Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4024,2,Mod(1,4024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4024 = 2^{3} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4024.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: | \(32.1318017734\) |
Analytic rank: | \(1\) |
Dimension: | \(29\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.29 | ||
Character | \(\chi\) | \(=\) | 4024.1 |
$q$-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 | ||||||||
\(3\) | 3.11496 | 1.79842 | 0.899212 | − | 0.437513i | \(-0.144141\pi\) | ||||
0.899212 | + | 0.437513i | \(0.144141\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.544032 | 0.243298 | 0.121649 | − | 0.992573i | \(-0.461182\pi\) | ||||
0.121649 | + | 0.992573i | \(0.461182\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.06617 | −1.53687 | −0.768435 | − | 0.639928i | \(-0.778964\pi\) | ||||
−0.768435 | + | 0.639928i | \(0.778964\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.70298 | 2.23433 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.60847 | −0.786483 | −0.393241 | − | 0.919435i | \(-0.628646\pi\) | ||||
−0.393241 | + | 0.919435i | \(0.628646\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.55433 | −0.708444 | −0.354222 | − | 0.935161i | \(-0.615254\pi\) | ||||
−0.354222 | + | 0.935161i | \(0.615254\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.69464 | 0.437553 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.12126 | −1.72716 | −0.863579 | − | 0.504213i | \(-0.831783\pi\) | ||||
−0.863579 | + | 0.504213i | \(0.831783\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.832421 | −0.190970 | −0.0954852 | − | 0.995431i | \(-0.530440\pi\) | ||||
−0.0954852 | + | 0.995431i | \(0.530440\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −12.6660 | −2.76394 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.370152 | 0.0771820 | 0.0385910 | − | 0.999255i | \(-0.487713\pi\) | ||||
0.0385910 | + | 0.999255i | \(0.487713\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.70403 | −0.940806 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 11.5347 | 2.21985 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.116099 | 0.0215590 | 0.0107795 | − | 0.999942i | \(-0.496569\pi\) | ||||
0.0107795 | + | 0.999942i | \(0.496569\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.33684 | 0.778920 | 0.389460 | − | 0.921043i | \(-0.372662\pi\) | ||||
0.389460 | + | 0.921043i | \(0.372662\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.12528 | −1.41443 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.21213 | −0.373918 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.0662 | 1.65487 | 0.827437 | − | 0.561559i | \(-0.189798\pi\) | ||||
0.827437 | + | 0.561559i | \(0.189798\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.95665 | −1.27408 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.49744 | −1.17090 | −0.585452 | − | 0.810707i | \(-0.699083\pi\) | ||||
−0.585452 | + | 0.810707i | \(0.699083\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.6950 | −1.78347 | −0.891733 | − | 0.452562i | \(-0.850510\pi\) | ||||
−0.891733 | + | 0.452562i | \(0.850510\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.64663 | 0.543608 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.33828 | 0.632803 | 0.316401 | − | 0.948625i | \(-0.397525\pi\) | ||||
0.316401 | + | 0.948625i | \(0.397525\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.53378 | 1.36197 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −22.1824 | −3.10616 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.218817 | −0.0300569 | −0.0150284 | − | 0.999887i | \(-0.504784\pi\) | ||||
−0.0150284 | + | 0.999887i | \(0.504784\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.41909 | −0.191350 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.59296 | −0.343446 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.73530 | −1.13724 | −0.568619 | − | 0.822601i | \(-0.692522\pi\) | ||||
−0.568619 | + | 0.822601i | \(0.692522\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.76890 | −0.354521 | −0.177260 | − | 0.984164i | \(-0.556723\pi\) | ||||
−0.177260 | + | 0.984164i | \(0.556723\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −27.2555 | −3.43387 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.38964 | −0.172363 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.35707 | −0.776639 | −0.388320 | − | 0.921525i | \(-0.626944\pi\) | ||||
−0.388320 | + | 0.921525i | \(0.626944\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.15301 | 0.138806 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.8476 | −1.52473 | −0.762367 | − | 0.647145i | \(-0.775963\pi\) | ||||
−0.762367 | + | 0.647145i | \(0.775963\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.0547269 | −0.00640529 | −0.00320265 | − | 0.999995i | \(-0.501019\pi\) | ||||
−0.00320265 | + | 0.999995i | \(0.501019\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −14.6529 | −1.69197 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.6065 | 1.20872 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.48916 | 0.842596 | 0.421298 | − | 0.906922i | \(-0.361575\pi\) | ||||
0.421298 | + | 0.906922i | \(0.361575\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 15.8211 | 1.75789 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.01360 | −0.111257 | −0.0556286 | − | 0.998452i | \(-0.517716\pi\) | ||||
−0.0556286 | + | 0.998452i | \(0.517716\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.87419 | −0.420215 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.361643 | 0.0387722 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.49359 | −0.264320 | −0.132160 | − | 0.991228i | \(-0.542191\pi\) | ||||
−0.132160 | + | 0.991228i | \(0.542191\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.3864 | 1.08879 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 13.5091 | 1.40083 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.452863 | −0.0464628 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.239287 | 0.0242959 | 0.0121480 | − | 0.999926i | \(-0.496133\pi\) | ||||
0.0121480 | + | 0.999926i | \(0.496133\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −17.4845 | −1.75726 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.28642 | −0.426515 | −0.213257 | − | 0.976996i | \(-0.568407\pi\) | ||||
−0.213257 | + | 0.976996i | \(0.568407\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.43439 | −0.535467 | −0.267733 | − | 0.963493i | \(-0.586275\pi\) | ||||
−0.267733 | + | 0.963493i | \(0.586275\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.89069 | −0.672463 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.3026 | 1.47936 | 0.739680 | − | 0.672958i | \(-0.234977\pi\) | ||||
0.739680 | + | 0.672958i | \(0.234977\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.49708 | 0.813873 | 0.406936 | − | 0.913456i | \(-0.366597\pi\) | ||||
0.406936 | + | 0.913456i | \(0.366597\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 31.3558 | 2.97616 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.72334 | 0.444335 | 0.222167 | − | 0.975009i | \(-0.428687\pi\) | ||||
0.222167 | + | 0.975009i | \(0.428687\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.201374 | 0.0187782 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −17.1217 | −1.58290 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 28.9563 | 2.65442 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.19589 | −0.381445 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −23.3542 | −2.10578 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.27930 | −0.472195 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.5536 | −1.64637 | −0.823183 | − | 0.567775i | \(-0.807804\pi\) | ||||
−0.823183 | + | 0.567775i | \(0.807804\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −36.4294 | −3.20743 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.36136 | −0.293683 | −0.146842 | − | 0.989160i | \(-0.546911\pi\) | ||||
−0.146842 | + | 0.989160i | \(0.546911\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.38477 | 0.293497 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.27522 | 0.540085 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.6541 | 1.08111 | 0.540557 | − | 0.841307i | \(-0.318213\pi\) | ||||
0.540557 | + | 0.841307i | \(0.318213\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.90938 | 0.161951 | 0.0809757 | − | 0.996716i | \(-0.474196\pi\) | ||||
0.0809757 | + | 0.996716i | \(0.474196\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.5136 | 1.13805 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.66289 | 0.557179 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.0631614 | 0.00524527 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 29.6973 | 2.44940 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.93385 | −0.731889 | −0.365945 | − | 0.930637i | \(-0.619254\pi\) | ||||
−0.365945 | + | 0.930637i | \(0.619254\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.476372 | 0.0387666 | 0.0193833 | − | 0.999812i | \(-0.493830\pi\) | ||||
0.0193833 | + | 0.999812i | \(0.493830\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −47.7337 | −3.85904 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.35938 | 0.189510 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.99854 | 0.239310 | 0.119655 | − | 0.992816i | \(-0.461821\pi\) | ||||
0.119655 | + | 0.992816i | \(0.461821\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.681608 | −0.0540550 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.50510 | −0.118619 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.0849 | −1.49485 | −0.747424 | − | 0.664347i | \(-0.768710\pi\) | ||||
−0.747424 | + | 0.664347i | \(0.768710\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.42041 | −0.344128 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.857327 | 0.0663420 | 0.0331710 | − | 0.999450i | \(-0.489439\pi\) | ||||
0.0331710 | + | 0.999450i | \(0.489439\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.47539 | −0.498107 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.57970 | −0.426691 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.35691 | 0.711392 | 0.355696 | − | 0.934602i | \(-0.384244\pi\) | ||||
0.355696 | + | 0.934602i | \(0.384244\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 19.1274 | 1.44590 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −27.2101 | −2.04524 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.5381 | 0.862400 | 0.431200 | − | 0.902256i | \(-0.358090\pi\) | ||||
0.431200 | + | 0.902256i | \(0.358090\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.5774 | 1.82682 | 0.913410 | − | 0.407040i | \(-0.133439\pi\) | ||||
0.913410 | + | 0.407040i | \(0.133439\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.62501 | −0.637579 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.47633 | 0.402628 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.5756 | 1.35838 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −46.9019 | −3.41161 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.99705 | 0.289216 | 0.144608 | − | 0.989489i | \(-0.453808\pi\) | ||||
0.144608 | + | 0.989489i | \(0.453808\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.52415 | −0.181692 | −0.0908460 | − | 0.995865i | \(-0.528957\pi\) | ||||
−0.0908460 | + | 0.995865i | \(0.528957\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.32867 | −0.309982 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.5250 | 0.892370 | 0.446185 | − | 0.894941i | \(-0.352782\pi\) | ||||
0.446185 | + | 0.894941i | \(0.352782\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.3111 | 1.36893 | 0.684464 | − | 0.729047i | \(-0.260036\pi\) | ||||
0.684464 | + | 0.729047i | \(0.260036\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.8020 | −1.39673 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.472078 | −0.0331334 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.07884 | −0.284879 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.48112 | 0.172450 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.17134 | 0.150195 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.9644 | −1.09903 | −0.549517 | − | 0.835483i | \(-0.685188\pi\) | ||||
−0.549517 | + | 0.835483i | \(0.685188\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −40.0199 | −2.74212 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.36243 | −0.433914 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.6344 | −1.19710 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.170472 | −0.0115194 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.1901 | 1.22360 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.28709 | −0.220120 | −0.110060 | − | 0.993925i | \(-0.535104\pi\) | ||||
−0.110060 | + | 0.993925i | \(0.535104\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −31.5310 | −2.10207 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.49893 | −0.232232 | −0.116116 | − | 0.993236i | \(-0.537045\pi\) | ||||
−0.116116 | + | 0.993236i | \(0.537045\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.3346 | 1.27767 | 0.638834 | − | 0.769345i | \(-0.279417\pi\) | ||||
0.638834 | + | 0.769345i | \(0.279417\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 33.0388 | 2.17379 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.60251 | 0.236009 | 0.118004 | − | 0.993013i | \(-0.462350\pi\) | ||||
0.118004 | + | 0.993013i | \(0.462350\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.36016 | 0.153960 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 23.3284 | 1.51534 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.8720 | −0.832619 | −0.416310 | − | 0.909223i | \(-0.636677\pi\) | ||||
−0.416310 | + | 0.909223i | \(0.636677\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.0737 | −1.09982 | −0.549908 | − | 0.835226i | \(-0.685337\pi\) | ||||
−0.549908 | + | 0.835226i | \(0.685337\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.6780 | 0.941594 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.18667 | 0.331364 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.12628 | 0.135292 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.15733 | −0.200088 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.4865 | −1.73493 | −0.867466 | − | 0.497496i | \(-0.834253\pi\) | ||||
−0.867466 | + | 0.497496i | \(0.834253\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.965529 | −0.0607023 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −12.0679 | −0.755724 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.74116 | 0.233367 | 0.116683 | − | 0.993169i | \(-0.462774\pi\) | ||||
0.116683 | + | 0.993169i | \(0.462774\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −40.9309 | −2.54332 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.778209 | 0.0481699 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.02615 | 0.433251 | 0.216625 | − | 0.976255i | \(-0.430495\pi\) | ||||
0.216625 | + | 0.976255i | \(0.430495\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.119044 | −0.00731279 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.76745 | −0.475360 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.55451 | −0.399635 | −0.199818 | − | 0.979833i | \(-0.564035\pi\) | ||||
−0.199818 | + | 0.979833i | \(0.564035\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.14696 | 0.494893 | 0.247446 | − | 0.968902i | \(-0.420409\pi\) | ||||
0.247446 | + | 0.968902i | \(0.420409\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 32.3531 | 1.95810 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.2703 | 0.739928 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.85761 | 0.291866 | 0.145933 | − | 0.989295i | \(-0.453382\pi\) | ||||
0.145933 | + | 0.989295i | \(0.453382\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 29.0698 | 1.74036 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.4279 | 1.27828 | 0.639141 | − | 0.769089i | \(-0.279290\pi\) | ||||
0.639141 | + | 0.769089i | \(0.279290\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.7790 | 1.41351 | 0.706757 | − | 0.707457i | \(-0.250158\pi\) | ||||
0.706757 | + | 0.707457i | \(0.250158\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.41065 | −0.0835597 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 30.4859 | 1.79953 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 33.7123 | 1.98308 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.745369 | 0.0436943 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.93680 | −0.580514 | −0.290257 | − | 0.956949i | \(-0.593741\pi\) | ||||
−0.290257 | + | 0.956949i | \(0.593741\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.75228 | −0.276688 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −30.0878 | −1.74587 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.945491 | −0.0546791 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 47.5538 | 2.74095 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.3520 | −0.767054 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.50637 | −0.0862543 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.8282 | −0.903361 | −0.451681 | − | 0.892180i | \(-0.649175\pi\) | ||||
−0.451681 | + | 0.892180i | \(0.649175\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.9279 | −0.962996 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.74402 | −0.0988942 | −0.0494471 | − | 0.998777i | \(-0.515746\pi\) | ||||
−0.0494471 | + | 0.998777i | \(0.515746\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.9429 | 1.63595 | 0.817975 | − | 0.575254i | \(-0.195097\pi\) | ||||
0.817975 | + | 0.575254i | \(0.195097\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −14.8279 | −0.835455 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.504520 | −0.0283366 | −0.0141683 | − | 0.999900i | \(-0.504510\pi\) | ||||
−0.0141683 | + | 0.999900i | \(0.504510\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.302840 | −0.0169558 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 47.6671 | 2.66052 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.92788 | 0.329836 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.0157 | 0.666509 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 26.4681 | 1.46369 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.6402 | −0.972535 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.07805 | 0.444010 | 0.222005 | − | 0.975046i | \(-0.428740\pi\) | ||||
0.222005 | + | 0.975046i | \(0.428740\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 67.4736 | 3.69753 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.45844 | −0.188955 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.0352 | 1.85402 | 0.927008 | − | 0.375041i | \(-0.122372\pi\) | ||||
0.927008 | + | 0.375041i | \(0.122372\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.7130 | 0.799102 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.3125 | −0.612607 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.3028 | −0.556298 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.627273 | 0.0337712 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.3874 | 1.41655 | 0.708275 | − | 0.705936i | \(-0.249474\pi\) | ||||
0.708275 | + | 0.705936i | \(0.249474\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −36.3265 | −1.94452 | −0.972258 | − | 0.233912i | \(-0.924847\pi\) | ||||
−0.972258 | + | 0.233912i | \(0.924847\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −29.4633 | −1.57264 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.6978 | 0.835511 | 0.417755 | − | 0.908560i | \(-0.362817\pi\) | ||||
0.417755 | + | 0.908560i | \(0.362817\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.98952 | −0.370965 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 90.1977 | 4.77377 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.9202 | 1.20968 | 0.604841 | − | 0.796346i | \(-0.293237\pi\) | ||||
0.604841 | + | 0.796346i | \(0.293237\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.3071 | −0.963530 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13.0700 | −0.685999 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.0297731 | −0.00155840 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.1516 | −1.05190 | −0.525952 | − | 0.850514i | \(-0.676291\pi\) | ||||
−0.525952 | + | 0.850514i | \(0.676291\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −50.2552 | −2.61618 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.889750 | 0.0461935 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.84927 | 0.302864 | 0.151432 | − | 0.988468i | \(-0.451612\pi\) | ||||
0.151432 | + | 0.988468i | \(0.451612\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −16.4448 | −0.849206 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.296555 | −0.0152734 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.02864 | 0.463770 | 0.231885 | − | 0.972743i | \(-0.425511\pi\) | ||||
0.231885 | + | 0.972743i | \(0.425511\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −57.7938 | −2.96087 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.8573 | −1.47454 | −0.737270 | − | 0.675598i | \(-0.763886\pi\) | ||||
−0.737270 | + | 0.675598i | \(0.763886\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.77026 | 0.294080 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −78.3912 | −3.98485 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −33.4134 | −1.69413 | −0.847063 | − | 0.531492i | \(-0.821631\pi\) | ||||
−0.847063 | + | 0.531492i | \(0.821631\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.63595 | −0.133306 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.4705 | −0.528167 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.07434 | 0.205002 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.3461 | −1.42265 | −0.711324 | − | 0.702864i | \(-0.751904\pi\) | ||||
−0.711324 | + | 0.702864i | \(0.751904\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.5434 | 0.527831 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 38.4895 | 1.92207 | 0.961036 | − | 0.276422i | \(-0.0891486\pi\) | ||||
0.961036 | + | 0.276422i | \(0.0891486\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.0777 | −0.551822 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.60715 | 0.427693 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −26.2574 | −1.30153 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.43137 | 0.0707767 | 0.0353884 | − | 0.999374i | \(-0.488733\pi\) | ||||
0.0353884 | + | 0.999374i | \(0.488733\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 39.4171 | 1.94430 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 35.5192 | 1.74779 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.551431 | −0.0270687 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.94764 | 0.291257 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.6655 | −1.25384 | −0.626921 | − | 0.779082i | \(-0.715685\pi\) | ||||
−0.626921 | + | 0.779082i | \(0.715685\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.4672 | −0.607616 | −0.303808 | − | 0.952733i | \(-0.598258\pi\) | ||||
−0.303808 | + | 0.952733i | \(0.598258\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 29.0794 | 1.41389 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 33.4986 | 1.62492 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.2588 | 0.544852 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 20.7547 | 1.00204 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.84481 | −0.329703 | −0.164852 | − | 0.986318i | \(-0.552715\pi\) | ||||
−0.164852 | + | 0.986318i | \(0.552715\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.0106 | 1.44222 | 0.721108 | − | 0.692822i | \(-0.243633\pi\) | ||||
0.721108 | + | 0.692822i | \(0.243633\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.196745 | 0.00943322 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.308122 | −0.0147395 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.3539 | 1.49644 | 0.748219 | − | 0.663451i | \(-0.230909\pi\) | ||||
0.748219 | + | 0.663451i | \(0.230909\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 63.9048 | 3.04308 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.4312 | −0.590626 | −0.295313 | − | 0.955401i | \(-0.595424\pi\) | ||||
−0.295313 | + | 0.955401i | \(0.595424\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.35659 | −0.0643087 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −27.8286 | −1.31625 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.488482 | 0.0230529 | 0.0115265 | − | 0.999934i | \(-0.496331\pi\) | ||||
0.0115265 | + | 0.999934i | \(0.496331\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.5568 | 0.920895 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.48388 | 0.0697187 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.65051 | 0.264900 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.7703 | −1.11193 | −0.555963 | − | 0.831207i | \(-0.687650\pi\) | ||||
−0.555963 | + | 0.831207i | \(0.687650\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −82.1413 | −3.83403 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.58507 | −0.399847 | −0.199923 | − | 0.979812i | \(-0.564069\pi\) | ||||
−0.199923 | + | 0.979812i | \(0.564069\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.2154 | −0.985963 | −0.492981 | − | 0.870040i | \(-0.664093\pi\) | ||||
−0.492981 | + | 0.870040i | \(0.664093\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.34938 | 0.340819 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.69231 | 0.402232 | 0.201116 | − | 0.979567i | \(-0.435543\pi\) | ||||
0.201116 | + | 0.979567i | \(0.435543\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25.8489 | 1.19359 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.34034 | 0.430380 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 30.5060 | 1.40267 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.91573 | 0.179666 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.46673 | −0.0671569 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.2454 | −0.696581 | −0.348291 | − | 0.937387i | \(-0.613238\pi\) | ||||
−0.348291 | + | 0.937387i | \(0.613238\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.7124 | −1.17239 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.68834 | −0.213327 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.130180 | 0.00591115 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.7583 | −0.668761 | −0.334380 | − | 0.942438i | \(-0.608527\pi\) | ||||
−0.334380 | + | 0.942438i | \(0.608527\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −59.4489 | −2.68837 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.88193 | 0.220318 | 0.110159 | − | 0.993914i | \(-0.464864\pi\) | ||||
0.110159 | + | 0.993914i | \(0.464864\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.826770 | −0.0372358 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.51213 | −0.427539 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 52.2408 | 2.34332 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −39.8728 | −1.78495 | −0.892475 | − | 0.451096i | \(-0.851033\pi\) | ||||
−0.892475 | + | 0.451096i | \(0.851033\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.67054 | 0.119311 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.33195 | −0.103770 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −20.1706 | −0.895807 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −38.3023 | −1.69772 | −0.848860 | − | 0.528618i | \(-0.822710\pi\) | ||||
−0.848860 | + | 0.528618i | \(0.822710\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.222529 | 0.00984410 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.60168 | −0.423925 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.95648 | −0.130278 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.3163 | −0.497688 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 29.1464 | 1.27939 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.1754 | 0.664847 | 0.332424 | − | 0.943130i | \(-0.392134\pi\) | ||||
0.332424 | + | 0.943130i | \(0.392134\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 38.9182 | 1.70177 | 0.850887 | − | 0.525349i | \(-0.176065\pi\) | ||||
0.850887 | + | 0.525349i | \(0.176065\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 59.5811 | 2.60033 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −30.8838 | −1.34532 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8630 | −0.994043 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −58.5526 | −2.54096 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.1510 | 0.829520 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.32511 | 0.359926 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 35.9408 | 1.55096 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −24.8686 | −1.07116 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.1147 | 1.50970 | 0.754850 | − | 0.655898i | \(-0.227710\pi\) | ||||
0.754850 | + | 0.655898i | \(0.227710\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 76.5575 | 3.28540 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.62268 | 0.198014 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.1530 | −1.20373 | −0.601867 | − | 0.798596i | \(-0.705576\pi\) | ||||
−0.601867 | + | 0.798596i | \(0.705576\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −18.5599 | −0.792116 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.0966430 | −0.00411713 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −30.4522 | −1.29496 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 17.0586 | 0.724096 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.7916 | −0.626740 | −0.313370 | − | 0.949631i | \(-0.601458\pi\) | ||||
−0.313370 | + | 0.949631i | \(0.601458\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 29.8728 | 1.26349 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 57.8622 | 2.44294 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −38.3498 | −1.61625 | −0.808125 | − | 0.589011i | \(-0.799518\pi\) | ||||
−0.808125 | + | 0.589011i | \(0.799518\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.56965 | 0.108106 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −64.3312 | −2.70165 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −31.2247 | −1.30901 | −0.654504 | − | 0.756059i | \(-0.727122\pi\) | ||||
−0.654504 | + | 0.756059i | \(0.727122\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.85600 | 0.370612 | 0.185306 | − | 0.982681i | \(-0.440672\pi\) | ||||
0.185306 | + | 0.982681i | \(0.440672\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.4506 | 0.520133 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.74121 | −0.0726133 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.0244 | 0.916889 | 0.458445 | − | 0.888723i | \(-0.348407\pi\) | ||||
0.458445 | + | 0.888723i | \(0.348407\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.86262 | −0.326759 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.12148 | 0.170988 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.570778 | 0.0236392 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.31472 | −0.385116 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.2179 | −0.917030 | −0.458515 | − | 0.888687i | \(-0.651618\pi\) | ||||
−0.458515 | + | 0.888687i | \(0.651618\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.61008 | −0.148751 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 39.0149 | 1.60486 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 38.3818 | 1.57615 | 0.788076 | − | 0.615578i | \(-0.211078\pi\) | ||||
0.788076 | + | 0.615578i | \(0.211078\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.7531 | 0.645815 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 60.1534 | 2.46191 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.8958 | 0.649486 | 0.324743 | − | 0.945802i | \(-0.394722\pi\) | ||||
0.324743 | + | 0.945802i | \(0.394722\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.6843 | 1.37401 | 0.687006 | − | 0.726652i | \(-0.258925\pi\) | ||||
0.687006 | + | 0.726652i | \(0.258925\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −42.6113 | −1.73527 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.28270 | −0.0928049 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.28606 | −0.0927883 | −0.0463941 | − | 0.998923i | \(-0.514773\pi\) | ||||
−0.0463941 | + | 0.998923i | \(0.514773\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.47050 | −0.0595879 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.0814 | −0.448305 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.7993 | 0.638127 | 0.319063 | − | 0.947733i | \(-0.396632\pi\) | ||||
0.319063 | + | 0.947733i | \(0.396632\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −12.7054 | −0.512333 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.6329 | −0.790390 | −0.395195 | − | 0.918597i | \(-0.629323\pi\) | ||||
−0.395195 | + | 0.918597i | \(0.629323\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.1487 | −1.33236 | −0.666180 | − | 0.745791i | \(-0.732072\pi\) | ||||
−0.666180 | + | 0.745791i | \(0.732072\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.26957 | 0.171332 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.1394 | 0.406226 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.6480 | 0.825922 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.76365 | 0.270114 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −71.6840 | −2.85823 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.4604 | −0.734898 | −0.367449 | − | 0.930044i | \(-0.619769\pi\) | ||||
−0.367449 | + | 0.930044i | \(0.619769\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −49.7285 | −1.97653 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.0938 | −0.400558 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.3524 | −0.964878 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −86.1175 | −3.40676 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.9324 | −1.10326 | −0.551632 | − | 0.834087i | \(-0.685995\pi\) | ||||
−0.551632 | + | 0.834087i | \(0.685995\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.9331 | 0.628340 | 0.314170 | − | 0.949367i | \(-0.398274\pi\) | ||||
0.314170 | + | 0.949367i | \(0.398274\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −19.8187 | −0.780362 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28.7045 | −1.12849 | −0.564246 | − | 0.825607i | \(-0.690833\pi\) | ||||
−0.564246 | + | 0.825607i | \(0.690833\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.7857 | 0.894419 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −54.9304 | −2.15289 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.9511 | −0.428551 | −0.214276 | − | 0.976773i | \(-0.568739\pi\) | ||||
−0.214276 | + | 0.976773i | \(0.568739\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.82869 | −0.0714527 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.366833 | −0.0143115 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −45.7335 | −1.78152 | −0.890762 | − | 0.454470i | \(-0.849829\pi\) | ||||
−0.890762 | + | 0.454470i | \(0.849829\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.40358 | 0.0545928 | 0.0272964 | − | 0.999627i | \(-0.491310\pi\) | ||||
0.0272964 | + | 0.999627i | \(0.491310\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 56.6613 | 2.20054 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.84142 | 0.0714072 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.0429742 | 0.00166397 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.2392 | −0.395869 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.22258 | 0.278825 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.36295 | −0.129632 | −0.0648160 | − | 0.997897i | \(-0.520646\pi\) | ||||
−0.0648160 | + | 0.997897i | \(0.520646\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −54.2594 | −2.08844 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.0645 | 0.386811 | 0.193405 | − | 0.981119i | \(-0.438047\pi\) | ||||
0.193405 | + | 0.981119i | \(0.438047\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.972982 | −0.0373396 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.8990 | −0.417652 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 49.5438 | 1.89574 | 0.947871 | − | 0.318653i | \(-0.103231\pi\) | ||||
0.947871 | + | 0.318653i | \(0.103231\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.88424 | 0.263033 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 60.2266 | 2.29779 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.558932 | 0.0212936 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.3212 | −1.68606 | −0.843029 | − | 0.537868i | \(-0.819230\pi\) | ||||
−0.843029 | + | 0.537868i | \(0.819230\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 71.0951 | 2.70068 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.03876 | 0.0394025 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 53.3912 | 2.02234 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.2217 | 0.424443 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33.6302 | −1.27020 | −0.635098 | − | 0.772431i | \(-0.719040\pi\) | ||||
−0.635098 | + | 0.772431i | \(0.719040\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.37931 | −0.316032 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.35180 | 0.276885 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17.4293 | 0.655498 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.8225 | −1.34534 | −0.672670 | − | 0.739942i | \(-0.734853\pi\) | ||||
−0.672670 | + | 0.739942i | \(0.734853\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 50.1997 | 1.88264 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.60529 | 0.0601186 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.62482 | 0.135561 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −40.0957 | −1.49740 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 49.4640 | 1.84470 | 0.922348 | − | 0.386359i | \(-0.126267\pi\) | ||||
0.922348 | + | 0.386359i | \(0.126267\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.0972 | 0.822942 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −53.1840 | −1.97793 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.546132 | −0.0202828 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.3440 | −0.420726 | −0.210363 | − | 0.977623i | \(-0.567465\pi\) | ||||
−0.210363 | + | 0.977623i | \(0.567465\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.74176 | −0.0645095 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 83.2829 | 3.08033 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.1414 | 0.522325 | 0.261162 | − | 0.965295i | \(-0.415894\pi\) | ||||
0.261162 | + | 0.965295i | \(0.415894\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 16.1563 | 0.595934 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.5822 | 0.610813 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.5404 | −0.608447 | −0.304223 | − | 0.952601i | \(-0.598397\pi\) | ||||
−0.304223 | + | 0.952601i | \(0.598397\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.62328 | 0.243312 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28.8396 | −1.05802 | −0.529012 | − | 0.848614i | \(-0.677437\pi\) | ||||
−0.529012 | + | 0.848614i | \(0.677437\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.86029 | −0.178067 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.79415 | −0.248585 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −62.2232 | −2.27358 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.44249 | −0.162109 | −0.0810544 | − | 0.996710i | \(-0.525829\pi\) | ||||
−0.0810544 | + | 0.996710i | \(0.525829\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −85.6194 | −3.12014 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.259161 | 0.00943184 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.21775 | −0.298679 | −0.149340 | − | 0.988786i | \(-0.547715\pi\) | ||||
−0.149340 | + | 0.988786i | \(0.547715\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.00759 | −0.109168 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −48.5835 | −1.76115 | −0.880576 | − | 0.473905i | \(-0.842844\pi\) | ||||
−0.880576 | + | 0.473905i | \(0.842844\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −34.5506 | −1.25082 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −25.9686 | −0.938898 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 22.3128 | 0.805670 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.96818 | 0.359462 | 0.179731 | − | 0.983716i | \(-0.442477\pi\) | ||||
0.179731 | + | 0.983716i | \(0.442477\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.6536 | 0.419693 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 35.3040 | 1.26980 | 0.634899 | − | 0.772595i | \(-0.281042\pi\) | ||||
0.634899 | + | 0.772595i | \(0.281042\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −20.4006 | −0.732813 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −127.498 | −4.57398 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.24102 | 0.223608 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 33.5127 | 1.19918 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.33916 | 0.0478577 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.63130 | 0.0582236 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.9639 | 0.996804 | 0.498402 | − | 0.866946i | \(-0.333920\pi\) | ||||
0.498402 | + | 0.866946i | \(0.333920\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.8862 | 0.779169 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.2059 | −0.682884 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.07268 | 0.251158 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.370816 | −0.0131515 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.0070 | 1.16917 | 0.584583 | − | 0.811334i | \(-0.301258\pi\) | ||||
0.584583 | + | 0.811334i | \(0.301258\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30.8940 | −1.09295 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.7145 | −0.590579 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.142753 | 0.00503765 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.818823 | −0.0288597 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.4170 | −0.718714 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.6876 | −0.938288 | −0.469144 | − | 0.883122i | \(-0.655437\pi\) | ||||
−0.469144 | + | 0.883122i | \(0.655437\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.8883 | 0.698371 | 0.349186 | − | 0.937054i | \(-0.386458\pi\) | ||||
0.349186 | + | 0.937054i | \(0.386458\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.3775 | 0.890027 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.3828 | −0.363694 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.73513 | 0.340589 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 69.6196 | 2.43271 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 41.9862 | 1.46533 | 0.732664 | − | 0.680590i | \(-0.238277\pi\) | ||||
0.732664 | + | 0.680590i | \(0.238277\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.3429 | −0.709108 | −0.354554 | − | 0.935036i | \(-0.615367\pi\) | ||||
−0.354554 | + | 0.935036i | \(0.615367\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 38.2216 | 1.33070 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21.0590 | −0.732292 | −0.366146 | − | 0.930558i | \(-0.619323\pi\) | ||||
−0.366146 | + | 0.930558i | \(0.619323\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44.7041 | 1.55264 | 0.776319 | − | 0.630341i | \(-0.217085\pi\) | ||||
0.776319 | + | 0.630341i | \(0.217085\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.1313 | 0.524898 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −67.8925 | −2.35233 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.466413 | 0.0161409 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 50.0240 | 1.72908 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −52.0847 | −1.79816 | −0.899081 | − | 0.437781i | \(-0.855764\pi\) | ||||
−0.899081 | + | 0.437781i | \(0.855764\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9865 | −0.999535 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 66.7471 | 2.29889 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.52281 | −0.121188 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.0612 | 0.586231 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 74.0706 | 2.54210 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.72602 | 0.127726 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.4155 | −0.699012 | −0.349506 | − | 0.936934i | \(-0.613651\pi\) | ||||
−0.349506 | + | 0.936934i | \(0.613651\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.03553 | −0.103813 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29.9634 | −1.02353 | −0.511765 | − | 0.859126i | \(-0.671008\pi\) | ||||
−0.511765 | + | 0.859126i | \(0.671008\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.1094 | −1.26616 | −0.633079 | − | 0.774087i | \(-0.718209\pi\) | ||||
−0.633079 | + | 0.774087i | \(0.718209\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 94.9624 | 3.23631 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20.3550 | −0.692893 | −0.346446 | − | 0.938070i | \(-0.612612\pi\) | ||||
−0.346446 | + | 0.938070i | \(0.612612\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.09045 | 0.173081 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 105.013 | 3.56641 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19.5352 | −0.662687 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.2381 | 0.550206 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.60394 | 0.0542850 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 21.4665 | 0.725702 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.27733 | 0.245738 | 0.122869 | − | 0.992423i | \(-0.460790\pi\) | ||||
0.122869 | + | 0.992423i | \(0.460790\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −30.9527 | −1.04401 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.9712 | 0.908684 | 0.454342 | − | 0.890827i | \(-0.349874\pi\) | ||||
0.454342 | + | 0.890827i | \(0.349874\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.7951 | −1.06999 | −0.534995 | − | 0.844855i | \(-0.679686\pi\) | ||||
−0.534995 | + | 0.844855i | \(0.679686\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14.8032 | −0.497603 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 56.9627 | 1.91262 | 0.956310 | − | 0.292354i | \(-0.0944384\pi\) | ||||
0.956310 | + | 0.292354i | \(0.0944384\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 75.4422 | 2.53025 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −41.2687 | −1.38255 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.61127 | −0.120847 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.27710 | 0.209820 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.94517 | −0.0983363 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.503502 | 0.0167927 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.55825 | 0.0519130 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 148.128 | 4.92940 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.3709 | 0.444462 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.6342 | 0.751556 | 0.375778 | − | 0.926710i | \(-0.377376\pi\) | ||||
0.375778 | + | 0.926710i | \(0.377376\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −28.7318 | −0.952974 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.2195 | −0.968084 | −0.484042 | − | 0.875045i | \(-0.660832\pi\) | ||||
−0.484042 | + | 0.875045i | \(0.660832\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.64395 | 0.0875019 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.69227 | −0.155122 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.6679 | 0.451353 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.3423 | 0.868952 | 0.434476 | − | 0.900683i | \(-0.356934\pi\) | ||||
0.434476 | + | 0.900683i | \(0.356934\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −49.3041 | −1.62463 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 32.8171 | 1.08019 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −47.3517 | −1.55691 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −36.4267 | −1.19641 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 37.6392 | 1.23490 | 0.617451 | − | 0.786610i | \(-0.288166\pi\) | ||||
0.617451 | + | 0.786610i | \(0.288166\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.93611 | −0.260096 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.43255 | −0.177854 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.1057 | 0.330492 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.6564 | 0.707483 | 0.353742 | − | 0.935343i | \(-0.384909\pi\) | ||||
0.353742 | + | 0.935343i | \(0.384909\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 90.1560 | 2.94213 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36.8472 | −1.20118 | −0.600592 | − | 0.799556i | \(-0.705068\pi\) | ||||
−0.600592 | + | 0.799556i | \(0.705068\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.77519 | −0.0903727 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −25.5161 | −0.830040 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.3700 | 0.824414 | 0.412207 | − | 0.911090i | \(-0.364758\pi\) | ||||
0.412207 | + | 0.911090i | \(0.364758\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.139791 | 0.00453779 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.57156 | −0.0509613 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.2401 | −1.33590 | −0.667950 | − | 0.744207i | \(-0.732828\pi\) | ||||
−0.667950 | + | 0.744207i | \(0.732828\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.17452 | 0.0703658 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.943335 | −0.0304937 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −51.4539 | −1.66153 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.1918 | −0.393283 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 102.573 | 3.30538 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.37321 | −0.0442053 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.9090 | 1.37986 | 0.689930 | − | 0.723876i | \(-0.257641\pi\) | ||||
0.689930 | + | 0.723876i | \(0.257641\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.4651 | 0.593185 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.734797 | −0.0235808 | −0.0117904 | − | 0.999930i | \(-0.503753\pi\) | ||||
−0.0117904 | + | 0.999930i | \(0.503753\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.76387 | −0.248898 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 37.4283 | 1.19866 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −33.0223 | −1.05648 | −0.528239 | − | 0.849096i | \(-0.677147\pi\) | ||||
−0.528239 | + | 0.849096i | \(0.677147\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.50446 | 0.207883 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 56.9558 | 1.81846 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.13640 | −0.131931 | −0.0659653 | − | 0.997822i | \(-0.521013\pi\) | ||||
−0.0659653 | + | 0.997822i | \(0.521013\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.81400 | 0.217112 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −54.9485 | −1.74903 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.32891 | −0.137651 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.6651 | −1.38707 | −0.693533 | − | 0.720425i | \(-0.743947\pi\) | ||||
−0.693533 | + | 0.720425i | \(0.743947\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25.1628 | 0.798518 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.5059 | 0.333058 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.0119 | 0.728795 | 0.364397 | − | 0.931244i | \(-0.381275\pi\) | ||||
0.364397 | + | 0.931244i | \(0.381275\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 116.110 | 3.67356 |
(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 | 4024.2.a.e.1.29 | ✓ | 29 | |
4.3 | odd | 2 | 8048.2.a.w.1.1 | 29 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.e.1.29 | ✓ | 29 | 1.1 | even | 1 | trivial | |
8048.2.a.w.1.1 | 29 | 4.3 | odd | 2 |