300\) | −170000. | −0.109055 | ||||||||
\(301\) | −110642. | −0.0703888 | ||||||||
\(302\) | 1.88633e6 | 1.19015 | ||||||||
\(303\) | 497250. | 0.311149 | ||||||||
\(304\) | −439808. | −0.272948 | ||||||||
\(305\) | 979700. | 0.603036 | ||||||||
\(306\) | −312616. | −0.190857 | ||||||||
\(307\) | −27043.0 | −0.0163760 | −0.00818802 | − | 0.999966i | \(-0.502606\pi\) | ||||
−0.00818802 | + | 0.999966i | \(0.502606\pi\) | |||||||
\(308\) | 560560. | 0.336702 | ||||||||
\(309\) | 2.53621e6 | 1.51109 | ||||||||
\(310\) | 675600. | 0.399287 | ||||||||
\(311\) | 2.14919e6 | 1.26001 | 0.630004 | − | 0.776592i | \(-0.283053\pi\) | ||||
0.630004 | + | 0.776592i | \(0.283053\pi\) | |||||||
\(312\) | −360128. | −0.209445 | ||||||||
\(313\) | −2.67052e6 | −1.54076 | −0.770381 | − | 0.637583i | \(-0.779934\pi\) | ||||
−0.770381 | + | 0.637583i | \(0.779934\pi\) | |||||||
\(314\) | −288216. | −0.164966 | ||||||||
\(315\) | −56350.0 | −0.0319976 | ||||||||
\(316\) | −447632. | −0.252176 | ||||||||
\(317\) | −250514. | −0.140018 | −0.0700090 | − | 0.997546i | \(-0.522303\pi\) | ||||
−0.0700090 | + | 0.997546i | \(0.522303\pi\) | |||||||
\(318\) | 746912. | 0.414192 | ||||||||
\(319\) | −3.27398e6 | −1.80136 | ||||||||
\(320\) | 102400. | 0.0559017 | ||||||||
\(321\) | −1.42361e6 | −0.771134 | ||||||||
\(322\) | 774200. | 0.416115 | ||||||||
\(323\) | 2.91888e6 | 1.55672 | ||||||||
\(324\) | −1.08978e6 | −0.576733 | ||||||||
\(325\) | 206875. | 0.108642 | ||||||||
\(326\) | 1.54134e6 | 0.803255 | ||||||||
\(327\) | −1.79141e6 | −0.926457 | ||||||||
\(328\) | 1.20806e6 | 0.620019 | ||||||||
\(329\) | 26313.0 | 0.0134023 | ||||||||
\(330\) | 1.21550e6 | 0.614427 | ||||||||
\(331\) | 1.05899e6 | 0.531277 | 0.265639 | − | 0.964073i | \(-0.414417\pi\) | ||||
0.265639 | + | 0.964073i | \(0.414417\pi\) | |||||||
\(332\) | 602304. | 0.299896 | ||||||||
\(333\) | −759828. | −0.375495 | ||||||||
\(334\) | −2.17183e6 | −1.06527 | ||||||||
\(335\) | 110400. | 0.0537473 | ||||||||
\(336\) | 213248. | 0.103047 | ||||||||
\(337\) | −2.85025e6 | −1.36712 | −0.683562 | − | 0.729893i | \(-0.739570\pi\) | ||||
−0.683562 | + | 0.729893i | \(0.739570\pi\) | |||||||
\(338\) | −1.04693e6 | −0.498454 | ||||||||
\(339\) | 2.08682e6 | 0.986246 | ||||||||
\(340\) | −679600. | −0.318828 | ||||||||
\(341\) | −4.83054e6 | −2.24962 | ||||||||
\(342\) | −316112. | −0.146142 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | 144512. | 0.0658427 | ||||||||
\(345\) | 1.67875e6 | 0.759344 | ||||||||
\(346\) | 1.48381e6 | 0.666329 | ||||||||
\(347\) | 1.89141e6 | 0.843259 | 0.421630 | − | 0.906768i | \(-0.361458\pi\) | ||||
0.421630 | + | 0.906768i | \(0.361458\pi\) | |||||||
\(348\) | −1.24549e6 | −0.551304 | ||||||||
\(349\) | −1.04232e6 | −0.458075 | −0.229038 | − | 0.973418i | \(-0.573558\pi\) | ||||
−0.229038 | + | 0.973418i | \(0.573558\pi\) | |||||||
\(350\) | −122500. | −0.0534522 | ||||||||
\(351\) | 1.10852e6 | 0.480259 | ||||||||
\(352\) | −732160. | −0.314956 | ||||||||
\(353\) | −2.30309e6 | −0.983725 | −0.491862 | − | 0.870673i | \(-0.663684\pi\) | ||||
−0.491862 | + | 0.870673i | \(0.663684\pi\) | |||||||
\(354\) | 1.76501e6 | 0.748581 | ||||||||
\(355\) | −797000. | −0.335651 | ||||||||
\(356\) | −275456. | −0.115193 | ||||||||
\(357\) | −1.41527e6 | −0.587716 | ||||||||
\(358\) | −3.01669e6 | −1.24401 | ||||||||
\(359\) | −1.67594e6 | −0.686315 | −0.343157 | − | 0.939278i | \(-0.611496\pi\) | ||||
−0.343157 | + | 0.939278i | \(0.611496\pi\) | |||||||
\(360\) | 73600.0 | 0.0299310 | ||||||||
\(361\) | 475425. | 0.192006 | ||||||||
\(362\) | 1.21536e6 | 0.487454 | ||||||||
\(363\) | −5.95296e6 | −2.37119 | ||||||||
\(364\) | −259504. | −0.102657 | ||||||||
\(365\) | −125450. | −0.0492877 | ||||||||
\(366\) | −2.66478e6 | −1.03982 | ||||||||
\(367\) | 94663.0 | 0.0366872 | 0.0183436 | − | 0.999832i | \(-0.494161\pi\) | ||||
0.0183436 | + | 0.999832i | \(0.494161\pi\) | |||||||
\(368\) | −1.01120e6 | −0.389240 | ||||||||
\(369\) | 868296. | 0.331972 | ||||||||
\(370\) | −1.65180e6 | −0.627268 | ||||||||
\(371\) | 538216. | 0.203012 | ||||||||
\(372\) | −1.83763e6 | −0.688496 | ||||||||
\(373\) | −953536. | −0.354867 | −0.177433 | − | 0.984133i | \(-0.556779\pi\) | ||||
−0.177433 | + | 0.984133i | \(0.556779\pi\) | |||||||
\(374\) | 4.85914e6 | 1.79631 | ||||||||
\(375\) | −265625. | −0.0975418 | ||||||||
\(376\) | −34368.0 | −0.0125367 | ||||||||
\(377\) | 1.51565e6 | 0.549219 | ||||||||
\(378\) | −656404. | −0.236288 | ||||||||
\(379\) | 3.88824e6 | 1.39045 | 0.695225 | − | 0.718792i | \(-0.255305\pi\) | ||||
0.695225 | + | 0.718792i | \(0.255305\pi\) | |||||||
\(380\) | −687200. | −0.244132 | ||||||||
\(381\) | 3.72633e6 | 1.31513 | ||||||||
\(382\) | −745084. | −0.261244 | ||||||||
\(383\) | 2.93636e6 | 1.02285 | 0.511425 | − | 0.859328i | \(-0.329118\pi\) | ||||
0.511425 | + | 0.859328i | \(0.329118\pi\) | |||||||
\(384\) | −278528. | −0.0963920 | ||||||||
\(385\) | 875875. | 0.301155 | ||||||||
\(386\) | 370016. | 0.126402 | ||||||||
\(387\) | 103868. | 0.0352537 | ||||||||
\(388\) | −1.01080e6 | −0.340868 | ||||||||
\(389\) | 1.70377e6 | 0.570871 | 0.285435 | − | 0.958398i | \(-0.407862\pi\) | ||||
0.285435 | + | 0.958398i | \(0.407862\pi\) | |||||||
\(390\) | −562700. | −0.187333 | ||||||||
\(391\) | 6.71105e6 | 2.21998 | ||||||||
\(392\) | 153664. | 0.0505076 | ||||||||
\(393\) | 1.64359e6 | 0.536801 | ||||||||
\(394\) | −2.94547e6 | −0.955904 | ||||||||
\(395\) | −699425. | −0.225553 | ||||||||
\(396\) | −526240. | −0.168634 | ||||||||
\(397\) | 1.19110e6 | 0.379292 | 0.189646 | − | 0.981853i | \(-0.439266\pi\) | ||||
0.189646 | + | 0.981853i | \(0.439266\pi\) | |||||||
\(398\) | −1.92648e6 | −0.609617 | ||||||||
\(399\) | −1.43109e6 | −0.450024 | ||||||||
\(400\) | 160000. | 0.0500000 | ||||||||
\(401\) | −3.38330e6 | −1.05070 | −0.525351 | − | 0.850885i | \(-0.676066\pi\) | ||||
−0.525351 | + | 0.850885i | \(0.676066\pi\) | |||||||
\(402\) | −300288. | −0.0926772 | ||||||||
\(403\) | 2.23624e6 | 0.685891 | ||||||||
\(404\) | −468000. | −0.142657 | ||||||||
\(405\) | −1.70278e6 | −0.515846 | ||||||||
\(406\) | −897484. | −0.270216 | ||||||||
\(407\) | 1.18104e7 | 3.53409 | ||||||||
\(408\) | 1.84851e6 | 0.549758 | ||||||||
\(409\) | −1.33185e6 | −0.393682 | −0.196841 | − | 0.980435i | \(-0.563068\pi\) | ||||
−0.196841 | + | 0.980435i | \(0.563068\pi\) | |||||||
\(410\) | 1.88760e6 | 0.554562 | ||||||||
\(411\) | −3.18390e6 | −0.929725 | ||||||||
\(412\) | −2.38702e6 | −0.692809 | ||||||||
\(413\) | 1.27184e6 | 0.366909 | ||||||||
\(414\) | −726800. | −0.208408 | ||||||||
\(415\) | 941100. | 0.268235 | ||||||||
\(416\) | 338944. | 0.0960273 | ||||||||
\(417\) | −3.00720e6 | −0.846880 | ||||||||
\(418\) | 4.91348e6 | 1.37546 | ||||||||
\(419\) | 5.82786e6 | 1.62171 | 0.810856 | − | 0.585246i | \(-0.199002\pi\) | ||||
0.810856 | + | 0.585246i | \(0.199002\pi\) | |||||||
\(420\) | 333200. | 0.0921683 | ||||||||
\(421\) | 2.47430e6 | 0.680374 | 0.340187 | − | 0.940358i | \(-0.389510\pi\) | ||||
0.340187 | + | 0.940358i | \(0.389510\pi\) | |||||||
\(422\) | 758124. | 0.207233 | ||||||||
\(423\) | −24702.0 | −0.00671245 | ||||||||
\(424\) | −702976. | −0.189900 | ||||||||
\(425\) | −1.06188e6 | −0.285168 | ||||||||
\(426\) | 2.16784e6 | 0.578766 | ||||||||
\(427\) | −1.92021e6 | −0.509659 | ||||||||
\(428\) | 1.33987e6 | 0.353552 | ||||||||
\(429\) | 4.02331e6 | 1.05546 | ||||||||
\(430\) | 225800. | 0.0588915 | ||||||||
\(431\) | 4.61851e6 | 1.19759 | 0.598796 | − | 0.800902i | \(-0.295646\pi\) | ||||
0.598796 | + | 0.800902i | \(0.295646\pi\) | |||||||
\(432\) | 857344. | 0.221027 | ||||||||
\(433\) | 58606.0 | 0.0150218 | 0.00751091 | − | 0.999972i | \(-0.497609\pi\) | ||||
0.00751091 | + | 0.999972i | \(0.497609\pi\) | |||||||
\(434\) | −1.32418e6 | −0.337459 | ||||||||
\(435\) | −1.94608e6 | −0.493102 | ||||||||
\(436\) | 1.68603e6 | 0.424766 | ||||||||
\(437\) | 6.78610e6 | 1.69987 | ||||||||
\(438\) | 341224. | 0.0849874 | ||||||||
\(439\) | 7.04298e6 | 1.74419 | 0.872097 | − | 0.489332i | \(-0.162759\pi\) | ||||
0.872097 | + | 0.489332i | \(0.162759\pi\) | |||||||
\(440\) | −1.14400e6 | −0.281705 | ||||||||
\(441\) | 110446. | 0.0270429 | ||||||||
\(442\) | −2.24948e6 | −0.547678 | ||||||||
\(443\) | 1.46894e6 | 0.355627 | 0.177813 | − | 0.984064i | \(-0.443098\pi\) | ||||
0.177813 | + | 0.984064i | \(0.443098\pi\) | |||||||
\(444\) | 4.49290e6 | 1.08161 | ||||||||
\(445\) | −430400. | −0.103032 | ||||||||
\(446\) | −90388.0 | −0.0215166 | ||||||||
\(447\) | 3.38433e6 | 0.801131 | ||||||||
\(448\) | −200704. | −0.0472456 | ||||||||
\(449\) | −7.48414e6 | −1.75197 | −0.875983 | − | 0.482341i | \(-0.839787\pi\) | ||||
−0.875983 | + | 0.482341i | \(0.839787\pi\) | |||||||
\(450\) | 115000. | 0.0267711 | ||||||||
\(451\) | −1.34963e7 | −3.12446 | ||||||||
\(452\) | −1.96406e6 | −0.452178 | ||||||||
\(453\) | −8.01691e6 | −1.83553 | ||||||||
\(454\) | −3.99247e6 | −0.909079 | ||||||||
\(455\) | −405475. | −0.0918196 | ||||||||
\(456\) | 1.86918e6 | 0.420959 | ||||||||
\(457\) | 170320. | 0.0381483 | 0.0190741 | − | 0.999818i | \(-0.493928\pi\) | ||||
0.0190741 | + | 0.999818i | \(0.493928\pi\) | |||||||
\(458\) | −3.41858e6 | −0.761520 | ||||||||
\(459\) | −5.68995e6 | −1.26060 | ||||||||
\(460\) | −1.58000e6 | −0.348147 | ||||||||
\(461\) | −4.28685e6 | −0.939476 | −0.469738 | − | 0.882806i | \(-0.655652\pi\) | ||||
−0.469738 | + | 0.882806i | \(0.655652\pi\) | |||||||
\(462\) | −2.38238e6 | −0.519285 | ||||||||
\(463\) | 3.38317e6 | 0.733452 | 0.366726 | − | 0.930329i | \(-0.380479\pi\) | ||||
0.366726 | + | 0.930329i | \(0.380479\pi\) | |||||||
\(464\) | 1.17222e6 | 0.252764 | ||||||||
\(465\) | −2.87130e6 | −0.615809 | ||||||||
\(466\) | 5.03274e6 | 1.07359 | ||||||||
\(467\) | 5.18029e6 | 1.09916 | 0.549581 | − | 0.835440i | \(-0.314787\pi\) | ||||
0.549581 | + | 0.835440i | \(0.314787\pi\) | |||||||
\(468\) | 243616. | 0.0514152 | ||||||||
\(469\) | −216384. | −0.0454248 | ||||||||
\(470\) | −53700.0 | −0.0112132 | ||||||||
\(471\) | 1.22492e6 | 0.254422 | ||||||||
\(472\) | −1.66118e6 | −0.343212 | ||||||||
\(473\) | −1.61447e6 | −0.331801 | ||||||||
\(474\) | 1.90244e6 | 0.388924 | ||||||||
\(475\) | −1.07375e6 | −0.218358 | ||||||||
\(476\) | 1.33202e6 | 0.269459 | ||||||||
\(477\) | −505264. | −0.101677 | ||||||||
\(478\) | −2.82632e6 | −0.565786 | ||||||||
\(479\) | −8.76779e6 | −1.74603 | −0.873014 | − | 0.487695i | \(-0.837838\pi\) | ||||
−0.873014 | + | 0.487695i | \(0.837838\pi\) | |||||||
\(480\) | −435200. | −0.0862156 | ||||||||
\(481\) | −5.46746e6 | −1.07751 | ||||||||
\(482\) | 2.46532e6 | 0.483343 | ||||||||
\(483\) | −3.29035e6 | −0.641762 | ||||||||
\(484\) | 5.60278e6 | 1.08715 | ||||||||
\(485\) | −1.57938e6 | −0.304881 | ||||||||
\(486\) | 1.37632e6 | 0.264319 | ||||||||
\(487\) | 270154. | 0.0516166 | 0.0258083 | − | 0.999667i | \(-0.491784\pi\) | ||||
0.0258083 | + | 0.999667i | \(0.491784\pi\) | |||||||
\(488\) | 2.50803e6 | 0.476742 | ||||||||
\(489\) | −6.55068e6 | −1.23884 | ||||||||
\(490\) | 240100. | 0.0451754 | ||||||||
\(491\) | 4.85550e6 | 0.908930 | 0.454465 | − | 0.890765i | \(-0.349830\pi\) | ||||
0.454465 | + | 0.890765i | \(0.349830\pi\) | |||||||
\(492\) | −5.13427e6 | −0.956238 | ||||||||
\(493\) | −7.77972e6 | −1.44161 | ||||||||
\(494\) | −2.27463e6 | −0.419367 | ||||||||
\(495\) | −822250. | −0.150831 | ||||||||
\(496\) | 1.72954e6 | 0.315664 | ||||||||
\(497\) | 1.56212e6 | 0.283677 | ||||||||
\(498\) | −2.55979e6 | −0.462521 | ||||||||
\(499\) | −2.98576e6 | −0.536789 | −0.268394 | − | 0.963309i | \(-0.586493\pi\) | ||||
−0.268394 | + | 0.963309i | \(0.586493\pi\) | |||||||
\(500\) | 250000. | 0.0447214 | ||||||||
\(501\) | 9.23027e6 | 1.64293 | ||||||||
\(502\) | 763368. | 0.135199 | ||||||||
\(503\) | −8.28783e6 | −1.46057 | −0.730283 | − | 0.683145i | \(-0.760612\pi\) | ||||
−0.730283 | + | 0.683145i | \(0.760612\pi\) | |||||||
\(504\) | −144256. | −0.0252963 | ||||||||
\(505\) | −731250. | −0.127596 | ||||||||
\(506\) | 1.12970e7 | 1.96149 | ||||||||
\(507\) | 4.44944e6 | 0.768751 | ||||||||
\(508\) | −3.50714e6 | −0.602967 | ||||||||
\(509\) | 6.24307e6 | 1.06808 | 0.534040 | − | 0.845459i | \(-0.320673\pi\) | ||||
0.534040 | + | 0.845459i | \(0.320673\pi\) | |||||||
\(510\) | 2.88830e6 | 0.491719 | ||||||||
\(511\) | 245882. | 0.0416557 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | −5.75358e6 | −0.965261 | ||||||||
\(514\) | −4.52377e6 | −0.755253 | ||||||||
\(515\) | −3.72972e6 | −0.619668 | ||||||||
\(516\) | −614176. | −0.101547 | ||||||||
\(517\) | 383955. | 0.0631763 | ||||||||
\(518\) | 3.23753e6 | 0.530138 | ||||||||
\(519\) | −6.30620e6 | −1.02766 | ||||||||
\(520\) | 529600. | 0.0858894 | ||||||||
\(521\) | 7.49509e6 | 1.20971 | 0.604856 | − | 0.796335i | \(-0.293230\pi\) | ||||
0.604856 | + | 0.796335i | \(0.293230\pi\) | |||||||
\(522\) | 842536. | 0.135336 | ||||||||
\(523\) | 3.80957e6 | 0.609007 | 0.304503 | − | 0.952511i | \(-0.401510\pi\) | ||||
0.304503 | + | 0.952511i | \(0.401510\pi\) | |||||||
\(524\) | −1.54691e6 | −0.246115 | ||||||||
\(525\) | 520625. | 0.0824379 | ||||||||
\(526\) | −6.69508e6 | −1.05509 | ||||||||
\(527\) | −1.14784e7 | −1.80035 | ||||||||
\(528\) | 3.11168e6 | 0.485747 | ||||||||
\(529\) | 9.16616e6 | 1.42413 | ||||||||
\(530\) | −1.09840e6 | −0.169852 | ||||||||
\(531\) | −1.19398e6 | −0.183764 | ||||||||
\(532\) | 1.34691e6 | 0.206329 | ||||||||
\(533\) | 6.24796e6 | 0.952621 | ||||||||
\(534\) | 1.17069e6 | 0.177659 | ||||||||
\(535\) | 2.09355e6 | 0.316227 | ||||||||
\(536\) | 282624. | 0.0424910 | ||||||||
\(537\) | 1.28209e7 | 1.91860 | ||||||||
\(538\) | −2.52377e6 | −0.375919 | ||||||||
\(539\) | −1.71672e6 | −0.254523 | ||||||||
\(540\) | 1.33960e6 | 0.197693 | ||||||||
\(541\) | 7.67156e6 | 1.12691 | 0.563457 | − | 0.826145i | \(-0.309471\pi\) | ||||
0.563457 | + | 0.826145i | \(0.309471\pi\) | |||||||
\(542\) | −1.48990e6 | −0.217851 | ||||||||
\(543\) | −5.16528e6 | −0.751786 | ||||||||
\(544\) | −1.73978e6 | −0.252055 | ||||||||
\(545\) | 2.63442e6 | 0.379922 | ||||||||
\(546\) | 1.10289e6 | 0.158326 | ||||||||
\(547\) | −9.53845e6 | −1.36304 | −0.681522 | − | 0.731798i | \(-0.738681\pi\) | ||||
−0.681522 | + | 0.731798i | \(0.738681\pi\) | |||||||
\(548\) | 2.99661e6 | 0.426264 | ||||||||
\(549\) | 1.80265e6 | 0.255258 | ||||||||
\(550\) | −1.78750e6 | −0.251964 | ||||||||
\(551\) | −7.86672e6 | −1.10386 | ||||||||
\(552\) | 4.29760e6 | 0.600314 | ||||||||
\(553\) | 1.37087e6 | 0.190627 | ||||||||
\(554\) | 3.46804e6 | 0.480076 | ||||||||
\(555\) | 7.02015e6 | 0.967417 | ||||||||
\(556\) | 2.83030e6 | 0.388281 | ||||||||
\(557\) | −7.45022e6 | −1.01749 | −0.508746 | − | 0.860916i | \(-0.669891\pi\) | ||||
−0.508746 | + | 0.860916i | \(0.669891\pi\) | |||||||
\(558\) | 1.24310e6 | 0.169014 | ||||||||
\(559\) | 747398. | 0.101163 | ||||||||
\(560\) | −313600. | −0.0422577 | ||||||||
\(561\) | −2.06513e7 | −2.77039 | ||||||||
\(562\) | −7.77992e6 | −1.03905 | ||||||||
\(563\) | 3.36698e6 | 0.447682 | 0.223841 | − | 0.974626i | \(-0.428140\pi\) | ||||
0.223841 | + | 0.974626i | \(0.428140\pi\) | |||||||
\(564\) | 146064. | 0.0193351 | ||||||||
\(565\) | −3.06885e6 | −0.404440 | ||||||||
\(566\) | 4.74005e6 | 0.621931 | ||||||||
\(567\) | 3.33744e6 | 0.435969 | ||||||||
\(568\) | −2.04032e6 | −0.265355 | ||||||||
\(569\) | −4.05501e6 | −0.525063 | −0.262532 | − | 0.964923i | \(-0.584557\pi\) | ||||
−0.262532 | + | 0.964923i | \(0.584557\pi\) | |||||||
\(570\) | 2.92060e6 | 0.376517 | ||||||||
\(571\) | 7.31585e6 | 0.939020 | 0.469510 | − | 0.882927i | \(-0.344431\pi\) | ||||
0.469510 | + | 0.882927i | \(0.344431\pi\) | |||||||
\(572\) | −3.78664e6 | −0.483909 | ||||||||
\(573\) | 3.16661e6 | 0.402910 | ||||||||
\(574\) | −3.69970e6 | −0.468691 | ||||||||
\(575\) | −2.46875e6 | −0.311392 | ||||||||
\(576\) | 188416. | 0.0236626 | ||||||||
\(577\) | −9.76895e6 | −1.22154 | −0.610771 | − | 0.791807i | \(-0.709140\pi\) | ||||
−0.610771 | + | 0.791807i | \(0.709140\pi\) | |||||||
\(578\) | 5.86698e6 | 0.730457 | ||||||||
\(579\) | −1.57257e6 | −0.194945 | ||||||||
\(580\) | 1.83160e6 | 0.226079 | ||||||||
\(581\) | −1.84456e6 | −0.226700 | ||||||||
\(582\) | 4.29590e6 | 0.525711 | ||||||||
\(583\) | 7.85356e6 | 0.956963 | ||||||||
\(584\) | −321152. | −0.0389653 | ||||||||
\(585\) | 380650. | 0.0459871 | ||||||||
\(586\) | 134676. | 0.0162012 | ||||||||
\(587\) | 3.75689e6 | 0.450021 | 0.225011 | − | 0.974356i | \(-0.427758\pi\) | ||||
0.225011 | + | 0.974356i | \(0.427758\pi\) | |||||||
\(588\) | −653072. | −0.0778965 | ||||||||
\(589\) | −1.16068e7 | −1.37856 | ||||||||
\(590\) | −2.59560e6 | −0.306978 | ||||||||
\(591\) | 1.25183e7 | 1.47426 | ||||||||
\(592\) | −4.22861e6 | −0.495899 | ||||||||
\(593\) | 2.89048e6 | 0.337546 | 0.168773 | − | 0.985655i | \(-0.446020\pi\) | ||||
0.168773 | + | 0.985655i | \(0.446020\pi\) | |||||||
\(594\) | −9.57814e6 | −1.11382 | ||||||||
\(595\) | 2.08128e6 | 0.241011 | ||||||||
\(596\) | −3.18525e6 | −0.367306 | ||||||||
\(597\) | 8.18754e6 | 0.940194 | ||||||||
\(598\) | −5.22980e6 | −0.598043 | ||||||||
\(599\) | 1.32233e7 | 1.50582 | 0.752910 | − | 0.658124i | \(-0.228650\pi\) | ||||
0.752910 | + | 0.658124i | \(0.228650\pi\) | |||||||
\(600\) | −680000. | −0.0771136 | ||||||||
\(601\) | 3.47399e6 | 0.392321 | 0.196161 | − | 0.980572i | \(-0.437153\pi\) | ||||
0.196161 | + | 0.980572i | \(0.437153\pi\) | |||||||
\(602\) | −442568. | −0.0497724 | ||||||||
\(603\) | 203136. | 0.0227506 | ||||||||
\(604\) | 7.54533e6 | 0.841561 | ||||||||
\(605\) | 8.75435e6 | 0.972379 | ||||||||
\(606\) | 1.98900e6 | 0.220015 | ||||||||
\(607\) | 6.45088e6 | 0.710636 | 0.355318 | − | 0.934746i | \(-0.384373\pi\) | ||||
0.355318 | + | 0.934746i | \(0.384373\pi\) | |||||||
\(608\) | −1.75923e6 | −0.193003 | ||||||||
\(609\) | 3.81431e6 | 0.416747 | ||||||||
\(610\) | 3.91880e6 | 0.426411 | ||||||||
\(611\) | −177747. | −0.0192619 | ||||||||
\(612\) | −1.25046e6 | −0.134956 | ||||||||
\(613\) | 8.43820e6 | 0.906982 | 0.453491 | − | 0.891261i | \(-0.350178\pi\) | ||||
0.453491 | + | 0.891261i | \(0.350178\pi\) | |||||||
\(614\) | −108172. | −0.0115796 | ||||||||
\(615\) | −8.02230e6 | −0.855285 | ||||||||
\(616\) | 2.24224e6 | 0.238084 | ||||||||
\(617\) | 9.45501e6 | 0.999882 | 0.499941 | − | 0.866059i | \(-0.333355\pi\) | ||||
0.499941 | + | 0.866059i | \(0.333355\pi\) | |||||||
\(618\) | 1.01449e7 | 1.06850 | ||||||||
\(619\) | 1.43145e6 | 0.150158 | 0.0750790 | − | 0.997178i | \(-0.476079\pi\) | ||||
0.0750790 | + | 0.997178i | \(0.476079\pi\) | |||||||
\(620\) | 2.70240e6 | 0.282339 | ||||||||
\(621\) | −1.32286e7 | −1.37652 | ||||||||
\(622\) | 8.59674e6 | 0.890960 | ||||||||
\(623\) | 843584. | 0.0870780 | ||||||||
\(624\) | −1.44051e6 | −0.148100 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −1.06821e7 | −1.08948 | ||||||||
\(627\) | −2.08823e7 | −2.12134 | ||||||||
\(628\) | −1.15286e6 | −0.116648 | ||||||||
\(629\) | 2.80641e7 | 2.82829 | ||||||||
\(630\) | −225400. | −0.0226257 | ||||||||
\(631\) | −1.01813e7 | −1.01795 | −0.508977 | − | 0.860780i | \(-0.669976\pi\) | ||||
−0.508977 | + | 0.860780i | \(0.669976\pi\) | |||||||
\(632\) | −1.79053e6 | −0.178315 | ||||||||
\(633\) | −3.22203e6 | −0.319610 | ||||||||
\(634\) | −1.00206e6 | −0.0990077 | ||||||||
\(635\) | −5.47990e6 | −0.539310 | ||||||||
\(636\) | 2.98765e6 | 0.292878 | ||||||||
\(637\) | 794731. | 0.0776018 | ||||||||
\(638\) | −1.30959e7 | −1.27375 | ||||||||
\(639\) | −1.46648e6 | −0.142077 | ||||||||
\(640\) | 409600. | 0.0395285 | ||||||||
\(641\) | −1.76908e7 | −1.70060 | −0.850300 | − | 0.526298i | \(-0.823580\pi\) | ||||
−0.850300 | + | 0.526298i | \(0.823580\pi\) | |||||||
\(642\) | −5.69446e6 | −0.545274 | ||||||||
\(643\) | 1.82748e7 | 1.74311 | 0.871556 | − | 0.490296i | \(-0.163111\pi\) | ||||
0.871556 | + | 0.490296i | \(0.163111\pi\) | |||||||
\(644\) | 3.09680e6 | 0.294238 | ||||||||
\(645\) | −959650. | −0.0908267 | ||||||||
\(646\) | 1.16755e7 | 1.10077 | ||||||||
\(647\) | 1.52897e6 | 0.143594 | 0.0717972 | − | 0.997419i | \(-0.477127\pi\) | ||||
0.0717972 | + | 0.997419i | \(0.477127\pi\) | |||||||
\(648\) | −4.35910e6 | −0.407812 | ||||||||
\(649\) | 1.85585e7 | 1.72955 | ||||||||
\(650\) | 827500. | 0.0768218 | ||||||||
\(651\) | 5.62775e6 | 0.520454 | ||||||||
\(652\) | 6.16534e6 | 0.567987 | ||||||||
\(653\) | −9.10088e6 | −0.835219 | −0.417610 | − | 0.908627i | \(-0.637132\pi\) | ||||
−0.417610 | + | 0.908627i | \(0.637132\pi\) | |||||||
\(654\) | −7.16564e6 | −0.655104 | ||||||||
\(655\) | −2.41705e6 | −0.220132 | ||||||||
\(656\) | 4.83226e6 | 0.438420 | ||||||||
\(657\) | −230828. | −0.0208629 | ||||||||
\(658\) | 105252. | 0.00947689 | ||||||||
\(659\) | −430119. | −0.0385811 | −0.0192906 | − | 0.999814i | \(-0.506141\pi\) | ||||
−0.0192906 | + | 0.999814i | \(0.506141\pi\) | |||||||
\(660\) | 4.86200e6 | 0.434465 | ||||||||
\(661\) | 7.65248e6 | 0.681238 | 0.340619 | − | 0.940202i | \(-0.389363\pi\) | ||||
0.340619 | + | 0.940202i | \(0.389363\pi\) | |||||||
\(662\) | 4.23595e6 | 0.375670 | ||||||||
\(663\) | 9.56027e6 | 0.844669 | ||||||||
\(664\) | 2.40922e6 | 0.212058 | ||||||||
\(665\) | 2.10455e6 | 0.184546 | ||||||||
\(666\) | −3.03931e6 | −0.265515 | ||||||||
\(667\) | −1.80870e7 | −1.57418 | ||||||||
\(668\) | −8.68731e6 | −0.753259 | ||||||||
\(669\) | 384149. | 0.0331844 | ||||||||
\(670\) | 441600. | 0.0380051 | ||||||||
\(671\) | −2.80194e7 | −2.40244 | ||||||||
\(672\) | 852992. | 0.0728655 | ||||||||
\(673\) | −2.18404e7 | −1.85876 | −0.929378 | − | 0.369128i | \(-0.879656\pi\) | ||||
−0.929378 | + | 0.369128i | \(0.879656\pi\) | |||||||
\(674\) | −1.14010e7 | −0.966702 | ||||||||
\(675\) | 2.09312e6 | 0.176822 | ||||||||
\(676\) | −4.18771e6 | −0.352460 | ||||||||
\(677\) | 1.39504e7 | 1.16981 | 0.584905 | − | 0.811102i | \(-0.301132\pi\) | ||||
0.584905 | + | 0.811102i | \(0.301132\pi\) | |||||||
\(678\) | 8.34727e6 | 0.697381 | ||||||||
\(679\) | 3.09558e6 | 0.257672 | ||||||||
\(680\) | −2.71840e6 | −0.225445 | ||||||||
\(681\) | 1.69680e7 | 1.40205 | ||||||||
\(682\) | −1.93222e7 | −1.59072 | ||||||||
\(683\) | 2.29121e7 | 1.87937 | 0.939686 | − | 0.342040i | \(-0.111118\pi\) | ||||
0.939686 | + | 0.342040i | \(0.111118\pi\) | |||||||
\(684\) | −1.26445e6 | −0.103338 | ||||||||
\(685\) | 4.68220e6 | 0.381262 | ||||||||
\(686\) | −470596. | −0.0381802 | ||||||||
\(687\) | 1.45289e7 | 1.17447 | ||||||||
\(688\) | 578048. | 0.0465578 | ||||||||
\(689\) | −3.63570e6 | −0.291770 | ||||||||
\(690\) | 6.71500e6 | 0.536937 | ||||||||
\(691\) | −1.69127e7 | −1.34747 | −0.673734 | − | 0.738974i | \(-0.735310\pi\) | ||||
−0.673734 | + | 0.738974i | \(0.735310\pi\) | |||||||
\(692\) | 5.93525e6 | 0.471166 | ||||||||
\(693\) | 1.61161e6 | 0.127476 | ||||||||
\(694\) | 7.56562e6 | 0.596274 | ||||||||
\(695\) | 4.42235e6 | 0.347289 | ||||||||
\(696\) | −4.98195e6 | −0.389831 | ||||||||
\(697\) | −3.20703e7 | −2.50047 | ||||||||
\(698\) | −4.16927e6 | −0.323908 | ||||||||
\(699\) | −2.13891e7 | −1.65577 | ||||||||
\(700\) | −490000. | −0.0377964 | ||||||||
\(701\) | −1.90087e7 | −1.46102 | −0.730510 | − | 0.682902i | \(-0.760718\pi\) | ||||
−0.730510 | + | 0.682902i | \(0.760718\pi\) | |||||||
\(702\) | 4.43408e6 | 0.339594 | ||||||||
\(703\) | 2.83779e7 | 2.16567 | ||||||||
\(704\) | −2.92864e6 | −0.222707 | ||||||||
\(705\) | 228225. | 0.0172938 | ||||||||
\(706\) | −9.21235e6 | −0.695598 | ||||||||
\(707\) | 1.43325e6 | 0.107838 | ||||||||
\(708\) | 7.06003e6 | 0.529326 | ||||||||
\(709\) | 1.66079e7 | 1.24079 | 0.620396 | − | 0.784289i | \(-0.286972\pi\) | ||||
0.620396 | + | 0.784289i | \(0.286972\pi\) | |||||||
\(710\) | −3.18800e6 | −0.237341 | ||||||||
\(711\) | −1.28694e6 | −0.0954740 | ||||||||
\(712\) | −1.10182e6 | −0.0814540 | ||||||||
\(713\) | −2.66862e7 | −1.96591 | ||||||||
\(714\) | −5.66107e6 | −0.415578 | ||||||||
\(715\) | −5.91662e6 | −0.432822 | ||||||||
\(716\) | −1.20668e7 | −0.879646 | ||||||||
\(717\) | 1.20119e7 | 0.872596 | ||||||||
\(718\) | −6.70378e6 | −0.485298 | ||||||||
\(719\) | 5.93610e6 | 0.428232 | 0.214116 | − | 0.976808i | \(-0.431313\pi\) | ||||
0.214116 | + | 0.976808i | \(0.431313\pi\) | |||||||
\(720\) | 294400. | 0.0211644 | ||||||||
\(721\) | 7.31026e6 | 0.523715 | ||||||||
\(722\) | 1.90170e6 | 0.135768 | ||||||||
\(723\) | −1.04776e7 | −0.745447 | ||||||||
\(724\) | 4.86144e6 | 0.344682 | ||||||||
\(725\) | 2.86188e6 | 0.202211 | ||||||||
\(726\) | −2.38118e7 | −1.67668 | ||||||||
\(727\) | 1.73276e7 | 1.21591 | 0.607957 | − | 0.793970i | \(-0.291989\pi\) | ||||
0.607957 | + | 0.793970i | \(0.291989\pi\) | |||||||
\(728\) | −1.03802e6 | −0.0725898 | ||||||||
\(729\) | 1.07016e7 | 0.745814 | ||||||||
\(730\) | −501800. | −0.0348517 | ||||||||
\(731\) | −3.83634e6 | −0.265536 | ||||||||
\(732\) | −1.06591e7 | −0.735266 | ||||||||
\(733\) | 1.39829e7 | 0.961255 | 0.480627 | − | 0.876925i | \(-0.340409\pi\) | ||||
0.480627 | + | 0.876925i | \(0.340409\pi\) | |||||||
\(734\) | 378652. | 0.0259418 | ||||||||
\(735\) | −1.02042e6 | −0.0696727 | ||||||||
\(736\) | −4.04480e6 | −0.275234 | ||||||||
\(737\) | −3.15744e6 | −0.214125 | ||||||||
\(738\) | 3.47318e6 | 0.234740 | ||||||||
\(739\) | −1.14263e7 | −0.769649 | −0.384824 | − | 0.922990i | \(-0.625738\pi\) | ||||
−0.384824 | + | 0.922990i | \(0.625738\pi\) | |||||||
\(740\) | −6.60720e6 | −0.443545 | ||||||||
\(741\) | 9.66719e6 | 0.646777 | ||||||||
\(742\) | 2.15286e6 | 0.143551 | ||||||||
\(743\) | 1.23126e7 | 0.818236 | 0.409118 | − | 0.912481i | \(-0.365836\pi\) | ||||
0.409118 | + | 0.912481i | \(0.365836\pi\) | |||||||
\(744\) | −7.35053e6 | −0.486840 | ||||||||
\(745\) | −4.97695e6 | −0.328528 | ||||||||
\(746\) | −3.81414e6 | −0.250929 | ||||||||
\(747\) | 1.73162e6 | 0.113541 | ||||||||
\(748\) | 1.94366e7 | 1.27018 | ||||||||
\(749\) | −4.10336e6 | −0.267261 | ||||||||
\(750\) | −1.06250e6 | −0.0689725 | ||||||||
\(751\) | −1.43093e7 | −0.925806 | −0.462903 | − | 0.886409i | \(-0.653192\pi\) | ||||
−0.462903 | + | 0.886409i | \(0.653192\pi\) | |||||||
\(752\) | −137472. | −0.00886481 | ||||||||
\(753\) | −3.24431e6 | −0.208514 | ||||||||
\(754\) | 6.06260e6 | 0.388356 | ||||||||
\(755\) | 1.17896e7 | 0.752715 | ||||||||
\(756\) | −2.62562e6 | −0.167081 | ||||||||
\(757\) | −5.34505e6 | −0.339010 | −0.169505 | − | 0.985529i | \(-0.554217\pi\) | ||||
−0.169505 | + | 0.985529i | \(0.554217\pi\) | |||||||
\(758\) | 1.55530e7 | 0.983197 | ||||||||
\(759\) | −4.80122e7 | −3.02515 | ||||||||
\(760\) | −2.74880e6 | −0.172627 | ||||||||
\(761\) | 6.22568e6 | 0.389695 | 0.194848 | − | 0.980834i | \(-0.437579\pi\) | ||||
0.194848 | + | 0.980834i | \(0.437579\pi\) | |||||||
\(762\) | 1.49053e7 | 0.929938 | ||||||||
\(763\) | −5.16347e6 | −0.321093 | ||||||||
\(764\) | −2.98034e6 | −0.184728 | ||||||||
\(765\) | −1.95385e6 | −0.120708 | ||||||||
\(766\) | 1.17454e7 | 0.723264 | ||||||||
\(767\) | −8.59144e6 | −0.527324 | ||||||||
\(768\) | −1.11411e6 | −0.0681594 | ||||||||
\(769\) | 1.57888e7 | 0.962793 | 0.481397 | − | 0.876503i | \(-0.340130\pi\) | ||||
0.481397 | + | 0.876503i | \(0.340130\pi\) | |||||||
\(770\) | 3.50350e6 | 0.212949 | ||||||||
\(771\) | 1.92260e7 | 1.16481 | ||||||||
\(772\) | 1.48006e6 | 0.0893794 | ||||||||
\(773\) | −2.50453e7 | −1.50757 | −0.753785 | − | 0.657121i | \(-0.771774\pi\) | ||||
−0.753785 | + | 0.657121i | \(0.771774\pi\) | |||||||
\(774\) | 415472. | 0.0249281 | ||||||||
\(775\) | 4.22250e6 | 0.252531 | ||||||||
\(776\) | −4.04320e6 | −0.241030 | ||||||||
\(777\) | −1.37595e7 | −0.817617 | ||||||||
\(778\) | 6.81509e6 | 0.403667 | ||||||||
\(779\) | −3.24290e7 | −1.91465 | ||||||||
\(780\) | −2.25080e6 | −0.132465 | ||||||||
\(781\) | 2.27942e7 | 1.33720 | ||||||||
\(782\) | 2.68442e7 | 1.56976 | ||||||||
\(783\) | 1.53351e7 | 0.893884 | ||||||||
\(784\) | 614656. | 0.0357143 | ||||||||
\(785\) | −1.80135e6 | −0.104334 | ||||||||
\(786\) | 6.57438e6 | 0.379576 | ||||||||
\(787\) | −1.28020e6 | −0.0736784 | −0.0368392 | − | 0.999321i | \(-0.511729\pi\) | ||||
−0.0368392 | + | 0.999321i | \(0.511729\pi\) | |||||||
\(788\) | −1.17819e7 | −0.675926 | ||||||||
\(789\) | 2.84541e7 | 1.62724 | ||||||||
\(790\) | −2.79770e6 | −0.159490 | ||||||||
\(791\) | 6.01495e6 | 0.341815 | ||||||||
\(792\) | −2.10496e6 | −0.119242 | ||||||||
\(793\) | 1.29712e7 | 0.732484 | ||||||||
\(794\) | 4.76442e6 | 0.268200 | ||||||||
\(795\) | 4.66820e6 | 0.261958 | ||||||||
\(796\) | −7.70592e6 | −0.431064 | ||||||||
\(797\) | −1.13798e7 | −0.634584 | −0.317292 | − | 0.948328i | \(-0.602774\pi\) | ||||
−0.317292 | + | 0.948328i | \(0.602774\pi\) | |||||||
\(798\) | −5.72438e6 | −0.318215 | ||||||||
\(799\) | 912363. | 0.0505593 | ||||||||
\(800\) | 640000. | 0.0353553 | ||||||||
\(801\) | −791936. | −0.0436123 | ||||||||
\(802\) | −1.35332e7 | −0.742959 | ||||||||
\(803\) | 3.58787e6 | 0.196358 | ||||||||
\(804\) | −1.20115e6 | −0.0655327 | ||||||||
\(805\) | 4.83875e6 | 0.263174 | ||||||||
\(806\) | 8.94494e6 | 0.484998 | ||||||||
\(807\) | 1.07260e7 | 0.579768 | ||||||||
\(808\) | −1.87200e6 | −0.100874 | ||||||||
\(809\) | −1.70542e7 | −0.916138 | −0.458069 | − | 0.888917i | \(-0.651459\pi\) | ||||
−0.458069 | + | 0.888917i | \(0.651459\pi\) | |||||||
\(810\) | −6.81110e6 | −0.364758 | ||||||||
\(811\) | −2.21494e7 | −1.18252 | −0.591262 | − | 0.806480i | \(-0.701370\pi\) | ||||
−0.591262 | + | 0.806480i | \(0.701370\pi\) | |||||||
\(812\) | −3.58994e6 | −0.191072 | ||||||||
\(813\) | 6.33209e6 | 0.335986 | ||||||||
\(814\) | 4.72415e7 | 2.49898 | ||||||||
\(815\) | 9.63335e6 | 0.508023 | ||||||||
\(816\) | 7.39405e6 | 0.388738 | ||||||||
\(817\) | −3.87924e6 | −0.203326 | ||||||||
\(818\) | −5.32738e6 | −0.278375 | ||||||||
\(819\) | −746074. | −0.0388662 | ||||||||
\(820\) | 7.55040e6 | 0.392135 | ||||||||
\(821\) | −1.01068e7 | −0.523307 | −0.261654 | − | 0.965162i | \(-0.584268\pi\) | ||||
−0.261654 | + | 0.965162i | \(0.584268\pi\) | |||||||
\(822\) | −1.27356e7 | −0.657415 | ||||||||
\(823\) | −1.83993e7 | −0.946895 | −0.473447 | − | 0.880822i | \(-0.656991\pi\) | ||||
−0.473447 | + | 0.880822i | \(0.656991\pi\) | |||||||
\(824\) | −9.54810e6 | −0.489890 | ||||||||
\(825\) | 7.59688e6 | 0.388598 | ||||||||
\(826\) | 5.08738e6 | 0.259444 | ||||||||
\(827\) | −2.48056e7 | −1.26121 | −0.630604 | − | 0.776105i | \(-0.717193\pi\) | ||||
−0.630604 | + | 0.776105i | \(0.717193\pi\) | |||||||
\(828\) | −2.90720e6 | −0.147367 | ||||||||
\(829\) | −1.19708e6 | −0.0604976 | −0.0302488 | − | 0.999542i | \(-0.509630\pi\) | ||||
−0.0302488 | + | 0.999542i | \(0.509630\pi\) | |||||||
\(830\) | 3.76440e6 | 0.189671 | ||||||||
\(831\) | −1.47392e7 | −0.740407 | ||||||||
\(832\) | 1.35578e6 | 0.0679015 | ||||||||
\(833\) | −4.07930e6 | −0.203692 | ||||||||
\(834\) | −1.20288e7 | −0.598835 | ||||||||
\(835\) | −1.35739e7 | −0.673735 | ||||||||
\(836\) | 1.96539e7 | 0.972598 | ||||||||
\(837\) | 2.26258e7 | 1.11633 | ||||||||
\(838\) | 2.33114e7 | 1.14672 | ||||||||
\(839\) | −3.17171e7 | −1.55557 | −0.777783 | − | 0.628533i | \(-0.783656\pi\) | ||||
−0.777783 | + | 0.628533i | \(0.783656\pi\) | |||||||
\(840\) | 1.33280e6 | 0.0651729 | ||||||||
\(841\) | 456092. | 0.0222363 | ||||||||
\(842\) | 9.89722e6 | 0.481097 | ||||||||
\(843\) | 3.30647e7 | 1.60249 | ||||||||
\(844\) | 3.03250e6 | 0.146536 | ||||||||
\(845\) | −6.54330e6 | −0.315250 | ||||||||
\(846\) | −98808.0 | −0.00474642 | ||||||||
\(847\) | −1.71585e7 | −0.821810 | ||||||||
\(848\) | −2.81190e6 | −0.134280 | ||||||||
\(849\) | −2.01452e7 | −0.959186 | ||||||||
\(850\) | −4.24750e6 | −0.201644 | ||||||||
\(851\) | 6.52461e7 | 3.08838 | ||||||||
\(852\) | 8.67136e6 | 0.409250 | ||||||||
\(853\) | 3.18237e7 | 1.49754 | 0.748769 | − | 0.662831i | \(-0.230645\pi\) | ||||
0.748769 | + | 0.662831i | \(0.230645\pi\) | |||||||
\(854\) | −7.68085e6 | −0.360383 | ||||||||
\(855\) | −1.97570e6 | −0.0924285 | ||||||||
\(856\) | 5.35949e6 | 0.249999 | ||||||||
\(857\) | 2.27853e7 | 1.05975 | 0.529874 | − | 0.848076i | \(-0.322239\pi\) | ||||
0.529874 | + | 0.848076i | \(0.322239\pi\) | |||||||
\(858\) | 1.60932e7 | 0.746319 | ||||||||
\(859\) | −1.85966e7 | −0.859907 | −0.429953 | − | 0.902851i | \(-0.641470\pi\) | ||||
−0.429953 | + | 0.902851i | \(0.641470\pi\) | |||||||
\(860\) | 903200. | 0.0416426 | ||||||||
\(861\) | 1.57237e7 | 0.722848 | ||||||||
\(862\) | 1.84740e7 | 0.846825 | ||||||||
\(863\) | −2.77046e7 | −1.26627 | −0.633133 | − | 0.774043i | \(-0.718231\pi\) | ||||
−0.633133 | + | 0.774043i | \(0.718231\pi\) | |||||||
\(864\) | 3.42938e6 | 0.156290 | ||||||||
\(865\) | 9.27382e6 | 0.421423 | ||||||||
\(866\) | 234424. | 0.0106220 | ||||||||
\(867\) | −2.49346e7 | −1.12656 | ||||||||
\(868\) | −5.29670e6 | −0.238620 | ||||||||
\(869\) | 2.00036e7 | 0.898582 | ||||||||
\(870\) | −7.78430e6 | −0.348676 | ||||||||
\(871\) | 1.46170e6 | 0.0652847 | ||||||||
\(872\) | 6.74413e6 | 0.300355 | ||||||||
\(873\) | −2.90605e6 | −0.129053 | ||||||||
\(874\) | 2.71444e7 | 1.20199 | ||||||||
\(875\) | −765625. | −0.0338062 | ||||||||
\(876\) | 1.36490e6 | 0.0600951 | ||||||||
\(877\) | −2.41150e7 | −1.05874 | −0.529370 | − | 0.848391i | \(-0.677572\pi\) | ||||
−0.529370 | + | 0.848391i | \(0.677572\pi\) | |||||||
\(878\) | 2.81719e7 | 1.23333 | ||||||||
\(879\) | −572373. | −0.0249866 | ||||||||
\(880\) | −4.57600e6 | −0.199195 | ||||||||
\(881\) | −1.26207e7 | −0.547827 | −0.273914 | − | 0.961754i | \(-0.588318\pi\) | ||||
−0.273914 | + | 0.961754i | \(0.588318\pi\) | |||||||
\(882\) | 441784. | 0.0191222 | ||||||||
\(883\) | −6.01876e6 | −0.259780 | −0.129890 | − | 0.991528i | \(-0.541462\pi\) | ||||
−0.129890 | + | 0.991528i | \(0.541462\pi\) | |||||||
\(884\) | −8.99790e6 | −0.387267 | ||||||||
\(885\) | 1.10313e7 | 0.473444 | ||||||||
\(886\) | 5.87575e6 | 0.251466 | ||||||||
\(887\) | 2.36901e7 | 1.01102 | 0.505509 | − | 0.862821i | \(-0.331305\pi\) | ||||
0.505509 | + | 0.862821i | \(0.331305\pi\) | |||||||
\(888\) | 1.79716e7 | 0.764811 | ||||||||
\(889\) | 1.07406e7 | 0.455800 | ||||||||
\(890\) | −1.72160e6 | −0.0728546 | ||||||||
\(891\) | 4.86994e7 | 2.05508 | ||||||||
\(892\) | −361552. | −0.0152145 | ||||||||
\(893\) | 922566. | 0.0387141 | ||||||||
\(894\) | 1.35373e7 | 0.566485 | ||||||||
\(895\) | −1.88543e7 | −0.786779 | ||||||||
\(896\) | −802816. | −0.0334077 | ||||||||
\(897\) | 2.22266e7 | 0.922344 | ||||||||
\(898\) | −2.99365e7 | −1.23883 | ||||||||
\(899\) | 3.09357e7 | 1.27662 | ||||||||
\(900\) | 460000. | 0.0189300 | ||||||||
\(901\) | 1.86618e7 | 0.765847 | ||||||||
\(902\) | −5.39854e7 | −2.20933 | ||||||||
\(903\) | 1.88091e6 | 0.0767626 | ||||||||
\(904\) | −7.85626e6 | −0.319738 | ||||||||
\(905\) | 7.59600e6 | 0.308293 | ||||||||
\(906\) | −3.20676e7 | −1.29792 | ||||||||
\(907\) | −1.10583e7 | −0.446346 | −0.223173 | − | 0.974779i | \(-0.571641\pi\) | ||||
−0.223173 | + | 0.974779i | \(0.571641\pi\) | |||||||
\(908\) | −1.59699e7 | −0.642816 | ||||||||
\(909\) | −1.34550e6 | −0.0540100 | ||||||||
\(910\) | −1.62190e6 | −0.0649263 | ||||||||
\(911\) | 3.07573e6 | 0.122787 | 0.0613934 | − | 0.998114i | \(-0.480446\pi\) | ||||
0.0613934 | + | 0.998114i | \(0.480446\pi\) | |||||||
\(912\) | 7.47674e6 | 0.297663 | ||||||||
\(913\) | −2.69155e7 | −1.06862 | ||||||||
\(914\) | 681280. | 0.0269749 | ||||||||
\(915\) | −1.66549e7 | −0.657642 | ||||||||
\(916\) | −1.36743e7 | −0.538476 | ||||||||
\(917\) | 4.73742e6 | 0.186045 | ||||||||
\(918\) | −2.27598e7 | −0.891378 | ||||||||
\(919\) | −1.89018e7 | −0.738270 | −0.369135 | − | 0.929376i | \(-0.620346\pi\) | ||||
−0.369135 | + | 0.929376i | \(0.620346\pi\) | |||||||
\(920\) | −6.32000e6 | −0.246177 | ||||||||
\(921\) | 459731. | 0.0178589 | ||||||||
\(922\) | −1.71474e7 | −0.664310 | ||||||||
\(923\) | −1.05523e7 | −0.407701 | ||||||||
\(924\) | −9.52952e6 | −0.367190 | ||||||||
\(925\) | −1.03238e7 | −0.396719 | ||||||||
\(926\) | 1.35327e7 | 0.518629 | ||||||||
\(927\) | −6.86269e6 | −0.262298 | ||||||||
\(928\) | 4.68890e6 | 0.178731 | ||||||||
\(929\) | −1.81458e7 | −0.689821 | −0.344911 | − | 0.938636i | \(-0.612091\pi\) | ||||
−0.344911 | + | 0.938636i | \(0.612091\pi\) | |||||||
\(930\) | −1.14852e7 | −0.435443 | ||||||||
\(931\) | −4.12492e6 | −0.155970 | ||||||||
\(932\) | 2.01309e7 | 0.759144 | ||||||||
\(933\) | −3.65362e7 | −1.37410 | ||||||||
\(934\) | 2.07212e7 | 0.777225 | ||||||||
\(935\) | 3.03696e7 | 1.13608 | ||||||||
\(936\) | 974464. | 0.0363560 | ||||||||
\(937\) | −2.17350e7 | −0.808744 | −0.404372 | − | 0.914595i | \(-0.632510\pi\) | ||||
−0.404372 | + | 0.914595i | \(0.632510\pi\) | |||||||
\(938\) | −865536. | −0.0321202 | ||||||||
\(939\) | 4.53989e7 | 1.68028 | ||||||||
\(940\) | −214800. | −0.00792893 | ||||||||
\(941\) | 1.86808e7 | 0.687735 | 0.343868 | − | 0.939018i | \(-0.388263\pi\) | ||||
0.343868 | + | 0.939018i | \(0.388263\pi\) | |||||||
\(942\) | 4.89967e6 | 0.179904 | ||||||||
\(943\) | −7.45602e7 | −2.73041 | ||||||||
\(944\) | −6.64474e6 | −0.242688 | ||||||||
\(945\) | −4.10252e6 | −0.149442 | ||||||||
\(946\) | −6.45788e6 | −0.234618 | ||||||||
\(947\) | −2.24778e6 | −0.0814476 | −0.0407238 | − | 0.999170i | \(-0.512966\pi\) | ||||
−0.0407238 | + | 0.999170i | \(0.512966\pi\) | |||||||
\(948\) | 7.60974e6 | 0.275010 | ||||||||
\(949\) | −1.66096e6 | −0.0598678 | ||||||||
\(950\) | −4.29500e6 | −0.154402 | ||||||||
\(951\) | 4.25874e6 | 0.152697 | ||||||||
\(952\) | 5.32806e6 | 0.190536 | ||||||||
\(953\) | −3.73293e7 | −1.33143 | −0.665714 | − | 0.746207i | \(-0.731873\pi\) | ||||
−0.665714 | + | 0.746207i | \(0.731873\pi\) | |||||||
\(954\) | −2.02106e6 | −0.0718964 | ||||||||
\(955\) | −4.65678e6 | −0.165225 | ||||||||
\(956\) | −1.13053e7 | −0.400071 | ||||||||
\(957\) | 5.56577e7 | 1.96447 | ||||||||
\(958\) | −3.50711e7 | −1.23463 | ||||||||
\(959\) | −9.17711e6 | −0.322225 | ||||||||
\(960\) | −1.74080e6 | −0.0609636 | ||||||||
\(961\) | 1.70144e7 | 0.594303 | ||||||||
\(962\) | −2.18698e7 | −0.761917 | ||||||||
\(963\) | 3.85213e6 | 0.133855 | ||||||||
\(964\) | 9.86128e6 | 0.341775 | ||||||||
\(965\) | 2.31260e6 | 0.0799433 | ||||||||
\(966\) | −1.31614e7 | −0.453795 | ||||||||
\(967\) | 2.61870e7 | 0.900573 | 0.450287 | − | 0.892884i | \(-0.351322\pi\) | ||||
0.450287 | + | 0.892884i | \(0.351322\pi\) | |||||||
\(968\) | 2.24111e7 | 0.768733 | ||||||||
\(969\) | −4.96210e7 | −1.69768 | ||||||||
\(970\) | −6.31750e6 | −0.215584 | ||||||||
\(971\) | −3.91957e7 | −1.33410 | −0.667052 | − | 0.745011i | \(-0.732444\pi\) | ||||
−0.667052 | + | 0.745011i | \(0.732444\pi\) | |||||||
\(972\) | 5.50528e6 | 0.186902 | ||||||||
\(973\) | −8.66781e6 | −0.293513 | ||||||||
\(974\) | 1.08062e6 | 0.0364984 | ||||||||
\(975\) | −3.51688e6 | −0.118480 | ||||||||
\(976\) | 1.00321e7 | 0.337108 | ||||||||
\(977\) | 3.03935e6 | 0.101870 | 0.0509348 | − | 0.998702i | \(-0.483780\pi\) | ||||
0.0509348 | + | 0.998702i | \(0.483780\pi\) | |||||||
\(978\) | −2.62027e7 | −0.875990 | ||||||||
\(979\) | 1.23094e7 | 0.410470 | ||||||||
\(980\) | 960400. | 0.0319438 | ||||||||
\(981\) | 4.84734e6 | 0.160817 | ||||||||
\(982\) | 1.94220e7 | 0.642711 | ||||||||
\(983\) | −1.59937e7 | −0.527915 | −0.263957 | − | 0.964534i | \(-0.585028\pi\) | ||||
−0.263957 | + | 0.964534i | \(0.585028\pi\) | |||||||
\(984\) | −2.05371e7 | −0.676163 | ||||||||
\(985\) | −1.84092e7 | −0.604567 | ||||||||
\(986\) | −3.11189e7 | −1.01937 | ||||||||
\(987\) | −447321. | −0.0146159 | ||||||||
\(988\) | −9.09853e6 | −0.296537 | ||||||||
\(989\) | −8.91910e6 | −0.289955 | ||||||||
\(990\) | −3.28900e6 | −0.106654 | ||||||||
\(991\) | 3.63186e6 | 0.117475 | 0.0587375 | − | 0.998273i | \(-0.481293\pi\) | ||||
0.0587375 | + | 0.998273i | \(0.481293\pi\) | |||||||
\(992\) | 6.91814e6 | 0.223208 | ||||||||
\(993\) | −1.80028e7 | −0.579384 | ||||||||
\(994\) | 6.24848e6 | 0.200590 | ||||||||
\(995\) | −1.20405e7 | −0.385555 | ||||||||
\(996\) | −1.02392e7 | −0.327052 | ||||||||
\(997\) | −4.33287e7 | −1.38051 | −0.690253 | − | 0.723568i | \(-0.742501\pi\) | ||||
−0.690253 | + | 0.723568i | \(0.742501\pi\) | |||||||
\(998\) | −1.19430e7 | −0.379567 | ||||||||
\(999\) | −5.53188e7 | −1.75371 |
(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 | 70.6.a.e.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 630.6.a.b.1.1 | 1 | |||
4.3 | odd | 2 | 560.6.a.h.1.1 | 1 | |||
5.2 | odd | 4 | 350.6.c.a.99.2 | 2 | |||
5.3 | odd | 4 | 350.6.c.a.99.1 | 2 | |||
5.4 | even | 2 | 350.6.a.e.1.1 | 1 | |||
7.6 | odd | 2 | 490.6.a.m.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.6.a.e.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
350.6.a.e.1.1 | 1 | 5.4 | even | 2 | |||
350.6.c.a.99.1 | 2 | 5.3 | odd | 4 | |||
350.6.c.a.99.2 | 2 | 5.2 | odd | 4 | |||
490.6.a.m.1.1 | 1 | 7.6 | odd | 2 | |||
560.6.a.h.1.1 | 1 | 4.3 | odd | 2 | |||
630.6.a.b.1.1 | 1 | 3.2 | odd | 2 |