Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8100,2,Mod(1,8100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8100.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8100 = 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8100.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: | \(64.6788256372\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.28356903014400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 37x^{6} + 399x^{4} - 1195x^{2} + 400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 1620) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(4.46736\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8100.1 |
$q$-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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.28148 | 0.484353 | 0.242176 | − | 0.970232i | \(-0.422139\pi\) | ||||
0.242176 | + | 0.970232i | \(0.422139\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.14474 | 1.24969 | 0.624844 | − | 0.780750i | \(-0.285163\pi\) | ||||
0.624844 | + | 0.780750i | \(0.285163\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.52202 | −1.80888 | −0.904441 | − | 0.426598i | \(-0.859712\pi\) | ||||
−0.904441 | + | 0.426598i | \(0.859712\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.98507 | 1.45159 | 0.725797 | − | 0.687909i | \(-0.241471\pi\) | ||||
0.725797 | + | 0.687909i | \(0.241471\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.17891 | 1.64695 | 0.823477 | − | 0.567349i | \(-0.192031\pi\) | ||||
0.823477 | + | 0.567349i | \(0.192031\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.53098 | −1.57032 | −0.785159 | − | 0.619295i | \(-0.787419\pi\) | ||||
−0.785159 | + | 0.619295i | \(0.787419\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.19615 | 0.964901 | 0.482451 | − | 0.875923i | \(-0.339747\pi\) | ||||
0.482451 | + | 0.875923i | \(0.339747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.17891 | 0.930159 | 0.465080 | − | 0.885269i | \(-0.346026\pi\) | ||||
0.465080 | + | 0.885269i | \(0.346026\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.24054 | −0.861540 | −0.430770 | − | 0.902462i | \(-0.641758\pi\) | ||||
−0.430770 | + | 0.902462i | \(0.641758\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.680643 | 0.106299 | 0.0531493 | − | 0.998587i | \(-0.483074\pi\) | ||||
0.0531493 | + | 0.998587i | \(0.483074\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.28148 | 0.195423 | 0.0977117 | − | 0.995215i | \(-0.468848\pi\) | ||||
0.0977117 | + | 0.995215i | \(0.468848\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.31139 | 0.774747 | 0.387373 | − | 0.921923i | \(-0.373382\pi\) | ||||
0.387373 | + | 0.921923i | \(0.373382\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.35782 | −0.765402 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.21958 | 0.304883 | 0.152442 | − | 0.988312i | \(-0.451286\pi\) | ||||
0.152442 | + | 0.988312i | \(0.451286\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.60885 | −0.990587 | −0.495294 | − | 0.868726i | \(-0.664940\pi\) | ||||
−0.495294 | + | 0.868726i | \(0.664940\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.17891 | −0.278981 | −0.139490 | − | 0.990223i | \(-0.544546\pi\) | ||||
−0.139490 | + | 0.990223i | \(0.544546\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.6070 | 1.90670 | 0.953349 | − | 0.301871i | \(-0.0976113\pi\) | ||||
0.953349 | + | 0.301871i | \(0.0976113\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.50603 | 0.653446 | 0.326723 | − | 0.945120i | \(-0.394056\pi\) | ||||
0.326723 | + | 0.945120i | \(0.394056\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.80350 | 0.913330 | 0.456665 | − | 0.889639i | \(-0.349044\pi\) | ||||
0.456665 | + | 0.889639i | \(0.349044\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.31139 | 0.605290 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.00000 | 0.675053 | 0.337526 | − | 0.941316i | \(-0.390410\pi\) | ||||
0.337526 | + | 0.941316i | \(0.390410\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.75056 | −1.07026 | −0.535132 | − | 0.844769i | \(-0.679738\pi\) | ||||
−0.535132 | + | 0.844769i | \(0.679738\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.0215 | −1.06228 | −0.531141 | − | 0.847284i | \(-0.678236\pi\) | ||||
−0.531141 | + | 0.847284i | \(0.678236\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.35782 | −0.876137 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.3255 | −1.45454 | −0.727268 | − | 0.686354i | \(-0.759210\pi\) | ||||
−0.727268 | + | 0.686354i | \(0.759210\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.680643 | −0.0677265 | −0.0338633 | − | 0.999426i | \(-0.510781\pi\) | ||||
−0.0338633 | + | 0.999426i | \(0.510781\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.56295 | 0.252535 | 0.126268 | − | 0.991996i | \(-0.459700\pi\) | ||||
0.126268 | + | 0.991996i | \(0.459700\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.00000 | 0.670478 | 0.335239 | − | 0.942133i | \(-0.391183\pi\) | ||||
0.335239 | + | 0.942133i | \(0.391183\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.07688 | 0.853881 | 0.426941 | − | 0.904280i | \(-0.359591\pi\) | ||||
0.426941 | + | 0.904280i | \(0.359591\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.66973 | 0.703083 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.17891 | 0.561719 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.28148 | 0.113713 | 0.0568563 | − | 0.998382i | \(-0.481892\pi\) | ||||
0.0568563 | + | 0.998382i | \(0.481892\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.50603 | 0.481064 | 0.240532 | − | 0.970641i | \(-0.422678\pi\) | ||||
0.240532 | + | 0.970641i | \(0.422678\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.19961 | 0.797707 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.2965 | −0.965122 | −0.482561 | − | 0.875862i | \(-0.660293\pi\) | ||||
−0.482561 | + | 0.875862i | \(0.660293\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.1789 | 1.45710 | 0.728548 | − | 0.684995i | \(-0.240196\pi\) | ||||
0.728548 | + | 0.684995i | \(0.240196\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −27.0321 | −2.26054 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.7332 | −1.61661 | −0.808303 | − | 0.588766i | \(-0.799614\pi\) | ||||
−0.808303 | + | 0.588766i | \(0.799614\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.17891 | 0.421454 | 0.210727 | − | 0.977545i | \(-0.432417\pi\) | ||||
0.210727 | + | 0.977545i | \(0.432417\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.24054 | 0.418241 | 0.209120 | − | 0.977890i | \(-0.432940\pi\) | ||||
0.209120 | + | 0.977890i | \(0.432940\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.65078 | −0.760588 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.7626 | 0.921315 | 0.460657 | − | 0.887578i | \(-0.347614\pi\) | ||||
0.460657 | + | 0.887578i | \(0.347614\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.21958 | 0.171757 | 0.0858783 | − | 0.996306i | \(-0.472630\pi\) | ||||
0.0858783 | + | 0.996306i | \(0.472630\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 29.5367 | 2.27206 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.673677 | 0.0512187 | 0.0256094 | − | 0.999672i | \(-0.491847\pi\) | ||||
0.0256094 | + | 0.999672i | \(0.491847\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.5370 | −1.08655 | −0.543275 | − | 0.839555i | \(-0.682816\pi\) | ||||
−0.543275 | + | 0.839555i | \(0.682816\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.1789 | 1.12824 | 0.564120 | − | 0.825693i | \(-0.309216\pi\) | ||||
0.564120 | + | 0.825693i | \(0.309216\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.8066 | 1.81404 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 26.2906 | 1.90232 | 0.951162 | − | 0.308692i | \(-0.0998913\pi\) | ||||
0.951162 | + | 0.308692i | \(0.0998913\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.9294 | −0.930679 | −0.465339 | − | 0.885132i | \(-0.654068\pi\) | ||||
−0.465339 | + | 0.885132i | \(0.654068\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.20466 | −0.584558 | −0.292279 | − | 0.956333i | \(-0.594414\pi\) | ||||
−0.292279 | + | 0.956333i | \(0.594414\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.35782 | −0.167141 | −0.0835706 | − | 0.996502i | \(-0.526632\pi\) | ||||
−0.0835706 | + | 0.996502i | \(0.526632\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.65875 | 0.467353 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 29.7547 | 2.05818 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.82109 | 0.331898 | 0.165949 | − | 0.986134i | \(-0.446931\pi\) | ||||
0.165949 | + | 0.986134i | \(0.446931\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.63665 | 0.450525 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −39.0348 | −2.62576 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.91813 | −0.530237 | −0.265119 | − | 0.964216i | \(-0.585411\pi\) | ||||
−0.265119 | + | 0.964216i | \(0.585411\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.7207 | 1.44165 | 0.720827 | − | 0.693115i | \(-0.243762\pi\) | ||||
0.720827 | + | 0.693115i | \(0.243762\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.1789 | 1.20130 | 0.600648 | − | 0.799514i | \(-0.294909\pi\) | ||||
0.600648 | + | 0.799514i | \(0.294909\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.0470 | 1.37884 | 0.689418 | − | 0.724363i | \(-0.257866\pi\) | ||||
0.689418 | + | 0.724363i | \(0.257866\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.1459 | −1.43250 | −0.716249 | − | 0.697844i | \(-0.754143\pi\) | ||||
−0.716249 | + | 0.697844i | \(0.754143\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.0000 | 1.22390 | 0.611949 | − | 0.790897i | \(-0.290386\pi\) | ||||
0.611949 | + | 0.790897i | \(0.290386\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −46.8210 | −2.97915 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.3205 | −1.09326 | −0.546630 | − | 0.837374i | \(-0.684090\pi\) | ||||
−0.546630 | + | 0.837374i | \(0.684090\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −31.2140 | −1.96241 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.85730 | −0.427747 | −0.213873 | − | 0.976861i | \(-0.568608\pi\) | ||||
−0.213873 | + | 0.976861i | \(0.568608\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.71563 | −0.417289 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.0620 | 0.928760 | 0.464380 | − | 0.885636i | \(-0.346277\pi\) | ||||
0.464380 | + | 0.885636i | \(0.346277\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.28001 | 0.565812 | 0.282906 | − | 0.959148i | \(-0.408702\pi\) | ||||
0.282906 | + | 0.959148i | \(0.408702\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.357817 | 0.0217358 | 0.0108679 | − | 0.999941i | \(-0.496541\pi\) | ||||
0.0108679 | + | 0.999941i | \(0.496541\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.7626 | −0.706744 | −0.353372 | − | 0.935483i | \(-0.614965\pi\) | ||||
−0.353372 | + | 0.935483i | \(0.614965\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.23808 | −0.431788 | −0.215894 | − | 0.976417i | \(-0.569267\pi\) | ||||
−0.215894 | + | 0.976417i | \(0.569267\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.6510 | 1.70313 | 0.851563 | − | 0.524252i | \(-0.175655\pi\) | ||||
0.851563 | + | 0.524252i | \(0.175655\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.872228 | 0.0514860 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 18.8211 | 1.10712 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.9552 | −1.04895 | −0.524477 | − | 0.851424i | \(-0.675739\pi\) | ||||
−0.524477 | + | 0.851424i | \(0.675739\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 49.1172 | 2.84052 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.64218 | 0.0946539 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.8885 | −0.963876 | −0.481938 | − | 0.876205i | \(-0.660067\pi\) | ||||
−0.481938 | + | 0.876205i | \(0.660067\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.97013 | 0.508650 | 0.254325 | − | 0.967119i | \(-0.418147\pi\) | ||||
0.254325 | + | 0.967119i | \(0.418147\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.08497 | −0.513513 | −0.256757 | − | 0.966476i | \(-0.582654\pi\) | ||||
−0.256757 | + | 0.966476i | \(0.582654\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.1687 | −0.683462 | −0.341731 | − | 0.939798i | \(-0.611013\pi\) | ||||
−0.341731 | + | 0.939798i | \(0.611013\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.5367 | 1.20583 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 42.9663 | 2.39071 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.80643 | 0.375251 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.53673 | 0.0844660 | 0.0422330 | − | 0.999108i | \(-0.486553\pi\) | ||||
0.0422330 | + | 0.999108i | \(0.486553\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.56295 | −0.139613 | −0.0698065 | − | 0.997561i | \(-0.522238\pi\) | ||||
−0.0698065 | + | 0.997561i | \(0.522238\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.4653 | 1.16241 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.8363 | −0.855078 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.21958 | 0.119153 | 0.0595767 | − | 0.998224i | \(-0.481025\pi\) | ||||
0.0595767 | + | 0.998224i | \(0.481025\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.82109 | 0.472182 | 0.236091 | − | 0.971731i | \(-0.424134\pi\) | ||||
0.236091 | + | 0.971731i | \(0.424134\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 27.9043 | 1.48520 | 0.742599 | − | 0.669737i | \(-0.233593\pi\) | ||||
0.742599 | + | 0.669737i | \(0.233593\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.3624 | −1.02191 | −0.510955 | − | 0.859607i | \(-0.670708\pi\) | ||||
−0.510955 | + | 0.859607i | \(0.670708\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 32.5367 | 1.71246 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.56295 | −0.133785 | −0.0668926 | − | 0.997760i | \(-0.521308\pi\) | ||||
−0.0668926 | + | 0.997760i | \(0.521308\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.84434 | 0.147671 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.8885 | 0.874452 | 0.437226 | − | 0.899352i | \(-0.355961\pi\) | ||||
0.437226 | + | 0.899352i | \(0.355961\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −33.8894 | −1.74539 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.3578 | 1.14844 | 0.574222 | − | 0.818700i | \(-0.305305\pi\) | ||||
0.574222 | + | 0.818700i | \(0.305305\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.9701 | 0.611646 | 0.305823 | − | 0.952088i | \(-0.401068\pi\) | ||||
0.305823 | + | 0.952088i | \(0.401068\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.4951 | 0.633528 | 0.316764 | − | 0.948504i | \(-0.397404\pi\) | ||||
0.316764 | + | 0.948504i | \(0.397404\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −45.0735 | −2.27946 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.6920 | 1.23925 | 0.619627 | − | 0.784896i | \(-0.287284\pi\) | ||||
0.619627 | + | 0.784896i | \(0.287284\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.0635 | 0.602421 | 0.301210 | − | 0.953558i | \(-0.402609\pi\) | ||||
0.301210 | + | 0.953558i | \(0.402609\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −33.7769 | −1.68255 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.7207 | −1.07666 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.1789 | 0.898889 | 0.449445 | − | 0.893308i | \(-0.351622\pi\) | ||||
0.449445 | + | 0.893308i | \(0.351622\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.75056 | −0.479794 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.65078 | 0.471471 | 0.235736 | − | 0.971817i | \(-0.424250\pi\) | ||||
0.235736 | + | 0.971817i | \(0.424250\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.7156 | −0.765933 | −0.382967 | − | 0.923762i | \(-0.625098\pi\) | ||||
−0.382967 | + | 0.923762i | \(0.625098\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.79222 | −0.135125 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.1160 | −1.49881 | −0.749403 | − | 0.662114i | \(-0.769659\pi\) | ||||
−0.749403 | + | 0.662114i | \(0.769659\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.7738 | −0.806099 | −0.403050 | − | 0.915178i | \(-0.632050\pi\) | ||||
−0.403050 | + | 0.915178i | \(0.632050\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −54.0642 | −2.58624 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.5367 | −0.741527 | −0.370764 | − | 0.928727i | \(-0.620904\pi\) | ||||
−0.370764 | + | 0.928727i | \(0.620904\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.3734 | −0.967967 | −0.483984 | − | 0.875077i | \(-0.660811\pi\) | ||||
−0.483984 | + | 0.875077i | \(0.660811\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.8386 | 1.59694 | 0.798471 | − | 0.602033i | \(-0.205642\pi\) | ||||
0.798471 | + | 0.602033i | \(0.205642\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.82109 | 0.132840 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.114633 | 0.00536233 | 0.00268116 | − | 0.999996i | \(-0.499147\pi\) | ||||
0.00268116 | + | 0.999996i | \(0.499147\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.97013 | −0.417781 | −0.208890 | − | 0.977939i | \(-0.566985\pi\) | ||||
−0.208890 | + | 0.977939i | \(0.566985\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.68886 | −0.357332 | −0.178666 | − | 0.983910i | \(-0.557178\pi\) | ||||
−0.178666 | + | 0.983910i | \(0.557178\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 29.2517 | 1.35361 | 0.676803 | − | 0.736164i | \(-0.263365\pi\) | ||||
0.676803 | + | 0.736164i | \(0.263365\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.0000 | 0.923514 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.31139 | 0.244218 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 31.8576 | 1.45561 | 0.727804 | − | 0.685785i | \(-0.240541\pi\) | ||||
0.727804 | + | 0.685785i | \(0.240541\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.1789 | 1.55842 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.7769 | 1.53058 | 0.765290 | − | 0.643686i | \(-0.222596\pi\) | ||||
0.765290 | + | 0.643686i | \(0.222596\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.4463 | −1.05812 | −0.529058 | − | 0.848586i | \(-0.677455\pi\) | ||||
−0.529058 | + | 0.848586i | \(0.677455\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31.0993 | 1.40064 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.05585 | 0.316498 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.17891 | −0.321372 | −0.160686 | − | 0.987006i | \(-0.551371\pi\) | ||||
−0.160686 | + | 0.987006i | \(0.551371\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −40.7467 | −1.81681 | −0.908403 | − | 0.418096i | \(-0.862698\pi\) | ||||
−0.908403 | + | 0.418096i | \(0.862698\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.7967 | −1.40936 | −0.704681 | − | 0.709524i | \(-0.748910\pi\) | ||||
−0.704681 | + | 0.709524i | \(0.748910\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.0000 | 0.442374 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.0144 | 0.968191 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.1459 | 0.970229 | 0.485115 | − | 0.874451i | \(-0.338778\pi\) | ||||
0.485115 | + | 0.874451i | \(0.338778\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 41.6951 | 1.82320 | 0.911599 | − | 0.411081i | \(-0.134849\pi\) | ||||
0.911599 | + | 0.411081i | \(0.134849\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 30.9961 | 1.35021 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 33.7156 | 1.46590 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.43917 | −0.192282 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −22.2068 | −0.956514 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.3578 | −0.832258 | −0.416129 | − | 0.909306i | \(-0.636613\pi\) | ||||
−0.416129 | + | 0.909306i | \(0.636613\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.12591 | 0.219168 | 0.109584 | − | 0.993978i | \(-0.465048\pi\) | ||||
0.109584 | + | 0.993978i | \(0.465048\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 37.3027 | 1.58915 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.68886 | 0.326964 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.41813 | −0.102460 | −0.0512298 | − | 0.998687i | \(-0.516314\pi\) | ||||
−0.0512298 | + | 0.998687i | \(0.516314\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.35782 | −0.353498 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.31139 | 0.223849 | 0.111924 | − | 0.993717i | \(-0.464299\pi\) | ||||
0.111924 | + | 0.993717i | \(0.464299\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.7751 | 0.912861 | 0.456430 | − | 0.889759i | \(-0.349128\pi\) | ||||
0.456430 | + | 0.889759i | \(0.349128\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.82109 | −0.285454 | −0.142727 | − | 0.989762i | \(-0.545587\pi\) | ||||
−0.142727 | + | 0.989762i | \(0.545587\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.24054 | −0.218167 | −0.109083 | − | 0.994033i | \(-0.534792\pi\) | ||||
−0.109083 | + | 0.994033i | \(0.534792\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.4951 | −0.518385 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.19961 | 0.381009 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −47.4055 | −1.95663 | −0.978316 | − | 0.207117i | \(-0.933592\pi\) | ||||
−0.978316 | + | 0.207117i | \(0.933592\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 37.1789 | 1.53193 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.2965 | −0.463890 | −0.231945 | − | 0.972729i | \(-0.574509\pi\) | ||||
−0.231945 | + | 0.972729i | \(0.574509\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −36.6829 | −1.49882 | −0.749412 | − | 0.662104i | \(-0.769664\pi\) | ||||
−0.749412 | + | 0.662104i | \(0.769664\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.3578 | 0.789622 | 0.394811 | − | 0.918762i | \(-0.370810\pi\) | ||||
0.394811 | + | 0.918762i | \(0.370810\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.28148 | −0.0520135 | −0.0260068 | − | 0.999662i | \(-0.508279\pi\) | ||||
−0.0260068 | + | 0.999662i | \(0.508279\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −34.6410 | −1.40143 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.9028 | 1.57127 | 0.785636 | − | 0.618690i | \(-0.212336\pi\) | ||||
0.785636 | + | 0.618690i | \(0.212336\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.7976 | 1.23986 | 0.619932 | − | 0.784655i | \(-0.287160\pi\) | ||||
0.619932 | + | 0.784655i | \(0.287160\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.3578 | 1.38096 | 0.690479 | − | 0.723353i | \(-0.257400\pi\) | ||||
0.690479 | + | 0.723353i | \(0.257400\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.8424 | −0.514519 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −31.3650 | −1.25061 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.5367 | 0.459270 | 0.229635 | − | 0.973277i | \(-0.426247\pi\) | ||||
0.229635 | + | 0.973277i | \(0.426247\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 34.9438 | 1.38452 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.91872 | 0.312771 | 0.156385 | − | 0.987696i | \(-0.450016\pi\) | ||||
0.156385 | + | 0.987696i | \(0.450016\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.19961 | −0.362797 | −0.181399 | − | 0.983410i | \(-0.558062\pi\) | ||||
−0.181399 | + | 0.983410i | \(0.558062\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13.7146 | −0.539177 | −0.269588 | − | 0.962976i | \(-0.586888\pi\) | ||||
−0.269588 | + | 0.962976i | \(0.586888\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −31.5367 | −1.23792 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 42.0941 | 1.64727 | 0.823634 | − | 0.567122i | \(-0.191943\pi\) | ||||
0.823634 | + | 0.567122i | \(0.191943\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.1269 | −0.939852 | −0.469926 | − | 0.882706i | \(-0.655719\pi\) | ||||
−0.469926 | + | 0.882706i | \(0.655719\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.4313 | 1.72818 | 0.864088 | − | 0.503341i | \(-0.167896\pi\) | ||||
0.864088 | + | 0.503341i | \(0.167896\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −39.1321 | −1.51520 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.03102 | −0.348639 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.6101 | 1.25703 | 0.628513 | − | 0.777799i | \(-0.283664\pi\) | ||||
0.628513 | + | 0.777799i | \(0.283664\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 50.9724 | 1.95903 | 0.979514 | − | 0.201376i | \(-0.0645412\pi\) | ||||
0.979514 | + | 0.201376i | \(0.0645412\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.3578 | −0.704508 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.3795 | 1.08591 | 0.542955 | − | 0.839762i | \(-0.317305\pi\) | ||||
0.542955 | + | 0.839762i | \(0.317305\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.4762 | −0.551498 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.7156 | 0.559809 | 0.279905 | − | 0.960028i | \(-0.409697\pi\) | ||||
0.279905 | + | 0.960028i | \(0.409697\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.07370 | 0.154302 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.2272 | 0.537353 | 0.268676 | − | 0.963230i | \(-0.413414\pi\) | ||||
0.268676 | + | 0.963230i | \(0.413414\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −37.6214 | −1.41892 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.872228 | −0.0328035 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.5367 | −0.696161 | −0.348081 | − | 0.937465i | \(-0.613166\pi\) | ||||
−0.348081 | + | 0.937465i | \(0.613166\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −39.0022 | −1.46065 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.7358 | −1.18355 | −0.591773 | − | 0.806105i | \(-0.701572\pi\) | ||||
−0.591773 | + | 0.806105i | \(0.701572\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.28437 | 0.122316 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.4432 | −1.16617 | −0.583083 | − | 0.812413i | \(-0.698154\pi\) | ||||
−0.583083 | + | 0.812413i | \(0.698154\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.66973 | 0.283675 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.12591 | −0.189330 | −0.0946649 | − | 0.995509i | \(-0.530178\pi\) | ||||
−0.0946649 | + | 0.995509i | \(0.530178\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 64.6870 | 2.38278 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.8945 | 1.24683 | 0.623415 | − | 0.781891i | \(-0.285745\pi\) | ||||
0.623415 | + | 0.781891i | \(0.285745\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −38.1300 | −1.39885 | −0.699427 | − | 0.714704i | \(-0.746562\pi\) | ||||
−0.699427 | + | 0.714704i | \(0.746562\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.3578 | 0.596905 | 0.298453 | − | 0.954424i | \(-0.403530\pi\) | ||||
0.298453 | + | 0.954424i | \(0.403530\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.6510 | −1.04134 | −0.520670 | − | 0.853758i | \(-0.674318\pi\) | ||||
−0.520670 | + | 0.853758i | \(0.674318\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.73205 | 0.0627868 | 0.0313934 | − | 0.999507i | \(-0.490006\pi\) | ||||
0.0313934 | + | 0.999507i | \(0.490006\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.97034 | 0.324748 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 49.6250 | 1.79186 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.7156 | −0.710964 | −0.355482 | − | 0.934683i | \(-0.615683\pi\) | ||||
−0.355482 | + | 0.934683i | \(0.615683\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.63772 | 0.166807 | 0.0834036 | − | 0.996516i | \(-0.473421\pi\) | ||||
0.0834036 | + | 0.996516i | \(0.473421\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.88627 | 0.175069 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.8211 | 0.816603 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.7688 | 1.63148 | 0.815740 | − | 0.578419i | \(-0.196330\pi\) | ||||
0.815740 | + | 0.578419i | \(0.196330\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.6318 | 0.413580 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.2109 | 0.504643 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.3584 | 0.933663 | 0.466832 | − | 0.884346i | \(-0.345395\pi\) | ||||
0.466832 | + | 0.884346i | \(0.345395\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31.7891 | 1.12462 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.3435 | 1.14138 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.19615 | 0.182687 | 0.0913435 | − | 0.995819i | \(-0.470884\pi\) | ||||
0.0913435 | + | 0.995819i | \(0.470884\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −49.8945 | −1.75203 | −0.876017 | − | 0.482280i | \(-0.839809\pi\) | ||||
−0.876017 | + | 0.482280i | \(0.839809\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.19961 | 0.321853 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.248992 | 0.00868988 | 0.00434494 | − | 0.999991i | \(-0.498617\pi\) | ||||
0.00434494 | + | 0.999991i | \(0.498617\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.0881 | −0.909373 | −0.454687 | − | 0.890652i | \(-0.650249\pi\) | ||||
−0.454687 | + | 0.890652i | \(0.650249\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.9701 | −0.416243 | −0.208121 | − | 0.978103i | \(-0.566735\pi\) | ||||
−0.208121 | + | 0.978103i | \(0.566735\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.17891 | 0.249334 | 0.124667 | − | 0.992199i | \(-0.460214\pi\) | ||||
0.124667 | + | 0.992199i | \(0.460214\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −32.0669 | −1.11105 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.0850 | −0.762459 | −0.381230 | − | 0.924480i | \(-0.624499\pi\) | ||||
−0.381230 | + | 0.924480i | \(0.624499\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.00000 | −0.0689655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.91813 | 0.272070 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 39.4664 | 1.35289 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40.4136 | −1.38373 | −0.691867 | − | 0.722025i | \(-0.743212\pi\) | ||||
−0.691867 | + | 0.722025i | \(0.743212\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.02103 | −0.0690371 | −0.0345186 | − | 0.999404i | \(-0.510990\pi\) | ||||
−0.0345186 | + | 0.999404i | \(0.510990\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.46327 | 0.152285 | 0.0761425 | − | 0.997097i | \(-0.475740\pi\) | ||||
0.0761425 | + | 0.997097i | \(0.475740\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.21958 | −0.0755555 | −0.0377777 | − | 0.999286i | \(-0.512028\pi\) | ||||
−0.0377777 | + | 0.999286i | \(0.512028\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.8685 | 0.843605 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −101.789 | −3.44899 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.31424 | −0.314520 | −0.157260 | − | 0.987557i | \(-0.550266\pi\) | ||||
−0.157260 | + | 0.987557i | \(0.550266\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.6111 | 1.46930 | 0.734648 | − | 0.678448i | \(-0.237347\pi\) | ||||
0.734648 | + | 0.678448i | \(0.237347\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.51074 | 0.0508406 | 0.0254203 | − | 0.999677i | \(-0.491908\pi\) | ||||
0.0254203 | + | 0.999677i | \(0.491908\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.65875 | −0.223579 | −0.111789 | − | 0.993732i | \(-0.535658\pi\) | ||||
−0.111789 | + | 0.993732i | \(0.535658\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.64218 | 0.0550771 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 38.1300 | 1.27597 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26.9104 | 0.897512 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.2844 | 0.442566 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.3777 | −0.510609 | −0.255304 | − | 0.966861i | \(-0.582176\pi\) | ||||
−0.255304 | + | 0.966861i | \(0.582176\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.4463 | −0.776810 | −0.388405 | − | 0.921489i | \(-0.626974\pi\) | ||||
−0.388405 | + | 0.921489i | \(0.626974\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −40.4136 | −1.33749 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.05585 | 0.233005 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −31.1789 | −1.02850 | −0.514249 | − | 0.857641i | \(-0.671929\pi\) | ||||
−0.514249 | + | 0.857641i | \(0.671929\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −35.9104 | −1.18201 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26.6005 | −0.872735 | −0.436367 | − | 0.899769i | \(-0.643735\pi\) | ||||
−0.436367 | + | 0.899769i | \(0.643735\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −38.4633 | −1.26058 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.95906 | −0.129337 | −0.0646685 | − | 0.997907i | \(-0.520599\pi\) | ||||
−0.0646685 | + | 0.997907i | \(0.520599\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.3650 | 1.02247 | 0.511235 | − | 0.859441i | \(-0.329188\pi\) | ||||
0.511235 | + | 0.859441i | \(0.329188\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.12591 | −0.166923 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27.0321 | −0.878425 | −0.439213 | − | 0.898383i | \(-0.644743\pi\) | ||||
−0.439213 | + | 0.898383i | \(0.644743\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −50.8945 | −1.65211 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.3584 | −0.853833 | −0.426917 | − | 0.904291i | \(-0.640400\pi\) | ||||
−0.426917 | + | 0.904291i | \(0.640400\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.4762 | −0.467460 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.17891 | −0.134803 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.4955 | 1.04498 | 0.522492 | − | 0.852644i | \(-0.325003\pi\) | ||||
0.522492 | + | 0.852644i | \(0.325003\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37.3027 | −1.19710 | −0.598550 | − | 0.801085i | \(-0.704256\pi\) | ||||
−0.598550 | + | 0.801085i | \(0.704256\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.0144 | 0.705748 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.1538 | −0.580790 | −0.290395 | − | 0.956907i | \(-0.593787\pi\) | ||||
−0.290395 | + | 0.956907i | \(0.593787\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −41.5367 | −1.32752 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −48.7528 | −1.55497 | −0.777487 | − | 0.628900i | \(-0.783506\pi\) | ||||
−0.777487 | + | 0.628900i | \(0.783506\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.65078 | −0.306877 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.53673 | 0.0488157 | 0.0244078 | − | 0.999702i | \(-0.492230\pi\) | ||||
0.0244078 | + | 0.999702i | \(0.492230\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −44.1434 | −1.39804 | −0.699018 | − | 0.715105i | \(-0.746379\pi\) | ||||
−0.699018 | + | 0.715105i | \(0.746379\pi\) | |||||||
\(998\) | 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 | 8100.2.a.be.1.6 | 8 | ||
3.2 | odd | 2 | inner | 8100.2.a.be.1.5 | 8 | ||
5.2 | odd | 4 | 1620.2.d.e.649.5 | yes | 8 | ||
5.3 | odd | 4 | 1620.2.d.e.649.6 | yes | 8 | ||
5.4 | even | 2 | inner | 8100.2.a.be.1.4 | 8 | ||
15.2 | even | 4 | 1620.2.d.e.649.4 | yes | 8 | ||
15.8 | even | 4 | 1620.2.d.e.649.3 | ✓ | 8 | ||
15.14 | odd | 2 | inner | 8100.2.a.be.1.3 | 8 | ||
45.2 | even | 12 | 1620.2.r.h.109.3 | 16 | |||
45.7 | odd | 12 | 1620.2.r.h.109.6 | 16 | |||
45.13 | odd | 12 | 1620.2.r.h.1189.6 | 16 | |||
45.22 | odd | 12 | 1620.2.r.h.1189.1 | 16 | |||
45.23 | even | 12 | 1620.2.r.h.1189.3 | 16 | |||
45.32 | even | 12 | 1620.2.r.h.1189.8 | 16 | |||
45.38 | even | 12 | 1620.2.r.h.109.8 | 16 | |||
45.43 | odd | 12 | 1620.2.r.h.109.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1620.2.d.e.649.3 | ✓ | 8 | 15.8 | even | 4 | ||
1620.2.d.e.649.4 | yes | 8 | 15.2 | even | 4 | ||
1620.2.d.e.649.5 | yes | 8 | 5.2 | odd | 4 | ||
1620.2.d.e.649.6 | yes | 8 | 5.3 | odd | 4 | ||
1620.2.r.h.109.1 | 16 | 45.43 | odd | 12 | |||
1620.2.r.h.109.3 | 16 | 45.2 | even | 12 | |||
1620.2.r.h.109.6 | 16 | 45.7 | odd | 12 | |||
1620.2.r.h.109.8 | 16 | 45.38 | even | 12 | |||
1620.2.r.h.1189.1 | 16 | 45.22 | odd | 12 | |||
1620.2.r.h.1189.3 | 16 | 45.23 | even | 12 | |||
1620.2.r.h.1189.6 | 16 | 45.13 | odd | 12 | |||
1620.2.r.h.1189.8 | 16 | 45.32 | even | 12 | |||
8100.2.a.be.1.3 | 8 | 15.14 | odd | 2 | inner | ||
8100.2.a.be.1.4 | 8 | 5.4 | even | 2 | inner | ||
8100.2.a.be.1.5 | 8 | 3.2 | odd | 2 | inner | ||
8100.2.a.be.1.6 | 8 | 1.1 | even | 1 | trivial |