Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [18,6,Mod(1,18)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(18, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("18.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 18 = 2 \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 18.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: | \(2.88690875663\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 6) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 18.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 66.0000 | 1.18064 | 0.590322 | − | 0.807168i | \(-0.299001\pi\) | ||||
0.590322 | + | 0.807168i | \(0.299001\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 176.000 | 1.35759 | 0.678793 | − | 0.734329i | \(-0.262503\pi\) | ||||
0.678793 | + | 0.734329i | \(0.262503\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −264.000 | −0.834841 | ||||||||
\(11\) | 60.0000 | 0.149510 | 0.0747549 | − | 0.997202i | \(-0.476183\pi\) | ||||
0.0747549 | + | 0.997202i | \(0.476183\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −658.000 | −1.07986 | −0.539930 | − | 0.841710i | \(-0.681549\pi\) | ||||
−0.539930 | + | 0.841710i | \(0.681549\pi\) | |||||||
\(14\) | −704.000 | −0.959959 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 414.000 | 0.347439 | 0.173719 | − | 0.984795i | \(-0.444421\pi\) | ||||
0.173719 | + | 0.984795i | \(0.444421\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 956.000 | 0.607539 | 0.303769 | − | 0.952746i | \(-0.401755\pi\) | ||||
0.303769 | + | 0.952746i | \(0.401755\pi\) | |||||||
\(20\) | 1056.00 | 0.590322 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −240.000 | −0.105719 | ||||||||
\(23\) | −600.000 | −0.236500 | −0.118250 | − | 0.992984i | \(-0.537728\pi\) | ||||
−0.118250 | + | 0.992984i | \(0.537728\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1231.00 | 0.393920 | ||||||||
\(26\) | 2632.00 | 0.763576 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2816.00 | 0.678793 | ||||||||
\(29\) | −5574.00 | −1.23076 | −0.615378 | − | 0.788232i | \(-0.710997\pi\) | ||||
−0.615378 | + | 0.788232i | \(0.710997\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3592.00 | −0.671324 | −0.335662 | − | 0.941983i | \(-0.608960\pi\) | ||||
−0.335662 | + | 0.941983i | \(0.608960\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1656.00 | −0.245676 | ||||||||
\(35\) | 11616.0 | 1.60283 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8458.00 | −1.01570 | −0.507848 | − | 0.861447i | \(-0.669559\pi\) | ||||
−0.507848 | + | 0.861447i | \(0.669559\pi\) | |||||||
\(38\) | −3824.00 | −0.429595 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4224.00 | −0.417421 | ||||||||
\(41\) | −19194.0 | −1.78322 | −0.891612 | − | 0.452800i | \(-0.850425\pi\) | ||||
−0.891612 | + | 0.452800i | \(0.850425\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 13316.0 | 1.09825 | 0.549127 | − | 0.835739i | \(-0.314960\pi\) | ||||
0.549127 | + | 0.835739i | \(0.314960\pi\) | |||||||
\(44\) | 960.000 | 0.0747549 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2400.00 | 0.167231 | ||||||||
\(47\) | 19680.0 | 1.29951 | 0.649756 | − | 0.760143i | \(-0.274871\pi\) | ||||
0.649756 | + | 0.760143i | \(0.274871\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14169.0 | 0.843042 | ||||||||
\(50\) | −4924.00 | −0.278544 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −10528.0 | −0.539930 | ||||||||
\(53\) | 31266.0 | 1.52891 | 0.764456 | − | 0.644676i | \(-0.223008\pi\) | ||||
0.764456 | + | 0.644676i | \(0.223008\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3960.00 | 0.176518 | ||||||||
\(56\) | −11264.0 | −0.479979 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 22296.0 | 0.870276 | ||||||||
\(59\) | −26340.0 | −0.985112 | −0.492556 | − | 0.870281i | \(-0.663937\pi\) | ||||
−0.492556 | + | 0.870281i | \(0.663937\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −31090.0 | −1.06978 | −0.534892 | − | 0.844920i | \(-0.679648\pi\) | ||||
−0.534892 | + | 0.844920i | \(0.679648\pi\) | |||||||
\(62\) | 14368.0 | 0.474698 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −43428.0 | −1.27493 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −16804.0 | −0.457326 | −0.228663 | − | 0.973506i | \(-0.573435\pi\) | ||||
−0.228663 | + | 0.973506i | \(0.573435\pi\) | |||||||
\(68\) | 6624.00 | 0.173719 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −46464.0 | −1.13337 | ||||||||
\(71\) | −6120.00 | −0.144081 | −0.0720403 | − | 0.997402i | \(-0.522951\pi\) | ||||
−0.0720403 | + | 0.997402i | \(0.522951\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −25558.0 | −0.561332 | −0.280666 | − | 0.959806i | \(-0.590555\pi\) | ||||
−0.280666 | + | 0.959806i | \(0.590555\pi\) | |||||||
\(74\) | 33832.0 | 0.718205 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 15296.0 | 0.303769 | ||||||||
\(77\) | 10560.0 | 0.202972 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 74408.0 | 1.34138 | 0.670690 | − | 0.741738i | \(-0.265998\pi\) | ||||
0.670690 | + | 0.741738i | \(0.265998\pi\) | |||||||
\(80\) | 16896.0 | 0.295161 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 76776.0 | 1.26093 | ||||||||
\(83\) | 6468.00 | 0.103056 | 0.0515282 | − | 0.998672i | \(-0.483591\pi\) | ||||
0.0515282 | + | 0.998672i | \(0.483591\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 27324.0 | 0.410201 | ||||||||
\(86\) | −53264.0 | −0.776583 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3840.00 | −0.0528597 | ||||||||
\(89\) | 32742.0 | 0.438157 | 0.219079 | − | 0.975707i | \(-0.429695\pi\) | ||||
0.219079 | + | 0.975707i | \(0.429695\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −115808. | −1.46600 | ||||||||
\(92\) | −9600.00 | −0.118250 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −78720.0 | −0.918894 | ||||||||
\(95\) | 63096.0 | 0.717287 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 166082. | 1.79223 | 0.896114 | − | 0.443824i | \(-0.146378\pi\) | ||||
0.896114 | + | 0.443824i | \(0.146378\pi\) | |||||||
\(98\) | −56676.0 | −0.596120 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 19696.0 | 0.196960 | ||||||||
\(101\) | 22002.0 | 0.214614 | 0.107307 | − | 0.994226i | \(-0.465777\pi\) | ||||
0.107307 | + | 0.994226i | \(0.465777\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −79264.0 | −0.736178 | −0.368089 | − | 0.929791i | \(-0.619988\pi\) | ||||
−0.368089 | + | 0.929791i | \(0.619988\pi\) | |||||||
\(104\) | 42112.0 | 0.381788 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −125064. | −1.08110 | ||||||||
\(107\) | −227988. | −1.92510 | −0.962548 | − | 0.271110i | \(-0.912609\pi\) | ||||
−0.962548 | + | 0.271110i | \(0.912609\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8530.00 | −0.0687674 | −0.0343837 | − | 0.999409i | \(-0.510947\pi\) | ||||
−0.0343837 | + | 0.999409i | \(0.510947\pi\) | |||||||
\(110\) | −15840.0 | −0.124817 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 45056.0 | 0.339397 | ||||||||
\(113\) | 195438. | 1.43984 | 0.719918 | − | 0.694059i | \(-0.244179\pi\) | ||||
0.719918 | + | 0.694059i | \(0.244179\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −39600.0 | −0.279223 | ||||||||
\(116\) | −89184.0 | −0.615378 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 105360. | 0.696580 | ||||||||
\(119\) | 72864.0 | 0.471678 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −157451. | −0.977647 | ||||||||
\(122\) | 124360. | 0.756452 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −57472.0 | −0.335662 | ||||||||
\(125\) | −125004. | −0.715565 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 173000. | 0.951780 | 0.475890 | − | 0.879505i | \(-0.342126\pi\) | ||||
0.475890 | + | 0.879505i | \(0.342126\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 173712. | 0.901512 | ||||||||
\(131\) | −151260. | −0.770098 | −0.385049 | − | 0.922896i | \(-0.625815\pi\) | ||||
−0.385049 | + | 0.922896i | \(0.625815\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 168256. | 0.824786 | ||||||||
\(134\) | 67216.0 | 0.323378 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −26496.0 | −0.122838 | ||||||||
\(137\) | 128454. | 0.584718 | 0.292359 | − | 0.956309i | \(-0.405560\pi\) | ||||
0.292359 | + | 0.956309i | \(0.405560\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 154196. | 0.676918 | 0.338459 | − | 0.940981i | \(-0.390094\pi\) | ||||
0.338459 | + | 0.940981i | \(0.390094\pi\) | |||||||
\(140\) | 185856. | 0.801413 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 24480.0 | 0.101880 | ||||||||
\(143\) | −39480.0 | −0.161450 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −367884. | −1.45308 | ||||||||
\(146\) | 102232. | 0.396922 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −135328. | −0.507848 | ||||||||
\(149\) | −29454.0 | −0.108687 | −0.0543436 | − | 0.998522i | \(-0.517307\pi\) | ||||
−0.0543436 | + | 0.998522i | \(0.517307\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −203872. | −0.727638 | −0.363819 | − | 0.931470i | \(-0.618527\pi\) | ||||
−0.363819 | + | 0.931470i | \(0.618527\pi\) | |||||||
\(152\) | −61184.0 | −0.214797 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −42240.0 | −0.143523 | ||||||||
\(155\) | −237072. | −0.792594 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 136142. | 0.440801 | 0.220401 | − | 0.975409i | \(-0.429263\pi\) | ||||
0.220401 | + | 0.975409i | \(0.429263\pi\) | |||||||
\(158\) | −297632. | −0.948499 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −67584.0 | −0.208710 | ||||||||
\(161\) | −105600. | −0.321070 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −171124. | −0.504478 | −0.252239 | − | 0.967665i | \(-0.581167\pi\) | ||||
−0.252239 | + | 0.967665i | \(0.581167\pi\) | |||||||
\(164\) | −307104. | −0.891612 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −25872.0 | −0.0728718 | ||||||||
\(167\) | 676200. | 1.87622 | 0.938110 | − | 0.346336i | \(-0.112574\pi\) | ||||
0.938110 | + | 0.346336i | \(0.112574\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 61671.0 | 0.166098 | ||||||||
\(170\) | −109296. | −0.290056 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 213056. | 0.549127 | ||||||||
\(173\) | −133158. | −0.338261 | −0.169131 | − | 0.985594i | \(-0.554096\pi\) | ||||
−0.169131 | + | 0.985594i | \(0.554096\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 216656. | 0.534781 | ||||||||
\(176\) | 15360.0 | 0.0373774 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −130968. | −0.309824 | ||||||||
\(179\) | 693396. | 1.61752 | 0.808758 | − | 0.588141i | \(-0.200140\pi\) | ||||
0.808758 | + | 0.588141i | \(0.200140\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 377174. | 0.855747 | 0.427873 | − | 0.903839i | \(-0.359263\pi\) | ||||
0.427873 | + | 0.903839i | \(0.359263\pi\) | |||||||
\(182\) | 463232. | 1.03662 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 38400.0 | 0.0836155 | ||||||||
\(185\) | −558228. | −1.19917 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24840.0 | 0.0519455 | ||||||||
\(188\) | 314880. | 0.649756 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −252384. | −0.507198 | ||||||||
\(191\) | 265344. | 0.526291 | 0.263145 | − | 0.964756i | \(-0.415240\pi\) | ||||
0.263145 | + | 0.964756i | \(0.415240\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 295298. | 0.570647 | 0.285323 | − | 0.958431i | \(-0.407899\pi\) | ||||
0.285323 | + | 0.958431i | \(0.407899\pi\) | |||||||
\(194\) | −664328. | −1.26730 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 226704. | 0.421521 | ||||||||
\(197\) | −201294. | −0.369543 | −0.184772 | − | 0.982781i | \(-0.559155\pi\) | ||||
−0.184772 | + | 0.982781i | \(0.559155\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 652448. | 1.16792 | 0.583960 | − | 0.811782i | \(-0.301502\pi\) | ||||
0.583960 | + | 0.811782i | \(0.301502\pi\) | |||||||
\(200\) | −78784.0 | −0.139272 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −88008.0 | −0.151755 | ||||||||
\(203\) | −981024. | −1.67086 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.26680e6 | −2.10535 | ||||||||
\(206\) | 317056. | 0.520557 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −168448. | −0.269965 | ||||||||
\(209\) | 57360.0 | 0.0908330 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.14706e6 | −1.77370 | −0.886850 | − | 0.462058i | \(-0.847111\pi\) | ||||
−0.886850 | + | 0.462058i | \(0.847111\pi\) | |||||||
\(212\) | 500256. | 0.764456 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 911952. | 1.36125 | ||||||||
\(215\) | 878856. | 1.29665 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −632192. | −0.911380 | ||||||||
\(218\) | 34120.0 | 0.0486259 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 63360.0 | 0.0882589 | ||||||||
\(221\) | −272412. | −0.375185 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 701960. | 0.945258 | 0.472629 | − | 0.881262i | \(-0.343305\pi\) | ||||
0.472629 | + | 0.881262i | \(0.343305\pi\) | |||||||
\(224\) | −180224. | −0.239990 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −781752. | −1.01812 | ||||||||
\(227\) | −1.23611e6 | −1.59218 | −0.796089 | − | 0.605179i | \(-0.793101\pi\) | ||||
−0.796089 | + | 0.605179i | \(0.793101\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 105830. | 0.133358 | 0.0666792 | − | 0.997774i | \(-0.478760\pi\) | ||||
0.0666792 | + | 0.997774i | \(0.478760\pi\) | |||||||
\(230\) | 158400. | 0.197440 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 356736. | 0.435138 | ||||||||
\(233\) | 438678. | 0.529366 | 0.264683 | − | 0.964335i | \(-0.414733\pi\) | ||||
0.264683 | + | 0.964335i | \(0.414733\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.29888e6 | 1.53426 | ||||||||
\(236\) | −421440. | −0.492556 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −291456. | −0.333527 | ||||||||
\(239\) | −28464.0 | −0.0322330 | −0.0161165 | − | 0.999870i | \(-0.505130\pi\) | ||||
−0.0161165 | + | 0.999870i | \(0.505130\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 892562. | 0.989910 | 0.494955 | − | 0.868919i | \(-0.335185\pi\) | ||||
0.494955 | + | 0.868919i | \(0.335185\pi\) | |||||||
\(242\) | 629804. | 0.691301 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −497440. | −0.534892 | ||||||||
\(245\) | 935154. | 0.995332 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −629048. | −0.656057 | ||||||||
\(248\) | 229888. | 0.237349 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 500016. | 0.505981 | ||||||||
\(251\) | 110124. | 0.110331 | 0.0551655 | − | 0.998477i | \(-0.482431\pi\) | ||||
0.0551655 | + | 0.998477i | \(0.482431\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −36000.0 | −0.0353591 | ||||||||
\(254\) | −692000. | −0.673010 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −140802. | −0.132977 | −0.0664884 | − | 0.997787i | \(-0.521180\pi\) | ||||
−0.0664884 | + | 0.997787i | \(0.521180\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.48861e6 | −1.37889 | ||||||||
\(260\) | −694848. | −0.637465 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 605040. | 0.544541 | ||||||||
\(263\) | 938760. | 0.836884 | 0.418442 | − | 0.908244i | \(-0.362576\pi\) | ||||
0.418442 | + | 0.908244i | \(0.362576\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.06356e6 | 1.80510 | ||||||||
\(266\) | −673024. | −0.583212 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −268864. | −0.228663 | ||||||||
\(269\) | 1.11451e6 | 0.939078 | 0.469539 | − | 0.882912i | \(-0.344420\pi\) | ||||
0.469539 | + | 0.882912i | \(0.344420\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 567704. | 0.469568 | 0.234784 | − | 0.972048i | \(-0.424562\pi\) | ||||
0.234784 | + | 0.972048i | \(0.424562\pi\) | |||||||
\(272\) | 105984. | 0.0868596 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −513816. | −0.413458 | ||||||||
\(275\) | 73860.0 | 0.0588949 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.21326e6 | −0.950066 | −0.475033 | − | 0.879968i | \(-0.657564\pi\) | ||||
−0.475033 | + | 0.879968i | \(0.657564\pi\) | |||||||
\(278\) | −616784. | −0.478653 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −743424. | −0.566685 | ||||||||
\(281\) | −687738. | −0.519586 | −0.259793 | − | 0.965664i | \(-0.583654\pi\) | ||||
−0.259793 | + | 0.965664i | \(0.583654\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −830908. | −0.616718 | −0.308359 | − | 0.951270i | \(-0.599780\pi\) | ||||
−0.308359 | + | 0.951270i | \(0.599780\pi\) | |||||||
\(284\) | −97920.0 | −0.0720403 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 157920. | 0.114162 | ||||||||
\(287\) | −3.37814e6 | −2.42088 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.24846e6 | −0.879286 | ||||||||
\(290\) | 1.47154e6 | 1.02749 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −408928. | −0.280666 | ||||||||
\(293\) | 1.31263e6 | 0.893248 | 0.446624 | − | 0.894722i | \(-0.352626\pi\) | ||||
0.446624 | + | 0.894722i | \(0.352626\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.73844e6 | −1.16307 | ||||||||
\(296\) | 541312. | 0.359102 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 117816. | 0.0768535 | ||||||||
\(299\) | 394800. | 0.255387 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.34362e6 | 1.49097 | ||||||||
\(302\) | 815488. | 0.514518 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 244736. | 0.151885 | ||||||||
\(305\) | −2.05194e6 | −1.26303 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.69022e6 | 1.02352 | 0.511761 | − | 0.859128i | \(-0.328993\pi\) | ||||
0.511761 | + | 0.859128i | \(0.328993\pi\) | |||||||
\(308\) | 168960. | 0.101486 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 948288. | 0.560449 | ||||||||
\(311\) | 1.50204e6 | 0.880604 | 0.440302 | − | 0.897850i | \(-0.354871\pi\) | ||||
0.440302 | + | 0.897850i | \(0.354871\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 810842. | 0.467816 | 0.233908 | − | 0.972259i | \(-0.424848\pi\) | ||||
0.233908 | + | 0.972259i | \(0.424848\pi\) | |||||||
\(314\) | −544568. | −0.311694 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.19053e6 | 0.670690 | ||||||||
\(317\) | −903558. | −0.505019 | −0.252510 | − | 0.967594i | \(-0.581256\pi\) | ||||
−0.252510 | + | 0.967594i | \(0.581256\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −334440. | −0.184010 | ||||||||
\(320\) | 270336. | 0.147580 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 422400. | 0.227031 | ||||||||
\(323\) | 395784. | 0.211082 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −809998. | −0.425379 | ||||||||
\(326\) | 684496. | 0.356720 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.22842e6 | 0.630465 | ||||||||
\(329\) | 3.46368e6 | 1.76420 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.12197e6 | 0.562875 | 0.281438 | − | 0.959580i | \(-0.409189\pi\) | ||||
0.281438 | + | 0.959580i | \(0.409189\pi\) | |||||||
\(332\) | 103488. | 0.0515282 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.70480e6 | −1.32669 | ||||||||
\(335\) | −1.10906e6 | −0.539939 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.75217e6 | −1.32008 | −0.660041 | − | 0.751229i | \(-0.729461\pi\) | ||||
−0.660041 | + | 0.751229i | \(0.729461\pi\) | |||||||
\(338\) | −246684. | −0.117449 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 437184. | 0.205101 | ||||||||
\(341\) | −215520. | −0.100369 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −464288. | −0.213085 | ||||||||
\(344\) | −852224. | −0.388291 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 532632. | 0.239187 | ||||||||
\(347\) | −1.91749e6 | −0.854889 | −0.427445 | − | 0.904042i | \(-0.640586\pi\) | ||||
−0.427445 | + | 0.904042i | \(0.640586\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.83659e6 | 0.807140 | 0.403570 | − | 0.914949i | \(-0.367769\pi\) | ||||
0.403570 | + | 0.914949i | \(0.367769\pi\) | |||||||
\(350\) | −866624. | −0.378147 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −61440.0 | −0.0264298 | ||||||||
\(353\) | 622014. | 0.265683 | 0.132841 | − | 0.991137i | \(-0.457590\pi\) | ||||
0.132841 | + | 0.991137i | \(0.457590\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −403920. | −0.170108 | ||||||||
\(356\) | 523872. | 0.219079 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.77358e6 | −1.14376 | ||||||||
\(359\) | −3.74062e6 | −1.53182 | −0.765909 | − | 0.642949i | \(-0.777711\pi\) | ||||
−0.765909 | + | 0.642949i | \(0.777711\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.56216e6 | −0.630897 | ||||||||
\(362\) | −1.50870e6 | −0.605104 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.85293e6 | −0.733002 | ||||||||
\(365\) | −1.68683e6 | −0.662733 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16232.0 | 0.00629081 | 0.00314541 | − | 0.999995i | \(-0.498999\pi\) | ||||
0.00314541 | + | 0.999995i | \(0.498999\pi\) | |||||||
\(368\) | −153600. | −0.0591251 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.23291e6 | 0.847944 | ||||||||
\(371\) | 5.50282e6 | 2.07563 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 293606. | 0.109268 | 0.0546340 | − | 0.998506i | \(-0.482601\pi\) | ||||
0.0546340 | + | 0.998506i | \(0.482601\pi\) | |||||||
\(374\) | −99360.0 | −0.0367310 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.25952e6 | −0.459447 | ||||||||
\(377\) | 3.66769e6 | 1.32904 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.18012e6 | 1.13722 | 0.568611 | − | 0.822607i | \(-0.307481\pi\) | ||||
0.568611 | + | 0.822607i | \(0.307481\pi\) | |||||||
\(380\) | 1.00954e6 | 0.358643 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.06138e6 | −0.372144 | ||||||||
\(383\) | 2.97984e6 | 1.03800 | 0.518998 | − | 0.854775i | \(-0.326305\pi\) | ||||
0.518998 | + | 0.854775i | \(0.326305\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 696960. | 0.239638 | ||||||||
\(386\) | −1.18119e6 | −0.403508 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.65731e6 | 0.896114 | ||||||||
\(389\) | −3.45977e6 | −1.15924 | −0.579620 | − | 0.814887i | \(-0.696799\pi\) | ||||
−0.579620 | + | 0.814887i | \(0.696799\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −248400. | −0.0821693 | ||||||||
\(392\) | −906816. | −0.298060 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 805176. | 0.261307 | ||||||||
\(395\) | 4.91093e6 | 1.58369 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.90416e6 | −1.24323 | −0.621615 | − | 0.783323i | \(-0.713523\pi\) | ||||
−0.621615 | + | 0.783323i | \(0.713523\pi\) | |||||||
\(398\) | −2.60979e6 | −0.825844 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 315136. | 0.0984800 | ||||||||
\(401\) | −5.44115e6 | −1.68978 | −0.844890 | − | 0.534940i | \(-0.820334\pi\) | ||||
−0.844890 | + | 0.534940i | \(0.820334\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.36354e6 | 0.724936 | ||||||||
\(404\) | 352032. | 0.107307 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.92410e6 | 1.18148 | ||||||||
\(407\) | −507480. | −0.151856 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.96995e6 | 0.582299 | 0.291150 | − | 0.956678i | \(-0.405962\pi\) | ||||
0.291150 | + | 0.956678i | \(0.405962\pi\) | |||||||
\(410\) | 5.06722e6 | 1.48871 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.26822e6 | −0.368089 | ||||||||
\(413\) | −4.63584e6 | −1.33738 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 426888. | 0.121673 | ||||||||
\(416\) | 673792. | 0.190894 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −229440. | −0.0642286 | ||||||||
\(419\) | −139020. | −0.0386850 | −0.0193425 | − | 0.999813i | \(-0.506157\pi\) | ||||
−0.0193425 | + | 0.999813i | \(0.506157\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.32743e6 | 1.18994 | 0.594970 | − | 0.803748i | \(-0.297164\pi\) | ||||
0.594970 | + | 0.803748i | \(0.297164\pi\) | |||||||
\(422\) | 4.58824e6 | 1.25419 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.00102e6 | −0.540552 | ||||||||
\(425\) | 509634. | 0.136863 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.47184e6 | −1.45232 | ||||||||
\(428\) | −3.64781e6 | −0.962548 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.51542e6 | −0.916867 | ||||||||
\(431\) | 2.79936e6 | 0.725881 | 0.362941 | − | 0.931812i | \(-0.381773\pi\) | ||||
0.362941 | + | 0.931812i | \(0.381773\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.90241e6 | −1.51290 | −0.756449 | − | 0.654052i | \(-0.773068\pi\) | ||||
−0.756449 | + | 0.654052i | \(0.773068\pi\) | |||||||
\(434\) | 2.52877e6 | 0.644443 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −136480. | −0.0343837 | ||||||||
\(437\) | −573600. | −0.143683 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −446512. | −0.110579 | −0.0552894 | − | 0.998470i | \(-0.517608\pi\) | ||||
−0.0552894 | + | 0.998470i | \(0.517608\pi\) | |||||||
\(440\) | −253440. | −0.0624085 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.08965e6 | 0.265296 | ||||||||
\(443\) | −3.49525e6 | −0.846193 | −0.423096 | − | 0.906085i | \(-0.639057\pi\) | ||||
−0.423096 | + | 0.906085i | \(0.639057\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.16097e6 | 0.517308 | ||||||||
\(446\) | −2.80784e6 | −0.668398 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 720896. | 0.169698 | ||||||||
\(449\) | 1.20613e6 | 0.282343 | 0.141171 | − | 0.989985i | \(-0.454913\pi\) | ||||
0.141171 | + | 0.989985i | \(0.454913\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.15164e6 | −0.266609 | ||||||||
\(452\) | 3.12701e6 | 0.719918 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.94443e6 | 1.12584 | ||||||||
\(455\) | −7.64333e6 | −1.73083 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 233546. | 0.0523097 | 0.0261548 | − | 0.999658i | \(-0.491674\pi\) | ||||
0.0261548 | + | 0.999658i | \(0.491674\pi\) | |||||||
\(458\) | −423320. | −0.0942986 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −633600. | −0.139611 | ||||||||
\(461\) | 1.74489e6 | 0.382398 | 0.191199 | − | 0.981551i | \(-0.438762\pi\) | ||||
0.191199 | + | 0.981551i | \(0.438762\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.91786e6 | −0.632576 | −0.316288 | − | 0.948663i | \(-0.602437\pi\) | ||||
−0.316288 | + | 0.948663i | \(0.602437\pi\) | |||||||
\(464\) | −1.42694e6 | −0.307689 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.75471e6 | −0.374318 | ||||||||
\(467\) | 5.31076e6 | 1.12684 | 0.563422 | − | 0.826169i | \(-0.309484\pi\) | ||||
0.563422 | + | 0.826169i | \(0.309484\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.95750e6 | −0.620859 | ||||||||
\(470\) | −5.19552e6 | −1.08489 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.68576e6 | 0.348290 | ||||||||
\(473\) | 798960. | 0.164200 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.17684e6 | 0.239322 | ||||||||
\(476\) | 1.16582e6 | 0.235839 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 113856. | 0.0227922 | ||||||||
\(479\) | −2.34466e6 | −0.466918 | −0.233459 | − | 0.972367i | \(-0.575004\pi\) | ||||
−0.233459 | + | 0.972367i | \(0.575004\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.56536e6 | 1.09681 | ||||||||
\(482\) | −3.57025e6 | −0.699972 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.51922e6 | −0.488823 | ||||||||
\(485\) | 1.09614e7 | 2.11598 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.81531e6 | 1.87535 | 0.937674 | − | 0.347517i | \(-0.112975\pi\) | ||||
0.937674 | + | 0.347517i | \(0.112975\pi\) | |||||||
\(488\) | 1.98976e6 | 0.378226 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.74062e6 | −0.703806 | ||||||||
\(491\) | 5.94520e6 | 1.11292 | 0.556458 | − | 0.830876i | \(-0.312160\pi\) | ||||
0.556458 | + | 0.830876i | \(0.312160\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.30764e6 | −0.427612 | ||||||||
\(494\) | 2.51619e6 | 0.463902 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −919552. | −0.167831 | ||||||||
\(497\) | −1.07712e6 | −0.195602 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.47832e6 | 1.16469 | 0.582346 | − | 0.812941i | \(-0.302135\pi\) | ||||
0.582346 | + | 0.812941i | \(0.302135\pi\) | |||||||
\(500\) | −2.00006e6 | −0.357782 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −440496. | −0.0780158 | ||||||||
\(503\) | −4.71794e6 | −0.831444 | −0.415722 | − | 0.909492i | \(-0.636471\pi\) | ||||
−0.415722 | + | 0.909492i | \(0.636471\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.45213e6 | 0.253383 | ||||||||
\(506\) | 144000. | 0.0250027 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.76800e6 | 0.475890 | ||||||||
\(509\) | 1.90771e6 | 0.326375 | 0.163188 | − | 0.986595i | \(-0.447822\pi\) | ||||
0.163188 | + | 0.986595i | \(0.447822\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.49821e6 | −0.762057 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 563208. | 0.0940288 | ||||||||
\(515\) | −5.23142e6 | −0.869164 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.18080e6 | 0.194290 | ||||||||
\(518\) | 5.95443e6 | 0.975025 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.77939e6 | 0.450756 | ||||||||
\(521\) | −8.01974e6 | −1.29439 | −0.647196 | − | 0.762324i | \(-0.724059\pi\) | ||||
−0.647196 | + | 0.762324i | \(0.724059\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.91162e6 | 0.305596 | 0.152798 | − | 0.988257i | \(-0.451172\pi\) | ||||
0.152798 | + | 0.988257i | \(0.451172\pi\) | |||||||
\(524\) | −2.42016e6 | −0.385049 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.75504e6 | −0.591766 | ||||||||
\(527\) | −1.48709e6 | −0.233244 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.07634e6 | −0.944068 | ||||||||
\(530\) | −8.25422e6 | −1.27640 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.69210e6 | 0.412393 | ||||||||
\(533\) | 1.26297e7 | 1.92563 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.50472e7 | −2.27285 | ||||||||
\(536\) | 1.07546e6 | 0.161689 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.45802e6 | −0.664028 | ||||||||
\(539\) | 850140. | 0.126043 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.19900e7 | −1.76128 | −0.880639 | − | 0.473788i | \(-0.842886\pi\) | ||||
−0.880639 | + | 0.473788i | \(0.842886\pi\) | |||||||
\(542\) | −2.27082e6 | −0.332035 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −423936. | −0.0614190 | ||||||||
\(545\) | −562980. | −0.0811898 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.45809e6 | 0.637061 | 0.318530 | − | 0.947913i | \(-0.396811\pi\) | ||||
0.318530 | + | 0.947913i | \(0.396811\pi\) | |||||||
\(548\) | 2.05526e6 | 0.292359 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −295440. | −0.0416450 | ||||||||
\(551\) | −5.32874e6 | −0.747732 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.30958e7 | 1.82104 | ||||||||
\(554\) | 4.85303e6 | 0.671798 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.46714e6 | 0.338459 | ||||||||
\(557\) | −9.02612e6 | −1.23272 | −0.616358 | − | 0.787466i | \(-0.711393\pi\) | ||||
−0.616358 | + | 0.787466i | \(0.711393\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.76193e6 | −1.18596 | ||||||||
\(560\) | 2.97370e6 | 0.400707 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.75095e6 | 0.367403 | ||||||||
\(563\) | −6.84899e6 | −0.910658 | −0.455329 | − | 0.890323i | \(-0.650478\pi\) | ||||
−0.455329 | + | 0.890323i | \(0.650478\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.28989e7 | 1.69993 | ||||||||
\(566\) | 3.32363e6 | 0.436086 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 391680. | 0.0509402 | ||||||||
\(569\) | 5.46322e6 | 0.707405 | 0.353703 | − | 0.935358i | \(-0.384923\pi\) | ||||
0.353703 | + | 0.935358i | \(0.384923\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.02324e7 | −1.31337 | −0.656684 | − | 0.754166i | \(-0.728041\pi\) | ||||
−0.656684 | + | 0.754166i | \(0.728041\pi\) | |||||||
\(572\) | −631680. | −0.0807248 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.35126e7 | 1.71182 | ||||||||
\(575\) | −738600. | −0.0931622 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.59437e7 | 1.99365 | 0.996825 | − | 0.0796186i | \(-0.0253702\pi\) | ||||
0.996825 | + | 0.0796186i | \(0.0253702\pi\) | |||||||
\(578\) | 4.99384e6 | 0.621749 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.88614e6 | −0.726542 | ||||||||
\(581\) | 1.13837e6 | 0.139908 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.87596e6 | 0.228587 | ||||||||
\(584\) | 1.63571e6 | 0.198461 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.25050e6 | −0.631622 | ||||||||
\(587\) | 9.47713e6 | 1.13522 | 0.567612 | − | 0.823296i | \(-0.307867\pi\) | ||||
0.567612 | + | 0.823296i | \(0.307867\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.43395e6 | −0.407855 | ||||||||
\(590\) | 6.95376e6 | 0.822412 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.16525e6 | −0.253924 | ||||||||
\(593\) | −2.45349e6 | −0.286515 | −0.143258 | − | 0.989685i | \(-0.545758\pi\) | ||||
−0.143258 | + | 0.989685i | \(0.545758\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.80902e6 | 0.556884 | ||||||||
\(596\) | −471264. | −0.0543436 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.57920e6 | −0.180586 | ||||||||
\(599\) | 9.29978e6 | 1.05902 | 0.529512 | − | 0.848302i | \(-0.322375\pi\) | ||||
0.529512 | + | 0.848302i | \(0.322375\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.14617e7 | −1.29438 | −0.647192 | − | 0.762327i | \(-0.724057\pi\) | ||||
−0.647192 | + | 0.762327i | \(0.724057\pi\) | |||||||
\(602\) | −9.37446e6 | −1.05428 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.26195e6 | −0.363819 | ||||||||
\(605\) | −1.03918e7 | −1.15425 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.12784e7 | 1.24244 | 0.621219 | − | 0.783637i | \(-0.286638\pi\) | ||||
0.621219 | + | 0.783637i | \(0.286638\pi\) | |||||||
\(608\) | −978944. | −0.107399 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.20776e6 | 0.893100 | ||||||||
\(611\) | −1.29494e7 | −1.40329 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 93782.0 | 0.0100802 | 0.00504009 | − | 0.999987i | \(-0.498396\pi\) | ||||
0.00504009 | + | 0.999987i | \(0.498396\pi\) | |||||||
\(614\) | −6.76088e6 | −0.723740 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −675840. | −0.0717616 | ||||||||
\(617\) | 1.49642e7 | 1.58248 | 0.791242 | − | 0.611504i | \(-0.209435\pi\) | ||||
0.791242 | + | 0.611504i | \(0.209435\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.06888e6 | −0.531723 | −0.265861 | − | 0.964011i | \(-0.585656\pi\) | ||||
−0.265861 | + | 0.964011i | \(0.585656\pi\) | |||||||
\(620\) | −3.79315e6 | −0.396297 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.00816e6 | −0.622681 | ||||||||
\(623\) | 5.76259e6 | 0.594837 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.20971e7 | −1.23875 | ||||||||
\(626\) | −3.24337e6 | −0.330796 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.17827e6 | 0.220401 | ||||||||
\(629\) | −3.50161e6 | −0.352892 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.55919e7 | 1.55892 | 0.779462 | − | 0.626450i | \(-0.215493\pi\) | ||||
0.779462 | + | 0.626450i | \(0.215493\pi\) | |||||||
\(632\) | −4.76211e6 | −0.474250 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.61423e6 | 0.357102 | ||||||||
\(635\) | 1.14180e7 | 1.12371 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.32320e6 | −0.910367 | ||||||||
\(638\) | 1.33776e6 | 0.130115 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.08134e6 | −0.104355 | ||||||||
\(641\) | −1.09701e7 | −1.05455 | −0.527274 | − | 0.849695i | \(-0.676786\pi\) | ||||
−0.527274 | + | 0.849695i | \(0.676786\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.83704e6 | −0.270607 | −0.135303 | − | 0.990804i | \(-0.543201\pi\) | ||||
−0.135303 | + | 0.990804i | \(0.543201\pi\) | |||||||
\(644\) | −1.68960e6 | −0.160535 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.58314e6 | −0.149258 | ||||||||
\(647\) | 6.05686e6 | 0.568835 | 0.284418 | − | 0.958700i | \(-0.408200\pi\) | ||||
0.284418 | + | 0.958700i | \(0.408200\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.58040e6 | −0.147284 | ||||||||
\(650\) | 3.23999e6 | 0.300788 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.73798e6 | −0.252239 | ||||||||
\(653\) | 1.08892e6 | 0.0999341 | 0.0499671 | − | 0.998751i | \(-0.484088\pi\) | ||||
0.0499671 | + | 0.998751i | \(0.484088\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.98316e6 | −0.909211 | ||||||||
\(656\) | −4.91366e6 | −0.445806 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.38547e7 | −1.24748 | ||||||||
\(659\) | −7.41803e6 | −0.665388 | −0.332694 | − | 0.943035i | \(-0.607958\pi\) | ||||
−0.332694 | + | 0.943035i | \(0.607958\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 767654. | 0.0683379 | 0.0341690 | − | 0.999416i | \(-0.489122\pi\) | ||||
0.0341690 | + | 0.999416i | \(0.489122\pi\) | |||||||
\(662\) | −4.48789e6 | −0.398013 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −413952. | −0.0364359 | ||||||||
\(665\) | 1.11049e7 | 0.973779 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.34440e6 | 0.291074 | ||||||||
\(668\) | 1.08192e7 | 0.938110 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.43626e6 | 0.381794 | ||||||||
\(671\) | −1.86540e6 | −0.159943 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.42263e6 | 0.121075 | 0.0605373 | − | 0.998166i | \(-0.480719\pi\) | ||||
0.0605373 | + | 0.998166i | \(0.480719\pi\) | |||||||
\(674\) | 1.10087e7 | 0.933439 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 986736. | 0.0830490 | ||||||||
\(677\) | 6.16231e6 | 0.516739 | 0.258370 | − | 0.966046i | \(-0.416815\pi\) | ||||
0.258370 | + | 0.966046i | \(0.416815\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.92304e7 | 2.43310 | ||||||||
\(680\) | −1.74874e6 | −0.145028 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 862080. | 0.0709719 | ||||||||
\(683\) | −1.50621e7 | −1.23548 | −0.617739 | − | 0.786383i | \(-0.711951\pi\) | ||||
−0.617739 | + | 0.786383i | \(0.711951\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.47796e6 | 0.690343 | ||||||||
\(686\) | 1.85715e6 | 0.150674 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.40890e6 | 0.274563 | ||||||||
\(689\) | −2.05730e7 | −1.65101 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.87636e6 | −0.468180 | −0.234090 | − | 0.972215i | \(-0.575211\pi\) | ||||
−0.234090 | + | 0.972215i | \(0.575211\pi\) | |||||||
\(692\) | −2.13053e6 | −0.169131 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.66997e6 | 0.604498 | ||||||||
\(695\) | 1.01769e7 | 0.799199 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.94632e6 | −0.619561 | ||||||||
\(698\) | −7.34636e6 | −0.570734 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.46650e6 | 0.267390 | ||||||||
\(701\) | −3.60077e6 | −0.276758 | −0.138379 | − | 0.990379i | \(-0.544189\pi\) | ||||
−0.138379 | + | 0.990379i | \(0.544189\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.08585e6 | −0.617074 | ||||||||
\(704\) | 245760. | 0.0186887 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.48806e6 | −0.187866 | ||||||||
\(707\) | 3.87235e6 | 0.291358 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.22516e6 | 0.689221 | 0.344610 | − | 0.938746i | \(-0.388011\pi\) | ||||
0.344610 | + | 0.938746i | \(0.388011\pi\) | |||||||
\(710\) | 1.61568e6 | 0.120284 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.09549e6 | −0.154912 | ||||||||
\(713\) | 2.15520e6 | 0.158768 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.60568e6 | −0.190615 | ||||||||
\(716\) | 1.10943e7 | 0.808758 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.49625e7 | 1.08316 | ||||||||
\(719\) | 2.63923e7 | 1.90395 | 0.951975 | − | 0.306177i | \(-0.0990500\pi\) | ||||
0.951975 | + | 0.306177i | \(0.0990500\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.39505e7 | −0.999426 | ||||||||
\(722\) | 6.24865e6 | 0.446111 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.03478e6 | 0.427873 | ||||||||
\(725\) | −6.86159e6 | −0.484819 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.79485e6 | −0.687324 | −0.343662 | − | 0.939093i | \(-0.611667\pi\) | ||||
−0.343662 | + | 0.939093i | \(0.611667\pi\) | |||||||
\(728\) | 7.41171e6 | 0.518311 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.74731e6 | 0.468623 | ||||||||
\(731\) | 5.51282e6 | 0.381576 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.07584e6 | 0.280193 | 0.140096 | − | 0.990138i | \(-0.455259\pi\) | ||||
0.140096 | + | 0.990138i | \(0.455259\pi\) | |||||||
\(734\) | −64928.0 | −0.00444828 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 614400. | 0.0418077 | ||||||||
\(737\) | −1.00824e6 | −0.0683747 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.65709e7 | −1.11618 | −0.558089 | − | 0.829781i | \(-0.688465\pi\) | ||||
−0.558089 | + | 0.829781i | \(0.688465\pi\) | |||||||
\(740\) | −8.93165e6 | −0.599587 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.20113e7 | −1.46769 | ||||||||
\(743\) | −1.44141e7 | −0.957892 | −0.478946 | − | 0.877844i | \(-0.658981\pi\) | ||||
−0.478946 | + | 0.877844i | \(0.658981\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.94396e6 | −0.128321 | ||||||||
\(746\) | −1.17442e6 | −0.0772641 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 397440. | 0.0259727 | ||||||||
\(749\) | −4.01259e7 | −2.61349 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.67944e7 | 1.08659 | 0.543295 | − | 0.839542i | \(-0.317177\pi\) | ||||
0.543295 | + | 0.839542i | \(0.317177\pi\) | |||||||
\(752\) | 5.03808e6 | 0.324878 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.46708e7 | −0.939776 | ||||||||
\(755\) | −1.34556e7 | −0.859081 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.32943e7 | 0.843188 | 0.421594 | − | 0.906785i | \(-0.361471\pi\) | ||||
0.421594 | + | 0.906785i | \(0.361471\pi\) | |||||||
\(758\) | −1.27205e7 | −0.804137 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.03814e6 | −0.253599 | ||||||||
\(761\) | 2.14786e6 | 0.134445 | 0.0672225 | − | 0.997738i | \(-0.478586\pi\) | ||||
0.0672225 | + | 0.997738i | \(0.478586\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.50128e6 | −0.0933577 | ||||||||
\(764\) | 4.24550e6 | 0.263145 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.19194e7 | −0.733975 | ||||||||
\(767\) | 1.73317e7 | 1.06378 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.31059e7 | −0.799193 | −0.399596 | − | 0.916691i | \(-0.630850\pi\) | ||||
−0.399596 | + | 0.916691i | \(0.630850\pi\) | |||||||
\(770\) | −2.78784e6 | −0.169450 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.72477e6 | 0.285323 | ||||||||
\(773\) | 2.37154e7 | 1.42752 | 0.713759 | − | 0.700392i | \(-0.246991\pi\) | ||||
0.713759 | + | 0.700392i | \(0.246991\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.42175e6 | −0.264448 | ||||||||
\(776\) | −1.06292e7 | −0.633648 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.38391e7 | 0.819707 | ||||||||
\(779\) | −1.83495e7 | −1.08338 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −367200. | −0.0215415 | ||||||||
\(782\) | 993600. | 0.0581025 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.62726e6 | 0.210760 | ||||||||
\(785\) | 8.98537e6 | 0.520430 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.40048e6 | −0.483468 | −0.241734 | − | 0.970343i | \(-0.577716\pi\) | ||||
−0.241734 | + | 0.970343i | \(0.577716\pi\) | |||||||
\(788\) | −3.22070e6 | −0.184772 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.96437e7 | −1.11984 | ||||||||
\(791\) | 3.43971e7 | 1.95470 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.04572e7 | 1.15522 | ||||||||
\(794\) | 1.56166e7 | 0.879097 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.04392e7 | 0.583960 | ||||||||
\(797\) | −5.41023e6 | −0.301696 | −0.150848 | − | 0.988557i | \(-0.548200\pi\) | ||||
−0.150848 | + | 0.988557i | \(0.548200\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.14752e6 | 0.451501 | ||||||||
\(800\) | −1.26054e6 | −0.0696359 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.17646e7 | 1.19485 | ||||||||
\(803\) | −1.53348e6 | −0.0839246 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.96960e6 | −0.379069 | ||||||||
\(806\) | −9.45414e6 | −0.512607 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.40813e6 | −0.0758776 | ||||||||
\(809\) | 2.60777e7 | 1.40087 | 0.700436 | − | 0.713715i | \(-0.252989\pi\) | ||||
0.700436 | + | 0.713715i | \(0.252989\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.90021e7 | 1.01449 | 0.507247 | − | 0.861800i | \(-0.330663\pi\) | ||||
0.507247 | + | 0.861800i | \(0.330663\pi\) | |||||||
\(812\) | −1.56964e7 | −0.835429 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.02992e6 | 0.107379 | ||||||||
\(815\) | −1.12942e7 | −0.595608 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.27301e7 | 0.667231 | ||||||||
\(818\) | −7.87978e6 | −0.411748 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.02689e7 | −1.05268 | ||||||||
\(821\) | 3.10173e7 | 1.60600 | 0.803001 | − | 0.595978i | \(-0.203236\pi\) | ||||
0.803001 | + | 0.595978i | \(0.203236\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.56290e7 | −0.804323 | −0.402162 | − | 0.915569i | \(-0.631741\pi\) | ||||
−0.402162 | + | 0.915569i | \(0.631741\pi\) | |||||||
\(824\) | 5.07290e6 | 0.260278 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.85434e7 | 0.945667 | ||||||||
\(827\) | −1.58421e7 | −0.805467 | −0.402733 | − | 0.915317i | \(-0.631940\pi\) | ||||
−0.402733 | + | 0.915317i | \(0.631940\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.06176e6 | 0.104196 | 0.0520980 | − | 0.998642i | \(-0.483409\pi\) | ||||
0.0520980 | + | 0.998642i | \(0.483409\pi\) | |||||||
\(830\) | −1.70755e6 | −0.0860357 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.69517e6 | −0.134983 | ||||||||
\(833\) | 5.86597e6 | 0.292905 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.46292e7 | 2.21515 | ||||||||
\(836\) | 917760. | 0.0454165 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 556080. | 0.0273544 | ||||||||
\(839\) | −3.03900e7 | −1.49048 | −0.745240 | − | 0.666796i | \(-0.767665\pi\) | ||||
−0.745240 | + | 0.666796i | \(0.767665\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.05583e7 | 0.514760 | ||||||||
\(842\) | −1.73097e7 | −0.841414 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.83530e7 | −0.886850 | ||||||||
\(845\) | 4.07029e6 | 0.196103 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.77114e7 | −1.32724 | ||||||||
\(848\) | 8.00410e6 | 0.382228 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.03854e6 | −0.0967768 | ||||||||
\(851\) | 5.07480e6 | 0.240212 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.97738e7 | −1.40108 | −0.700538 | − | 0.713615i | \(-0.747056\pi\) | ||||
−0.700538 | + | 0.713615i | \(0.747056\pi\) | |||||||
\(854\) | 2.18874e7 | 1.02695 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.45912e7 | 0.680624 | ||||||||
\(857\) | −8.64100e6 | −0.401894 | −0.200947 | − | 0.979602i | \(-0.564402\pi\) | ||||
−0.200947 | + | 0.979602i | \(0.564402\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.35663e7 | −1.55210 | −0.776051 | − | 0.630670i | \(-0.782780\pi\) | ||||
−0.776051 | + | 0.630670i | \(0.782780\pi\) | |||||||
\(860\) | 1.40617e7 | 0.648323 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.11974e7 | −0.513276 | ||||||||
\(863\) | −3.90191e7 | −1.78341 | −0.891703 | − | 0.452621i | \(-0.850489\pi\) | ||||
−0.891703 | + | 0.452621i | \(0.850489\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.78843e6 | −0.399366 | ||||||||
\(866\) | 2.36097e7 | 1.06978 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.01151e7 | −0.455690 | ||||||||
\(869\) | 4.46448e6 | 0.200549 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.10570e7 | 0.493848 | ||||||||
\(872\) | 545920. | 0.0243130 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.29440e6 | 0.101599 | ||||||||
\(875\) | −2.20007e7 | −0.971441 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.81382e7 | −0.796333 | −0.398166 | − | 0.917313i | \(-0.630353\pi\) | ||||
−0.398166 | + | 0.917313i | \(0.630353\pi\) | |||||||
\(878\) | 1.78605e6 | 0.0781910 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.01376e6 | 0.0441294 | ||||||||
\(881\) | −3.05312e7 | −1.32527 | −0.662634 | − | 0.748943i | \(-0.730562\pi\) | ||||
−0.662634 | + | 0.748943i | \(0.730562\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.35533e7 | −1.87983 | −0.939916 | − | 0.341405i | \(-0.889097\pi\) | ||||
−0.939916 | + | 0.341405i | \(0.889097\pi\) | |||||||
\(884\) | −4.35859e6 | −0.187593 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.39810e7 | 0.598348 | ||||||||
\(887\) | 1.34152e7 | 0.572515 | 0.286257 | − | 0.958153i | \(-0.407589\pi\) | ||||
0.286257 | + | 0.958153i | \(0.407589\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.04480e7 | 1.29212 | ||||||||
\(890\) | −8.64389e6 | −0.365792 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.12314e7 | 0.472629 | ||||||||
\(893\) | 1.88141e7 | 0.789504 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.57641e7 | 1.90971 | ||||||||
\(896\) | −2.88358e6 | −0.119995 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.82450e6 | −0.199647 | ||||||||
\(899\) | 2.00218e7 | 0.826236 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.29441e7 | 0.531203 | ||||||||
\(902\) | 4.60656e6 | 0.188521 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.25080e7 | −0.509059 | ||||||||
\(905\) | 2.48935e7 | 1.01033 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.10816e6 | 0.125454 | 0.0627272 | − | 0.998031i | \(-0.480020\pi\) | ||||
0.0627272 | + | 0.998031i | \(0.480020\pi\) | |||||||
\(908\) | −1.97777e7 | −0.796089 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.05733e7 | 1.22388 | ||||||||
\(911\) | −1.19035e6 | −0.0475203 | −0.0237602 | − | 0.999718i | \(-0.507564\pi\) | ||||
−0.0237602 | + | 0.999718i | \(0.507564\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 388080. | 0.0154079 | ||||||||
\(914\) | −934184. | −0.0369885 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.69328e6 | 0.0666792 | ||||||||
\(917\) | −2.66218e7 | −1.04547 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.71996e7 | −1.84353 | −0.921764 | − | 0.387752i | \(-0.873252\pi\) | ||||
−0.921764 | + | 0.387752i | \(0.873252\pi\) | |||||||
\(920\) | 2.53440e6 | 0.0987201 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6.97956e6 | −0.270396 | ||||||||
\(923\) | 4.02696e6 | 0.155587 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.04118e7 | −0.400103 | ||||||||
\(926\) | 1.16715e7 | 0.447299 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.70778e6 | 0.217569 | ||||||||
\(929\) | −1.33595e6 | −0.0507870 | −0.0253935 | − | 0.999678i | \(-0.508084\pi\) | ||||
−0.0253935 | + | 0.999678i | \(0.508084\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.35456e7 | 0.512180 | ||||||||
\(932\) | 7.01885e6 | 0.264683 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.12430e7 | −0.796800 | ||||||||
\(935\) | 1.63944e6 | 0.0613291 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.47238e7 | 0.547861 | 0.273931 | − | 0.961749i | \(-0.411676\pi\) | ||||
0.273931 | + | 0.961749i | \(0.411676\pi\) | |||||||
\(938\) | 1.18300e7 | 0.439014 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.07821e7 | 0.767131 | ||||||||
\(941\) | 2.69196e7 | 0.991049 | 0.495525 | − | 0.868594i | \(-0.334976\pi\) | ||||
0.495525 | + | 0.868594i | \(0.334976\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.15164e7 | 0.421733 | ||||||||
\(944\) | −6.74304e6 | −0.246278 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.19584e6 | −0.116107 | ||||||||
\(947\) | 3.73160e6 | 0.135214 | 0.0676068 | − | 0.997712i | \(-0.478464\pi\) | ||||
0.0676068 | + | 0.997712i | \(0.478464\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.68172e7 | 0.606160 | ||||||||
\(950\) | −4.70734e6 | −0.169226 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.66330e6 | −0.166763 | ||||||||
\(953\) | −2.18735e7 | −0.780166 | −0.390083 | − | 0.920780i | \(-0.627554\pi\) | ||||
−0.390083 | + | 0.920780i | \(0.627554\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.75127e7 | 0.621362 | ||||||||
\(956\) | −455424. | −0.0161165 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.37862e6 | 0.330161 | ||||||||
\(959\) | 2.26079e7 | 0.793805 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.57267e7 | −0.549324 | ||||||||
\(962\) | −2.22615e7 | −0.775561 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.42810e7 | 0.494955 | ||||||||
\(965\) | 1.94897e7 | 0.673730 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.76025e7 | 0.605352 | 0.302676 | − | 0.953093i | \(-0.402120\pi\) | ||||
0.302676 | + | 0.953093i | \(0.402120\pi\) | |||||||
\(968\) | 1.00769e7 | 0.345650 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.38456e7 | −1.49623 | ||||||||
\(971\) | −1.67317e7 | −0.569497 | −0.284749 | − | 0.958602i | \(-0.591910\pi\) | ||||
−0.284749 | + | 0.958602i | \(0.591910\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.71385e7 | 0.918975 | ||||||||
\(974\) | −3.92612e7 | −1.32607 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.95904e6 | −0.267446 | ||||||||
\(977\) | −5.55382e7 | −1.86147 | −0.930733 | − | 0.365699i | \(-0.880830\pi\) | ||||
−0.930733 | + | 0.365699i | \(0.880830\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.96452e6 | 0.0655088 | ||||||||
\(980\) | 1.49625e7 | 0.497666 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.37808e7 | −0.786951 | ||||||||
\(983\) | 3.86784e7 | 1.27669 | 0.638344 | − | 0.769751i | \(-0.279620\pi\) | ||||
0.638344 | + | 0.769751i | \(0.279620\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.32854e7 | −0.436299 | ||||||||
\(986\) | 9.23054e6 | 0.302367 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.00648e7 | −0.328028 | ||||||||
\(989\) | −7.98960e6 | −0.259737 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.58498e6 | 0.310033 | 0.155016 | − | 0.987912i | \(-0.450457\pi\) | ||||
0.155016 | + | 0.987912i | \(0.450457\pi\) | |||||||
\(992\) | 3.67821e6 | 0.118674 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.30848e6 | 0.138311 | ||||||||
\(995\) | 4.30616e7 | 1.37890 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.03650e7 | −0.330242 | −0.165121 | − | 0.986273i | \(-0.552802\pi\) | ||||
−0.165121 | + | 0.986273i | \(0.552802\pi\) | |||||||
\(998\) | −2.59133e7 | −0.823561 | ||||||||
\(999\) | 0 | 0 |
(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 | 18.6.a.b.1.1 | 1 | ||
3.2 | odd | 2 | 6.6.a.a.1.1 | ✓ | 1 | ||
4.3 | odd | 2 | 144.6.a.j.1.1 | 1 | |||
5.2 | odd | 4 | 450.6.c.j.199.1 | 2 | |||
5.3 | odd | 4 | 450.6.c.j.199.2 | 2 | |||
5.4 | even | 2 | 450.6.a.m.1.1 | 1 | |||
7.6 | odd | 2 | 882.6.a.a.1.1 | 1 | |||
8.3 | odd | 2 | 576.6.a.i.1.1 | 1 | |||
8.5 | even | 2 | 576.6.a.j.1.1 | 1 | |||
9.2 | odd | 6 | 162.6.c.e.109.1 | 2 | |||
9.4 | even | 3 | 162.6.c.h.55.1 | 2 | |||
9.5 | odd | 6 | 162.6.c.e.55.1 | 2 | |||
9.7 | even | 3 | 162.6.c.h.109.1 | 2 | |||
12.11 | even | 2 | 48.6.a.c.1.1 | 1 | |||
15.2 | even | 4 | 150.6.c.b.49.2 | 2 | |||
15.8 | even | 4 | 150.6.c.b.49.1 | 2 | |||
15.14 | odd | 2 | 150.6.a.d.1.1 | 1 | |||
21.2 | odd | 6 | 294.6.e.g.67.1 | 2 | |||
21.5 | even | 6 | 294.6.e.a.67.1 | 2 | |||
21.11 | odd | 6 | 294.6.e.g.79.1 | 2 | |||
21.17 | even | 6 | 294.6.e.a.79.1 | 2 | |||
21.20 | even | 2 | 294.6.a.m.1.1 | 1 | |||
24.5 | odd | 2 | 192.6.a.o.1.1 | 1 | |||
24.11 | even | 2 | 192.6.a.g.1.1 | 1 | |||
33.32 | even | 2 | 726.6.a.a.1.1 | 1 | |||
39.38 | odd | 2 | 1014.6.a.c.1.1 | 1 | |||
48.5 | odd | 4 | 768.6.d.c.385.2 | 2 | |||
48.11 | even | 4 | 768.6.d.p.385.1 | 2 | |||
48.29 | odd | 4 | 768.6.d.c.385.1 | 2 | |||
48.35 | even | 4 | 768.6.d.p.385.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.6.a.a.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
18.6.a.b.1.1 | 1 | 1.1 | even | 1 | trivial | ||
48.6.a.c.1.1 | 1 | 12.11 | even | 2 | |||
144.6.a.j.1.1 | 1 | 4.3 | odd | 2 | |||
150.6.a.d.1.1 | 1 | 15.14 | odd | 2 | |||
150.6.c.b.49.1 | 2 | 15.8 | even | 4 | |||
150.6.c.b.49.2 | 2 | 15.2 | even | 4 | |||
162.6.c.e.55.1 | 2 | 9.5 | odd | 6 | |||
162.6.c.e.109.1 | 2 | 9.2 | odd | 6 | |||
162.6.c.h.55.1 | 2 | 9.4 | even | 3 | |||
162.6.c.h.109.1 | 2 | 9.7 | even | 3 | |||
192.6.a.g.1.1 | 1 | 24.11 | even | 2 | |||
192.6.a.o.1.1 | 1 | 24.5 | odd | 2 | |||
294.6.a.m.1.1 | 1 | 21.20 | even | 2 | |||
294.6.e.a.67.1 | 2 | 21.5 | even | 6 | |||
294.6.e.a.79.1 | 2 | 21.17 | even | 6 | |||
294.6.e.g.67.1 | 2 | 21.2 | odd | 6 | |||
294.6.e.g.79.1 | 2 | 21.11 | odd | 6 | |||
450.6.a.m.1.1 | 1 | 5.4 | even | 2 | |||
450.6.c.j.199.1 | 2 | 5.2 | odd | 4 | |||
450.6.c.j.199.2 | 2 | 5.3 | odd | 4 | |||
576.6.a.i.1.1 | 1 | 8.3 | odd | 2 | |||
576.6.a.j.1.1 | 1 | 8.5 | even | 2 | |||
726.6.a.a.1.1 | 1 | 33.32 | even | 2 | |||
768.6.d.c.385.1 | 2 | 48.29 | odd | 4 | |||
768.6.d.c.385.2 | 2 | 48.5 | odd | 4 | |||
768.6.d.p.385.1 | 2 | 48.11 | even | 4 | |||
768.6.d.p.385.2 | 2 | 48.35 | even | 4 | |||
882.6.a.a.1.1 | 1 | 7.6 | odd | 2 | |||
1014.6.a.c.1.1 | 1 | 39.38 | odd | 2 |