Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(449,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.q (of order \(6\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.19269881856.9 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 15x^{6} - 2x^{5} + 133x^{4} - 84x^{3} + 276x^{2} + 144x + 144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1601.4 | ||
Root | \(0.831167 - 1.43962i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.1601 |
Dual form | 1728.3.q.j.449.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.44299 | − | 1.98781i | 0.688598 | − | 0.397562i | −0.114488 | − | 0.993425i | \(-0.536523\pi\) |
0.803087 | + | 0.595862i | \(0.203190\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.80469 | + | 3.12582i | −0.257813 | + | 0.446545i | −0.965656 | − | 0.259825i | \(-0.916335\pi\) |
0.707843 | + | 0.706370i | \(0.249669\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.8326 | + | 6.83153i | 1.07569 | + | 0.621048i | 0.929730 | − | 0.368243i | \(-0.120041\pi\) |
0.145957 | + | 0.989291i | \(0.453374\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 8.96435 | + | 15.5267i | 0.689565 | + | 1.19436i | 0.971979 | + | 0.235070i | \(0.0755318\pi\) |
−0.282413 | + | 0.959293i | \(0.591135\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 21.6750i | 1.27500i | 0.770449 | + | 0.637501i | \(0.220032\pi\) | ||||
−0.770449 | + | 0.637501i | \(0.779968\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 23.4245 | 1.23287 | 0.616435 | − | 0.787406i | \(-0.288576\pi\) | ||||
0.616435 | + | 0.787406i | \(0.288576\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −13.0662 | + | 7.54376i | −0.568095 | + | 0.327990i | −0.756388 | − | 0.654123i | \(-0.773038\pi\) |
0.188293 | + | 0.982113i | \(0.439704\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.59721 | + | 7.96260i | −0.183888 | + | 0.318504i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −20.4862 | − | 11.8277i | −0.706420 | − | 0.407852i | 0.103314 | − | 0.994649i | \(-0.467055\pi\) |
−0.809734 | + | 0.586797i | \(0.800389\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −23.5016 | − | 40.7060i | −0.758117 | − | 1.31310i | −0.943810 | − | 0.330489i | \(-0.892786\pi\) |
0.185693 | − | 0.982608i | \(-0.440547\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 14.3495i | 0.409987i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −54.6126 | −1.47602 | −0.738009 | − | 0.674791i | \(-0.764234\pi\) | ||||
−0.738009 | + | 0.674791i | \(0.764234\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −24.6459 | + | 14.2293i | −0.601118 | + | 0.347056i | −0.769481 | − | 0.638669i | \(-0.779485\pi\) |
0.168363 | + | 0.985725i | \(0.446152\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 23.8753 | − | 41.3532i | 0.555239 | − | 0.961702i | −0.442646 | − | 0.896696i | \(-0.645960\pi\) |
0.997885 | − | 0.0650055i | \(-0.0207065\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −30.5323 | − | 17.6278i | −0.649623 | − | 0.375060i | 0.138689 | − | 0.990336i | \(-0.455711\pi\) |
−0.788312 | + | 0.615276i | \(0.789045\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 17.9862 | + | 31.1530i | 0.367065 | + | 0.635775i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 65.0193i | 1.22678i | 0.789780 | + | 0.613390i | \(0.210195\pi\) | ||||
−0.789780 | + | 0.613390i | \(0.789805\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 54.3192 | 0.987621 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −76.0156 | + | 43.8876i | −1.28840 | + | 0.743858i | −0.978369 | − | 0.206869i | \(-0.933673\pi\) |
−0.310031 | + | 0.950726i | \(0.600339\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.46852 | − | 11.2038i | 0.106041 | − | 0.183669i | −0.808122 | − | 0.589015i | \(-0.799516\pi\) |
0.914163 | + | 0.405346i | \(0.132849\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 61.7284 | + | 35.6389i | 0.949667 | + | 0.548291i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.55595 | − | 2.69499i | −0.0232232 | − | 0.0402237i | 0.854180 | − | 0.519977i | \(-0.174059\pi\) |
−0.877403 | + | 0.479753i | \(0.840726\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 49.5089i | 0.697308i | 0.937251 | + | 0.348654i | \(0.113361\pi\) | ||||
−0.937251 | + | 0.348654i | \(0.886639\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 102.151 | 1.39932 | 0.699662 | − | 0.714474i | \(-0.253334\pi\) | ||||
0.699662 | + | 0.714474i | \(0.253334\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −42.7082 | + | 24.6576i | −0.554652 | + | 0.320228i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −18.7220 | + | 32.4275i | −0.236988 | + | 0.410475i | −0.959849 | − | 0.280519i | \(-0.909494\pi\) |
0.722861 | + | 0.690994i | \(0.242827\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.6999 | + | 8.48702i | 0.177108 | + | 0.102253i | 0.585933 | − | 0.810359i | \(-0.300728\pi\) |
−0.408825 | + | 0.912613i | \(0.634061\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 43.0859 | + | 74.6270i | 0.506893 | + | 0.877964i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.1990i | 0.159540i | 0.996813 | + | 0.0797698i | \(0.0254185\pi\) | ||||
−0.996813 | + | 0.0797698i | \(0.974581\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −64.7115 | −0.711116 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 80.6505 | − | 46.5636i | 0.848952 | − | 0.490143i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −24.1484 | + | 41.8262i | −0.248952 | + | 0.431198i | −0.963235 | − | 0.268659i | \(-0.913420\pi\) |
0.714283 | + | 0.699857i | \(0.246753\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −34.5980 | − | 19.9752i | −0.342554 | − | 0.197774i | 0.318847 | − | 0.947806i | \(-0.396704\pi\) |
−0.661401 | + | 0.750032i | \(0.730038\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.9749 | + | 19.0091i | 0.106552 | + | 0.184554i | 0.914371 | − | 0.404876i | \(-0.132685\pi\) |
−0.807819 | + | 0.589431i | \(0.799352\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.521299i | 0.00487195i | 0.999997 | + | 0.00243598i | \(0.000775396\pi\) | ||||
−0.999997 | + | 0.00243598i | \(0.999225\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 198.784 | 1.82371 | 0.911855 | − | 0.410513i | \(-0.134650\pi\) | ||||
0.911855 | + | 0.410513i | \(0.134650\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −115.971 | + | 66.9557i | −1.02629 | + | 0.592528i | −0.915919 | − | 0.401363i | \(-0.868537\pi\) |
−0.110369 | + | 0.993891i | \(0.535203\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −29.9912 | + | 51.9462i | −0.260793 | + | 0.451706i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −67.7522 | − | 39.1168i | −0.569346 | − | 0.328712i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 32.8395 | + | 56.8797i | 0.271401 | + | 0.470080i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 135.944i | 1.08755i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 45.8769 | 0.361235 | 0.180618 | − | 0.983553i | \(-0.442190\pi\) | ||||
0.180618 | + | 0.983553i | \(0.442190\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 167.914 | − | 96.9453i | 1.28179 | − | 0.740040i | 0.304612 | − | 0.952476i | \(-0.401473\pi\) |
0.977175 | + | 0.212436i | \(0.0681397\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −42.2741 | + | 73.2208i | −0.317850 | + | 0.550532i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −149.798 | − | 86.4859i | −1.09342 | − | 0.631284i | −0.158932 | − | 0.987289i | \(-0.550805\pi\) |
−0.934484 | + | 0.356005i | \(0.884138\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.803631 | − | 1.39193i | −0.00578151 | − | 0.0100139i | 0.863120 | − | 0.504999i | \(-0.168507\pi\) |
−0.868902 | + | 0.494985i | \(0.835174\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 244.961i | 1.71301i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −94.0450 | −0.648586 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 76.1133 | − | 43.9441i | 0.510828 | − | 0.294927i | −0.222346 | − | 0.974968i | \(-0.571371\pi\) |
0.733174 | + | 0.680041i | \(0.238038\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.64118 | − | 11.5029i | 0.0439813 | − | 0.0761778i | −0.843197 | − | 0.537605i | \(-0.819329\pi\) |
0.887178 | + | 0.461427i | \(0.152662\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −161.832 | − | 93.4336i | −1.04408 | − | 0.602798i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 93.8926 | + | 162.627i | 0.598042 | + | 1.03584i | 0.993110 | + | 0.117188i | \(0.0373879\pi\) |
−0.395068 | + | 0.918652i | \(0.629279\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 54.4566i | − | 0.338240i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 131.235 | 0.805123 | 0.402562 | − | 0.915393i | \(-0.368120\pi\) | ||||
0.402562 | + | 0.915393i | \(0.368120\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 158.636 | − | 91.5887i | 0.949918 | − | 0.548436i | 0.0568627 | − | 0.998382i | \(-0.481890\pi\) |
0.893056 | + | 0.449946i | \(0.148557\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −76.2192 | + | 132.015i | −0.451001 | + | 0.781157i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.6730 | + | 13.0903i | 0.131058 | + | 0.0756662i | 0.564095 | − | 0.825710i | \(-0.309225\pi\) |
−0.433038 | + | 0.901376i | \(0.642558\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.5931 | − | 28.7401i | −0.0948176 | − | 0.164229i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 175.092i | − | 0.978165i | −0.872238 | − | 0.489083i | \(-0.837332\pi\) | ||
0.872238 | − | 0.489083i | \(-0.162668\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 172.814 | 0.954772 | 0.477386 | − | 0.878694i | \(-0.341584\pi\) | ||||
0.477386 | + | 0.878694i | \(0.341584\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −188.031 | + | 108.560i | −1.01638 | + | 0.586809i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −148.074 | + | 256.471i | −0.791838 | + | 1.37150i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −76.1098 | − | 43.9420i | −0.398481 | − | 0.230063i | 0.287348 | − | 0.957826i | \(-0.407227\pi\) |
−0.685828 | + | 0.727764i | \(0.740560\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 68.6377 | + | 118.884i | 0.355636 | + | 0.615979i | 0.987227 | − | 0.159323i | \(-0.0509310\pi\) |
−0.631591 | + | 0.775302i | \(0.717598\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 239.073i | 1.21357i | 0.794867 | + | 0.606784i | \(0.207541\pi\) | ||||
−0.794867 | + | 0.606784i | \(0.792459\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −250.574 | −1.25916 | −0.629582 | − | 0.776934i | \(-0.716774\pi\) | ||||
−0.629582 | + | 0.776934i | \(0.716774\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 73.9425 | − | 42.6907i | 0.364249 | − | 0.210299i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −56.5703 | + | 97.9826i | −0.275953 | + | 0.477964i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 277.172 | + | 160.025i | 1.32618 | + | 0.765671i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −118.043 | − | 204.456i | −0.559445 | − | 0.968988i | −0.997543 | − | 0.0700601i | \(-0.977681\pi\) |
0.438098 | − | 0.898927i | \(-0.355652\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 189.838i | − | 0.882968i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 169.653 | 0.781810 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −336.542 | + | 194.303i | −1.52282 | + | 0.879198i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 42.8742 | − | 74.2603i | 0.192261 | − | 0.333006i | −0.753738 | − | 0.657175i | \(-0.771751\pi\) |
0.945999 | + | 0.324169i | \(0.105085\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 160.187 | + | 92.4841i | 0.705671 | + | 0.407419i | 0.809456 | − | 0.587181i | \(-0.199762\pi\) |
−0.103785 | + | 0.994600i | \(0.533095\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −128.199 | − | 222.048i | −0.559822 | − | 0.969640i | −0.997511 | − | 0.0705135i | \(-0.977536\pi\) |
0.437689 | − | 0.899126i | \(-0.355797\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 403.712i | 1.73267i | 0.499464 | + | 0.866335i | \(0.333530\pi\) | ||||
−0.499464 | + | 0.866335i | \(0.666470\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −140.163 | −0.596439 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 215.728 | − | 124.551i | 0.902630 | − | 0.521133i | 0.0245772 | − | 0.999698i | \(-0.492176\pi\) |
0.878052 | + | 0.478565i | \(0.158843\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 85.7023 | − | 148.441i | 0.355611 | − | 0.615937i | −0.631611 | − | 0.775285i | \(-0.717606\pi\) |
0.987222 | + | 0.159349i | \(0.0509394\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 123.852 | + | 71.5063i | 0.505520 | + | 0.291862i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 209.986 | + | 363.706i | 0.850145 | + | 1.47249i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 287.980i | 1.14733i | 0.819089 | + | 0.573666i | \(0.194479\pi\) | ||||
−0.819089 | + | 0.573666i | \(0.805521\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −206.142 | −0.814789 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 60.1268 | − | 34.7142i | 0.233957 | − | 0.135075i | −0.378439 | − | 0.925626i | \(-0.623539\pi\) |
0.612396 | + | 0.790551i | \(0.290206\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 98.5590 | − | 170.709i | 0.380537 | − | 0.659109i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −68.7357 | − | 39.6845i | −0.261352 | − | 0.150892i | 0.363599 | − | 0.931556i | \(-0.381548\pi\) |
−0.624951 | + | 0.780664i | \(0.714881\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 129.246 | + | 223.861i | 0.487722 | + | 0.844758i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 41.6217i | − | 0.154728i | −0.997003 | − | 0.0773638i | \(-0.975350\pi\) | ||
0.997003 | − | 0.0773638i | \(-0.0246503\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 98.0065 | 0.361648 | 0.180824 | − | 0.983516i | \(-0.442124\pi\) | ||||
0.180824 | + | 0.983516i | \(0.442124\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −108.793 | + | 62.8119i | −0.395612 | + | 0.228407i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −153.400 | + | 265.696i | −0.553790 | + | 0.959193i | 0.444206 | + | 0.895924i | \(0.353486\pi\) |
−0.997997 | + | 0.0632681i | \(0.979848\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 54.8876 | + | 31.6894i | 0.195330 | + | 0.112774i | 0.594475 | − | 0.804114i | \(-0.297360\pi\) |
−0.399146 | + | 0.916888i | \(0.630693\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 163.299 | + | 282.842i | 0.577027 | + | 0.999440i | 0.995818 | + | 0.0913578i | \(0.0291207\pi\) |
−0.418791 | + | 0.908083i | \(0.637546\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 102.718i | − | 0.357902i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −180.808 | −0.625632 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −62.3120 | + | 35.9759i | −0.212669 | + | 0.122784i | −0.602551 | − | 0.798080i | \(-0.705849\pi\) |
0.389882 | + | 0.920865i | \(0.372516\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −174.481 | + | 302.209i | −0.591460 | + | 1.02444i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −234.260 | − | 135.250i | −0.783477 | − | 0.452341i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 86.1750 | + | 149.259i | 0.286296 | + | 0.495879i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 51.4328i | − | 0.168632i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 161.023 | 0.524504 | 0.262252 | − | 0.964999i | \(-0.415535\pi\) | ||||
0.262252 | + | 0.964999i | \(0.415535\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −352.553 | + | 203.547i | −1.13361 | + | 0.654491i | −0.944841 | − | 0.327530i | \(-0.893784\pi\) |
−0.188771 | + | 0.982021i | \(0.560451\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 79.7548 | − | 138.139i | 0.254808 | − | 0.441340i | −0.710035 | − | 0.704166i | \(-0.751321\pi\) |
0.964843 | + | 0.262826i | \(0.0846545\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −364.877 | − | 210.662i | −1.15103 | − | 0.664549i | −0.201894 | − | 0.979407i | \(-0.564710\pi\) |
−0.949139 | + | 0.314859i | \(0.898043\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −161.602 | − | 279.904i | −0.506591 | − | 0.877441i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 507.728i | 1.57191i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −164.844 | −0.507212 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 110.203 | − | 63.6256i | 0.334963 | − | 0.193391i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 64.9715 | − | 112.534i | 0.196289 | − | 0.339982i | −0.751034 | − | 0.660264i | \(-0.770444\pi\) |
0.947322 | + | 0.320282i | \(0.103778\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.7143 | − | 6.18588i | −0.0319828 | − | 0.0184653i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 53.6006 | + | 92.8389i | 0.159052 | + | 0.275486i | 0.934527 | − | 0.355892i | \(-0.115823\pi\) |
−0.775475 | + | 0.631378i | \(0.782490\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 642.208i | − | 1.88331i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −306.698 | −0.894163 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 347.832 | − | 200.821i | 1.00240 | − | 0.578735i | 0.0934416 | − | 0.995625i | \(-0.470213\pi\) |
0.908957 | + | 0.416890i | \(0.136880\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 218.729 | − | 378.849i | 0.626730 | − | 1.08553i | −0.361474 | − | 0.932382i | \(-0.617726\pi\) |
0.988204 | − | 0.153146i | \(-0.0489404\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −303.639 | − | 175.306i | −0.860167 | − | 0.496618i | 0.00390098 | − | 0.999992i | \(-0.498758\pi\) |
−0.864068 | + | 0.503375i | \(0.832092\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 98.4143 | + | 170.459i | 0.277223 | + | 0.480165i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 529.816i | 1.47581i | 0.674904 | + | 0.737906i | \(0.264185\pi\) | ||||
−0.674904 | + | 0.737906i | \(0.735815\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 187.709 | 0.519969 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 351.704 | − | 203.056i | 0.963572 | − | 0.556319i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 361.971 | − | 626.953i | 0.986298 | − | 1.70832i | 0.350278 | − | 0.936646i | \(-0.386087\pi\) |
0.636020 | − | 0.771673i | \(-0.280580\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −203.239 | − | 117.340i | −0.547813 | − | 0.316280i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.6005 | + | 51.2696i | 0.0793580 | + | 0.137452i | 0.902973 | − | 0.429697i | \(-0.141380\pi\) |
−0.823615 | + | 0.567149i | \(0.808046\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 424.111i | − | 1.12496i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.5366 | −0.0858485 | −0.0429243 | − | 0.999078i | \(-0.513667\pi\) | ||||
−0.0429243 | + | 0.999078i | \(0.513667\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 188.264 | − | 108.694i | 0.491551 | − | 0.283797i | −0.233666 | − | 0.972317i | \(-0.575072\pi\) |
0.725218 | + | 0.688519i | \(0.241739\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −98.0293 | + | 169.792i | −0.254622 | + | 0.441017i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 579.712 | + | 334.697i | 1.49026 | + | 0.860403i | 0.999938 | − | 0.0111369i | \(-0.00354507\pi\) |
0.490324 | + | 0.871540i | \(0.336878\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −163.511 | − | 283.210i | −0.418188 | − | 0.724322i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 148.864i | 0.376870i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.3088 | −0.0561935 | −0.0280967 | − | 0.999605i | \(-0.508945\pi\) | ||||
−0.0280967 | + | 0.999605i | \(0.508945\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 77.7666 | − | 44.8986i | 0.193932 | − | 0.111967i | −0.399890 | − | 0.916563i | \(-0.630952\pi\) |
0.593822 | + | 0.804597i | \(0.297618\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 421.354 | − | 729.806i | 1.04554 | − | 1.81093i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −646.207 | − | 373.088i | −1.58773 | − | 0.916677i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −308.464 | − | 534.276i | −0.754191 | − | 1.30630i | −0.945775 | − | 0.324821i | \(-0.894696\pi\) |
0.191584 | − | 0.981476i | \(-0.438637\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 316.814i | − | 0.767105i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 67.4824 | 0.162608 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 566.501 | − | 327.069i | 1.35203 | − | 0.780595i | 0.363496 | − | 0.931596i | \(-0.381583\pi\) |
0.988534 | + | 0.151001i | \(0.0482496\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 209.287 | − | 362.495i | 0.497118 | − | 0.861033i | −0.502877 | − | 0.864358i | \(-0.667725\pi\) |
0.999994 | + | 0.00332489i | \(0.00105835\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −172.590 | − | 99.6447i | −0.406093 | − | 0.234458i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.3474 | + | 40.4388i | 0.0546777 | + | 0.0947045i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 111.970i | 0.259792i | 0.991528 | + | 0.129896i | \(0.0414644\pi\) | ||||
−0.991528 | + | 0.129896i | \(0.958536\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −158.770 | −0.366673 | −0.183337 | − | 0.983050i | \(-0.558690\pi\) | ||||
−0.183337 | + | 0.983050i | \(0.558690\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −306.069 | + | 176.709i | −0.700387 | + | 0.404369i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 61.8211 | − | 107.077i | 0.140823 | − | 0.243912i | −0.786984 | − | 0.616973i | \(-0.788359\pi\) |
0.927807 | + | 0.373061i | \(0.121692\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −680.397 | − | 392.827i | −1.53588 | − | 0.886743i | −0.999073 | − | 0.0430402i | \(-0.986296\pi\) |
−0.536811 | − | 0.843703i | \(-0.680371\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.2250 | + | 48.8871i | 0.0634269 | + | 0.109859i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 387.277i | 0.862533i | 0.902225 | + | 0.431266i | \(0.141933\pi\) | ||||
−0.902225 | + | 0.431266i | \(0.858067\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −388.831 | −0.862153 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −222.801 | + | 128.634i | −0.489673 | + | 0.282713i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 160.668 | − | 278.284i | 0.351570 | − | 0.608938i | −0.634954 | − | 0.772550i | \(-0.718981\pi\) |
0.986525 | + | 0.163612i | \(0.0523145\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 61.0565 | + | 35.2510i | 0.132444 | + | 0.0764663i | 0.564758 | − | 0.825257i | \(-0.308970\pi\) |
−0.432314 | + | 0.901723i | \(0.642303\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 181.170 | + | 313.796i | 0.391297 | + | 0.677746i | 0.992621 | − | 0.121259i | \(-0.0386933\pi\) |
−0.601324 | + | 0.799005i | \(0.705360\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 478.151i | 1.02388i | 0.859022 | + | 0.511939i | \(0.171073\pi\) | ||||
−0.859022 | + | 0.511939i | \(0.828927\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.2320 | 0.0239489 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 565.011 | − | 326.209i | 1.19453 | − | 0.689660i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −107.687 | + | 186.520i | −0.226710 | + | 0.392674i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 790.996 | + | 456.682i | 1.65135 | + | 0.953407i | 0.976518 | + | 0.215434i | \(0.0691166\pi\) |
0.674830 | + | 0.737973i | \(0.264217\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −489.567 | − | 847.955i | −1.01781 | − | 1.76290i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 192.010i | 0.395896i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 700.870 | 1.43916 | 0.719579 | − | 0.694411i | \(-0.244335\pi\) | ||||
0.719579 | + | 0.694411i | \(0.244335\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −479.646 | + | 276.924i | −0.976876 | + | 0.564000i | −0.901326 | − | 0.433142i | \(-0.857405\pi\) |
−0.0755505 | + | 0.997142i | \(0.524071\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 256.366 | − | 444.039i | 0.520012 | − | 0.900687i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −154.756 | − | 89.3482i | −0.311380 | − | 0.179775i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −162.874 | − | 282.107i | −0.326401 | − | 0.565344i | 0.655394 | − | 0.755287i | \(-0.272503\pi\) |
−0.981795 | + | 0.189944i | \(0.939169\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 610.492i | 1.21370i | 0.794816 | + | 0.606851i | \(0.207567\pi\) | ||||
−0.794816 | + | 0.606851i | \(0.792433\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −158.827 | −0.314510 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 774.630 | − | 447.233i | 1.52187 | − | 0.878650i | 0.522200 | − | 0.852823i | \(-0.325111\pi\) |
0.999666 | − | 0.0258270i | \(-0.00822190\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −184.350 | + | 319.304i | −0.360764 | + | 0.624862i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 75.5729 | + | 43.6320i | 0.146744 | + | 0.0847224i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −240.850 | − | 417.164i | −0.465860 | − | 0.806894i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 244.209i | − | 0.468732i | −0.972148 | − | 0.234366i | \(-0.924699\pi\) | ||
0.972148 | − | 0.234366i | \(-0.0753014\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.79146 | 0.00916150 | 0.00458075 | − | 0.999990i | \(-0.498542\pi\) | ||||
0.00458075 | + | 0.999990i | \(0.498542\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 882.305 | − | 509.399i | 1.67420 | − | 0.966601i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −150.683 | + | 260.991i | −0.284846 | + | 0.493367i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −441.868 | − | 255.113i | −0.829021 | − | 0.478636i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.03624 | + | 1.79483i | 0.00193690 | + | 0.00335482i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 491.492i | 0.911859i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −406.633 | −0.751633 | −0.375816 | − | 0.926694i | \(-0.622638\pi\) | ||||
−0.375816 | + | 0.926694i | \(0.622638\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 684.413 | − | 395.146i | 1.25580 | − | 0.725038i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −250.283 | + | 433.503i | −0.457556 | + | 0.792509i | −0.998831 | − | 0.0483358i | \(-0.984608\pi\) |
0.541276 | + | 0.840845i | \(0.317942\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −479.879 | − | 277.058i | −0.870924 | − | 0.502828i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −67.5750 | − | 117.043i | −0.122197 | − | 0.211652i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 549.645i | 0.986796i | 0.869804 | + | 0.493398i | \(0.164245\pi\) | ||||
−0.869804 | + | 0.493398i | \(0.835755\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 856.105 | 1.53149 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 799.025 | − | 461.317i | 1.41923 | − | 0.819391i | 0.422996 | − | 0.906132i | \(-0.360978\pi\) |
0.996231 | + | 0.0867404i | \(0.0276451\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −266.191 | + | 461.056i | −0.471134 | + | 0.816027i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −281.820 | − | 162.709i | −0.495289 | − | 0.285955i | 0.231477 | − | 0.972840i | \(-0.425644\pi\) |
−0.726766 | + | 0.686885i | \(0.758978\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −64.8487 | − | 112.321i | −0.113570 | − | 0.196710i | 0.803637 | − | 0.595120i | \(-0.202895\pi\) |
−0.917207 | + | 0.398410i | \(0.869562\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 138.721i | − | 0.241254i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 401.374 | 0.695621 | 0.347811 | − | 0.937565i | \(-0.386925\pi\) | ||||
0.347811 | + | 0.937565i | \(0.386925\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −53.0577 | + | 30.6329i | −0.0913214 | + | 0.0527244i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −444.181 | + | 769.345i | −0.761889 | + | 1.31963i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −650.079 | − | 375.323i | −1.10746 | − | 0.639392i | −0.169290 | − | 0.985566i | \(-0.554147\pi\) |
−0.938170 | + | 0.346174i | \(0.887481\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −550.515 | − | 953.519i | −0.934660 | − | 1.61888i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 969.193i | − | 1.63439i | −0.576362 | − | 0.817195i | \(-0.695528\pi\) | ||
0.576362 | − | 0.817195i | \(-0.304472\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −311.027 | −0.522735 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.76897 | − | 5.64012i | 0.0163088 | − | 0.00941589i | −0.491823 | − | 0.870695i | \(-0.663669\pi\) |
0.508132 | + | 0.861279i | \(0.330336\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −425.209 | + | 736.483i | −0.707502 | + | 1.22543i | 0.258279 | + | 0.966070i | \(0.416845\pi\) |
−0.965781 | + | 0.259359i | \(0.916489\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 226.132 | + | 130.557i | 0.373772 | + | 0.215797i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −91.2085 | − | 157.978i | −0.150261 | − | 0.260260i | 0.781062 | − | 0.624453i | \(-0.214678\pi\) |
−0.931323 | + | 0.364193i | \(0.881345\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 632.088i | − | 1.03451i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 334.345 | 0.545425 | 0.272712 | − | 0.962096i | \(-0.412079\pi\) | ||||
0.272712 | + | 0.962096i | \(0.412079\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 154.140 | − | 88.9929i | 0.249822 | − | 0.144235i | −0.369861 | − | 0.929087i | \(-0.620595\pi\) |
0.619683 | + | 0.784852i | \(0.287261\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −529.724 | + | 917.510i | −0.855775 | + | 1.48225i | 0.0201500 | + | 0.999797i | \(0.493586\pi\) |
−0.875925 | + | 0.482448i | \(0.839748\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −44.3836 | − | 25.6249i | −0.0712417 | − | 0.0411314i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 155.301 | + | 268.989i | 0.248482 | + | 0.430383i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1183.73i | − | 1.88193i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −950.275 | −1.50598 | −0.752991 | − | 0.658031i | \(-0.771390\pi\) | ||||
−0.752991 | + | 0.658031i | \(0.771390\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 157.954 | − | 91.1946i | 0.248746 | − | 0.143614i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −322.469 | + | 558.532i | −0.506230 | + | 0.876817i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 74.1661 | + | 42.8198i | 0.115704 | + | 0.0668016i | 0.556735 | − | 0.830690i | \(-0.312054\pi\) |
−0.441031 | + | 0.897492i | \(0.645387\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −139.447 | − | 241.529i | −0.216869 | − | 0.375629i | 0.736980 | − | 0.675915i | \(-0.236251\pi\) |
−0.953849 | + | 0.300286i | \(0.902918\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 654.758i | − | 1.01199i | −0.862536 | − | 0.505995i | \(-0.831125\pi\) | ||
0.862536 | − | 0.505995i | \(-0.168875\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1199.28 | −1.84789 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −159.696 | + | 92.2004i | −0.244557 | + | 0.141195i | −0.617269 | − | 0.786752i | \(-0.711761\pi\) |
0.372712 | + | 0.927947i | \(0.378428\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 385.418 | − | 667.563i | 0.588424 | − | 1.01918i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −165.641 | − | 95.6328i | −0.251352 | − | 0.145118i | 0.369031 | − | 0.929417i | \(-0.379690\pi\) |
−0.620383 | + | 0.784299i | \(0.713023\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −66.6012 | − | 115.357i | −0.100758 | − | 0.174518i | 0.811239 | − | 0.584715i | \(-0.198794\pi\) |
−0.911997 | + | 0.410196i | \(0.865460\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 336.131i | 0.505461i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 356.901 | 0.535085 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 153.078 | − | 88.3797i | 0.228134 | − | 0.131713i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 661.521 | − | 1145.79i | 0.982943 | − | 1.70251i | 0.332201 | − | 0.943208i | \(-0.392209\pi\) |
0.650742 | − | 0.759299i | \(-0.274458\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 288.213 | + | 166.400i | 0.425720 | + | 0.245790i | 0.697522 | − | 0.716564i | \(-0.254286\pi\) |
−0.271801 | + | 0.962353i | \(0.587619\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −87.1607 | − | 150.967i | −0.128366 | − | 0.222337i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 190.785i | − | 0.279333i | −0.990199 | − | 0.139667i | \(-0.955397\pi\) | ||
0.990199 | − | 0.139667i | \(-0.0446031\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −687.671 | −1.00390 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1009.54 | + | 582.856i | −1.46522 | + | 0.845945i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 360.135 | − | 623.771i | 0.521179 | − | 0.902708i | −0.478518 | − | 0.878078i | \(-0.658826\pi\) |
0.999697 | − | 0.0246304i | \(-0.00784089\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.53379 | − | 3.19493i | −0.00796228 | − | 0.00459703i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −308.421 | − | 534.200i | −0.442497 | − | 0.766428i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 145.736i | − | 0.207897i | −0.994583 | − | 0.103949i | \(-0.966852\pi\) | ||
0.994583 | − | 0.103949i | \(-0.0331477\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1279.28 | −1.81974 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 124.877 | − | 72.0980i | 0.176630 | − | 0.101977i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 394.430 | − | 683.173i | 0.556319 | − | 0.963572i | −0.441481 | − | 0.897271i | \(-0.645547\pi\) |
0.997800 | − | 0.0663017i | \(-0.0211200\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 614.153 | + | 354.581i | 0.861365 | + | 0.497309i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 486.936 | + | 843.398i | 0.681029 | + | 1.17958i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 721.671i | 1.00372i | 0.864950 | + | 0.501858i | \(0.167350\pi\) | ||||
−0.864950 | + | 0.501858i | \(0.832650\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −79.2252 | −0.109882 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 188.358 | − | 108.749i | 0.259805 | − | 0.149998i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −543.433 | + | 941.253i | −0.747500 | + | 1.29471i | 0.201518 | + | 0.979485i | \(0.435413\pi\) |
−0.949018 | + | 0.315223i | \(0.897921\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 896.332 | + | 517.498i | 1.22617 | + | 0.707931i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 352.753 | + | 610.985i | 0.481245 | + | 0.833541i | 0.999768 | − | 0.0215227i | \(-0.00685140\pi\) |
−0.518523 | + | 0.855063i | \(0.673518\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 42.5181i | − | 0.0576908i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1183.74 | 1.60182 | 0.800909 | − | 0.598786i | \(-0.204350\pi\) | ||||
0.800909 | + | 0.598786i | \(0.204350\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −187.727 | + | 108.384i | −0.252661 | + | 0.145874i | −0.620982 | − | 0.783825i | \(-0.713266\pi\) |
0.368321 | + | 0.929699i | \(0.379933\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 174.705 | − | 302.598i | 0.234503 | − | 0.406172i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.62949 | − | 0.940784i | −0.00217555 | − | 0.00125605i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 76.7045 | + | 132.856i | 0.102137 | + | 0.176906i | 0.912565 | − | 0.408932i | \(-0.134099\pi\) |
−0.810428 | + | 0.585838i | \(0.800765\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 52.8056i | − | 0.0699412i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 585.893 | 0.773967 | 0.386983 | − | 0.922087i | \(-0.373517\pi\) | ||||
0.386983 | + | 0.922087i | \(0.373517\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 290.563 | − | 167.757i | 0.381817 | − | 0.220442i | −0.296791 | − | 0.954942i | \(-0.595917\pi\) |
0.678609 | + | 0.734500i | \(0.262583\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −358.744 | + | 621.364i | −0.470176 | + | 0.814369i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1362.86 | − | 786.848i | −1.77687 | − | 1.02588i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 613.797 | + | 1063.13i | 0.798175 | + | 1.38248i | 0.920803 | + | 0.390028i | \(0.127535\pi\) |
−0.122628 | + | 0.992453i | \(0.539132\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 512.944i | − | 0.663576i | −0.943354 | − | 0.331788i | \(-0.892348\pi\) | ||
0.943354 | − | 0.331788i | \(-0.107652\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 432.168 | 0.557636 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −577.318 | + | 333.315i | −0.741101 | + | 0.427875i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −338.221 | + | 585.816i | −0.433062 | + | 0.750085i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 646.543 | + | 373.282i | 0.823622 | + | 0.475518i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −284.387 | − | 492.573i | −0.361356 | − | 0.625886i | 0.626828 | − | 0.779157i | \(-0.284353\pi\) |
−0.988184 | + | 0.153271i | \(0.951019\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 483.337i | − | 0.611046i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 231.944 | 0.292490 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1026.79 | − | 592.819i | 1.28832 | − | 0.743813i | 0.309967 | − | 0.950747i | \(-0.399682\pi\) |
0.978355 | + | 0.206934i | \(0.0663485\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 382.084 | − | 661.789i | 0.478203 | − | 0.828271i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1208.70 | + | 697.845i | 1.50523 | + | 0.869047i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −108.250 | − | 187.494i | −0.134471 | − | 0.232911i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 185.707i | 0.229552i | 0.993391 | + | 0.114776i | \(0.0366150\pi\) | ||||
−0.993391 | + | 0.114776i | \(0.963385\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −451.817 | −0.557111 | −0.278555 | − | 0.960420i | \(-0.589856\pi\) | ||||
−0.278555 | + | 0.960420i | \(0.589856\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 451.841 | − | 260.871i | 0.554406 | − | 0.320087i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 559.267 | − | 968.679i | 0.684537 | − | 1.18565i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1029.67 | − | 594.478i | −1.25416 | − | 0.724090i | −0.282228 | − | 0.959347i | \(-0.591073\pi\) |
−0.971933 | + | 0.235257i | \(0.924407\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 329.832 | + | 571.286i | 0.400768 | + | 0.694151i | 0.993819 | − | 0.111014i | \(-0.0354099\pi\) |
−0.593051 | + | 0.805165i | \(0.702077\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 291.986i | − | 0.353067i | −0.984295 | − | 0.176533i | \(-0.943512\pi\) | ||
0.984295 | − | 0.176533i | \(-0.0564883\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 452.809 | 0.546212 | 0.273106 | − | 0.961984i | \(-0.411949\pi\) | ||||
0.273106 | + | 0.961984i | \(0.411949\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −675.242 | + | 389.851i | −0.810615 | + | 0.468009i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 364.122 | − | 630.678i | 0.436075 | − | 0.755303i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −62.7098 | − | 36.2055i | −0.0747435 | − | 0.0431532i | 0.462162 | − | 0.886795i | \(-0.347074\pi\) |
−0.536906 | + | 0.843642i | \(0.680407\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −140.711 | − | 243.719i | −0.167314 | − | 0.289796i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 606.037i | 0.717204i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −237.061 | −0.279883 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 713.578 | − | 411.985i | 0.838518 | − | 0.484118i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 165.809 | − | 287.189i | 0.194383 | − | 0.336681i | −0.752315 | − | 0.658803i | \(-0.771063\pi\) |
0.946698 | + | 0.322122i | \(0.104396\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 426.279 | + | 246.112i | 0.497408 | + | 0.287179i | 0.727643 | − | 0.685956i | \(-0.240616\pi\) |
−0.230234 | + | 0.973135i | \(0.573949\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −379.885 | − | 657.980i | −0.442241 | − | 0.765984i | 0.555614 | − | 0.831440i | \(-0.312483\pi\) |
−0.997855 | + | 0.0654561i | \(0.979150\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 263.506i | − | 0.305337i | −0.988277 | − | 0.152668i | \(-0.951213\pi\) | ||
0.988277 | − | 0.152668i | \(-0.0487867\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 104.084 | 0.120328 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −443.059 | + | 255.800i | −0.509849 | + | 0.294362i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.8962 | − | 48.3176i | 0.0320278 | − | 0.0554737i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −424.936 | − | 245.337i | −0.485642 | − | 0.280385i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −707.946 | − | 1226.20i | −0.807236 | − | 1.39817i | −0.914771 | − | 0.403973i | \(-0.867629\pi\) |
0.107534 | − | 0.994201i | \(-0.465704\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 992.699i | − | 1.12679i | −0.826189 | − | 0.563393i | \(-0.809496\pi\) | ||
0.826189 | − | 0.563393i | \(-0.190504\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 800.265 | 0.906303 | 0.453151 | − | 0.891434i | \(-0.350300\pi\) | ||||
0.453151 | + | 0.891434i | \(0.350300\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 522.975 | − | 301.940i | 0.589600 | − | 0.340405i | −0.175340 | − | 0.984508i | \(-0.556102\pi\) |
0.764939 | + | 0.644103i | \(0.222769\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −82.7936 | + | 143.403i | −0.0931312 | + | 0.161308i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −715.205 | − | 412.924i | −0.800901 | − | 0.462400i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −348.049 | − | 602.839i | −0.388882 | − | 0.673563i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1111.88i | 1.23680i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1409.30 | −1.56415 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 594.996 | − | 343.521i | 0.657454 | − | 0.379581i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −327.494 | + | 567.237i | −0.361074 | + | 0.625399i | −0.988138 | − | 0.153569i | \(-0.950923\pi\) |
0.627064 | + | 0.778968i | \(0.284257\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1475.55 | + | 851.907i | 1.61970 | + | 0.935134i | 0.986997 | + | 0.160740i | \(0.0513880\pi\) |
0.632703 | + | 0.774394i | \(0.281945\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 115.959 | + | 200.846i | 0.127008 | + | 0.219985i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 699.825i | 0.763168i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −412.015 | −0.448330 | −0.224165 | − | 0.974551i | \(-0.571965\pi\) | ||||
−0.224165 | + | 0.974551i | \(0.571965\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −768.710 | + | 443.815i | −0.832839 | + | 0.480840i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 251.066 | − | 434.859i | 0.271422 | − | 0.470117i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −645.658 | − | 372.771i | −0.695003 | − | 0.401260i | 0.110480 | − | 0.993878i | \(-0.464761\pi\) |
−0.805484 | + | 0.592618i | \(0.798094\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 421.318 | + | 729.744i | 0.452543 | + | 0.783828i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1177.37i | 1.25922i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 227.643 | 0.242948 | 0.121474 | − | 0.992595i | \(-0.461238\pi\) | ||||
0.121474 | + | 0.992595i | \(0.461238\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −108.079 | + | 62.3995i | −0.114856 | + | 0.0663119i | −0.556327 | − | 0.830963i | \(-0.687790\pi\) |
0.441472 | + | 0.897275i | \(0.354457\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 214.685 | − | 371.845i | 0.227661 | − | 0.394321i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −508.817 | − | 293.766i | −0.537294 | − | 0.310207i | 0.206688 | − | 0.978407i | \(-0.433732\pi\) |
−0.743981 | + | 0.668200i | \(0.767065\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 915.715 | + | 1586.06i | 0.964926 | + | 1.67130i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 413.855i | 0.434266i | 0.976142 | + | 0.217133i | \(0.0696705\pi\) | ||||
−0.976142 | + | 0.217133i | \(0.930330\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −349.394 | −0.365857 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 540.678 | − | 312.161i | 0.563794 | − | 0.325507i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −624.153 | + | 1081.07i | −0.649483 | + | 1.12494i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 472.638 | + | 272.878i | 0.489780 | + | 0.282775i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 512.963 | + | 888.477i | 0.530468 | + | 0.918798i | 0.999368 | + | 0.0355464i | \(0.0113172\pi\) |
−0.468900 | + | 0.883251i | \(0.655350\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 610.884i | − | 0.629129i | −0.949236 | − | 0.314564i | \(-0.898142\pi\) | ||
0.949236 | − | 0.314564i | \(-0.101858\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.80122 | 0.00596220 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −408.200 | + | 235.674i | −0.417809 | + | 0.241222i | −0.694140 | − | 0.719840i | \(-0.744215\pi\) |
0.276330 | + | 0.961063i | \(0.410882\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −97.0010 | + | 168.011i | −0.0990817 | + | 0.171615i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −828.578 | − | 478.380i | −0.842908 | − | 0.486653i | 0.0153438 | − | 0.999882i | \(-0.495116\pi\) |
−0.858252 | + | 0.513229i | \(0.828449\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 475.232 | + | 823.126i | 0.482469 | + | 0.835661i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 720.437i | 0.728450i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1743.95 | 1.75978 | 0.879892 | − | 0.475174i | \(-0.157615\pi\) | ||||
0.879892 | + | 0.475174i | \(0.157615\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −862.723 | + | 498.093i | −0.867058 | + | 0.500596i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −81.8646 | + | 141.794i | −0.0821109 | + | 0.142220i | −0.904156 | − | 0.427201i | \(-0.859500\pi\) |
0.822046 | + | 0.569422i | \(0.192833\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1728.3.q.j.1601.4 | 8 | ||
3.2 | odd | 2 | 576.3.q.i.65.2 | 8 | |||
4.3 | odd | 2 | 1728.3.q.i.1601.4 | 8 | |||
8.3 | odd | 2 | 432.3.q.e.305.1 | 8 | |||
8.5 | even | 2 | 216.3.m.b.89.1 | 8 | |||
9.4 | even | 3 | 576.3.q.i.257.2 | 8 | |||
9.5 | odd | 6 | inner | 1728.3.q.j.449.4 | 8 | ||
12.11 | even | 2 | 576.3.q.j.65.3 | 8 | |||
24.5 | odd | 2 | 72.3.m.b.65.3 | yes | 8 | ||
24.11 | even | 2 | 144.3.q.e.65.2 | 8 | |||
36.23 | even | 6 | 1728.3.q.i.449.4 | 8 | |||
36.31 | odd | 6 | 576.3.q.j.257.3 | 8 | |||
72.5 | odd | 6 | 216.3.m.b.17.1 | 8 | |||
72.11 | even | 6 | 1296.3.e.i.161.7 | 8 | |||
72.13 | even | 6 | 72.3.m.b.41.3 | ✓ | 8 | ||
72.29 | odd | 6 | 648.3.e.c.161.7 | 8 | |||
72.43 | odd | 6 | 1296.3.e.i.161.2 | 8 | |||
72.59 | even | 6 | 432.3.q.e.17.1 | 8 | |||
72.61 | even | 6 | 648.3.e.c.161.2 | 8 | |||
72.67 | odd | 6 | 144.3.q.e.113.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.3.m.b.41.3 | ✓ | 8 | 72.13 | even | 6 | ||
72.3.m.b.65.3 | yes | 8 | 24.5 | odd | 2 | ||
144.3.q.e.65.2 | 8 | 24.11 | even | 2 | |||
144.3.q.e.113.2 | 8 | 72.67 | odd | 6 | |||
216.3.m.b.17.1 | 8 | 72.5 | odd | 6 | |||
216.3.m.b.89.1 | 8 | 8.5 | even | 2 | |||
432.3.q.e.17.1 | 8 | 72.59 | even | 6 | |||
432.3.q.e.305.1 | 8 | 8.3 | odd | 2 | |||
576.3.q.i.65.2 | 8 | 3.2 | odd | 2 | |||
576.3.q.i.257.2 | 8 | 9.4 | even | 3 | |||
576.3.q.j.65.3 | 8 | 12.11 | even | 2 | |||
576.3.q.j.257.3 | 8 | 36.31 | odd | 6 | |||
648.3.e.c.161.2 | 8 | 72.61 | even | 6 | |||
648.3.e.c.161.7 | 8 | 72.29 | odd | 6 | |||
1296.3.e.i.161.2 | 8 | 72.43 | odd | 6 | |||
1296.3.e.i.161.7 | 8 | 72.11 | even | 6 | |||
1728.3.q.i.449.4 | 8 | 36.23 | even | 6 | |||
1728.3.q.i.1601.4 | 8 | 4.3 | odd | 2 | |||
1728.3.q.j.449.4 | 8 | 9.5 | odd | 6 | inner | ||
1728.3.q.j.1601.4 | 8 | 1.1 | even | 1 | trivial |