Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8512,2,Mod(1,8512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8512.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8512 = 2^{6} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8512.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: | \(67.9686622005\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{21}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 5 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 532) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.79129\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8512.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.79129 | −1.03420 | −0.517100 | − | 0.855925i | \(-0.672989\pi\) | ||||
−0.517100 | + | 0.855925i | \(0.672989\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.00000 | −1.34164 | −0.670820 | − | 0.741620i | \(-0.734058\pi\) | ||||
−0.670820 | + | 0.741620i | \(0.734058\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.208712 | 0.0695707 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.791288 | −0.238582 | −0.119291 | − | 0.992859i | \(-0.538062\pi\) | ||||
−0.119291 | + | 0.992859i | \(0.538062\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | 0.138675 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138675 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.37386 | 1.38753 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.791288 | −0.191915 | −0.0959577 | − | 0.995385i | \(-0.530591\pi\) | ||||
−0.0959577 | + | 0.995385i | \(0.530591\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.79129 | −0.390891 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.58258 | −0.955533 | −0.477767 | − | 0.878487i | \(-0.658554\pi\) | ||||
−0.477767 | + | 0.878487i | \(0.658554\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00000 | 0.800000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.791288 | 0.146938 | 0.0734692 | − | 0.997297i | \(-0.476593\pi\) | ||||
0.0734692 | + | 0.997297i | \(0.476593\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.37386 | −1.14478 | −0.572390 | − | 0.819982i | \(-0.693984\pi\) | ||||
−0.572390 | + | 0.819982i | \(0.693984\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.41742 | 0.246742 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.00000 | −0.507093 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.00000 | −0.821995 | −0.410997 | − | 0.911636i | \(-0.634819\pi\) | ||||
−0.410997 | + | 0.911636i | \(0.634819\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.79129 | −0.286836 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.791288 | 0.123578 | 0.0617892 | − | 0.998089i | \(-0.480319\pi\) | ||||
0.0617892 | + | 0.998089i | \(0.480319\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | −0.304997 | −0.152499 | − | 0.988304i | \(-0.548732\pi\) | ||||
−0.152499 | + | 0.988304i | \(0.548732\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.626136 | −0.0933389 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.41742 | 0.206753 | 0.103376 | − | 0.994642i | \(-0.467035\pi\) | ||||
0.103376 | + | 0.994642i | \(0.467035\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.41742 | 0.198479 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.37386 | −0.738157 | −0.369078 | − | 0.929398i | \(-0.620327\pi\) | ||||
−0.369078 | + | 0.929398i | \(0.620327\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.37386 | 0.320092 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.79129 | 0.237262 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.16515 | 0.802634 | 0.401317 | − | 0.915939i | \(-0.368553\pi\) | ||||
0.401317 | + | 0.915939i | \(0.368553\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | 0.128037 | 0.0640184 | − | 0.997949i | \(-0.479608\pi\) | ||||
0.0640184 | + | 0.997949i | \(0.479608\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.208712 | 0.0262953 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.00000 | −0.372104 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.37386 | −0.534352 | −0.267176 | − | 0.963648i | \(-0.586091\pi\) | ||||
−0.267176 | + | 0.963648i | \(0.586091\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.20871 | 0.988213 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.16515 | 0.731669 | 0.365834 | − | 0.930680i | \(-0.380784\pi\) | ||||
0.365834 | + | 0.930680i | \(0.380784\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.62614 | 0.307366 | 0.153683 | − | 0.988120i | \(-0.450887\pi\) | ||||
0.153683 | + | 0.988120i | \(0.450887\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.16515 | −0.827360 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.791288 | −0.0901756 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.0000 | −1.12509 | −0.562544 | − | 0.826767i | \(-0.690177\pi\) | ||||
−0.562544 | + | 0.826767i | \(0.690177\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.58258 | −1.06473 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.626136 | −0.0687274 | −0.0343637 | − | 0.999409i | \(-0.510940\pi\) | ||||
−0.0343637 | + | 0.999409i | \(0.510940\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.37386 | 0.257482 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.41742 | −0.151964 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.58258 | −0.167753 | −0.0838763 | − | 0.996476i | \(-0.526730\pi\) | ||||
−0.0838763 | + | 0.996476i | \(0.526730\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.4174 | 1.18393 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.00000 | 0.307794 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.00000 | −0.710742 | −0.355371 | − | 0.934725i | \(-0.615646\pi\) | ||||
−0.355371 | + | 0.934725i | \(0.615646\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.165151 | −0.0165983 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −19.7477 | −1.96497 | −0.982486 | − | 0.186336i | \(-0.940339\pi\) | ||||
−0.982486 | + | 0.186336i | \(0.940339\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.0000 | −1.28093 | −0.640464 | − | 0.767988i | \(-0.721258\pi\) | ||||
−0.640464 | + | 0.767988i | \(0.721258\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.37386 | 0.524435 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.1652 | 1.75609 | 0.878046 | − | 0.478577i | \(-0.158847\pi\) | ||||
0.878046 | + | 0.478577i | \(0.158847\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.7477 | −1.50836 | −0.754179 | − | 0.656668i | \(-0.771965\pi\) | ||||
−0.754179 | + | 0.656668i | \(0.771965\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.95644 | 0.850108 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.37386 | −0.505531 | −0.252765 | − | 0.967528i | \(-0.581340\pi\) | ||||
−0.252765 | + | 0.967528i | \(0.581340\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.7477 | 1.28198 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.208712 | 0.0192954 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.791288 | −0.0725372 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3739 | −0.943079 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.41742 | −0.127805 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.7477 | −1.84106 | −0.920532 | − | 0.390668i | \(-0.872244\pi\) | ||||
−0.920532 | + | 0.390668i | \(0.872244\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.58258 | 0.315428 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.1216 | −1.67066 | −0.835331 | − | 0.549748i | \(-0.814724\pi\) | ||||
−0.835331 | + | 0.549748i | \(0.814724\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00000 | −0.0867110 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −15.0000 | −1.29099 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.00000 | 0.512615 | 0.256307 | − | 0.966595i | \(-0.417494\pi\) | ||||
0.256307 | + | 0.966595i | \(0.417494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.7477 | 1.50534 | 0.752671 | − | 0.658396i | \(-0.228765\pi\) | ||||
0.752671 | + | 0.658396i | \(0.228765\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.53901 | −0.213824 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.791288 | −0.0661708 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.37386 | −0.197139 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.79129 | −0.147743 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.00000 | −0.245770 | −0.122885 | − | 0.992421i | \(-0.539215\pi\) | ||||
−0.122885 | + | 0.992421i | \(0.539215\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.373864 | −0.0304246 | −0.0152123 | − | 0.999884i | \(-0.504842\pi\) | ||||
−0.0152123 | + | 0.999884i | \(0.504842\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.165151 | −0.0133517 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.1216 | 1.53588 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.1216 | −1.68569 | −0.842843 | − | 0.538159i | \(-0.819120\pi\) | ||||
−0.842843 | + | 0.538159i | \(0.819120\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.62614 | 0.763402 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.58258 | −0.361158 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.37386 | 0.734218 | 0.367109 | − | 0.930178i | \(-0.380348\pi\) | ||||
0.367109 | + | 0.930178i | \(0.380348\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.25227 | −0.331039 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.5826 | 1.74749 | 0.873746 | − | 0.486382i | \(-0.161684\pi\) | ||||
0.873746 | + | 0.486382i | \(0.161684\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.208712 | −0.0159606 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.74773 | 0.360963 | 0.180482 | − | 0.983578i | \(-0.442234\pi\) | ||||
0.180482 | + | 0.983578i | \(0.442234\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.00000 | 0.302372 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.0436 | −0.830085 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.2087 | 0.837778 | 0.418889 | − | 0.908037i | \(-0.362420\pi\) | ||||
0.418889 | + | 0.908037i | \(0.362420\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.37386 | −0.325107 | −0.162553 | − | 0.986700i | \(-0.551973\pi\) | ||||
−0.162553 | + | 0.986700i | \(0.551973\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.79129 | −0.132416 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.0000 | 1.10282 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.626136 | 0.0457876 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.00000 | 0.363696 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.53901 | −0.617861 | −0.308931 | − | 0.951085i | \(-0.599971\pi\) | ||||
−0.308931 | + | 0.951085i | \(0.599971\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.37386 | −0.458801 | −0.229400 | − | 0.973332i | \(-0.573677\pi\) | ||||
−0.229400 | + | 0.973332i | \(0.573677\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.37386 | 0.384830 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.3739 | −0.810354 | −0.405177 | − | 0.914238i | \(-0.632790\pi\) | ||||
−0.405177 | + | 0.914238i | \(0.632790\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.74773 | 0.265669 | 0.132835 | − | 0.991138i | \(-0.457592\pi\) | ||||
0.132835 | + | 0.991138i | \(0.457592\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.83485 | 0.552628 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.791288 | 0.0555375 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.37386 | −0.165798 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.956439 | −0.0664771 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.791288 | 0.0547345 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.6261 | 0.731533 | 0.365767 | − | 0.930707i | \(-0.380807\pi\) | ||||
0.365767 | + | 0.930707i | \(0.380807\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.0436 | −0.756692 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.00000 | 0.409197 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.37386 | −0.432686 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.70417 | −0.317878 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.791288 | −0.0532278 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.74773 | 0.250966 | 0.125483 | − | 0.992096i | \(-0.459952\pi\) | ||||
0.125483 | + | 0.992096i | \(0.459952\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.834849 | 0.0556566 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.791288 | −0.0525196 | −0.0262598 | − | 0.999655i | \(-0.508360\pi\) | ||||
−0.0262598 | + | 0.999655i | \(0.508360\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.0000 | 1.45380 | 0.726900 | − | 0.686743i | \(-0.240960\pi\) | ||||
0.726900 | + | 0.686743i | \(0.240960\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.41742 | 0.0932597 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.1216 | 0.859624 | 0.429812 | − | 0.902918i | \(-0.358580\pi\) | ||||
0.429812 | + | 0.902918i | \(0.358580\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.25227 | −0.277388 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 17.9129 | 1.16357 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.7477 | 1.27737 | 0.638687 | − | 0.769467i | \(-0.279478\pi\) | ||||
0.638687 | + | 0.769467i | \(0.279478\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.7477 | 1.20765 | 0.603824 | − | 0.797118i | \(-0.293643\pi\) | ||||
0.603824 | + | 0.797118i | \(0.293643\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.16515 | 0.138895 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.00000 | −0.191663 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.00000 | −0.0636285 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.12159 | 0.0710779 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.20871 | −0.328771 | −0.164385 | − | 0.986396i | \(-0.552564\pi\) | ||||
−0.164385 | + | 0.986396i | \(0.552564\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.62614 | 0.227973 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.25227 | −0.266288 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.7913 | 0.985033 | 0.492517 | − | 0.870303i | \(-0.336077\pi\) | ||||
0.492517 | + | 0.870303i | \(0.336077\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.00000 | −0.310685 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.165151 | 0.0102226 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.20871 | 0.136195 | 0.0680975 | − | 0.997679i | \(-0.478307\pi\) | ||||
0.0680975 | + | 0.997679i | \(0.478307\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.1216 | 0.990341 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.83485 | 0.173490 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.9564 | −0.789968 | −0.394984 | − | 0.918688i | \(-0.629250\pi\) | ||||
−0.394984 | + | 0.918688i | \(0.629250\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.1216 | 1.64752 | 0.823760 | − | 0.566939i | \(-0.191873\pi\) | ||||
0.823760 | + | 0.566939i | \(0.191873\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.79129 | −0.108414 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.16515 | −0.190866 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −30.7477 | −1.84745 | −0.923726 | − | 0.383054i | \(-0.874872\pi\) | ||||
−0.923726 | + | 0.383054i | \(0.874872\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.33030 | −0.0796431 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.5826 | 1.70509 | 0.852547 | − | 0.522651i | \(-0.175057\pi\) | ||||
0.852547 | + | 0.522651i | \(0.175057\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.37386 | −0.438331 | −0.219165 | − | 0.975688i | \(-0.570333\pi\) | ||||
−0.219165 | + | 0.975688i | \(0.570333\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.37386 | −0.318320 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.791288 | 0.0467082 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3739 | −0.963168 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.5390 | 0.735050 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.74773 | 0.452627 | 0.226314 | − | 0.974055i | \(-0.427333\pi\) | ||||
0.226314 | + | 0.974055i | \(0.427333\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18.4955 | −1.07685 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.95644 | −0.229576 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.58258 | −0.265017 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.00000 | −0.115278 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 35.3739 | 2.03218 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.00000 | −0.171780 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.6261 | 0.777685 | 0.388842 | − | 0.921304i | \(-0.372875\pi\) | ||||
0.388842 | + | 0.921304i | \(0.372875\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 23.2867 | 1.32474 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.7913 | 1.74601 | 0.873007 | − | 0.487708i | \(-0.162167\pi\) | ||||
0.873007 | + | 0.487708i | \(0.162167\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.7477 | −0.833591 | −0.416795 | − | 0.909000i | \(-0.636847\pi\) | ||||
−0.416795 | + | 0.909000i | \(0.636847\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.626136 | −0.0352788 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −33.1652 | −1.86274 | −0.931370 | − | 0.364073i | \(-0.881386\pi\) | ||||
−0.931370 | + | 0.364073i | \(0.881386\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.626136 | −0.0350569 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −32.5390 | −1.81615 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.791288 | 0.0440284 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.00000 | 0.221880 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 28.2087 | 1.55995 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.41742 | 0.0781451 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.6261 | −0.803925 | −0.401963 | − | 0.915656i | \(-0.631672\pi\) | ||||
−0.401963 | + | 0.915656i | \(0.631672\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.04356 | −0.0571868 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13.1216 | 0.716909 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.3739 | −0.674047 | −0.337024 | − | 0.941496i | \(-0.609420\pi\) | ||||
−0.337024 | + | 0.941496i | \(0.609420\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.62614 | 0.522820 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.04356 | 0.273124 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −24.6261 | −1.32583 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.79129 | 0.203527 | 0.101763 | − | 0.994809i | \(-0.467552\pi\) | ||||
0.101763 | + | 0.994809i | \(0.467552\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.3739 | 0.822944 | 0.411472 | − | 0.911422i | \(-0.365015\pi\) | ||||
0.411472 | + | 0.911422i | \(0.365015\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.00000 | 0.266880 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.5390 | 1.25286 | 0.626428 | − | 0.779480i | \(-0.284516\pi\) | ||||
0.626428 | + | 0.779480i | \(0.284516\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.4955 | −0.981637 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.41742 | 0.0750180 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.3739 | −0.758624 | −0.379312 | − | 0.925269i | \(-0.623839\pi\) | ||||
−0.379312 | + | 0.925269i | \(0.623839\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.5826 | 0.975332 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.87841 | −0.412375 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 32.4955 | 1.69625 | 0.848124 | − | 0.529797i | \(-0.177732\pi\) | ||||
0.848124 | + | 0.529797i | \(0.177732\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.165151 | 0.00859744 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.37386 | −0.278997 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.62614 | −0.135976 | −0.0679881 | − | 0.997686i | \(-0.521658\pi\) | ||||
−0.0679881 | + | 0.997686i | \(0.521658\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.37386 | −0.277505 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.791288 | 0.0407534 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.74773 | 0.295241 | 0.147620 | − | 0.989044i | \(-0.452839\pi\) | ||||
0.147620 | + | 0.989044i | \(0.452839\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 37.1652 | 1.90403 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.0000 | 1.07305 | 0.536525 | − | 0.843884i | \(-0.319737\pi\) | ||||
0.536525 | + | 0.843884i | \(0.319737\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.37386 | 0.120983 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.417424 | −0.0212189 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 32.3739 | 1.64142 | 0.820710 | − | 0.571345i | \(-0.193578\pi\) | ||||
0.820710 | + | 0.571345i | \(0.193578\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.62614 | 0.183382 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 34.2523 | 1.72780 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 30.0000 | 1.50946 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.7477 | 1.64356 | 0.821781 | − | 0.569804i | \(-0.192981\pi\) | ||||
0.821781 | + | 0.569804i | \(0.192981\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.79129 | 0.0896766 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.3739 | −1.31705 | −0.658524 | − | 0.752560i | \(-0.728819\pi\) | ||||
−0.658524 | + | 0.752560i | \(0.728819\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.37386 | −0.317505 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 28.7477 | 1.42849 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.95644 | 0.196113 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.1216 | −0.698268 | −0.349134 | − | 0.937073i | \(-0.613524\pi\) | ||||
−0.349134 | + | 0.937073i | \(0.613524\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.7477 | −0.530146 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.16515 | 0.303367 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.87841 | 0.0922075 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −31.7913 | −1.55683 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.74773 | −0.0853821 | −0.0426910 | − | 0.999088i | \(-0.513593\pi\) | ||||
−0.0426910 | + | 0.999088i | \(0.513593\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.0000 | 0.926003 | 0.463002 | − | 0.886357i | \(-0.346772\pi\) | ||||
0.463002 | + | 0.886357i | \(0.346772\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.295834 | 0.0143839 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.16515 | −0.153532 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.00000 | 0.0483934 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.41742 | 0.0684339 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.00000 | −0.289010 | −0.144505 | − | 0.989504i | \(-0.546159\pi\) | ||||
−0.144505 | + | 0.989504i | \(0.546159\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.7477 | −0.852901 | −0.426451 | − | 0.904511i | \(-0.640236\pi\) | ||||
−0.426451 | + | 0.904511i | \(0.640236\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.25227 | 0.203881 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.58258 | 0.219214 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.4955 | −0.644103 | −0.322051 | − | 0.946722i | \(-0.604372\pi\) | ||||
−0.322051 | + | 0.946722i | \(0.604372\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.208712 | 0.00993867 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 36.9564 | 1.75585 | 0.877927 | − | 0.478795i | \(-0.158926\pi\) | ||||
0.877927 | + | 0.478795i | \(0.158926\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.74773 | 0.225064 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.37386 | 0.254175 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.1216 | −0.760825 | −0.380412 | − | 0.924817i | \(-0.624218\pi\) | ||||
−0.380412 | + | 0.924817i | \(0.624218\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.626136 | −0.0294836 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.669697 | 0.0314651 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.00000 | −0.140642 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.8693 | 1.35045 | 0.675225 | − | 0.737612i | \(-0.264047\pi\) | ||||
0.675225 | + | 0.737612i | \(0.264047\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.95644 | −0.184671 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.5390 | −0.956597 | −0.478299 | − | 0.878197i | \(-0.658746\pi\) | ||||
−0.478299 | + | 0.878197i | \(0.658746\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.4955 | 0.952505 | 0.476252 | − | 0.879309i | \(-0.341995\pi\) | ||||
0.476252 | + | 0.879309i | \(0.341995\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −34.2523 | −1.58841 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.2867 | 1.17013 | 0.585065 | − | 0.810986i | \(-0.301069\pi\) | ||||
0.585065 | + | 0.810986i | \(0.301069\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.37386 | −0.201966 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 37.8348 | 1.74334 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.58258 | 0.0727669 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.00000 | −0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.12159 | −0.0513541 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.3739 | 1.20505 | 0.602526 | − | 0.798099i | \(-0.294161\pi\) | ||||
0.602526 | + | 0.798099i | \(0.294161\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.00000 | −0.227980 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.20871 | 0.373509 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.0000 | 0.953561 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.0000 | 0.498458 | 0.249229 | − | 0.968445i | \(-0.419823\pi\) | ||||
0.249229 | + | 0.968445i | \(0.419823\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.7913 | −0.759328 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.16515 | −0.142841 | −0.0714206 | − | 0.997446i | \(-0.522753\pi\) | ||||
−0.0714206 | + | 0.997446i | \(0.522753\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.626136 | −0.0281998 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.495454 | 0.0222690 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.16515 | 0.276545 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.3739 | −1.40449 | −0.702244 | − | 0.711937i | \(-0.747818\pi\) | ||||
−0.702244 | + | 0.711937i | \(0.747818\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −40.4519 | −1.80726 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.3303 | 1.35236 | 0.676181 | − | 0.736736i | \(-0.263634\pi\) | ||||
0.676181 | + | 0.736736i | \(0.263634\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 59.2432 | 2.63629 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 21.4955 | 0.954647 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 36.3303 | 1.61031 | 0.805156 | − | 0.593063i | \(-0.202081\pi\) | ||||
0.805156 | + | 0.593063i | \(0.202081\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.62614 | 0.116173 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.00000 | −0.220755 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 39.0000 | 1.71855 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.12159 | −0.0493275 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.50455 | −0.373308 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.5826 | −0.989361 | −0.494680 | − | 0.869075i | \(-0.664715\pi\) | ||||
−0.494680 | + | 0.869075i | \(0.664715\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.7477 | −1.21332 | −0.606662 | − | 0.794960i | \(-0.707492\pi\) | ||||
−0.606662 | + | 0.794960i | \(0.707492\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.16515 | −0.312713 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.04356 | 0.219701 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.00000 | −0.0869565 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.28674 | 0.0558398 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.791288 | 0.0342745 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −54.4955 | −2.35604 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −20.0780 | −0.866431 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.791288 | −0.0340832 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.00000 | −0.0859867 | −0.0429934 | − | 0.999075i | \(-0.513689\pi\) | ||||
−0.0429934 | + | 0.999075i | \(0.513689\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.83485 | 0.336226 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 47.2432 | 2.02368 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.37386 | −0.0587422 | −0.0293711 | − | 0.999569i | \(-0.509350\pi\) | ||||
−0.0293711 | + | 0.999569i | \(0.509350\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.208712 | 0.00890762 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.791288 | −0.0337100 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.0000 | −0.425243 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −26.8693 | −1.14054 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.3739 | −0.609040 | −0.304520 | − | 0.952506i | \(-0.598496\pi\) | ||||
−0.304520 | + | 0.952506i | \(0.598496\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.00000 | −0.0845910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.12159 | −0.0473536 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.16515 | −0.259830 | −0.129915 | − | 0.991525i | \(-0.541470\pi\) | ||||
−0.129915 | + | 0.991525i | \(0.541470\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.1216 | 0.678240 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.58258 | −0.402430 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.8348 | 0.496143 | 0.248071 | − | 0.968742i | \(-0.420203\pi\) | ||||
0.248071 | + | 0.968742i | \(0.420203\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.4955 | 0.941405 | 0.470703 | − | 0.882292i | \(-0.344000\pi\) | ||||
0.470703 | + | 0.882292i | \(0.344000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.2958 | 0.638993 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18.3303 | −0.764426 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.1216 | 0.754412 | 0.377206 | − | 0.926129i | \(-0.376885\pi\) | ||||
0.377206 | + | 0.926129i | \(0.376885\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.4174 | 0.474492 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.626136 | −0.0259765 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.25227 | 0.176111 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.626136 | −0.0258876 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.16515 | −0.378286 | −0.189143 | − | 0.981950i | \(-0.560571\pi\) | ||||
−0.189143 | + | 0.981950i | \(0.560571\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.37386 | 0.262630 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.3739 | 0.838069 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.9129 | 0.694529 | 0.347264 | − | 0.937767i | \(-0.387111\pi\) | ||||
0.347264 | + | 0.937767i | \(0.387111\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.37386 | 0.0973189 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.71326 | −0.274755 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.62614 | −0.270737 | −0.135368 | − | 0.990795i | \(-0.543222\pi\) | ||||
−0.135368 | + | 0.990795i | \(0.543222\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.3739 | 1.03502 | 0.517511 | − | 0.855677i | \(-0.326859\pi\) | ||||
0.517511 | + | 0.855677i | \(0.326859\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.912878 | −0.0371753 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 31.1216 | 1.26527 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.4955 | −1.15659 | −0.578297 | − | 0.815826i | \(-0.696283\pi\) | ||||
−0.578297 | + | 0.815826i | \(0.696283\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.41742 | −0.0574369 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.41742 | 0.0573428 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.6261 | −0.833082 | −0.416541 | − | 0.909117i | \(-0.636758\pi\) | ||||
−0.416541 | + | 0.909117i | \(0.636758\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.25227 | 0.171468 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.9564 | 0.642382 | 0.321191 | − | 0.947014i | \(-0.395917\pi\) | ||||
0.321191 | + | 0.947014i | \(0.395917\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.37386 | 0.376767 | 0.188384 | − | 0.982096i | \(-0.439675\pi\) | ||||
0.188384 | + | 0.982096i | \(0.439675\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −22.9129 | −0.919462 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.58258 | −0.0634046 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.41742 | −0.0566065 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.95644 | 0.157754 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.0000 | −0.995234 | −0.497617 | − | 0.867397i | \(-0.665792\pi\) | ||||
−0.497617 | + | 0.867397i | \(0.665792\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −19.0345 | −0.756552 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 62.2432 | 2.47005 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.28674 | 0.0509027 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.7913 | −0.979197 | −0.489598 | − | 0.871948i | \(-0.662857\pi\) | ||||
−0.489598 | + | 0.871948i | \(0.662857\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.0000 | −0.907031 | −0.453516 | − | 0.891248i | \(-0.649830\pi\) | ||||
−0.453516 | + | 0.891248i | \(0.649830\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.7477 | −0.423191 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.5826 | −0.887813 | −0.443906 | − | 0.896073i | \(-0.646408\pi\) | ||||
−0.443906 | + | 0.896073i | \(0.646408\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.87841 | −0.191494 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.4174 | 0.447484 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28.5826 | −1.11852 | −0.559261 | − | 0.828991i | \(-0.688915\pi\) | ||||
−0.559261 | + | 0.828991i | \(0.688915\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 57.3648 | 2.24143 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.548107 | 0.0213837 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.0436 | 0.547059 | 0.273530 | − | 0.961864i | \(-0.411809\pi\) | ||||
0.273530 | + | 0.961864i | \(0.411809\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.0000 | 1.32245 | 0.661223 | − | 0.750189i | \(-0.270038\pi\) | ||||
0.661223 | + | 0.750189i | \(0.270038\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.41742 | 0.0550482 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.00000 | 0.116335 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.62614 | −0.140405 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.71326 | −0.259550 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.791288 | −0.0305473 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.1216 | 0.929819 | 0.464909 | − | 0.885358i | \(-0.346087\pi\) | ||||
0.464909 | + | 0.885358i | \(0.346087\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 20.0000 | 0.769800 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.956439 | −0.0367589 | −0.0183795 | − | 0.999831i | \(-0.505851\pi\) | ||||
−0.0183795 | + | 0.999831i | \(0.505851\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.00000 | −0.268635 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.41742 | 0.0543158 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.8348 | 0.682432 | 0.341216 | − | 0.939985i | \(-0.389161\pi\) | ||||
0.341216 | + | 0.939985i | \(0.389161\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.0000 | −0.687745 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −39.4083 | −1.50352 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.37386 | −0.204728 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.2523 | −0.808475 | −0.404237 | − | 0.914654i | \(-0.632463\pi\) | ||||
−0.404237 | + | 0.914654i | \(0.632463\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.165151 | −0.00627358 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −53.2432 | −2.01963 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.626136 | −0.0237166 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.5045 | −0.889024 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.66970 | −0.214142 | −0.107071 | − | 0.994251i | \(-0.534147\pi\) | ||||
−0.107071 | + | 0.994251i | \(0.534147\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.00000 | 0.188579 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.61704 | 0.286875 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19.7477 | −0.742690 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 51.2432 | 1.92448 | 0.962239 | − | 0.272206i | \(-0.0877532\pi\) | ||||
0.962239 | + | 0.272206i | \(0.0877532\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.08712 | −0.0782732 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 29.2087 | 1.09387 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.37386 | 0.0887775 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −35.3739 | −1.32106 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.0000 | −0.447524 | −0.223762 | − | 0.974644i | \(-0.571834\pi\) | ||||
−0.223762 | + | 0.974644i | \(0.571834\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.0000 | −0.484145 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −33.5826 | −1.24895 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.16515 | 0.117551 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.0000 | 0.407967 | 0.203984 | − | 0.978974i | \(-0.434611\pi\) | ||||
0.203984 | + | 0.978974i | \(0.434611\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.8693 | 0.921086 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.58258 | 0.0585337 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.4955 | 0.498466 | 0.249233 | − | 0.968444i | \(-0.419822\pi\) | ||||
0.249233 | + | 0.968444i | \(0.419822\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.37386 | 0.198218 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.46099 | 0.127487 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.25227 | 0.303565 | 0.151782 | − | 0.988414i | \(-0.451499\pi\) | ||||
0.151782 | + | 0.988414i | \(0.451499\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.79129 | 0.0658046 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.3303 | −0.562414 | −0.281207 | − | 0.959647i | \(-0.590735\pi\) | ||||
−0.281207 | + | 0.959647i | \(0.590735\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.00000 | 0.329734 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.130682 | −0.00478141 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.1652 | 0.663740 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.3739 | 0.925905 | 0.462953 | − | 0.886383i | \(-0.346790\pi\) | ||||
0.462953 | + | 0.886383i | \(0.346790\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.33030 | 0.340015 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.12159 | 0.0408189 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.00000 | −0.0726912 | −0.0363456 | − | 0.999339i | \(-0.511572\pi\) | ||||
−0.0363456 | + | 0.999339i | \(0.511572\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.49545 | −0.235770 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.66970 | −0.0967764 | −0.0483882 | − | 0.998829i | \(-0.515408\pi\) | ||||
−0.0483882 | + | 0.998829i | \(0.515408\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.7477 | −0.570106 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.495454 | 0.0179132 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.16515 | 0.222611 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.4955 | 1.49636 | 0.748182 | − | 0.663493i | \(-0.230927\pi\) | ||||
0.748182 | + | 0.663493i | \(0.230927\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.2867 | −1.01872 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.7477 | 0.386569 | 0.193284 | − | 0.981143i | \(-0.438086\pi\) | ||||
0.193284 | + | 0.981143i | \(0.438086\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −25.4955 | −0.915824 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.95644 | 0.321310 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.791288 | −0.0283508 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.87841 | −0.174563 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.95644 | 0.141392 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 63.3648 | 2.26159 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.00000 | 0.142585 | 0.0712923 | − | 0.997455i | \(-0.477288\pi\) | ||||
0.0712923 | + | 0.997455i | \(0.477288\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.95644 | −0.140853 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.37386 | −0.191073 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.00000 | 0.0355110 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −28.8784 | −1.02421 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −35.8693 | −1.27056 | −0.635278 | − | 0.772283i | \(-0.719115\pi\) | ||||
−0.635278 | + | 0.772283i | \(0.719115\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.12159 | −0.0396790 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.330303 | −0.0116707 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.07803 | −0.0733321 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.7477 | 0.484544 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.2087 | 0.816985 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.9129 | 0.805574 | 0.402787 | − | 0.915294i | \(-0.368042\pi\) | ||||
0.402787 | + | 0.915294i | \(0.368042\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.4955 | −0.825037 | −0.412518 | − | 0.910949i | \(-0.635351\pi\) | ||||
−0.412518 | + | 0.910949i | \(0.635351\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −48.5826 | −1.70387 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −28.1216 | −0.985056 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.00000 | 0.0699711 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.208712 | 0.00729299 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.66970 | −0.197874 | −0.0989369 | − | 0.995094i | \(-0.531544\pi\) | ||||
−0.0989369 | + | 0.995094i | \(0.531544\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.2432 | 0.984495 | 0.492248 | − | 0.870455i | \(-0.336175\pi\) | ||||
0.492248 | + | 0.870455i | \(0.336175\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.66970 | 0.197394 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.6606 | 1.17049 | 0.585247 | − | 0.810855i | \(-0.300998\pi\) | ||||
0.585247 | + | 0.810855i | \(0.300998\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.00000 | 0.138926 | 0.0694629 | − | 0.997585i | \(-0.477871\pi\) | ||||
0.0694629 | + | 0.997585i | \(0.477871\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 55.0780 | 1.91064 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.791288 | −0.0274165 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −67.7477 | −2.34451 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −31.8693 | −1.10156 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.1652 | 0.937845 | 0.468923 | − | 0.883239i | \(-0.344642\pi\) | ||||
0.468923 | + | 0.883239i | \(0.344642\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3739 | −0.978409 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −51.1996 | −1.76341 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 36.0000 | 1.23844 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.3739 | −0.356450 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.2087 | 0.453322 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 22.9129 | 0.785443 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.1216 | 1.09982 | 0.549911 | − | 0.835223i | \(-0.314662\pi\) | ||||
0.549911 | + | 0.835223i | \(0.314662\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.626136 | 0.0214134 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 38.7042 | 1.32211 | 0.661055 | − | 0.750338i | \(-0.270109\pi\) | ||||
0.661055 | + | 0.750338i | \(0.270109\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.37386 | 0.217473 | 0.108737 | − | 0.994071i | \(-0.465319\pi\) | ||||
0.108737 | + | 0.994071i | \(0.465319\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.41742 | −0.0483057 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.7042 | 0.398414 | 0.199207 | − | 0.979957i | \(-0.436163\pi\) | ||||
0.199207 | + | 0.979957i | \(0.436163\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.2432 | −0.484283 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 29.3303 | 0.996109 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.91288 | 0.268426 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.37386 | −0.148203 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.46099 | −0.0494469 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.00000 | 0.101419 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.2523 | 0.379962 | 0.189981 | − | 0.981788i | \(-0.439157\pi\) | ||||
0.189981 | + | 0.981788i | \(0.439157\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13.8784 | −0.468107 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.3739 | −0.383195 | −0.191598 | − | 0.981474i | \(-0.561367\pi\) | ||||
−0.191598 | + | 0.981474i | \(0.561367\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −51.7477 | −1.74145 | −0.870725 | − | 0.491771i | \(-0.836350\pi\) | ||||
−0.870725 | + | 0.491771i | \(0.836350\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 33.1307 | 1.11368 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.58258 | −0.153868 | −0.0769339 | − | 0.997036i | \(-0.524513\pi\) | ||||
−0.0769339 | + | 0.997036i | \(0.524513\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.7477 | −0.695856 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.58258 | 0.254026 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.41742 | −0.0474323 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −33.6261 | −1.12400 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.20871 | 0.274081 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.04356 | −0.168212 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.25227 | 0.141664 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.58258 | 0.119221 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.1216 | 0.436176 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 51.2432 | 1.70150 | 0.850751 | − | 0.525569i | \(-0.176148\pi\) | ||||
0.850751 | + | 0.525569i | \(0.176148\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.12159 | −0.136705 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.4955 | −1.70612 | −0.853060 | − | 0.521812i | \(-0.825256\pi\) | ||||
−0.853060 | + | 0.521812i | \(0.825256\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.495454 | 0.0163971 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.37386 | 0.177654 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −19.1216 | −0.631451 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.4955 | 0.676083 | 0.338041 | − | 0.941131i | \(-0.390236\pi\) | ||||
0.338041 | + | 0.941131i | \(0.390236\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.4083 | −0.804282 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.16515 | 0.202928 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.0000 | −0.657596 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.71326 | −0.0891151 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.8693 | −0.684700 | −0.342350 | − | 0.939572i | \(-0.611223\pi\) | ||||
−0.342350 | + | 0.939572i | \(0.611223\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.00000 | −0.0327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −55.1561 | −1.80573 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.87841 | −0.0614306 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.62614 | −0.0531236 | −0.0265618 | − | 0.999647i | \(-0.508456\pi\) | ||||
−0.0265618 | + | 0.999647i | \(0.508456\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.4174 | 0.862100 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.4955 | 0.896326 | 0.448163 | − | 0.893952i | \(-0.352078\pi\) | ||||
0.448163 | + | 0.893952i | \(0.352078\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.62614 | −0.118083 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −15.0000 | −0.487950 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −43.6170 | −1.41736 | −0.708682 | − | 0.705528i | \(-0.750710\pi\) | ||||
−0.708682 | + | 0.705528i | \(0.750710\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.62614 | 0.0852480 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 59.4083 | 1.92645 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 53.5390 | 1.73430 | 0.867149 | − | 0.498048i | \(-0.165950\pi\) | ||||
0.867149 | + | 0.498048i | \(0.165950\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25.6170 | 0.828948 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.12159 | 0.0362559 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.00000 | 0.193750 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.62614 | 0.310521 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.79129 | 0.122173 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.1216 | 0.615546 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.1216 | −0.936487 | −0.468244 | − | 0.883599i | \(-0.655113\pi\) | ||||
−0.468244 | + | 0.883599i | \(0.655113\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.41742 | −0.0455342 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.0000 | −0.481373 | −0.240686 | − | 0.970603i | \(-0.577373\pi\) | ||||
−0.240686 | + | 0.970603i | \(0.577373\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.7477 | 0.568966 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.16515 | −0.229468 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43.5826 | −1.39433 | −0.697165 | − | 0.716911i | \(-0.745556\pi\) | ||||
−0.697165 | + | 0.716911i | \(0.745556\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.25227 | 0.0400228 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.28674 | −0.104938 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 45.3303 | 1.44581 | 0.722906 | − | 0.690946i | \(-0.242806\pi\) | ||||
0.722906 | + | 0.690946i | \(0.242806\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 34.1216 | 1.08720 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.53901 | −0.0808177 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.16515 | 0.291435 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.7477 | 0.595541 | 0.297771 | − | 0.954637i | \(-0.403757\pi\) | ||||
0.297771 | + | 0.954637i | \(0.403757\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 26.1996 | 0.831420 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.2432 | −0.356433 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44.1216 | 1.39734 | 0.698672 | − | 0.715442i | \(-0.253775\pi\) | ||||
0.698672 | + | 0.715442i | \(0.253775\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −25.0000 | −0.790965 |
(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 | 8512.2.a.t.1.1 | 2 | ||
4.3 | odd | 2 | 8512.2.a.m.1.2 | 2 | |||
8.3 | odd | 2 | 2128.2.a.k.1.1 | 2 | |||
8.5 | even | 2 | 532.2.a.c.1.2 | ✓ | 2 | ||
24.5 | odd | 2 | 4788.2.a.g.1.1 | 2 | |||
56.13 | odd | 2 | 3724.2.a.e.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
532.2.a.c.1.2 | ✓ | 2 | 8.5 | even | 2 | ||
2128.2.a.k.1.1 | 2 | 8.3 | odd | 2 | |||
3724.2.a.e.1.1 | 2 | 56.13 | odd | 2 | |||
4788.2.a.g.1.1 | 2 | 24.5 | odd | 2 | |||
8512.2.a.m.1.2 | 2 | 4.3 | odd | 2 | |||
8512.2.a.t.1.1 | 2 | 1.1 | even | 1 | trivial |