Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [150,6,Mod(1,150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(150, 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("150.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 150 = 2 \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 150.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: | \(24.0575729719\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 150.1 |
$q$-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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −36.0000 | −0.408248 | ||||||||
\(7\) | 1.00000 | 0.00771356 | 0.00385678 | − | 0.999993i | \(-0.498772\pi\) | ||||
0.00385678 | + | 0.999993i | \(0.498772\pi\) | |||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −210.000 | −0.523284 | −0.261642 | − | 0.965165i | \(-0.584264\pi\) | ||||
−0.261642 | + | 0.965165i | \(0.584264\pi\) | |||||||
\(12\) | −144.000 | −0.288675 | ||||||||
\(13\) | 667.000 | 1.09463 | 0.547315 | − | 0.836927i | \(-0.315650\pi\) | ||||
0.547315 | + | 0.836927i | \(0.315650\pi\) | |||||||
\(14\) | 4.00000 | 0.00545431 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −114.000 | −0.0956715 | −0.0478357 | − | 0.998855i | \(-0.515232\pi\) | ||||
−0.0478357 | + | 0.998855i | \(0.515232\pi\) | |||||||
\(18\) | 324.000 | 0.235702 | ||||||||
\(19\) | 581.000 | 0.369226 | 0.184613 | − | 0.982811i | \(-0.440897\pi\) | ||||
0.184613 | + | 0.982811i | \(0.440897\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −9.00000 | −0.00445343 | ||||||||
\(22\) | −840.000 | −0.370018 | ||||||||
\(23\) | 4350.00 | 1.71463 | 0.857314 | − | 0.514795i | \(-0.172132\pi\) | ||||
0.857314 | + | 0.514795i | \(0.172132\pi\) | |||||||
\(24\) | −576.000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2668.00 | 0.774020 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 16.0000 | 0.00385678 | ||||||||
\(29\) | −126.000 | −0.0278212 | −0.0139106 | − | 0.999903i | \(-0.504428\pi\) | ||||
−0.0139106 | + | 0.999903i | \(0.504428\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7583.00 | 1.41722 | 0.708609 | − | 0.705601i | \(-0.249323\pi\) | ||||
0.708609 | + | 0.705601i | \(0.249323\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | 1890.00 | 0.302118 | ||||||||
\(34\) | −456.000 | −0.0676500 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | 3742.00 | 0.449365 | 0.224683 | − | 0.974432i | \(-0.427865\pi\) | ||||
0.224683 | + | 0.974432i | \(0.427865\pi\) | |||||||
\(38\) | 2324.00 | 0.261082 | ||||||||
\(39\) | −6003.00 | −0.631985 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2856.00 | −0.265337 | −0.132669 | − | 0.991160i | \(-0.542355\pi\) | ||||
−0.132669 | + | 0.991160i | \(0.542355\pi\) | |||||||
\(42\) | −36.0000 | −0.00314905 | ||||||||
\(43\) | 18241.0 | 1.50445 | 0.752225 | − | 0.658907i | \(-0.228981\pi\) | ||||
0.752225 | + | 0.658907i | \(0.228981\pi\) | |||||||
\(44\) | −3360.00 | −0.261642 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 17400.0 | 1.21242 | ||||||||
\(47\) | 23370.0 | 1.54317 | 0.771586 | − | 0.636126i | \(-0.219464\pi\) | ||||
0.771586 | + | 0.636126i | \(0.219464\pi\) | |||||||
\(48\) | −2304.00 | −0.144338 | ||||||||
\(49\) | −16806.0 | −0.999941 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1026.00 | 0.0552360 | ||||||||
\(52\) | 10672.0 | 0.547315 | ||||||||
\(53\) | 21684.0 | 1.06035 | 0.530176 | − | 0.847888i | \(-0.322126\pi\) | ||||
0.530176 | + | 0.847888i | \(0.322126\pi\) | |||||||
\(54\) | −2916.00 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 64.0000 | 0.00272716 | ||||||||
\(57\) | −5229.00 | −0.213173 | ||||||||
\(58\) | −504.000 | −0.0196725 | ||||||||
\(59\) | −32310.0 | −1.20839 | −0.604195 | − | 0.796837i | \(-0.706505\pi\) | ||||
−0.604195 | + | 0.796837i | \(0.706505\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7165.00 | −0.246542 | −0.123271 | − | 0.992373i | \(-0.539339\pi\) | ||||
−0.123271 | + | 0.992373i | \(0.539339\pi\) | |||||||
\(62\) | 30332.0 | 1.00212 | ||||||||
\(63\) | 81.0000 | 0.00257119 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7560.00 | 0.213630 | ||||||||
\(67\) | −59579.0 | −1.62146 | −0.810730 | − | 0.585420i | \(-0.800929\pi\) | ||||
−0.810730 | + | 0.585420i | \(0.800929\pi\) | |||||||
\(68\) | −1824.00 | −0.0478357 | ||||||||
\(69\) | −39150.0 | −0.989940 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −43080.0 | −1.01421 | −0.507107 | − | 0.861883i | \(-0.669285\pi\) | ||||
−0.507107 | + | 0.861883i | \(0.669285\pi\) | |||||||
\(72\) | 5184.00 | 0.117851 | ||||||||
\(73\) | 28942.0 | 0.635655 | 0.317827 | − | 0.948149i | \(-0.397047\pi\) | ||||
0.317827 | + | 0.948149i | \(0.397047\pi\) | |||||||
\(74\) | 14968.0 | 0.317749 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9296.00 | 0.184613 | ||||||||
\(77\) | −210.000 | −0.00403638 | ||||||||
\(78\) | −24012.0 | −0.446881 | ||||||||
\(79\) | 27608.0 | 0.497700 | 0.248850 | − | 0.968542i | \(-0.419947\pi\) | ||||
0.248850 | + | 0.968542i | \(0.419947\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −11424.0 | −0.187622 | ||||||||
\(83\) | 1782.00 | 0.0283931 | 0.0141965 | − | 0.999899i | \(-0.495481\pi\) | ||||
0.0141965 | + | 0.999899i | \(0.495481\pi\) | |||||||
\(84\) | −144.000 | −0.00222671 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 72964.0 | 1.06381 | ||||||||
\(87\) | 1134.00 | 0.0160626 | ||||||||
\(88\) | −13440.0 | −0.185009 | ||||||||
\(89\) | 50208.0 | 0.671890 | 0.335945 | − | 0.941882i | \(-0.390944\pi\) | ||||
0.335945 | + | 0.941882i | \(0.390944\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 667.000 | 0.00844350 | ||||||||
\(92\) | 69600.0 | 0.857314 | ||||||||
\(93\) | −68247.0 | −0.818231 | ||||||||
\(94\) | 93480.0 | 1.09119 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −9216.00 | −0.102062 | ||||||||
\(97\) | −142793. | −1.54091 | −0.770456 | − | 0.637494i | \(-0.779971\pi\) | ||||
−0.770456 | + | 0.637494i | \(0.779971\pi\) | |||||||
\(98\) | −67224.0 | −0.707065 | ||||||||
\(99\) | −17010.0 | −0.174428 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −164052. | −1.60021 | −0.800107 | − | 0.599857i | \(-0.795224\pi\) | ||||
−0.800107 | + | 0.599857i | \(0.795224\pi\) | |||||||
\(102\) | 4104.00 | 0.0390577 | ||||||||
\(103\) | 107236. | 0.995973 | 0.497986 | − | 0.867185i | \(-0.334073\pi\) | ||||
0.497986 | + | 0.867185i | \(0.334073\pi\) | |||||||
\(104\) | 42688.0 | 0.387010 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 86736.0 | 0.749782 | ||||||||
\(107\) | −21012.0 | −0.177422 | −0.0887111 | − | 0.996057i | \(-0.528275\pi\) | ||||
−0.0887111 | + | 0.996057i | \(0.528275\pi\) | |||||||
\(108\) | −11664.0 | −0.0962250 | ||||||||
\(109\) | 237545. | 1.91505 | 0.957524 | − | 0.288354i | \(-0.0931079\pi\) | ||||
0.957524 | + | 0.288354i | \(0.0931079\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −33678.0 | −0.259441 | ||||||||
\(112\) | 256.000 | 0.00192839 | ||||||||
\(113\) | −233388. | −1.71942 | −0.859711 | − | 0.510781i | \(-0.829356\pi\) | ||||
−0.859711 | + | 0.510781i | \(0.829356\pi\) | |||||||
\(114\) | −20916.0 | −0.150736 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2016.00 | −0.0139106 | ||||||||
\(117\) | 54027.0 | 0.364877 | ||||||||
\(118\) | −129240. | −0.854460 | ||||||||
\(119\) | −114.000 | −0.000737968 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −116951. | −0.726174 | ||||||||
\(122\) | −28660.0 | −0.174332 | ||||||||
\(123\) | 25704.0 | 0.153193 | ||||||||
\(124\) | 121328. | 0.708609 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 324.000 | 0.00181810 | ||||||||
\(127\) | −138800. | −0.763625 | −0.381813 | − | 0.924240i | \(-0.624700\pi\) | ||||
−0.381813 | + | 0.924240i | \(0.624700\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | −164169. | −0.868594 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −161340. | −0.821417 | −0.410709 | − | 0.911767i | \(-0.634719\pi\) | ||||
−0.410709 | + | 0.911767i | \(0.634719\pi\) | |||||||
\(132\) | 30240.0 | 0.151059 | ||||||||
\(133\) | 581.000 | 0.00284805 | ||||||||
\(134\) | −238316. | −1.14655 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7296.00 | −0.0338250 | ||||||||
\(137\) | −69054.0 | −0.314331 | −0.157166 | − | 0.987572i | \(-0.550236\pi\) | ||||
−0.157166 | + | 0.987572i | \(0.550236\pi\) | |||||||
\(138\) | −156600. | −0.699994 | ||||||||
\(139\) | 224396. | 0.985095 | 0.492547 | − | 0.870286i | \(-0.336066\pi\) | ||||
0.492547 | + | 0.870286i | \(0.336066\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −210330. | −0.890950 | ||||||||
\(142\) | −172320. | −0.717158 | ||||||||
\(143\) | −140070. | −0.572803 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 115768. | 0.449476 | ||||||||
\(147\) | 151254. | 0.577316 | ||||||||
\(148\) | 59872.0 | 0.224683 | ||||||||
\(149\) | −407646. | −1.50424 | −0.752121 | − | 0.659025i | \(-0.770969\pi\) | ||||
−0.752121 | + | 0.659025i | \(0.770969\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 216053. | 0.771113 | 0.385556 | − | 0.922684i | \(-0.374010\pi\) | ||||
0.385556 | + | 0.922684i | \(0.374010\pi\) | |||||||
\(152\) | 37184.0 | 0.130541 | ||||||||
\(153\) | −9234.00 | −0.0318905 | ||||||||
\(154\) | −840.000 | −0.00285415 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −96048.0 | −0.315993 | ||||||||
\(157\) | 188617. | 0.610705 | 0.305353 | − | 0.952239i | \(-0.401226\pi\) | ||||
0.305353 | + | 0.952239i | \(0.401226\pi\) | |||||||
\(158\) | 110432. | 0.351927 | ||||||||
\(159\) | −195156. | −0.612194 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4350.00 | 0.0132259 | ||||||||
\(162\) | 26244.0 | 0.0785674 | ||||||||
\(163\) | 422251. | 1.24481 | 0.622403 | − | 0.782697i | \(-0.286157\pi\) | ||||
0.622403 | + | 0.782697i | \(0.286157\pi\) | |||||||
\(164\) | −45696.0 | −0.132669 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7128.00 | 0.0200769 | ||||||||
\(167\) | −41700.0 | −0.115703 | −0.0578515 | − | 0.998325i | \(-0.518425\pi\) | ||||
−0.0578515 | + | 0.998325i | \(0.518425\pi\) | |||||||
\(168\) | −576.000 | −0.00157452 | ||||||||
\(169\) | 73596.0 | 0.198215 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 47061.0 | 0.123075 | ||||||||
\(172\) | 291856. | 0.752225 | ||||||||
\(173\) | −266142. | −0.676080 | −0.338040 | − | 0.941132i | \(-0.609764\pi\) | ||||
−0.338040 | + | 0.941132i | \(0.609764\pi\) | |||||||
\(174\) | 4536.00 | 0.0113579 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −53760.0 | −0.130821 | ||||||||
\(177\) | 290790. | 0.697664 | ||||||||
\(178\) | 200832. | 0.475098 | ||||||||
\(179\) | −51846.0 | −0.120944 | −0.0604718 | − | 0.998170i | \(-0.519261\pi\) | ||||
−0.0604718 | + | 0.998170i | \(0.519261\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 499349. | 1.13294 | 0.566471 | − | 0.824082i | \(-0.308308\pi\) | ||||
0.566471 | + | 0.824082i | \(0.308308\pi\) | |||||||
\(182\) | 2668.00 | 0.00597045 | ||||||||
\(183\) | 64485.0 | 0.142341 | ||||||||
\(184\) | 278400. | 0.606212 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −272988. | −0.578577 | ||||||||
\(187\) | 23940.0 | 0.0500634 | ||||||||
\(188\) | 373920. | 0.771586 | ||||||||
\(189\) | −729.000 | −0.00148448 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 705906. | 1.40011 | 0.700057 | − | 0.714087i | \(-0.253158\pi\) | ||||
0.700057 | + | 0.714087i | \(0.253158\pi\) | |||||||
\(192\) | −36864.0 | −0.0721688 | ||||||||
\(193\) | 519973. | 1.00482 | 0.502409 | − | 0.864630i | \(-0.332447\pi\) | ||||
0.502409 | + | 0.864630i | \(0.332447\pi\) | |||||||
\(194\) | −571172. | −1.08959 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −268896. | −0.499970 | ||||||||
\(197\) | 200394. | 0.367891 | 0.183945 | − | 0.982936i | \(-0.441113\pi\) | ||||
0.183945 | + | 0.982936i | \(0.441113\pi\) | |||||||
\(198\) | −68040.0 | −0.123339 | ||||||||
\(199\) | 553673. | 0.991107 | 0.495554 | − | 0.868577i | \(-0.334965\pi\) | ||||
0.495554 | + | 0.868577i | \(0.334965\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 536211. | 0.936150 | ||||||||
\(202\) | −656208. | −1.13152 | ||||||||
\(203\) | −126.000 | −0.000214600 0 | ||||||||
\(204\) | 16416.0 | 0.0276180 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 428944. | 0.704259 | ||||||||
\(207\) | 352350. | 0.571542 | ||||||||
\(208\) | 170752. | 0.273658 | ||||||||
\(209\) | −122010. | −0.193210 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 777365. | 1.20204 | 0.601020 | − | 0.799234i | \(-0.294761\pi\) | ||||
0.601020 | + | 0.799234i | \(0.294761\pi\) | |||||||
\(212\) | 346944. | 0.530176 | ||||||||
\(213\) | 387720. | 0.585557 | ||||||||
\(214\) | −84048.0 | −0.125456 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −46656.0 | −0.0680414 | ||||||||
\(217\) | 7583.00 | 0.0109318 | ||||||||
\(218\) | 950180. | 1.35414 | ||||||||
\(219\) | −260478. | −0.366996 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −76038.0 | −0.104725 | ||||||||
\(222\) | −134712. | −0.183453 | ||||||||
\(223\) | 776185. | 1.04521 | 0.522604 | − | 0.852575i | \(-0.324960\pi\) | ||||
0.522604 | + | 0.852575i | \(0.324960\pi\) | |||||||
\(224\) | 1024.00 | 0.00136358 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −933552. | −1.21581 | ||||||||
\(227\) | −919992. | −1.18500 | −0.592501 | − | 0.805569i | \(-0.701860\pi\) | ||||
−0.592501 | + | 0.805569i | \(0.701860\pi\) | |||||||
\(228\) | −83664.0 | −0.106586 | ||||||||
\(229\) | −1.13220e6 | −1.42670 | −0.713350 | − | 0.700808i | \(-0.752823\pi\) | ||||
−0.713350 | + | 0.700808i | \(0.752823\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1890.00 | 0.00233041 | ||||||||
\(232\) | −8064.00 | −0.00983627 | ||||||||
\(233\) | −823128. | −0.993293 | −0.496647 | − | 0.867953i | \(-0.665436\pi\) | ||||
−0.496647 | + | 0.867953i | \(0.665436\pi\) | |||||||
\(234\) | 216108. | 0.258007 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −516960. | −0.604195 | ||||||||
\(237\) | −248472. | −0.287347 | ||||||||
\(238\) | −456.000 | −0.000521822 0 | ||||||||
\(239\) | 1.32836e6 | 1.50426 | 0.752129 | − | 0.659016i | \(-0.229027\pi\) | ||||
0.752129 | + | 0.659016i | \(0.229027\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 94937.0 | 0.105291 | 0.0526457 | − | 0.998613i | \(-0.483235\pi\) | ||||
0.0526457 | + | 0.998613i | \(0.483235\pi\) | |||||||
\(242\) | −467804. | −0.513482 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | −114640. | −0.123271 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 102816. | 0.108324 | ||||||||
\(247\) | 387527. | 0.404166 | ||||||||
\(248\) | 485312. | 0.501062 | ||||||||
\(249\) | −16038.0 | −0.0163928 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −128124. | −0.128365 | −0.0641824 | − | 0.997938i | \(-0.520444\pi\) | ||||
−0.0641824 | + | 0.997938i | \(0.520444\pi\) | |||||||
\(252\) | 1296.00 | 0.00128559 | ||||||||
\(253\) | −913500. | −0.897237 | ||||||||
\(254\) | −555200. | −0.539964 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 1.72285e6 | 1.62710 | 0.813552 | − | 0.581493i | \(-0.197531\pi\) | ||||
0.813552 | + | 0.581493i | \(0.197531\pi\) | |||||||
\(258\) | −656676. | −0.614189 | ||||||||
\(259\) | 3742.00 | 0.00346621 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10206.0 | −0.00927373 | ||||||||
\(262\) | −645360. | −0.580830 | ||||||||
\(263\) | −692160. | −0.617045 | −0.308523 | − | 0.951217i | \(-0.599835\pi\) | ||||
−0.308523 | + | 0.951217i | \(0.599835\pi\) | |||||||
\(264\) | 120960. | 0.106815 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2324.00 | 0.00201387 | ||||||||
\(267\) | −451872. | −0.387916 | ||||||||
\(268\) | −953264. | −0.810730 | ||||||||
\(269\) | 690894. | 0.582144 | 0.291072 | − | 0.956701i | \(-0.405988\pi\) | ||||
0.291072 | + | 0.956701i | \(0.405988\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.04690e6 | −0.865925 | −0.432963 | − | 0.901412i | \(-0.642532\pi\) | ||||
−0.432963 | + | 0.901412i | \(0.642532\pi\) | |||||||
\(272\) | −29184.0 | −0.0239179 | ||||||||
\(273\) | −6003.00 | −0.00487486 | ||||||||
\(274\) | −276216. | −0.222266 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −626400. | −0.494970 | ||||||||
\(277\) | 1.07137e6 | 0.838955 | 0.419478 | − | 0.907766i | \(-0.362213\pi\) | ||||
0.419478 | + | 0.907766i | \(0.362213\pi\) | |||||||
\(278\) | 897584. | 0.696567 | ||||||||
\(279\) | 614223. | 0.472406 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.40416e6 | −1.06084 | −0.530422 | − | 0.847734i | \(-0.677966\pi\) | ||||
−0.530422 | + | 0.847734i | \(0.677966\pi\) | |||||||
\(282\) | −841320. | −0.629997 | ||||||||
\(283\) | −1.68203e6 | −1.24844 | −0.624221 | − | 0.781248i | \(-0.714584\pi\) | ||||
−0.624221 | + | 0.781248i | \(0.714584\pi\) | |||||||
\(284\) | −689280. | −0.507107 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −560280. | −0.405033 | ||||||||
\(287\) | −2856.00 | −0.00204670 | ||||||||
\(288\) | 82944.0 | 0.0589256 | ||||||||
\(289\) | −1.40686e6 | −0.990847 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.28514e6 | 0.889645 | ||||||||
\(292\) | 463072. | 0.317827 | ||||||||
\(293\) | −1.76293e6 | −1.19968 | −0.599839 | − | 0.800120i | \(-0.704769\pi\) | ||||
−0.599839 | + | 0.800120i | \(0.704769\pi\) | |||||||
\(294\) | 605016. | 0.408224 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 239488. | 0.158875 | ||||||||
\(297\) | 153090. | 0.100706 | ||||||||
\(298\) | −1.63058e6 | −1.06366 | ||||||||
\(299\) | 2.90145e6 | 1.87688 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18241.0 | 0.0116047 | ||||||||
\(302\) | 864212. | 0.545259 | ||||||||
\(303\) | 1.47647e6 | 0.923884 | ||||||||
\(304\) | 148736. | 0.0923065 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −36936.0 | −0.0225500 | ||||||||
\(307\) | −471905. | −0.285765 | −0.142882 | − | 0.989740i | \(-0.545637\pi\) | ||||
−0.142882 | + | 0.989740i | \(0.545637\pi\) | |||||||
\(308\) | −3360.00 | −0.00201819 | ||||||||
\(309\) | −965124. | −0.575025 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.64439e6 | −0.964060 | −0.482030 | − | 0.876155i | \(-0.660100\pi\) | ||||
−0.482030 | + | 0.876155i | \(0.660100\pi\) | |||||||
\(312\) | −384192. | −0.223440 | ||||||||
\(313\) | −2.37908e6 | −1.37262 | −0.686308 | − | 0.727311i | \(-0.740770\pi\) | ||||
−0.686308 | + | 0.727311i | \(0.740770\pi\) | |||||||
\(314\) | 754468. | 0.431834 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 441728. | 0.248850 | ||||||||
\(317\) | −1.32679e6 | −0.741574 | −0.370787 | − | 0.928718i | \(-0.620912\pi\) | ||||
−0.370787 | + | 0.928718i | \(0.620912\pi\) | |||||||
\(318\) | −780624. | −0.432887 | ||||||||
\(319\) | 26460.0 | 0.0145584 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 189108. | 0.102435 | ||||||||
\(322\) | 17400.0 | 0.00935211 | ||||||||
\(323\) | −66234.0 | −0.0353244 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.68900e6 | 0.880211 | ||||||||
\(327\) | −2.13790e6 | −1.10565 | ||||||||
\(328\) | −182784. | −0.0938110 | ||||||||
\(329\) | 23370.0 | 0.0119033 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 661172. | 0.331699 | 0.165850 | − | 0.986151i | \(-0.446963\pi\) | ||||
0.165850 | + | 0.986151i | \(0.446963\pi\) | |||||||
\(332\) | 28512.0 | 0.0141965 | ||||||||
\(333\) | 303102. | 0.149788 | ||||||||
\(334\) | −166800. | −0.0818144 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2304.00 | −0.00111336 | ||||||||
\(337\) | 1.53675e6 | 0.737104 | 0.368552 | − | 0.929607i | \(-0.379854\pi\) | ||||
0.368552 | + | 0.929607i | \(0.379854\pi\) | |||||||
\(338\) | 294384. | 0.140159 | ||||||||
\(339\) | 2.10049e6 | 0.992709 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.59243e6 | −0.741608 | ||||||||
\(342\) | 188244. | 0.0870274 | ||||||||
\(343\) | −33613.0 | −0.0154267 | ||||||||
\(344\) | 1.16742e6 | 0.531903 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.06457e6 | −0.478061 | ||||||||
\(347\) | −3.86576e6 | −1.72350 | −0.861749 | − | 0.507334i | \(-0.830631\pi\) | ||||
−0.861749 | + | 0.507334i | \(0.830631\pi\) | |||||||
\(348\) | 18144.0 | 0.00803128 | ||||||||
\(349\) | −4.23391e6 | −1.86071 | −0.930354 | − | 0.366663i | \(-0.880500\pi\) | ||||
−0.930354 | + | 0.366663i | \(0.880500\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −486243. | −0.210662 | ||||||||
\(352\) | −215040. | −0.0925044 | ||||||||
\(353\) | 2.41459e6 | 1.03135 | 0.515675 | − | 0.856784i | \(-0.327541\pi\) | ||||
0.515675 | + | 0.856784i | \(0.327541\pi\) | |||||||
\(354\) | 1.16316e6 | 0.493323 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 803328. | 0.335945 | ||||||||
\(357\) | 1026.00 | 0.000426066 0 | ||||||||
\(358\) | −207384. | −0.0855200 | ||||||||
\(359\) | 2.94802e6 | 1.20724 | 0.603620 | − | 0.797272i | \(-0.293724\pi\) | ||||
0.603620 | + | 0.797272i | \(0.293724\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.13854e6 | −0.863672 | ||||||||
\(362\) | 1.99740e6 | 0.801111 | ||||||||
\(363\) | 1.05256e6 | 0.419257 | ||||||||
\(364\) | 10672.0 | 0.00422175 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 257940. | 0.100651 | ||||||||
\(367\) | −679793. | −0.263458 | −0.131729 | − | 0.991286i | \(-0.542053\pi\) | ||||
−0.131729 | + | 0.991286i | \(0.542053\pi\) | |||||||
\(368\) | 1.11360e6 | 0.428657 | ||||||||
\(369\) | −231336. | −0.0884458 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21684.0 | 0.00817908 | ||||||||
\(372\) | −1.09195e6 | −0.409116 | ||||||||
\(373\) | 3.60888e6 | 1.34308 | 0.671538 | − | 0.740970i | \(-0.265634\pi\) | ||||
0.671538 | + | 0.740970i | \(0.265634\pi\) | |||||||
\(374\) | 95760.0 | 0.0354002 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.49568e6 | 0.545593 | ||||||||
\(377\) | −84042.0 | −0.0304539 | ||||||||
\(378\) | −2916.00 | −0.00104968 | ||||||||
\(379\) | −386809. | −0.138324 | −0.0691622 | − | 0.997605i | \(-0.522033\pi\) | ||||
−0.0691622 | + | 0.997605i | \(0.522033\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.24920e6 | 0.440879 | ||||||||
\(382\) | 2.82362e6 | 0.990030 | ||||||||
\(383\) | 645060. | 0.224700 | 0.112350 | − | 0.993669i | \(-0.464162\pi\) | ||||
0.112350 | + | 0.993669i | \(0.464162\pi\) | |||||||
\(384\) | −147456. | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.07989e6 | 0.710514 | ||||||||
\(387\) | 1.47752e6 | 0.501483 | ||||||||
\(388\) | −2.28469e6 | −0.770456 | ||||||||
\(389\) | −812976. | −0.272398 | −0.136199 | − | 0.990682i | \(-0.543489\pi\) | ||||
−0.136199 | + | 0.990682i | \(0.543489\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −495900. | −0.164041 | ||||||||
\(392\) | −1.07558e6 | −0.353532 | ||||||||
\(393\) | 1.45206e6 | 0.474245 | ||||||||
\(394\) | 801576. | 0.260138 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −272160. | −0.0872140 | ||||||||
\(397\) | 988813. | 0.314875 | 0.157437 | − | 0.987529i | \(-0.449677\pi\) | ||||
0.157437 | + | 0.987529i | \(0.449677\pi\) | |||||||
\(398\) | 2.21469e6 | 0.700819 | ||||||||
\(399\) | −5229.00 | −0.00164432 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.14580e6 | 0.666391 | 0.333195 | − | 0.942858i | \(-0.391873\pi\) | ||||
0.333195 | + | 0.942858i | \(0.391873\pi\) | |||||||
\(402\) | 2.14484e6 | 0.661958 | ||||||||
\(403\) | 5.05786e6 | 1.55133 | ||||||||
\(404\) | −2.62483e6 | −0.800107 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −504.000 | −0.000151745 0 | ||||||||
\(407\) | −785820. | −0.235146 | ||||||||
\(408\) | 65664.0 | 0.0195289 | ||||||||
\(409\) | −5.77658e6 | −1.70751 | −0.853753 | − | 0.520678i | \(-0.825679\pi\) | ||||
−0.853753 | + | 0.520678i | \(0.825679\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 621486. | 0.181479 | ||||||||
\(412\) | 1.71578e6 | 0.497986 | ||||||||
\(413\) | −32310.0 | −0.00932099 | ||||||||
\(414\) | 1.40940e6 | 0.404141 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 683008. | 0.193505 | ||||||||
\(417\) | −2.01956e6 | −0.568745 | ||||||||
\(418\) | −488040. | −0.136620 | ||||||||
\(419\) | −5.07318e6 | −1.41171 | −0.705855 | − | 0.708357i | \(-0.749437\pi\) | ||||
−0.705855 | + | 0.708357i | \(0.749437\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.01297e6 | −0.828494 | −0.414247 | − | 0.910164i | \(-0.635955\pi\) | ||||
−0.414247 | + | 0.910164i | \(0.635955\pi\) | |||||||
\(422\) | 3.10946e6 | 0.849970 | ||||||||
\(423\) | 1.89297e6 | 0.514390 | ||||||||
\(424\) | 1.38778e6 | 0.374891 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.55088e6 | 0.414051 | ||||||||
\(427\) | −7165.00 | −0.00190172 | ||||||||
\(428\) | −336192. | −0.0887111 | ||||||||
\(429\) | 1.26063e6 | 0.330708 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.59449e6 | 1.45067 | 0.725333 | − | 0.688398i | \(-0.241686\pi\) | ||||
0.725333 | + | 0.688398i | \(0.241686\pi\) | |||||||
\(432\) | −186624. | −0.0481125 | ||||||||
\(433\) | −5.63454e6 | −1.44424 | −0.722119 | − | 0.691769i | \(-0.756832\pi\) | ||||
−0.722119 | + | 0.691769i | \(0.756832\pi\) | |||||||
\(434\) | 30332.0 | 0.00772995 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.80072e6 | 0.957524 | ||||||||
\(437\) | 2.52735e6 | 0.633085 | ||||||||
\(438\) | −1.04191e6 | −0.259505 | ||||||||
\(439\) | 860663. | 0.213143 | 0.106572 | − | 0.994305i | \(-0.466013\pi\) | ||||
0.106572 | + | 0.994305i | \(0.466013\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.36129e6 | −0.333314 | ||||||||
\(442\) | −304152. | −0.0740517 | ||||||||
\(443\) | 2.75335e6 | 0.666580 | 0.333290 | − | 0.942824i | \(-0.391841\pi\) | ||||
0.333290 | + | 0.942824i | \(0.391841\pi\) | |||||||
\(444\) | −538848. | −0.129721 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.10474e6 | 0.739074 | ||||||||
\(447\) | 3.66881e6 | 0.868474 | ||||||||
\(448\) | 4096.00 | 0.000964195 0 | ||||||||
\(449\) | −2.83168e6 | −0.662869 | −0.331434 | − | 0.943478i | \(-0.607533\pi\) | ||||
−0.331434 | + | 0.943478i | \(0.607533\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 599760. | 0.138847 | ||||||||
\(452\) | −3.73421e6 | −0.859711 | ||||||||
\(453\) | −1.94448e6 | −0.445202 | ||||||||
\(454\) | −3.67997e6 | −0.837924 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −334656. | −0.0753679 | ||||||||
\(457\) | 4.66235e6 | 1.04427 | 0.522136 | − | 0.852862i | \(-0.325135\pi\) | ||||
0.522136 | + | 0.852862i | \(0.325135\pi\) | |||||||
\(458\) | −4.52878e6 | −1.00883 | ||||||||
\(459\) | 83106.0 | 0.0184120 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.27154e6 | −1.15527 | −0.577637 | − | 0.816294i | \(-0.696025\pi\) | ||||
−0.577637 | + | 0.816294i | \(0.696025\pi\) | |||||||
\(462\) | 7560.00 | 0.00164785 | ||||||||
\(463\) | 7.16954e6 | 1.55431 | 0.777157 | − | 0.629307i | \(-0.216661\pi\) | ||||
0.777157 | + | 0.629307i | \(0.216661\pi\) | |||||||
\(464\) | −32256.0 | −0.00695530 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.29251e6 | −0.702365 | ||||||||
\(467\) | −4.30441e6 | −0.913316 | −0.456658 | − | 0.889642i | \(-0.650954\pi\) | ||||
−0.456658 | + | 0.889642i | \(0.650954\pi\) | |||||||
\(468\) | 864432. | 0.182438 | ||||||||
\(469\) | −59579.0 | −0.0125072 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.69755e6 | −0.352591 | ||||||||
\(472\) | −2.06784e6 | −0.427230 | ||||||||
\(473\) | −3.83061e6 | −0.787254 | ||||||||
\(474\) | −993888. | −0.203185 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1824.00 | −0.000368984 0 | ||||||||
\(477\) | 1.75640e6 | 0.353450 | ||||||||
\(478\) | 5.31346e6 | 1.06367 | ||||||||
\(479\) | 190506. | 0.0379376 | 0.0189688 | − | 0.999820i | \(-0.493962\pi\) | ||||
0.0189688 | + | 0.999820i | \(0.493962\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.49591e6 | 0.491889 | ||||||||
\(482\) | 379748. | 0.0744523 | ||||||||
\(483\) | −39150.0 | −0.00763597 | ||||||||
\(484\) | −1.87122e6 | −0.363087 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −236196. | −0.0453609 | ||||||||
\(487\) | 128887. | 0.0246256 | 0.0123128 | − | 0.999924i | \(-0.496081\pi\) | ||||
0.0123128 | + | 0.999924i | \(0.496081\pi\) | |||||||
\(488\) | −458560. | −0.0871659 | ||||||||
\(489\) | −3.80026e6 | −0.718689 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −304296. | −0.0569630 | −0.0284815 | − | 0.999594i | \(-0.509067\pi\) | ||||
−0.0284815 | + | 0.999594i | \(0.509067\pi\) | |||||||
\(492\) | 411264. | 0.0765963 | ||||||||
\(493\) | 14364.0 | 0.00266169 | ||||||||
\(494\) | 1.55011e6 | 0.285788 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.94125e6 | 0.354305 | ||||||||
\(497\) | −43080.0 | −0.00782321 | ||||||||
\(498\) | −64152.0 | −0.0115914 | ||||||||
\(499\) | 6.41974e6 | 1.15416 | 0.577080 | − | 0.816688i | \(-0.304192\pi\) | ||||
0.577080 | + | 0.816688i | \(0.304192\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 375300. | 0.0668012 | ||||||||
\(502\) | −512496. | −0.0907677 | ||||||||
\(503\) | 1.55534e6 | 0.274098 | 0.137049 | − | 0.990564i | \(-0.456238\pi\) | ||||
0.137049 | + | 0.990564i | \(0.456238\pi\) | |||||||
\(504\) | 5184.00 | 0.000909052 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.65400e6 | −0.634442 | ||||||||
\(507\) | −662364. | −0.114440 | ||||||||
\(508\) | −2.22080e6 | −0.381813 | ||||||||
\(509\) | −541506. | −0.0926422 | −0.0463211 | − | 0.998927i | \(-0.514750\pi\) | ||||
−0.0463211 | + | 0.998927i | \(0.514750\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28942.0 | 0.00490316 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | −423549. | −0.0710576 | ||||||||
\(514\) | 6.89141e6 | 1.15054 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.62670e6 | −0.434297 | ||||||||
\(517\) | −4.90770e6 | −0.807517 | ||||||||
\(518\) | 14968.0 | 0.00245098 | ||||||||
\(519\) | 2.39528e6 | 0.390335 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −888762. | −0.143447 | −0.0717235 | − | 0.997425i | \(-0.522850\pi\) | ||||
−0.0717235 | + | 0.997425i | \(0.522850\pi\) | |||||||
\(522\) | −40824.0 | −0.00655752 | ||||||||
\(523\) | −7.69950e6 | −1.23086 | −0.615430 | − | 0.788192i | \(-0.711018\pi\) | ||||
−0.615430 | + | 0.788192i | \(0.711018\pi\) | |||||||
\(524\) | −2.58144e6 | −0.410709 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.76864e6 | −0.436317 | ||||||||
\(527\) | −864462. | −0.135587 | ||||||||
\(528\) | 483840. | 0.0755296 | ||||||||
\(529\) | 1.24862e7 | 1.93995 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.61711e6 | −0.402796 | ||||||||
\(532\) | 9296.00 | 0.00142402 | ||||||||
\(533\) | −1.90495e6 | −0.290446 | ||||||||
\(534\) | −1.80749e6 | −0.274298 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.81306e6 | −0.573273 | ||||||||
\(537\) | 466614. | 0.0698268 | ||||||||
\(538\) | 2.76358e6 | 0.411638 | ||||||||
\(539\) | 3.52926e6 | 0.523253 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.01878e6 | −0.443443 | −0.221721 | − | 0.975110i | \(-0.571168\pi\) | ||||
−0.221721 | + | 0.975110i | \(0.571168\pi\) | |||||||
\(542\) | −4.18758e6 | −0.612301 | ||||||||
\(543\) | −4.49414e6 | −0.654104 | ||||||||
\(544\) | −116736. | −0.0169125 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −24012.0 | −0.00344704 | ||||||||
\(547\) | −7.23481e6 | −1.03385 | −0.516926 | − | 0.856030i | \(-0.672924\pi\) | ||||
−0.516926 | + | 0.856030i | \(0.672924\pi\) | |||||||
\(548\) | −1.10486e6 | −0.157166 | ||||||||
\(549\) | −580365. | −0.0821808 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −73206.0 | −0.0102723 | ||||||||
\(552\) | −2.50560e6 | −0.349997 | ||||||||
\(553\) | 27608.0 | 0.00383904 | ||||||||
\(554\) | 4.28547e6 | 0.593231 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.59034e6 | 0.492547 | ||||||||
\(557\) | 9.88712e6 | 1.35030 | 0.675152 | − | 0.737678i | \(-0.264078\pi\) | ||||
0.675152 | + | 0.737678i | \(0.264078\pi\) | |||||||
\(558\) | 2.45689e6 | 0.334042 | ||||||||
\(559\) | 1.21667e7 | 1.64682 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −215460. | −0.0289041 | ||||||||
\(562\) | −5.61665e6 | −0.750130 | ||||||||
\(563\) | −946362. | −0.125831 | −0.0629153 | − | 0.998019i | \(-0.520040\pi\) | ||||
−0.0629153 | + | 0.998019i | \(0.520040\pi\) | |||||||
\(564\) | −3.36528e6 | −0.445475 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.72813e6 | −0.882782 | ||||||||
\(567\) | 6561.00 | 0.000857062 0 | ||||||||
\(568\) | −2.75712e6 | −0.358579 | ||||||||
\(569\) | −4.51552e6 | −0.584692 | −0.292346 | − | 0.956313i | \(-0.594436\pi\) | ||||
−0.292346 | + | 0.956313i | \(0.594436\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.57824e6 | 0.972699 | 0.486349 | − | 0.873764i | \(-0.338328\pi\) | ||||
0.486349 | + | 0.873764i | \(0.338328\pi\) | |||||||
\(572\) | −2.24112e6 | −0.286401 | ||||||||
\(573\) | −6.35315e6 | −0.808356 | ||||||||
\(574\) | −11424.0 | −0.00144723 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | −1.11688e7 | −1.39659 | −0.698295 | − | 0.715811i | \(-0.746057\pi\) | ||||
−0.698295 | + | 0.715811i | \(0.746057\pi\) | |||||||
\(578\) | −5.62744e6 | −0.700635 | ||||||||
\(579\) | −4.67976e6 | −0.580132 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1782.00 | 0.000219012 0 | ||||||||
\(582\) | 5.14055e6 | 0.629074 | ||||||||
\(583\) | −4.55364e6 | −0.554865 | ||||||||
\(584\) | 1.85229e6 | 0.224738 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.05170e6 | −0.848301 | ||||||||
\(587\) | −1.01053e6 | −0.121047 | −0.0605236 | − | 0.998167i | \(-0.519277\pi\) | ||||
−0.0605236 | + | 0.998167i | \(0.519277\pi\) | |||||||
\(588\) | 2.42006e6 | 0.288658 | ||||||||
\(589\) | 4.40572e6 | 0.523274 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.80355e6 | −0.212402 | ||||||||
\(592\) | 957952. | 0.112341 | ||||||||
\(593\) | −1.13674e7 | −1.32746 | −0.663732 | − | 0.747970i | \(-0.731029\pi\) | ||||
−0.663732 | + | 0.747970i | \(0.731029\pi\) | |||||||
\(594\) | 612360. | 0.0712100 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.52234e6 | −0.752121 | ||||||||
\(597\) | −4.98306e6 | −0.572216 | ||||||||
\(598\) | 1.16058e7 | 1.32716 | ||||||||
\(599\) | 2.56732e6 | 0.292356 | 0.146178 | − | 0.989258i | \(-0.453303\pi\) | ||||
0.146178 | + | 0.989258i | \(0.453303\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.59837e7 | 1.80506 | 0.902530 | − | 0.430626i | \(-0.141707\pi\) | ||||
0.902530 | + | 0.430626i | \(0.141707\pi\) | |||||||
\(602\) | 72964.0 | 0.00820573 | ||||||||
\(603\) | −4.82590e6 | −0.540487 | ||||||||
\(604\) | 3.45685e6 | 0.385556 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.90587e6 | 0.653285 | ||||||||
\(607\) | 1.01626e7 | 1.11952 | 0.559760 | − | 0.828655i | \(-0.310893\pi\) | ||||
0.559760 | + | 0.828655i | \(0.310893\pi\) | |||||||
\(608\) | 594944. | 0.0652705 | ||||||||
\(609\) | 1134.00 | 0.000123900 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.55878e7 | 1.68920 | ||||||||
\(612\) | −147744. | −0.0159452 | ||||||||
\(613\) | −5.83042e6 | −0.626684 | −0.313342 | − | 0.949640i | \(-0.601449\pi\) | ||||
−0.313342 | + | 0.949640i | \(0.601449\pi\) | |||||||
\(614\) | −1.88762e6 | −0.202066 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −13440.0 | −0.00142708 | ||||||||
\(617\) | 1.51029e7 | 1.59716 | 0.798578 | − | 0.601891i | \(-0.205586\pi\) | ||||
0.798578 | + | 0.601891i | \(0.205586\pi\) | |||||||
\(618\) | −3.86050e6 | −0.406604 | ||||||||
\(619\) | −5.38515e6 | −0.564900 | −0.282450 | − | 0.959282i | \(-0.591147\pi\) | ||||
−0.282450 | + | 0.959282i | \(0.591147\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.17115e6 | −0.329980 | ||||||||
\(622\) | −6.57756e6 | −0.681693 | ||||||||
\(623\) | 50208.0 | 0.00518266 | ||||||||
\(624\) | −1.53677e6 | −0.157996 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −9.51633e6 | −0.970585 | ||||||||
\(627\) | 1.09809e6 | 0.111550 | ||||||||
\(628\) | 3.01787e6 | 0.305353 | ||||||||
\(629\) | −426588. | −0.0429914 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.59345e6 | −0.559251 | −0.279625 | − | 0.960109i | \(-0.590210\pi\) | ||||
−0.279625 | + | 0.960109i | \(0.590210\pi\) | |||||||
\(632\) | 1.76691e6 | 0.175963 | ||||||||
\(633\) | −6.99628e6 | −0.693998 | ||||||||
\(634\) | −5.30717e6 | −0.524372 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.12250e6 | −0.306097 | ||||||||
\(637\) | −1.12096e7 | −1.09457 | ||||||||
\(638\) | 105840. | 0.0102943 | ||||||||
\(639\) | −3.48948e6 | −0.338072 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.00072e7 | −0.961985 | −0.480993 | − | 0.876725i | \(-0.659724\pi\) | ||||
−0.480993 | + | 0.876725i | \(0.659724\pi\) | |||||||
\(642\) | 756432. | 0.0724323 | ||||||||
\(643\) | 9.95036e6 | 0.949098 | 0.474549 | − | 0.880229i | \(-0.342611\pi\) | ||||
0.474549 | + | 0.880229i | \(0.342611\pi\) | |||||||
\(644\) | 69600.0 | 0.00661294 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −264936. | −0.0249781 | ||||||||
\(647\) | 9.16904e6 | 0.861119 | 0.430560 | − | 0.902562i | \(-0.358316\pi\) | ||||
0.430560 | + | 0.902562i | \(0.358316\pi\) | |||||||
\(648\) | 419904. | 0.0392837 | ||||||||
\(649\) | 6.78510e6 | 0.632331 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −68247.0 | −0.00631148 | ||||||||
\(652\) | 6.75602e6 | 0.622403 | ||||||||
\(653\) | 1.77127e7 | 1.62555 | 0.812777 | − | 0.582575i | \(-0.197955\pi\) | ||||
0.812777 | + | 0.582575i | \(0.197955\pi\) | |||||||
\(654\) | −8.55162e6 | −0.781815 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −731136. | −0.0663344 | ||||||||
\(657\) | 2.34430e6 | 0.211885 | ||||||||
\(658\) | 93480.0 | 0.00841693 | ||||||||
\(659\) | −2.07949e7 | −1.86527 | −0.932637 | − | 0.360816i | \(-0.882498\pi\) | ||||
−0.932637 | + | 0.360816i | \(0.882498\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.51745e6 | −0.135086 | −0.0675429 | − | 0.997716i | \(-0.521516\pi\) | ||||
−0.0675429 | + | 0.997716i | \(0.521516\pi\) | |||||||
\(662\) | 2.64469e6 | 0.234547 | ||||||||
\(663\) | 684342. | 0.0604630 | ||||||||
\(664\) | 114048. | 0.0100385 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.21241e6 | 0.105916 | ||||||||
\(667\) | −548100. | −0.0477029 | ||||||||
\(668\) | −667200. | −0.0578515 | ||||||||
\(669\) | −6.98566e6 | −0.603452 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.50465e6 | 0.129012 | ||||||||
\(672\) | −9216.00 | −0.000787262 0 | ||||||||
\(673\) | 2.90483e6 | 0.247219 | 0.123610 | − | 0.992331i | \(-0.460553\pi\) | ||||
0.123610 | + | 0.992331i | \(0.460553\pi\) | |||||||
\(674\) | 6.14700e6 | 0.521211 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.17754e6 | 0.0991077 | ||||||||
\(677\) | 7.06049e6 | 0.592057 | 0.296028 | − | 0.955179i | \(-0.404338\pi\) | ||||
0.296028 | + | 0.955179i | \(0.404338\pi\) | |||||||
\(678\) | 8.40197e6 | 0.701951 | ||||||||
\(679\) | −142793. | −0.0118859 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.27993e6 | 0.684162 | ||||||||
\(682\) | −6.36972e6 | −0.524396 | ||||||||
\(683\) | −3.81415e6 | −0.312857 | −0.156429 | − | 0.987689i | \(-0.549998\pi\) | ||||
−0.156429 | + | 0.987689i | \(0.549998\pi\) | |||||||
\(684\) | 752976. | 0.0615376 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −134452. | −0.0109083 | ||||||||
\(687\) | 1.01898e7 | 0.823705 | ||||||||
\(688\) | 4.66970e6 | 0.376112 | ||||||||
\(689\) | 1.44632e7 | 1.16069 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.95166e6 | −0.713195 | −0.356597 | − | 0.934258i | \(-0.616063\pi\) | ||||
−0.356597 | + | 0.934258i | \(0.616063\pi\) | |||||||
\(692\) | −4.25827e6 | −0.338040 | ||||||||
\(693\) | −17010.0 | −0.00134546 | ||||||||
\(694\) | −1.54630e7 | −1.21870 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 72576.0 | 0.00567897 | ||||||||
\(697\) | 325584. | 0.0253852 | ||||||||
\(698\) | −1.69356e7 | −1.31572 | ||||||||
\(699\) | 7.40815e6 | 0.573478 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.45297e6 | 0.649702 | 0.324851 | − | 0.945765i | \(-0.394686\pi\) | ||||
0.324851 | + | 0.945765i | \(0.394686\pi\) | |||||||
\(702\) | −1.94497e6 | −0.148960 | ||||||||
\(703\) | 2.17410e6 | 0.165917 | ||||||||
\(704\) | −860160. | −0.0654105 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.65834e6 | 0.729274 | ||||||||
\(707\) | −164052. | −0.0123433 | ||||||||
\(708\) | 4.65264e6 | 0.348832 | ||||||||
\(709\) | −1.18033e7 | −0.881834 | −0.440917 | − | 0.897548i | \(-0.645347\pi\) | ||||
−0.440917 | + | 0.897548i | \(0.645347\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.23625e6 | 0.165900 | ||||||||
\(712\) | 3.21331e6 | 0.237549 | ||||||||
\(713\) | 3.29861e7 | 2.43000 | ||||||||
\(714\) | 4104.00 | 0.000301274 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −829536. | −0.0604718 | ||||||||
\(717\) | −1.19553e7 | −0.868484 | ||||||||
\(718\) | 1.17921e7 | 0.853648 | ||||||||
\(719\) | −2.68089e7 | −1.93400 | −0.967000 | − | 0.254778i | \(-0.917998\pi\) | ||||
−0.967000 | + | 0.254778i | \(0.917998\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 107236. | 0.00768250 | ||||||||
\(722\) | −8.55415e6 | −0.610709 | ||||||||
\(723\) | −854433. | −0.0607900 | ||||||||
\(724\) | 7.98958e6 | 0.566471 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.21024e6 | 0.296459 | ||||||||
\(727\) | 2.00638e6 | 0.140792 | 0.0703958 | − | 0.997519i | \(-0.477574\pi\) | ||||
0.0703958 | + | 0.997519i | \(0.477574\pi\) | |||||||
\(728\) | 42688.0 | 0.00298523 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.07947e6 | −0.143933 | ||||||||
\(732\) | 1.03176e6 | 0.0711707 | ||||||||
\(733\) | 9.16554e6 | 0.630083 | 0.315042 | − | 0.949078i | \(-0.397981\pi\) | ||||
0.315042 | + | 0.949078i | \(0.397981\pi\) | |||||||
\(734\) | −2.71917e6 | −0.186293 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.45440e6 | 0.303106 | ||||||||
\(737\) | 1.25116e7 | 0.848484 | ||||||||
\(738\) | −925344. | −0.0625406 | ||||||||
\(739\) | 1.55897e7 | 1.05009 | 0.525047 | − | 0.851073i | \(-0.324048\pi\) | ||||
0.525047 | + | 0.851073i | \(0.324048\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.48774e6 | −0.233345 | ||||||||
\(742\) | 86736.0 | 0.00578349 | ||||||||
\(743\) | 3.78304e6 | 0.251402 | 0.125701 | − | 0.992068i | \(-0.459882\pi\) | ||||
0.125701 | + | 0.992068i | \(0.459882\pi\) | |||||||
\(744\) | −4.36781e6 | −0.289289 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.44355e7 | 0.949698 | ||||||||
\(747\) | 144342. | 0.00946436 | ||||||||
\(748\) | 383040. | 0.0250317 | ||||||||
\(749\) | −21012.0 | −0.00136856 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.24726e7 | 0.806972 | 0.403486 | − | 0.914986i | \(-0.367798\pi\) | ||||
0.403486 | + | 0.914986i | \(0.367798\pi\) | |||||||
\(752\) | 5.98272e6 | 0.385793 | ||||||||
\(753\) | 1.15312e6 | 0.0741115 | ||||||||
\(754\) | −336168. | −0.0215342 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −11664.0 | −0.000742238 0 | ||||||||
\(757\) | −1.87121e6 | −0.118682 | −0.0593408 | − | 0.998238i | \(-0.518900\pi\) | ||||
−0.0593408 | + | 0.998238i | \(0.518900\pi\) | |||||||
\(758\) | −1.54724e6 | −0.0978101 | ||||||||
\(759\) | 8.22150e6 | 0.518020 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.53638e7 | 1.58764 | 0.793821 | − | 0.608152i | \(-0.208089\pi\) | ||||
0.793821 | + | 0.608152i | \(0.208089\pi\) | |||||||
\(762\) | 4.99680e6 | 0.311749 | ||||||||
\(763\) | 237545. | 0.0147718 | ||||||||
\(764\) | 1.12945e7 | 0.700057 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.58024e6 | 0.158887 | ||||||||
\(767\) | −2.15508e7 | −1.32274 | ||||||||
\(768\) | −589824. | −0.0360844 | ||||||||
\(769\) | −1.43729e7 | −0.876452 | −0.438226 | − | 0.898865i | \(-0.644393\pi\) | ||||
−0.438226 | + | 0.898865i | \(0.644393\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.55057e7 | −0.939409 | ||||||||
\(772\) | 8.31957e6 | 0.502409 | ||||||||
\(773\) | 1.64185e7 | 0.988289 | 0.494145 | − | 0.869380i | \(-0.335481\pi\) | ||||
0.494145 | + | 0.869380i | \(0.335481\pi\) | |||||||
\(774\) | 5.91008e6 | 0.354602 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −9.13875e6 | −0.544794 | ||||||||
\(777\) | −33678.0 | −0.00200121 | ||||||||
\(778\) | −3.25190e6 | −0.192614 | ||||||||
\(779\) | −1.65934e6 | −0.0979695 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.04680e6 | 0.530722 | ||||||||
\(782\) | −1.98360e6 | −0.115994 | ||||||||
\(783\) | 91854.0 | 0.00535419 | ||||||||
\(784\) | −4.30234e6 | −0.249985 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 5.80824e6 | 0.335342 | ||||||||
\(787\) | 1.46320e7 | 0.842106 | 0.421053 | − | 0.907036i | \(-0.361661\pi\) | ||||
0.421053 | + | 0.907036i | \(0.361661\pi\) | |||||||
\(788\) | 3.20630e6 | 0.183945 | ||||||||
\(789\) | 6.22944e6 | 0.356251 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −233388. | −0.0132629 | ||||||||
\(792\) | −1.08864e6 | −0.0616696 | ||||||||
\(793\) | −4.77906e6 | −0.269873 | ||||||||
\(794\) | 3.95525e6 | 0.222650 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.85877e6 | 0.495554 | ||||||||
\(797\) | −2.61796e7 | −1.45988 | −0.729941 | − | 0.683511i | \(-0.760452\pi\) | ||||
−0.729941 | + | 0.683511i | \(0.760452\pi\) | |||||||
\(798\) | −20916.0 | −0.00116271 | ||||||||
\(799\) | −2.66418e6 | −0.147637 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.06685e6 | 0.223963 | ||||||||
\(802\) | 8.58322e6 | 0.471210 | ||||||||
\(803\) | −6.07782e6 | −0.332628 | ||||||||
\(804\) | 8.57938e6 | 0.468075 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.02314e7 | 1.09696 | ||||||||
\(807\) | −6.21805e6 | −0.336101 | ||||||||
\(808\) | −1.04993e7 | −0.565761 | ||||||||
\(809\) | 2.99051e7 | 1.60648 | 0.803238 | − | 0.595658i | \(-0.203109\pi\) | ||||
0.803238 | + | 0.595658i | \(0.203109\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.12873e7 | −1.67038 | −0.835190 | − | 0.549961i | \(-0.814642\pi\) | ||||
−0.835190 | + | 0.549961i | \(0.814642\pi\) | |||||||
\(812\) | −2016.00 | −0.000107300 0 | ||||||||
\(813\) | 9.42206e6 | 0.499942 | ||||||||
\(814\) | −3.14328e6 | −0.166273 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 262656. | 0.0138090 | ||||||||
\(817\) | 1.05980e7 | 0.555482 | ||||||||
\(818\) | −2.31063e7 | −1.20739 | ||||||||
\(819\) | 54027.0 | 0.00281450 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.24291e7 | −1.67910 | −0.839550 | − | 0.543282i | \(-0.817182\pi\) | ||||
−0.839550 | + | 0.543282i | \(0.817182\pi\) | |||||||
\(822\) | 2.48594e6 | 0.128325 | ||||||||
\(823\) | −1.91700e7 | −0.986560 | −0.493280 | − | 0.869871i | \(-0.664202\pi\) | ||||
−0.493280 | + | 0.869871i | \(0.664202\pi\) | |||||||
\(824\) | 6.86310e6 | 0.352130 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −129240. | −0.00659093 | ||||||||
\(827\) | 98052.0 | 0.00498532 | 0.00249266 | − | 0.999997i | \(-0.499207\pi\) | ||||
0.00249266 | + | 0.999997i | \(0.499207\pi\) | |||||||
\(828\) | 5.63760e6 | 0.285771 | ||||||||
\(829\) | 5.77426e6 | 0.291817 | 0.145908 | − | 0.989298i | \(-0.453390\pi\) | ||||
0.145908 | + | 0.989298i | \(0.453390\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.64230e6 | −0.484371 | ||||||||
\(832\) | 2.73203e6 | 0.136829 | ||||||||
\(833\) | 1.91588e6 | 0.0956658 | ||||||||
\(834\) | −8.07826e6 | −0.402163 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.95216e6 | −0.0966050 | ||||||||
\(837\) | −5.52801e6 | −0.272744 | ||||||||
\(838\) | −2.02927e7 | −0.998229 | ||||||||
\(839\) | −1.69354e7 | −0.830599 | −0.415299 | − | 0.909685i | \(-0.636323\pi\) | ||||
−0.415299 | + | 0.909685i | \(0.636323\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.04953e7 | −0.999226 | ||||||||
\(842\) | −1.20519e7 | −0.585834 | ||||||||
\(843\) | 1.26375e7 | 0.612478 | ||||||||
\(844\) | 1.24378e7 | 0.601020 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.57188e6 | 0.363729 | ||||||||
\(847\) | −116951. | −0.00560138 | ||||||||
\(848\) | 5.55110e6 | 0.265088 | ||||||||
\(849\) | 1.51383e7 | 0.720788 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.62777e7 | 0.770494 | ||||||||
\(852\) | 6.20352e6 | 0.292779 | ||||||||
\(853\) | −5.04391e6 | −0.237353 | −0.118677 | − | 0.992933i | \(-0.537865\pi\) | ||||
−0.118677 | + | 0.992933i | \(0.537865\pi\) | |||||||
\(854\) | −28660.0 | −0.00134472 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.34477e6 | −0.0627282 | ||||||||
\(857\) | −1.28829e7 | −0.599188 | −0.299594 | − | 0.954067i | \(-0.596851\pi\) | ||||
−0.299594 | + | 0.954067i | \(0.596851\pi\) | |||||||
\(858\) | 5.04252e6 | 0.233846 | ||||||||
\(859\) | −3.59522e7 | −1.66243 | −0.831213 | − | 0.555954i | \(-0.812353\pi\) | ||||
−0.831213 | + | 0.555954i | \(0.812353\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 25704.0 | 0.00118166 | ||||||||
\(862\) | 2.23780e7 | 1.02578 | ||||||||
\(863\) | −2.20345e7 | −1.00711 | −0.503554 | − | 0.863964i | \(-0.667975\pi\) | ||||
−0.503554 | + | 0.863964i | \(0.667975\pi\) | |||||||
\(864\) | −746496. | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.25382e7 | −1.02123 | ||||||||
\(867\) | 1.26617e7 | 0.572066 | ||||||||
\(868\) | 121328. | 0.00546590 | ||||||||
\(869\) | −5.79768e6 | −0.260438 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.97392e7 | −1.77490 | ||||||||
\(872\) | 1.52029e7 | 0.677072 | ||||||||
\(873\) | −1.15662e7 | −0.513637 | ||||||||
\(874\) | 1.01094e7 | 0.447658 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.16765e6 | −0.183498 | ||||||||
\(877\) | −1.34531e7 | −0.590641 | −0.295320 | − | 0.955398i | \(-0.595426\pi\) | ||||
−0.295320 | + | 0.955398i | \(0.595426\pi\) | |||||||
\(878\) | 3.44265e6 | 0.150715 | ||||||||
\(879\) | 1.58663e7 | 0.692635 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.36331e7 | 1.02584 | 0.512922 | − | 0.858435i | \(-0.328563\pi\) | ||||
0.512922 | + | 0.858435i | \(0.328563\pi\) | |||||||
\(882\) | −5.44514e6 | −0.235688 | ||||||||
\(883\) | −3.49588e7 | −1.50888 | −0.754439 | − | 0.656370i | \(-0.772091\pi\) | ||||
−0.754439 | + | 0.656370i | \(0.772091\pi\) | |||||||
\(884\) | −1.21661e6 | −0.0523625 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.10134e7 | 0.471343 | ||||||||
\(887\) | −3.11168e7 | −1.32796 | −0.663982 | − | 0.747749i | \(-0.731135\pi\) | ||||
−0.663982 | + | 0.747749i | \(0.731135\pi\) | |||||||
\(888\) | −2.15539e6 | −0.0917263 | ||||||||
\(889\) | −138800. | −0.00589027 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.37781e6 | −0.0581427 | ||||||||
\(892\) | 1.24190e7 | 0.522604 | ||||||||
\(893\) | 1.35780e7 | 0.569779 | ||||||||
\(894\) | 1.46753e7 | 0.614104 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 16384.0 | 0.000681789 0 | ||||||||
\(897\) | −2.61130e7 | −1.08362 | ||||||||
\(898\) | −1.13267e7 | −0.468719 | ||||||||
\(899\) | −955458. | −0.0394287 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.47198e6 | −0.101445 | ||||||||
\(902\) | 2.39904e6 | 0.0981796 | ||||||||
\(903\) | −164169. | −0.00669995 | ||||||||
\(904\) | −1.49368e7 | −0.607907 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −7.77791e6 | −0.314805 | ||||||||
\(907\) | 1.97320e7 | 0.796438 | 0.398219 | − | 0.917290i | \(-0.369628\pi\) | ||||
0.398219 | + | 0.917290i | \(0.369628\pi\) | |||||||
\(908\) | −1.47199e7 | −0.592501 | ||||||||
\(909\) | −1.32882e7 | −0.533405 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.40720e7 | −1.75941 | −0.879704 | − | 0.475521i | \(-0.842260\pi\) | ||||
−0.879704 | + | 0.475521i | \(0.842260\pi\) | |||||||
\(912\) | −1.33862e6 | −0.0532932 | ||||||||
\(913\) | −374220. | −0.0148576 | ||||||||
\(914\) | 1.86494e7 | 0.738412 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.81151e7 | −0.713350 | ||||||||
\(917\) | −161340. | −0.00633605 | ||||||||
\(918\) | 332424. | 0.0130192 | ||||||||
\(919\) | −4.33621e7 | −1.69364 | −0.846821 | − | 0.531879i | \(-0.821486\pi\) | ||||
−0.846821 | + | 0.531879i | \(0.821486\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.24714e6 | 0.164986 | ||||||||
\(922\) | −2.10862e7 | −0.816902 | ||||||||
\(923\) | −2.87344e7 | −1.11019 | ||||||||
\(924\) | 30240.0 | 0.00116520 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.86781e7 | 1.09907 | ||||||||
\(927\) | 8.68612e6 | 0.331991 | ||||||||
\(928\) | −129024. | −0.00491814 | ||||||||
\(929\) | 1.65235e7 | 0.628147 | 0.314074 | − | 0.949399i | \(-0.398306\pi\) | ||||
0.314074 | + | 0.949399i | \(0.398306\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.76429e6 | −0.369204 | ||||||||
\(932\) | −1.31700e7 | −0.496647 | ||||||||
\(933\) | 1.47995e7 | 0.556600 | ||||||||
\(934\) | −1.72176e7 | −0.645812 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.45773e6 | 0.129003 | ||||||||
\(937\) | −2.03546e7 | −0.757381 | −0.378691 | − | 0.925523i | \(-0.623626\pi\) | ||||
−0.378691 | + | 0.925523i | \(0.623626\pi\) | |||||||
\(938\) | −238316. | −0.00884395 | ||||||||
\(939\) | 2.14117e7 | 0.792480 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.12406e7 | −1.88643 | −0.943215 | − | 0.332184i | \(-0.892214\pi\) | ||||
−0.943215 | + | 0.332184i | \(0.892214\pi\) | |||||||
\(942\) | −6.79021e6 | −0.249319 | ||||||||
\(943\) | −1.24236e7 | −0.454955 | ||||||||
\(944\) | −8.27136e6 | −0.302097 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.53224e7 | −0.556673 | ||||||||
\(947\) | −2.79736e7 | −1.01361 | −0.506807 | − | 0.862059i | \(-0.669174\pi\) | ||||
−0.506807 | + | 0.862059i | \(0.669174\pi\) | |||||||
\(948\) | −3.97555e6 | −0.143673 | ||||||||
\(949\) | 1.93043e7 | 0.695807 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.19411e7 | 0.428148 | ||||||||
\(952\) | −7296.00 | −0.000260911 0 | ||||||||
\(953\) | −2.68337e7 | −0.957080 | −0.478540 | − | 0.878066i | \(-0.658834\pi\) | ||||
−0.478540 | + | 0.878066i | \(0.658834\pi\) | |||||||
\(954\) | 7.02562e6 | 0.249927 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.12538e7 | 0.752129 | ||||||||
\(957\) | −238140. | −0.00840529 | ||||||||
\(958\) | 762024. | 0.0268259 | ||||||||
\(959\) | −69054.0 | −0.00242461 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.88727e7 | 1.00851 | ||||||||
\(962\) | 9.98366e6 | 0.347818 | ||||||||
\(963\) | −1.70197e6 | −0.0591407 | ||||||||
\(964\) | 1.51899e6 | 0.0526457 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −156600. | −0.00539944 | ||||||||
\(967\) | 5.24831e7 | 1.80490 | 0.902450 | − | 0.430794i | \(-0.141766\pi\) | ||||
0.902450 | + | 0.430794i | \(0.141766\pi\) | |||||||
\(968\) | −7.48486e6 | −0.256741 | ||||||||
\(969\) | 596106. | 0.0203945 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.01029e7 | 1.70536 | 0.852678 | − | 0.522437i | \(-0.174977\pi\) | ||||
0.852678 | + | 0.522437i | \(0.174977\pi\) | |||||||
\(972\) | −944784. | −0.0320750 | ||||||||
\(973\) | 224396. | 0.00759859 | ||||||||
\(974\) | 515548. | 0.0174129 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.83424e6 | −0.0616356 | ||||||||
\(977\) | 4.50181e7 | 1.50887 | 0.754433 | − | 0.656377i | \(-0.227912\pi\) | ||||
0.754433 | + | 0.656377i | \(0.227912\pi\) | |||||||
\(978\) | −1.52010e7 | −0.508190 | ||||||||
\(979\) | −1.05437e7 | −0.351589 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.92411e7 | 0.638349 | ||||||||
\(982\) | −1.21718e6 | −0.0402789 | ||||||||
\(983\) | 3.26907e7 | 1.07905 | 0.539523 | − | 0.841971i | \(-0.318605\pi\) | ||||
0.539523 | + | 0.841971i | \(0.318605\pi\) | |||||||
\(984\) | 1.64506e6 | 0.0541618 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 57456.0 | 0.00188210 | ||||||||
\(987\) | −210330. | −0.00687240 | ||||||||
\(988\) | 6.20043e6 | 0.202083 | ||||||||
\(989\) | 7.93484e7 | 2.57957 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.24606e6 | 0.202033 | 0.101016 | − | 0.994885i | \(-0.467791\pi\) | ||||
0.101016 | + | 0.994885i | \(0.467791\pi\) | |||||||
\(992\) | 7.76499e6 | 0.250531 | ||||||||
\(993\) | −5.95055e6 | −0.191507 | ||||||||
\(994\) | −172320. | −0.00553184 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −256608. | −0.00819638 | ||||||||
\(997\) | −2.85010e7 | −0.908077 | −0.454039 | − | 0.890982i | \(-0.650017\pi\) | ||||
−0.454039 | + | 0.890982i | \(0.650017\pi\) | |||||||
\(998\) | 2.56790e7 | 0.816115 | ||||||||
\(999\) | −2.72792e6 | −0.0864804 |
(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 | 150.6.a.k.1.1 | yes | 1 | |
3.2 | odd | 2 | 450.6.a.g.1.1 | 1 | |||
5.2 | odd | 4 | 150.6.c.a.49.2 | 2 | |||
5.3 | odd | 4 | 150.6.c.a.49.1 | 2 | |||
5.4 | even | 2 | 150.6.a.e.1.1 | ✓ | 1 | ||
15.2 | even | 4 | 450.6.c.k.199.1 | 2 | |||
15.8 | even | 4 | 450.6.c.k.199.2 | 2 | |||
15.14 | odd | 2 | 450.6.a.r.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.6.a.e.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
150.6.a.k.1.1 | yes | 1 | 1.1 | even | 1 | trivial | |
150.6.c.a.49.1 | 2 | 5.3 | odd | 4 | |||
150.6.c.a.49.2 | 2 | 5.2 | odd | 4 | |||
450.6.a.g.1.1 | 1 | 3.2 | odd | 2 | |||
450.6.a.r.1.1 | 1 | 15.14 | odd | 2 | |||
450.6.c.k.199.1 | 2 | 15.2 | even | 4 | |||
450.6.c.k.199.2 | 2 | 15.8 | even | 4 |