Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6032,2,Mod(1,6032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6032, 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("6032.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6032 = 2^{4} \cdot 13 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6032.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: | \(48.1657624992\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 21x^{8} + 40x^{7} + 138x^{6} - 243x^{5} - 318x^{4} + 448x^{3} + 312x^{2} - 240x - 128 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 3016) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-0.866798\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6032.1 |
$q$-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 | ||||||||
\(3\) | 0.866798 | 0.500446 | 0.250223 | − | 0.968188i | \(-0.419496\pi\) | ||||
0.250223 | + | 0.968188i | \(0.419496\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.19814 | 0.983037 | 0.491519 | − | 0.870867i | \(-0.336442\pi\) | ||||
0.491519 | + | 0.870867i | \(0.336442\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.35947 | 1.64772 | 0.823862 | − | 0.566791i | \(-0.191815\pi\) | ||||
0.823862 | + | 0.566791i | \(0.191815\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.24866 | −0.749554 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.62729 | 1.09367 | 0.546835 | − | 0.837241i | \(-0.315833\pi\) | ||||
0.546835 | + | 0.837241i | \(0.315833\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.90534 | 0.491957 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.809117 | 0.196240 | 0.0981198 | − | 0.995175i | \(-0.468717\pi\) | ||||
0.0981198 | + | 0.995175i | \(0.468717\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.53409 | 1.26961 | 0.634803 | − | 0.772674i | \(-0.281081\pi\) | ||||
0.634803 | + | 0.772674i | \(0.281081\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.77878 | 0.824597 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.43856 | −0.716989 | −0.358495 | − | 0.933532i | \(-0.616710\pi\) | ||||
−0.358495 | + | 0.933532i | \(0.616710\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.168191 | −0.0336382 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.54953 | −0.875557 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.227533 | −0.0408662 | −0.0204331 | − | 0.999791i | \(-0.506505\pi\) | ||||
−0.0204331 | + | 0.999791i | \(0.506505\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.14413 | 0.547322 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.58271 | 1.61977 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.90883 | 0.807007 | 0.403504 | − | 0.914978i | \(-0.367792\pi\) | ||||
0.403504 | + | 0.914978i | \(0.367792\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.866798 | 0.138799 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.88191 | 1.07477 | 0.537387 | − | 0.843336i | \(-0.319411\pi\) | ||||
0.537387 | + | 0.843336i | \(0.319411\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.53289 | −0.386262 | −0.193131 | − | 0.981173i | \(-0.561864\pi\) | ||||
−0.193131 | + | 0.981173i | \(0.561864\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.94287 | −0.736839 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.69537 | 0.393160 | 0.196580 | − | 0.980488i | \(-0.437016\pi\) | ||||
0.196580 | + | 0.980488i | \(0.437016\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.0049 | 1.71499 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.701341 | 0.0982074 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.14083 | −0.431427 | −0.215713 | − | 0.976457i | \(-0.569208\pi\) | ||||
−0.215713 | + | 0.976457i | \(0.569208\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.97328 | 1.07512 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.79694 | 0.635370 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.9502 | −1.68598 | −0.842989 | − | 0.537930i | \(-0.819206\pi\) | ||||
−0.842989 | + | 0.537930i | \(0.819206\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.54000 | 0.965398 | 0.482699 | − | 0.875786i | \(-0.339656\pi\) | ||||
0.482699 | + | 0.875786i | \(0.339656\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.80296 | −1.23506 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.19814 | 0.272645 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.95057 | −1.09349 | −0.546743 | − | 0.837300i | \(-0.684133\pi\) | ||||
−0.546743 | + | 0.837300i | \(0.684133\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.98054 | −0.358815 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.11287 | 0.844143 | 0.422071 | − | 0.906563i | \(-0.361303\pi\) | ||||
0.422071 | + | 0.906563i | \(0.361303\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.6224 | 1.82847 | 0.914235 | − | 0.405185i | \(-0.132793\pi\) | ||||
0.914235 | + | 0.405185i | \(0.132793\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.145788 | −0.0168341 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 15.8130 | 1.80206 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.98066 | −0.222841 | −0.111421 | − | 0.993773i | \(-0.535540\pi\) | ||||
−0.111421 | + | 0.993773i | \(0.535540\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.80246 | 0.311384 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.59895 | 0.175508 | 0.0877538 | − | 0.996142i | \(-0.472031\pi\) | ||||
0.0877538 | + | 0.996142i | \(0.472031\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.77855 | 0.192911 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.866798 | −0.0929305 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.71529 | −0.923818 | −0.461909 | − | 0.886927i | \(-0.652835\pi\) | ||||
−0.461909 | + | 0.886927i | \(0.652835\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.35947 | 0.456996 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.197225 | −0.0204513 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.1647 | 1.24807 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.3323 | −1.55676 | −0.778378 | − | 0.627796i | \(-0.783957\pi\) | ||||
−0.778378 | + | 0.627796i | \(0.783957\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.15655 | −0.819764 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.74668 | 0.173801 | 0.0869005 | − | 0.996217i | \(-0.472304\pi\) | ||||
0.0869005 | + | 0.996217i | \(0.472304\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.96219 | 0.390406 | 0.195203 | − | 0.980763i | \(-0.437463\pi\) | ||||
0.195203 | + | 0.980763i | \(0.437463\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.30627 | 0.810609 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.9317 | −1.05681 | −0.528406 | − | 0.848992i | \(-0.677210\pi\) | ||||
−0.528406 | + | 0.848992i | \(0.677210\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.21484 | −0.307926 | −0.153963 | − | 0.988077i | \(-0.549204\pi\) | ||||
−0.153963 | + | 0.988077i | \(0.549204\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.25497 | 0.403864 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.0885 | 1.23127 | 0.615633 | − | 0.788033i | \(-0.288900\pi\) | ||||
0.615633 | + | 0.788033i | \(0.288900\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.55843 | −0.704827 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.24866 | −0.207889 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.52732 | 0.323349 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.15723 | 0.196112 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.96523 | 0.537867 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.3604 | −1.01610 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.79424 | 0.159213 | 0.0796066 | − | 0.996826i | \(-0.474634\pi\) | ||||
0.0796066 | + | 0.996826i | \(0.474634\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.19551 | −0.193304 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.50063 | 0.218481 | 0.109241 | − | 0.994015i | \(-0.465158\pi\) | ||||
0.109241 | + | 0.994015i | \(0.465158\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 24.1257 | 2.09196 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.0005 | −0.860705 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.2810 | −0.963798 | −0.481899 | − | 0.876227i | \(-0.660053\pi\) | ||||
−0.481899 | + | 0.876227i | \(0.660053\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.1314 | −1.53789 | −0.768945 | − | 0.639315i | \(-0.779218\pi\) | ||||
−0.768945 | + | 0.639315i | \(0.779218\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.33634 | 0.196756 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.62729 | 0.303329 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.19814 | −0.182545 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.4059 | 0.858261 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.47830 | −0.530723 | −0.265361 | − | 0.964149i | \(-0.585491\pi\) | ||||
−0.265361 | + | 0.964149i | \(0.585491\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.449097 | 0.0365470 | 0.0182735 | − | 0.999833i | \(-0.494183\pi\) | ||||
0.0182735 | + | 0.999833i | \(0.494183\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.81943 | −0.147092 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.500149 | −0.0401729 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.05118 | 0.163702 | 0.0818508 | − | 0.996645i | \(-0.473917\pi\) | ||||
0.0818508 | + | 0.996645i | \(0.473917\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.72247 | −0.215906 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.9903 | −1.18140 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.0998 | 1.02606 | 0.513029 | − | 0.858371i | \(-0.328523\pi\) | ||||
0.513029 | + | 0.858371i | \(0.328523\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.91123 | 0.538038 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.02735 | 0.234264 | 0.117132 | − | 0.993116i | \(-0.462630\pi\) | ||||
0.117132 | + | 0.993116i | \(0.462630\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.4443 | −0.951638 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.87327 | 0.218451 | 0.109225 | − | 0.994017i | \(-0.465163\pi\) | ||||
0.109225 | + | 0.994017i | \(0.465163\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.733223 | −0.0554264 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.2252 | −0.843741 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.33055 | −0.0994501 | −0.0497250 | − | 0.998763i | \(-0.515834\pi\) | ||||
−0.0497250 | + | 0.998763i | \(0.515834\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.5300 | 1.15433 | 0.577167 | − | 0.816626i | \(-0.304158\pi\) | ||||
0.577167 | + | 0.816626i | \(0.304158\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.53566 | 0.483130 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.7903 | 0.793318 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.93490 | 0.214621 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −19.8335 | −1.44268 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.87561 | −0.642216 | −0.321108 | − | 0.947043i | \(-0.604055\pi\) | ||||
−0.321108 | + | 0.947043i | \(0.604055\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.7284 | 1.06018 | 0.530088 | − | 0.847943i | \(-0.322159\pi\) | ||||
0.530088 | + | 0.847943i | \(0.322159\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.90534 | 0.136444 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.728224 | 0.0518838 | 0.0259419 | − | 0.999663i | \(-0.491742\pi\) | ||||
0.0259419 | + | 0.999663i | \(0.491742\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.75714 | 0.691665 | 0.345833 | − | 0.938296i | \(-0.387597\pi\) | ||||
0.345833 | + | 0.938296i | \(0.387597\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.75834 | −0.547231 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.35947 | −0.305975 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.1274 | 1.05654 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.73216 | 0.537422 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 20.0737 | 1.38853 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.49906 | −0.378571 | −0.189285 | − | 0.981922i | \(-0.560617\pi\) | ||||
−0.189285 | + | 0.981922i | \(0.560617\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.16543 | 0.422448 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.56764 | −0.379710 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.991923 | −0.0673361 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.5415 | 0.915050 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.809117 | 0.0544271 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.6940 | −1.18488 | −0.592440 | − | 0.805615i | \(-0.701835\pi\) | ||||
−0.592440 | + | 0.805615i | \(0.701835\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.378205 | 0.0252136 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.78798 | 0.384162 | 0.192081 | − | 0.981379i | \(-0.438476\pi\) | ||||
0.192081 | + | 0.981379i | \(0.438476\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.8632 | 1.51084 | 0.755422 | − | 0.655239i | \(-0.227432\pi\) | ||||
0.755422 | + | 0.655239i | \(0.227432\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.7067 | 0.901836 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.8442 | −0.906963 | −0.453482 | − | 0.891266i | \(-0.649818\pi\) | ||||
−0.453482 | + | 0.891266i | \(0.649818\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.92480 | 0.386491 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.71683 | −0.111520 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.74900 | −0.565926 | −0.282963 | − | 0.959131i | \(-0.591317\pi\) | ||||
−0.282963 | + | 0.959131i | \(0.591317\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.5363 | −1.19403 | −0.597014 | − | 0.802231i | \(-0.703646\pi\) | ||||
−0.597014 | + | 0.802231i | \(0.703646\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.0778 | 1.03139 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 26.3885 | 1.68590 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.53409 | 0.352126 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.38597 | 0.0878321 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.68464 | 0.421931 | 0.210965 | − | 0.977494i | \(-0.432339\pi\) | ||||
0.210965 | + | 0.977494i | \(0.432339\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.4727 | −0.784149 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.54164 | 0.0965415 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.9053 | 1.30404 | 0.652019 | − | 0.758203i | \(-0.273922\pi\) | ||||
0.652019 | + | 0.758203i | \(0.273922\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.3999 | 1.32972 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.24866 | 0.139189 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.7095 | −1.46199 | −0.730995 | − | 0.682383i | \(-0.760944\pi\) | ||||
−0.730995 | + | 0.682383i | \(0.760944\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.90398 | −0.424108 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.55439 | −0.462321 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.7389 | −0.654763 | −0.327381 | − | 0.944892i | \(-0.606166\pi\) | ||||
−0.327381 | + | 0.944892i | \(0.606166\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.5160 | −1.67148 | −0.835739 | − | 0.549127i | \(-0.814960\pi\) | ||||
−0.835739 | + | 0.549127i | \(0.814960\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.77878 | 0.228702 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.610077 | −0.0367891 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.4171 | −1.10658 | −0.553289 | − | 0.832989i | \(-0.686628\pi\) | ||||
−0.553289 | + | 0.832989i | \(0.686628\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.511645 | 0.0306314 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.07889 | 0.183671 | 0.0918356 | − | 0.995774i | \(-0.470727\pi\) | ||||
0.0918356 | + | 0.995774i | \(0.470727\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.30920 | 0.315599 | 0.157800 | − | 0.987471i | \(-0.449560\pi\) | ||||
0.157800 | + | 0.987471i | \(0.449560\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.5443 | 0.624592 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 30.0015 | 1.77093 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3453 | −0.961490 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.2900 | −0.779072 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.8332 | 0.983405 | 0.491702 | − | 0.870763i | \(-0.336375\pi\) | ||||
0.491702 | + | 0.870763i | \(0.336375\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −28.4664 | −1.65738 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −16.5025 | −0.957570 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.43856 | −0.198857 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.0421 | −0.636454 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.51402 | 0.0869780 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.5740 | 0.949022 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.9689 | −1.48213 | −0.741063 | − | 0.671436i | \(-0.765678\pi\) | ||||
−0.741063 | + | 0.671436i | \(0.765678\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.43442 | 0.195377 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.3043 | −0.584304 | −0.292152 | − | 0.956372i | \(-0.594371\pi\) | ||||
−0.292152 | + | 0.956372i | \(0.594371\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 30.2526 | 1.70998 | 0.854989 | − | 0.518646i | \(-0.173564\pi\) | ||||
0.854989 | + | 0.518646i | \(0.173564\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −21.5483 | −1.21411 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.4428 | −1.03585 | −0.517926 | − | 0.855425i | \(-0.673296\pi\) | ||||
−0.517926 | + | 0.855425i | \(0.673296\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.62729 | −0.203089 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.47561 | −0.528877 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.47772 | 0.249147 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.168191 | −0.00932956 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.78662 | −0.154100 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.7504 | 0.647820 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.65331 | 0.310734 | 0.155367 | − | 0.987857i | \(-0.450344\pi\) | ||||
0.155367 | + | 0.987857i | \(0.450344\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.0383 | −0.604895 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.6746 | −1.07494 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.5324 | −1.06400 | −0.532000 | − | 0.846744i | \(-0.678559\pi\) | ||||
−0.532000 | + | 0.846744i | \(0.678559\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.3451 | 0.616183 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.825329 | −0.0446941 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 21.8189 | 1.17811 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.55163 | −0.352728 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.63857 | 0.356377 | 0.178189 | − | 0.983996i | \(-0.442976\pi\) | ||||
0.178189 | + | 0.983996i | \(0.442976\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.45417 | −0.238426 | −0.119213 | − | 0.992869i | \(-0.538037\pi\) | ||||
−0.119213 | + | 0.992869i | \(0.538037\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.54953 | −0.242836 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.34190 | 0.390770 | 0.195385 | − | 0.980727i | \(-0.437404\pi\) | ||||
0.195385 | + | 0.980727i | \(0.437404\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.6351 | 0.829824 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.05747 | 0.161819 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.0325 | −1.21561 | −0.607804 | − | 0.794087i | \(-0.707949\pi\) | ||||
−0.607804 | + | 0.794087i | \(0.707949\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.6261 | 0.611901 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.86988 | 0.0981435 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 34.3403 | 1.79745 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.9306 | −1.40576 | −0.702882 | − | 0.711306i | \(-0.748104\pi\) | ||||
−0.702882 | + | 0.711306i | \(0.748104\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −15.4751 | −0.805601 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.6924 | −0.710872 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.9916 | 1.65646 | 0.828230 | − | 0.560388i | \(-0.189348\pi\) | ||||
0.828230 | + | 0.560388i | \(0.189348\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.84717 | −0.508506 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.00000 | −0.0515026 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.4552 | 0.588413 | 0.294207 | − | 0.955742i | \(-0.404945\pi\) | ||||
0.294207 | + | 0.955742i | \(0.404945\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.55525 | 0.0796777 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.901149 | −0.0460466 | −0.0230233 | − | 0.999735i | \(-0.507329\pi\) | ||||
−0.0230233 | + | 0.999735i | \(0.507329\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 34.7593 | 1.77150 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.69561 | 0.289524 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.198850 | 0.0100821 | 0.00504104 | − | 0.999987i | \(-0.498395\pi\) | ||||
0.00504104 | + | 0.999987i | \(0.498395\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.78220 | −0.140702 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.16754 | 0.109338 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.35376 | −0.219061 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.6657 | 1.13756 | 0.568780 | − | 0.822490i | \(-0.307416\pi\) | ||||
0.568780 | + | 0.822490i | \(0.307416\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 20.9121 | 1.04691 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.32964 | −0.166274 | −0.0831372 | − | 0.996538i | \(-0.526494\pi\) | ||||
−0.0831372 | + | 0.996538i | \(0.526494\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.227533 | −0.0113342 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.16019 | 0.306102 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.8058 | 0.882599 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.47625 | −0.270783 | −0.135391 | − | 0.990792i | \(-0.543229\pi\) | ||||
−0.135391 | + | 0.990792i | \(0.543229\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.77833 | −0.482329 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −56.4562 | −2.77803 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.51471 | 0.172531 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.7163 | −0.769631 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.9483 | −0.534860 | −0.267430 | − | 0.963577i | \(-0.586174\pi\) | ||||
−0.267430 | + | 0.963577i | \(0.586174\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.726095 | 0.0353877 | 0.0176939 | − | 0.999843i | \(-0.494368\pi\) | ||||
0.0176939 | + | 0.999843i | \(0.494368\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.06098 | −0.294695 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.136086 | −0.00660115 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 32.8704 | 1.59071 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.14413 | 0.151800 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.7541 | 0.710680 | 0.355340 | − | 0.934737i | \(-0.384365\pi\) | ||||
0.355340 | + | 0.934737i | \(0.384365\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.8348 | 1.43377 | 0.716884 | − | 0.697193i | \(-0.245568\pi\) | ||||
0.716884 | + | 0.697193i | \(0.245568\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.90534 | −0.0913541 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −19.0293 | −0.910294 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 37.5016 | 1.78985 | 0.894927 | − | 0.446212i | \(-0.147227\pi\) | ||||
0.894927 | + | 0.446212i | \(0.147227\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −26.9951 | −1.28548 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.3849 | 1.63368 | 0.816839 | − | 0.576866i | \(-0.195725\pi\) | ||||
0.816839 | + | 0.576866i | \(0.195725\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.1574 | −0.908148 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.61538 | −0.265598 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.6260 | 1.25656 | 0.628280 | − | 0.777988i | \(-0.283759\pi\) | ||||
0.628280 | + | 0.777988i | \(0.283759\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.9627 | 1.17545 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.389276 | 0.0182898 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.58271 | 0.449244 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.49872 | 0.0701071 | 0.0350535 | − | 0.999385i | \(-0.488840\pi\) | ||||
0.0350535 | + | 0.999385i | \(0.488840\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.68110 | −0.171819 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.9893 | −0.558397 | −0.279198 | − | 0.960233i | \(-0.590069\pi\) | ||||
−0.279198 | + | 0.960233i | \(0.590069\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.20541 | 0.427812 | 0.213906 | − | 0.976854i | \(-0.431381\pi\) | ||||
0.213906 | + | 0.976854i | \(0.431381\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.433528 | −0.0201044 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.9910 | −0.925072 | −0.462536 | − | 0.886601i | \(-0.653060\pi\) | ||||
−0.462536 | + | 0.886601i | \(0.653060\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −39.0197 | −1.80176 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.77796 | 0.0819238 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.18753 | −0.422443 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.930784 | −0.0427073 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.06267 | 0.323377 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.9438 | 1.64231 | 0.821157 | − | 0.570702i | \(-0.193329\pi\) | ||||
0.821157 | + | 0.570702i | \(0.193329\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.90883 | 0.223823 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.9936 | −0.591227 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −33.7024 | −1.53035 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.9734 | 0.723822 | 0.361911 | − | 0.932213i | \(-0.382124\pi\) | ||||
0.361911 | + | 0.932213i | \(0.382124\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.3549 | 0.513486 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.28873 | −0.419194 | −0.209597 | − | 0.977788i | \(-0.567215\pi\) | ||||
−0.209597 | + | 0.977788i | \(0.567215\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.809117 | −0.0364408 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −17.9292 | −0.805858 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 31.0083 | 1.39091 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.2188 | −0.636519 | −0.318259 | − | 0.948004i | \(-0.603098\pi\) | ||||
−0.318259 | + | 0.948004i | \(0.603098\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.62411 | 0.117236 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.0456 | −0.982963 | −0.491482 | − | 0.870888i | \(-0.663545\pi\) | ||||
−0.491482 | + | 0.870888i | \(0.663545\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.83944 | 0.170853 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.866798 | 0.0384959 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.1535 | 0.937614 | 0.468807 | − | 0.883301i | \(-0.344684\pi\) | ||||
0.468807 | + | 0.883301i | \(0.344684\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 68.1055 | 3.01281 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −25.1775 | −1.11161 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.70943 | 0.383783 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.77690 | 0.429987 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.49055 | 0.109323 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.5905 | 1.69068 | 0.845341 | − | 0.534227i | \(-0.179397\pi\) | ||||
0.845341 | + | 0.534227i | \(0.179397\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.8645 | 1.08725 | 0.543625 | − | 0.839328i | \(-0.317051\pi\) | ||||
0.543625 | + | 0.839328i | \(0.317051\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.635556 | −0.0277380 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.184101 | −0.00801956 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.1763 | −0.485926 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 29.1207 | 1.26373 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.88191 | 0.298089 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.0295 | −1.03888 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.15332 | −0.0497694 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 43.5454 | 1.87563 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.6371 | 0.500317 | 0.250158 | − | 0.968205i | \(-0.419517\pi\) | ||||
0.250158 | + | 0.968205i | \(0.419517\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.4614 | 0.577682 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.06666 | −0.302703 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.690340 | 0.0295168 | 0.0147584 | − | 0.999891i | \(-0.495302\pi\) | ||||
0.0147584 | + | 0.999891i | \(0.495302\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.9549 | −0.723618 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.53409 | −0.235760 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.63461 | −0.367181 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.35300 | 0.397013 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −40.1097 | −1.69950 | −0.849751 | − | 0.527184i | \(-0.823248\pi\) | ||||
−0.849751 | + | 0.527184i | \(0.823248\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.53289 | −0.107130 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.54397 | 0.107406 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.1905 | 1.35667 | 0.678333 | − | 0.734754i | \(-0.262703\pi\) | ||||
0.678333 | + | 0.734754i | \(0.262703\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 28.7704 | 1.21038 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12.2172 | 0.513075 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.1691 | 0.845531 | 0.422766 | − | 0.906239i | \(-0.361059\pi\) | ||||
0.422766 | + | 0.906239i | \(0.361059\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.43260 | 0.269196 | 0.134598 | − | 0.990900i | \(-0.457026\pi\) | ||||
0.134598 | + | 0.990900i | \(0.457026\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.69336 | −0.321395 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.578335 | 0.0241182 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.4692 | −1.14356 | −0.571779 | − | 0.820408i | \(-0.693747\pi\) | ||||
−0.571779 | + | 0.820408i | \(0.693747\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.7666 | 0.530561 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.97057 | 0.289188 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.3927 | −0.471838 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.94287 | −0.204362 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.2797 | 1.33233 | 0.666163 | − | 0.745806i | \(-0.267935\pi\) | ||||
0.666163 | + | 0.745806i | \(0.267935\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.25919 | −0.0518839 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.631223 | 0.0259650 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −29.9968 | −1.23182 | −0.615911 | − | 0.787815i | \(-0.711212\pi\) | ||||
−0.615911 | + | 0.787815i | \(0.711212\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.75353 | 0.317864 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.45747 | 0.346141 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −38.5665 | −1.57579 | −0.787893 | − | 0.615812i | \(-0.788828\pi\) | ||||
−0.787893 | + | 0.615812i | \(0.788828\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.5601 | 0.512337 | 0.256169 | − | 0.966632i | \(-0.417540\pi\) | ||||
0.256169 | + | 0.966632i | \(0.417540\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 20.1268 | 0.819627 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.74189 | 0.192785 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 36.0082 | 1.46153 | 0.730764 | − | 0.682630i | \(-0.239164\pi\) | ||||
0.730764 | + | 0.682630i | \(0.239164\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.77878 | −0.153124 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.69537 | 0.109043 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.4848 | −1.39283 | −0.696414 | − | 0.717640i | \(-0.745222\pi\) | ||||
−0.696414 | + | 0.717640i | \(0.745222\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13.1124 | 0.528743 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.81984 | 0.0732639 | 0.0366319 | − | 0.999329i | \(-0.488337\pi\) | ||||
0.0366319 | + | 0.999329i | \(0.488337\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.718328 | −0.0288720 | −0.0144360 | − | 0.999896i | \(-0.504595\pi\) | ||||
−0.0144360 | + | 0.999896i | \(0.504595\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.6438 | 0.627765 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −37.9940 | −1.52220 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.1308 | −0.965230 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17.3999 | 0.694884 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.97182 | 0.158367 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.1962 | −0.724378 | −0.362189 | − | 0.932105i | \(-0.617970\pi\) | ||||
−0.362189 | + | 0.932105i | \(0.617970\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.76658 | −0.189454 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.94399 | 0.156513 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.0049 | 0.475653 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.9944 | −0.632730 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.321087 | −0.0126822 | −0.00634109 | − | 0.999980i | \(-0.502018\pi\) | ||||
−0.00634109 | + | 0.999980i | \(0.502018\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.4353 | 0.766455 | 0.383227 | − | 0.923654i | \(-0.374813\pi\) | ||||
0.383227 | + | 0.923654i | \(0.374813\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.82602 | −0.190025 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30.5532 | −1.20117 | −0.600585 | − | 0.799561i | \(-0.705065\pi\) | ||||
−0.600585 | + | 0.799561i | \(0.705065\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −46.9743 | −1.84390 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.859797 | −0.0336981 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26.0930 | −1.02110 | −0.510549 | − | 0.859848i | \(-0.670558\pi\) | ||||
−0.510549 | + | 0.859848i | \(0.670558\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.49674 | 0.214775 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −35.1296 | −1.37054 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.22719 | 0.0867591 | 0.0433796 | − | 0.999059i | \(-0.486188\pi\) | ||||
0.0433796 | + | 0.999059i | \(0.486188\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.6483 | 1.38656 | 0.693279 | − | 0.720669i | \(-0.256165\pi\) | ||||
0.693279 | + | 0.720669i | \(0.256165\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.701341 | 0.0272378 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 53.0315 | 2.05647 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.43856 | 0.133142 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.3371 | −0.592968 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.3498 | 1.05583 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.4224 | −0.633039 | −0.316519 | − | 0.948586i | \(-0.602514\pi\) | ||||
−0.316519 | + | 0.948586i | \(0.602514\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.765190 | 0.0294522 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.9119 | −0.880576 | −0.440288 | − | 0.897857i | \(-0.645124\pi\) | ||||
−0.440288 | + | 0.897857i | \(0.645124\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −66.8405 | −2.56510 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.01701 | 0.192252 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −41.4800 | −1.58719 | −0.793594 | − | 0.608447i | \(-0.791793\pi\) | ||||
−0.793594 | + | 0.608447i | \(0.791793\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24.7971 | −0.947450 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.8178 | 0.756096 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.14083 | −0.119656 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.4177 | 0.966933 | 0.483467 | − | 0.875363i | \(-0.339377\pi\) | ||||
0.483467 | + | 0.875363i | \(0.339377\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −35.5582 | −1.35074 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −39.8554 | −1.51180 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.56827 | 0.210913 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.0001 | −0.453886 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.16013 | −0.0438175 | −0.0219087 | − | 0.999760i | \(-0.506974\pi\) | ||||
−0.0219087 | + | 0.999760i | \(0.506974\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27.1659 | 1.02458 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.13561 | 0.193418 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.61459 | 0.286376 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.32344 | 0.275038 | 0.137519 | − | 0.990499i | \(-0.456087\pi\) | ||||
0.137519 | + | 0.990499i | \(0.456087\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.45383 | 0.167032 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.782386 | 0.0293006 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.97328 | 0.298184 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.58362 | −0.283215 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.4802 | 0.540019 | 0.270010 | − | 0.962858i | \(-0.412973\pi\) | ||||
0.270010 | + | 0.962858i | \(0.412973\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.2730 | 0.643281 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16.0672 | −0.597546 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.168191 | 0.00624646 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −43.5365 | −1.61468 | −0.807340 | − | 0.590087i | \(-0.799094\pi\) | ||||
−0.807340 | + | 0.590087i | \(0.799094\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.52879 | 0.204770 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.04940 | −0.0758000 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.72585 | −0.137617 | −0.0688086 | − | 0.997630i | \(-0.521920\pi\) | ||||
−0.0688086 | + | 0.997630i | \(0.521920\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 22.8735 | 0.843703 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −32.4663 | −1.19591 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.10272 | −0.298063 | −0.149032 | − | 0.988832i | \(-0.547616\pi\) | ||||
−0.149032 | + | 0.988832i | \(0.547616\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.79694 | 0.176220 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.480988 | −0.0176457 | −0.00882287 | − | 0.999961i | \(-0.502808\pi\) | ||||
−0.00882287 | + | 0.999961i | \(0.502808\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.2402 | −0.521720 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.59550 | −0.131552 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −47.6565 | −1.74133 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.5082 | −1.77009 | −0.885044 | − | 0.465507i | \(-0.845872\pi\) | ||||
−0.885044 | + | 0.465507i | \(0.845872\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.79423 | 0.211154 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.987177 | 0.0359270 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −42.0009 | −1.52655 | −0.763274 | − | 0.646075i | \(-0.776410\pi\) | ||||
−0.763274 | + | 0.646075i | \(0.776410\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.8113 | −0.392424 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.9513 | −0.904484 | −0.452242 | − | 0.891895i | \(-0.649376\pi\) | ||||
−0.452242 | + | 0.891895i | \(0.649376\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.0150 | −0.507377 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.99936 | −0.144597 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.9502 | −0.467606 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.0942 | 1.51796 | 0.758978 | − | 0.651116i | \(-0.225699\pi\) | ||||
0.758978 | + | 0.651116i | \(0.225699\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.1207 | 0.652601 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.24607 | 0.296590 | 0.148295 | − | 0.988943i | \(-0.452621\pi\) | ||||
0.148295 | + | 0.988943i | \(0.452621\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.0382690 | 0.00137466 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 18.5494 | 0.665456 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 38.0851 | 1.36454 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.8005 | 0.923213 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.54953 | 0.162587 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.50877 | 0.160925 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 40.8478 | 1.45607 | 0.728033 | − | 0.685542i | \(-0.240435\pi\) | ||||
0.728033 | + | 0.685542i | \(0.240435\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20.5514 | −0.731647 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 57.0591 | 2.02879 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.54000 | 0.267753 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.98436 | −0.212243 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 38.3461 | 1.35829 | 0.679144 | − | 0.734005i | \(-0.262351\pi\) | ||||
0.679144 | + | 0.734005i | \(0.262351\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.18087 | 0.0771537 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 19.5977 | 0.692452 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 56.6671 | 1.99974 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −32.9507 | −1.16136 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.30847 | −0.327674 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.31360 | −0.0461837 | −0.0230919 | − | 0.999733i | \(-0.507351\pi\) | ||||
−0.0230919 | + | 0.999733i | \(0.507351\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −55.3838 | −1.94479 | −0.972395 | − | 0.233342i | \(-0.925034\pi\) | ||||
−0.972395 | + | 0.233342i | \(0.925034\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −23.8508 | −0.836485 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 28.7952 | 1.00865 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.0172 | −0.490401 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.80296 | −0.342543 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.8984 | 1.28776 | 0.643882 | − | 0.765125i | \(-0.277323\pi\) | ||||
0.643882 | + | 0.765125i | \(0.277323\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.9170 | 1.46113 | 0.730567 | − | 0.682841i | \(-0.239256\pi\) | ||||
0.730567 | + | 0.682841i | \(0.239256\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.528814 | −0.0184109 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.12791 | −0.143542 | −0.0717708 | − | 0.997421i | \(-0.522865\pi\) | ||||
−0.0717708 | + | 0.997421i | \(0.522865\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43.6665 | 1.51660 | 0.758300 | − | 0.651905i | \(-0.226030\pi\) | ||||
0.758300 | + | 0.651905i | \(0.226030\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.9639 | −0.553783 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.71340 | 0.336549 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.65454 | 0.230290 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.03517 | 0.0357807 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −52.3291 | −1.80660 | −0.903300 | − | 0.429008i | \(-0.858863\pi\) | ||||
−0.903300 | + | 0.429008i | \(0.858863\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.66878 | 0.0919175 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.19814 | 0.0756182 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.40438 | 0.323138 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.60201 | 0.157941 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16.8793 | −0.578616 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.7742 | −0.574339 | −0.287169 | − | 0.957880i | \(-0.592714\pi\) | ||||
−0.287169 | + | 0.957880i | \(0.592714\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −27.3543 | −0.935496 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.2516 | 0.452667 | 0.226334 | − | 0.974050i | \(-0.427326\pi\) | ||||
0.226334 | + | 0.974050i | \(0.427326\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.3091 | 0.692936 | 0.346468 | − | 0.938062i | \(-0.387381\pi\) | ||||
0.346468 | + | 0.938062i | \(0.387381\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 26.0052 | 0.886256 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.0234 | 0.409280 | 0.204640 | − | 0.978837i | \(-0.434398\pi\) | ||||
0.204640 | + | 0.978837i | \(0.434398\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.31584 | 0.214745 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.1681 | −0.481174 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.18442 | −0.243715 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.95057 | −0.303279 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 34.4771 | 1.16687 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −49.5253 | −1.67426 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.5918 | −1.16808 | −0.584041 | − | 0.811724i | \(-0.698529\pi\) | ||||
−0.584041 | + | 0.811724i | \(0.698529\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.5910 | 0.492141 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.5740 | 1.13114 | 0.565569 | − | 0.824701i | \(-0.308657\pi\) | ||||
0.565569 | + | 0.824701i | \(0.308657\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.7440 | 0.462522 | 0.231261 | − | 0.972892i | \(-0.425715\pi\) | ||||
0.231261 | + | 0.972892i | \(0.425715\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −24.6746 | −0.829429 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.4578 | −0.451868 | −0.225934 | − | 0.974143i | \(-0.572543\pi\) | ||||
−0.225934 | + | 0.974143i | \(0.572543\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.82194 | 0.262339 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.1653 | 0.340551 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.9164 | 0.499159 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.92473 | −0.0977631 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.98054 | −0.0995173 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.227533 | 0.00758865 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.54130 | −0.0846630 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.57123 | −0.318511 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 34.1370 | 1.13475 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.3789 | 0.709875 | 0.354937 | − | 0.934890i | \(-0.384502\pi\) | ||||
0.354937 | + | 0.934890i | \(0.384502\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.92769 | −0.130273 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.4415 | −1.53868 | −0.769338 | − | 0.638841i | \(-0.779414\pi\) | ||||
−0.769338 | + | 0.638841i | \(0.779414\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.79986 | 0.191947 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14.3663 | 0.474935 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.9014 | 0.359997 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.1716 | −0.896307 | −0.448154 | − | 0.893957i | \(-0.647918\pi\) | ||||
−0.448154 | + | 0.893957i | \(0.647918\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.5098 | −0.741724 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.11287 | 0.234123 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.825621 | −0.0271463 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.90962 | −0.292630 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.7343 | 0.942743 | 0.471372 | − | 0.881935i | \(-0.343759\pi\) | ||||
0.471372 | + | 0.881935i | \(0.343759\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 66.4364 | 2.17737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.93176 | −0.292413 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.45132 | 0.210981 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.0740 | −1.37450 | −0.687249 | − | 0.726422i | \(-0.741182\pi\) | ||||
−0.687249 | + | 0.726422i | \(0.741182\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.2229 | 0.855752 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −37.8989 | −1.23547 | −0.617734 | − | 0.786387i | \(-0.711949\pi\) | ||||
−0.617734 | + | 0.786387i | \(0.711949\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.6639 | −0.770602 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −43.5968 | −1.41820 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.7705 | −0.967411 | −0.483706 | − | 0.875231i | \(-0.660709\pi\) | ||||
−0.483706 | + | 0.875231i | \(0.660709\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.6224 | 0.507126 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.9862 | −0.518388 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 47.3380 | 1.53343 | 0.766714 | − | 0.641989i | \(-0.221890\pi\) | ||||
0.766714 | + | 0.641989i | \(0.221890\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.5098 | −0.631322 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.14413 | −0.101635 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −49.1790 | −1.58807 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9482 | −0.998330 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 24.5818 | 0.792137 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 32.3751 | 1.04219 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.6621 | 1.08250 | 0.541249 | − | 0.840862i | \(-0.317952\pi\) | ||||
0.541249 | + | 0.840862i | \(0.317952\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.88128 | 0.124685 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −51.1600 | −1.64180 | −0.820901 | − | 0.571070i | \(-0.806528\pi\) | ||||
−0.820901 | + | 0.571070i | \(0.806528\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −79.0434 | −2.53402 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.145788 | −0.00466894 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 50.3817 | 1.61185 | 0.805926 | − | 0.592016i | \(-0.201668\pi\) | ||||
0.805926 | + | 0.592016i | \(0.201668\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −31.6129 | −1.01035 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.22909 | 0.230807 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.0901 | −0.513194 | −0.256597 | − | 0.966518i | \(-0.582601\pi\) | ||||
−0.256597 | + | 0.966518i | \(0.582601\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.60074 | 0.0510037 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.1852 | 0.324199 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.70950 | 0.276946 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.2136 | −0.991533 | −0.495766 | − | 0.868456i | \(-0.665113\pi\) | ||||
−0.495766 | + | 0.868456i | \(0.665113\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.90028 | 0.155506 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.4475 | 0.679932 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −61.7232 | −1.95479 | −0.977397 | − | 0.211414i | \(-0.932193\pi\) | ||||
−0.977397 | + | 0.211414i | \(0.932193\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −22.3329 | −0.706581 |
(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 | 6032.2.a.ba.1.7 | 10 | ||
4.3 | odd | 2 | 3016.2.a.g.1.4 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3016.2.a.g.1.4 | ✓ | 10 | 4.3 | odd | 2 | ||
6032.2.a.ba.1.7 | 10 | 1.1 | even | 1 | trivial |