Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5625,2,Mod(1,5625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5625, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5625 = 3^{2} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5625.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: | \(44.9158511370\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.5444000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 2x^{6} + 20x^{5} - 4x^{4} - 30x^{3} + 7x^{2} + 12x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 75) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(1.53655\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5625.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.53655 | 1.08650 | 0.543251 | − | 0.839570i | \(-0.317193\pi\) | ||||
0.543251 | + | 0.839570i | \(0.317193\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.360976 | 0.180488 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.49550 | −0.565244 | −0.282622 | − | 0.959231i | \(-0.591204\pi\) | ||||
−0.282622 | + | 0.959231i | \(0.591204\pi\) | |||||||
\(8\) | −2.51844 | −0.890402 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.35626 | 0.710438 | 0.355219 | − | 0.934783i | \(-0.384406\pi\) | ||||
0.355219 | + | 0.934783i | \(0.384406\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.34951 | −0.374286 | −0.187143 | − | 0.982333i | \(-0.559923\pi\) | ||||
−0.187143 | + | 0.982333i | \(0.559923\pi\) | |||||||
\(14\) | −2.29790 | −0.614140 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.59165 | −1.14791 | ||||||||
\(17\) | −2.19405 | −0.532135 | −0.266068 | − | 0.963954i | \(-0.585724\pi\) | ||||
−0.266068 | + | 0.963954i | \(0.585724\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.71069 | 1.31012 | 0.655061 | − | 0.755576i | \(-0.272643\pi\) | ||||
0.655061 | + | 0.755576i | \(0.272643\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.62050 | 0.771892 | ||||||||
\(23\) | 8.79501 | 1.83389 | 0.916943 | − | 0.399018i | \(-0.130649\pi\) | ||||
0.916943 | + | 0.399018i | \(0.130649\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.07358 | −0.406662 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.539839 | −0.102020 | ||||||||
\(29\) | −7.90017 | −1.46702 | −0.733512 | − | 0.679676i | \(-0.762120\pi\) | ||||
−0.733512 | + | 0.679676i | \(0.762120\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.69717 | −0.664031 | −0.332016 | − | 0.943274i | \(-0.607729\pi\) | ||||
−0.332016 | + | 0.943274i | \(0.607729\pi\) | |||||||
\(32\) | −2.01841 | −0.356808 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.37126 | −0.578167 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.75097 | −1.60305 | −0.801525 | − | 0.597962i | \(-0.795977\pi\) | ||||
−0.801525 | + | 0.597962i | \(0.795977\pi\) | |||||||
\(38\) | 8.77474 | 1.42345 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.85550 | −0.289780 | −0.144890 | − | 0.989448i | \(-0.546283\pi\) | ||||
−0.144890 | + | 0.989448i | \(0.546283\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.01874 | 1.22285 | 0.611423 | − | 0.791304i | \(-0.290597\pi\) | ||||
0.611423 | + | 0.791304i | \(0.290597\pi\) | |||||||
\(44\) | 0.850553 | 0.128226 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 13.5139 | 1.99252 | ||||||||
\(47\) | 6.66298 | 0.971895 | 0.485948 | − | 0.873988i | \(-0.338475\pi\) | ||||
0.485948 | + | 0.873988i | \(0.338475\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.76349 | −0.680499 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.487140 | −0.0675542 | ||||||||
\(53\) | 4.17153 | 0.573003 | 0.286502 | − | 0.958080i | \(-0.407508\pi\) | ||||
0.286502 | + | 0.958080i | \(0.407508\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.76631 | 0.503295 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −12.1390 | −1.59393 | ||||||||
\(59\) | −11.0647 | −1.44050 | −0.720248 | − | 0.693716i | \(-0.755972\pi\) | ||||
−0.720248 | + | 0.693716i | \(0.755972\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.2372 | −1.56682 | −0.783408 | − | 0.621508i | \(-0.786520\pi\) | ||||
−0.783408 | + | 0.621508i | \(0.786520\pi\) | |||||||
\(62\) | −5.68088 | −0.721472 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.08192 | 0.760239 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.31358 | −0.526988 | −0.263494 | − | 0.964661i | \(-0.584875\pi\) | ||||
−0.263494 | + | 0.964661i | \(0.584875\pi\) | |||||||
\(68\) | −0.792000 | −0.0960442 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.77750 | −0.685663 | −0.342832 | − | 0.939397i | \(-0.611386\pi\) | ||||
−0.342832 | + | 0.939397i | \(0.611386\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.92684 | −0.810725 | −0.405362 | − | 0.914156i | \(-0.632855\pi\) | ||||
−0.405362 | + | 0.914156i | \(0.632855\pi\) | |||||||
\(74\) | −14.9828 | −1.74172 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.06142 | 0.236461 | ||||||||
\(77\) | −3.52377 | −0.401571 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.6687 | −1.20033 | −0.600163 | − | 0.799878i | \(-0.704898\pi\) | ||||
−0.600163 | + | 0.799878i | \(0.704898\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.85106 | −0.314846 | ||||||||
\(83\) | 0.224003 | 0.0245875 | 0.0122938 | − | 0.999924i | \(-0.496087\pi\) | ||||
0.0122938 | + | 0.999924i | \(0.496087\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 12.3212 | 1.32863 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.93408 | −0.632575 | ||||||||
\(89\) | −0.429167 | −0.0454916 | −0.0227458 | − | 0.999741i | \(-0.507241\pi\) | ||||
−0.0227458 | + | 0.999741i | \(0.507241\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.01818 | 0.211563 | ||||||||
\(92\) | 3.17479 | 0.330995 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.2380 | 1.05597 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.4945 | −1.26863 | −0.634315 | − | 0.773075i | \(-0.718718\pi\) | ||||
−0.634315 | + | 0.773075i | \(0.718718\pi\) | |||||||
\(98\) | −7.31933 | −0.739364 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.19767 | −0.815698 | −0.407849 | − | 0.913049i | \(-0.633721\pi\) | ||||
−0.407849 | + | 0.913049i | \(0.633721\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.50005 | −0.246337 | −0.123169 | − | 0.992386i | \(-0.539306\pi\) | ||||
−0.123169 | + | 0.992386i | \(0.539306\pi\) | |||||||
\(104\) | 3.39865 | 0.333265 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.40975 | 0.622570 | ||||||||
\(107\) | −1.81004 | −0.174983 | −0.0874914 | − | 0.996165i | \(-0.527885\pi\) | ||||
−0.0874914 | + | 0.996165i | \(0.527885\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.94778 | −0.282346 | −0.141173 | − | 0.989985i | \(-0.545087\pi\) | ||||
−0.141173 | + | 0.989985i | \(0.545087\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 6.86679 | 0.648851 | ||||||||
\(113\) | 13.8365 | 1.30163 | 0.650813 | − | 0.759238i | \(-0.274428\pi\) | ||||
0.650813 | + | 0.759238i | \(0.274428\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.85178 | −0.264781 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −17.0014 | −1.56510 | ||||||||
\(119\) | 3.28119 | 0.300787 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.44806 | −0.495278 | ||||||||
\(122\) | −18.8031 | −1.70235 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.33459 | −0.119850 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.73995 | −0.509338 | −0.254669 | − | 0.967028i | \(-0.581967\pi\) | ||||
−0.254669 | + | 0.967028i | \(0.581967\pi\) | |||||||
\(128\) | 13.3820 | 1.18281 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.35756 | 0.380722 | 0.190361 | − | 0.981714i | \(-0.439034\pi\) | ||||
0.190361 | + | 0.981714i | \(0.439034\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.54031 | −0.740539 | ||||||||
\(134\) | −6.62802 | −0.572574 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.52558 | 0.473814 | ||||||||
\(137\) | 1.97461 | 0.168702 | 0.0843510 | − | 0.996436i | \(-0.473118\pi\) | ||||
0.0843510 | + | 0.996436i | \(0.473118\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.67910 | 0.142419 | 0.0712095 | − | 0.997461i | \(-0.477314\pi\) | ||||
0.0712095 | + | 0.997461i | \(0.477314\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.87740 | −0.744975 | ||||||||
\(143\) | −3.17978 | −0.265907 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −10.6434 | −0.880855 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.51987 | −0.289331 | ||||||||
\(149\) | 7.38524 | 0.605023 | 0.302511 | − | 0.953146i | \(-0.402175\pi\) | ||||
0.302511 | + | 0.953146i | \(0.402175\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.26137 | −0.346785 | −0.173393 | − | 0.984853i | \(-0.555473\pi\) | ||||
−0.173393 | + | 0.984853i | \(0.555473\pi\) | |||||||
\(152\) | −14.3820 | −1.16653 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.41444 | −0.436308 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.0573 | −1.28152 | −0.640758 | − | 0.767743i | \(-0.721380\pi\) | ||||
−0.640758 | + | 0.767743i | \(0.721380\pi\) | |||||||
\(158\) | −16.3930 | −1.30416 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.1529 | −1.03659 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.2938 | 1.74618 | 0.873092 | − | 0.487556i | \(-0.162111\pi\) | ||||
0.873092 | + | 0.487556i | \(0.162111\pi\) | |||||||
\(164\) | −0.669790 | −0.0523018 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.344191 | 0.0267144 | ||||||||
\(167\) | −6.46601 | −0.500355 | −0.250177 | − | 0.968200i | \(-0.580489\pi\) | ||||
−0.250177 | + | 0.968200i | \(0.580489\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.1788 | −0.859910 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.89458 | 0.220709 | ||||||||
\(173\) | −11.8180 | −0.898509 | −0.449255 | − | 0.893404i | \(-0.648310\pi\) | ||||
−0.449255 | + | 0.893404i | \(0.648310\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −10.8191 | −0.815520 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.659435 | −0.0494268 | ||||||||
\(179\) | −15.5746 | −1.16410 | −0.582049 | − | 0.813154i | \(-0.697749\pi\) | ||||
−0.582049 | + | 0.813154i | \(0.697749\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.5797 | −1.08370 | −0.541851 | − | 0.840475i | \(-0.682276\pi\) | ||||
−0.541851 | + | 0.840475i | \(0.682276\pi\) | |||||||
\(182\) | 3.10103 | 0.229864 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −22.1497 | −1.63290 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.16974 | −0.378049 | ||||||||
\(188\) | 2.40518 | 0.175416 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.9884 | 1.51867 | 0.759333 | − | 0.650702i | \(-0.225525\pi\) | ||||
0.759333 | + | 0.650702i | \(0.225525\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.7094 | −1.63466 | −0.817328 | − | 0.576173i | \(-0.804546\pi\) | ||||
−0.817328 | + | 0.576173i | \(0.804546\pi\) | |||||||
\(194\) | −19.1985 | −1.37837 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.71951 | −0.122822 | ||||||||
\(197\) | 1.35341 | 0.0964268 | 0.0482134 | − | 0.998837i | \(-0.484647\pi\) | ||||
0.0482134 | + | 0.998837i | \(0.484647\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.96061 | −0.635201 | −0.317600 | − | 0.948225i | \(-0.602877\pi\) | ||||
−0.317600 | + | 0.948225i | \(0.602877\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −12.5961 | −0.886259 | ||||||||
\(203\) | 11.8147 | 0.829228 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.84145 | −0.267646 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.19646 | 0.429647 | ||||||||
\(209\) | 13.4558 | 0.930760 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.83983 | 0.402031 | 0.201015 | − | 0.979588i | \(-0.435576\pi\) | ||||
0.201015 | + | 0.979588i | \(0.435576\pi\) | |||||||
\(212\) | 1.50582 | 0.103420 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.78121 | −0.190119 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.52910 | 0.375340 | ||||||||
\(218\) | −4.52939 | −0.306769 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.96088 | 0.199171 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.82097 | 0.523731 | 0.261865 | − | 0.965104i | \(-0.415662\pi\) | ||||
0.261865 | + | 0.965104i | \(0.415662\pi\) | |||||||
\(224\) | 3.01853 | 0.201684 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 21.2604 | 1.41422 | ||||||||
\(227\) | 16.3090 | 1.08246 | 0.541232 | − | 0.840873i | \(-0.317958\pi\) | ||||
0.541232 | + | 0.840873i | \(0.317958\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.7088 | −1.43456 | −0.717278 | − | 0.696787i | \(-0.754612\pi\) | ||||
−0.717278 | + | 0.696787i | \(0.754612\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 19.8961 | 1.30624 | ||||||||
\(233\) | −13.5341 | −0.886646 | −0.443323 | − | 0.896362i | \(-0.646201\pi\) | ||||
−0.443323 | + | 0.896362i | \(0.646201\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.99408 | −0.259993 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.04171 | 0.326805 | ||||||||
\(239\) | 10.5338 | 0.681377 | 0.340689 | − | 0.940176i | \(-0.389340\pi\) | ||||
0.340689 | + | 0.940176i | \(0.389340\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.4838 | 1.25506 | 0.627530 | − | 0.778592i | \(-0.284066\pi\) | ||||
0.627530 | + | 0.778592i | \(0.284066\pi\) | |||||||
\(242\) | −8.37120 | −0.538121 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.41735 | −0.282792 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.70661 | −0.490360 | ||||||||
\(248\) | 9.31109 | 0.591255 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.9446 | 1.32201 | 0.661007 | − | 0.750380i | \(-0.270129\pi\) | ||||
0.661007 | + | 0.750380i | \(0.270129\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.7233 | 1.30286 | ||||||||
\(254\) | −8.81971 | −0.553398 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.39819 | 0.524887 | ||||||||
\(257\) | −1.67121 | −0.104247 | −0.0521237 | − | 0.998641i | \(-0.516599\pi\) | ||||
−0.0521237 | + | 0.998641i | \(0.516599\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.5825 | 0.906115 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.69559 | 0.413655 | ||||||||
\(263\) | 7.55667 | 0.465964 | 0.232982 | − | 0.972481i | \(-0.425152\pi\) | ||||
0.232982 | + | 0.972481i | \(0.425152\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −13.1226 | −0.804597 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.55710 | −0.0951151 | ||||||||
\(269\) | 11.2841 | 0.688005 | 0.344002 | − | 0.938969i | \(-0.388217\pi\) | ||||
0.344002 | + | 0.938969i | \(0.388217\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.9752 | −0.666696 | −0.333348 | − | 0.942804i | \(-0.608178\pi\) | ||||
−0.333348 | + | 0.942804i | \(0.608178\pi\) | |||||||
\(272\) | 10.0743 | 0.610845 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.03407 | 0.183295 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.75112 | 0.345551 | 0.172776 | − | 0.984961i | \(-0.444726\pi\) | ||||
0.172776 | + | 0.984961i | \(0.444726\pi\) | |||||||
\(278\) | 2.58001 | 0.154739 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.49962 | −0.507045 | −0.253522 | − | 0.967330i | \(-0.581589\pi\) | ||||
−0.253522 | + | 0.967330i | \(0.581589\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.2248 | 1.02391 | 0.511955 | − | 0.859013i | \(-0.328922\pi\) | ||||
0.511955 | + | 0.859013i | \(0.328922\pi\) | |||||||
\(284\) | −2.08554 | −0.123754 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.88588 | −0.288908 | ||||||||
\(287\) | 2.77489 | 0.163796 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.1861 | −0.716832 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.50042 | −0.146326 | ||||||||
\(293\) | 9.38764 | 0.548432 | 0.274216 | − | 0.961668i | \(-0.411582\pi\) | ||||
0.274216 | + | 0.961668i | \(0.411582\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 24.5572 | 1.42736 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 11.3478 | 0.657359 | ||||||||
\(299\) | −11.8689 | −0.686397 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.9920 | −0.691207 | ||||||||
\(302\) | −6.54779 | −0.376783 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −26.2215 | −1.50390 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.6465 | −0.607627 | −0.303814 | − | 0.952731i | \(-0.598260\pi\) | ||||
−0.303814 | + | 0.952731i | \(0.598260\pi\) | |||||||
\(308\) | −1.27200 | −0.0724788 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.3572 | 1.55128 | 0.775641 | − | 0.631174i | \(-0.217427\pi\) | ||||
0.775641 | + | 0.631174i | \(0.217427\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.99509 | 0.112769 | 0.0563846 | − | 0.998409i | \(-0.482043\pi\) | ||||
0.0563846 | + | 0.998409i | \(0.482043\pi\) | |||||||
\(314\) | −24.6729 | −1.39237 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.85116 | −0.216645 | ||||||||
\(317\) | 8.64876 | 0.485763 | 0.242881 | − | 0.970056i | \(-0.421907\pi\) | ||||
0.242881 | + | 0.970056i | \(0.421907\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.6148 | −1.04223 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −20.2101 | −1.12626 | ||||||||
\(323\) | −12.5295 | −0.697162 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 34.2554 | 1.89723 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.67295 | 0.258020 | ||||||||
\(329\) | −9.96446 | −0.549358 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.94331 | −0.216744 | −0.108372 | − | 0.994110i | \(-0.534564\pi\) | ||||
−0.108372 | + | 0.994110i | \(0.534564\pi\) | |||||||
\(332\) | 0.0808598 | 0.00443776 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −9.93532 | −0.543637 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.95471 | −0.215427 | −0.107713 | − | 0.994182i | \(-0.534353\pi\) | ||||
−0.107713 | + | 0.994182i | \(0.534353\pi\) | |||||||
\(338\) | −17.1768 | −0.934295 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.71148 | −0.471753 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.5923 | 0.949893 | ||||||||
\(344\) | −20.1947 | −1.08882 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.1590 | −0.976233 | ||||||||
\(347\) | −9.99596 | −0.536611 | −0.268306 | − | 0.963334i | \(-0.586464\pi\) | ||||
−0.268306 | + | 0.963334i | \(0.586464\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.4534 | 0.987789 | 0.493895 | − | 0.869522i | \(-0.335573\pi\) | ||||
0.493895 | + | 0.869522i | \(0.335573\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.75589 | −0.253490 | ||||||||
\(353\) | 9.32398 | 0.496265 | 0.248133 | − | 0.968726i | \(-0.420183\pi\) | ||||
0.248133 | + | 0.968726i | \(0.420183\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.154919 | −0.00821070 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −23.9311 | −1.26480 | ||||||||
\(359\) | −28.9438 | −1.52759 | −0.763797 | − | 0.645457i | \(-0.776667\pi\) | ||||
−0.763797 | + | 0.645457i | \(0.776667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.6119 | 0.716418 | ||||||||
\(362\) | −22.4024 | −1.17744 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.728516 | 0.0381846 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.99869 | 0.208730 | 0.104365 | − | 0.994539i | \(-0.466719\pi\) | ||||
0.104365 | + | 0.994539i | \(0.466719\pi\) | |||||||
\(368\) | −40.3836 | −2.10514 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.23850 | −0.323887 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.17260 | 0.164271 | 0.0821354 | − | 0.996621i | \(-0.473826\pi\) | ||||
0.0821354 | + | 0.996621i | \(0.473826\pi\) | |||||||
\(374\) | −7.94355 | −0.410751 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −16.7803 | −0.865377 | ||||||||
\(377\) | 10.6613 | 0.549086 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.5206 | 1.46500 | 0.732501 | − | 0.680766i | \(-0.238353\pi\) | ||||
0.732501 | + | 0.680766i | \(0.238353\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 32.2497 | 1.65004 | ||||||||
\(383\) | −11.4611 | −0.585636 | −0.292818 | − | 0.956168i | \(-0.594593\pi\) | ||||
−0.292818 | + | 0.956168i | \(0.594593\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −34.8940 | −1.77606 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.51024 | −0.228973 | ||||||||
\(389\) | −34.2463 | −1.73636 | −0.868179 | − | 0.496252i | \(-0.834709\pi\) | ||||
−0.868179 | + | 0.496252i | \(0.834709\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.2967 | −0.975876 | ||||||||
\(392\) | 11.9966 | 0.605917 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.07958 | 0.104768 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.0333 | 1.00545 | 0.502723 | − | 0.864448i | \(-0.332332\pi\) | ||||
0.502723 | + | 0.864448i | \(0.332332\pi\) | |||||||
\(398\) | −13.7684 | −0.690148 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.98200 | −0.248789 | −0.124395 | − | 0.992233i | \(-0.539699\pi\) | ||||
−0.124395 | + | 0.992233i | \(0.539699\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.98935 | 0.248537 | ||||||||
\(404\) | −2.95916 | −0.147224 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 18.1538 | 0.900958 | ||||||||
\(407\) | −22.9758 | −1.13887 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.8591 | 1.17976 | 0.589878 | − | 0.807493i | \(-0.299176\pi\) | ||||
0.589878 | + | 0.807493i | \(0.299176\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.902460 | −0.0444610 | ||||||||
\(413\) | 16.5472 | 0.814233 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.72386 | 0.133548 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 20.6755 | 1.01127 | ||||||||
\(419\) | −0.482550 | −0.0235741 | −0.0117871 | − | 0.999931i | \(-0.503752\pi\) | ||||
−0.0117871 | + | 0.999931i | \(0.503752\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.7183 | −0.863537 | −0.431769 | − | 0.901984i | \(-0.642110\pi\) | ||||
−0.431769 | + | 0.901984i | \(0.642110\pi\) | |||||||
\(422\) | 8.97317 | 0.436807 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10.5057 | −0.510203 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.3007 | 0.885634 | ||||||||
\(428\) | −0.653380 | −0.0315823 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.8061 | −1.29121 | −0.645603 | − | 0.763673i | \(-0.723394\pi\) | ||||
−0.645603 | + | 0.763673i | \(0.723394\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.23115 | 0.443621 | 0.221810 | − | 0.975090i | \(-0.428803\pi\) | ||||
0.221810 | + | 0.975090i | \(0.428803\pi\) | |||||||
\(434\) | 8.49573 | 0.407808 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.06408 | −0.0509601 | ||||||||
\(437\) | 50.2255 | 2.40261 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.00240 | 0.0478421 | 0.0239211 | − | 0.999714i | \(-0.492385\pi\) | ||||
0.0239211 | + | 0.999714i | \(0.492385\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.54954 | 0.216399 | ||||||||
\(443\) | −26.2872 | −1.24894 | −0.624471 | − | 0.781048i | \(-0.714685\pi\) | ||||
−0.624471 | + | 0.781048i | \(0.714685\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 12.0173 | 0.569035 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −9.09548 | −0.429721 | ||||||||
\(449\) | −4.75449 | −0.224378 | −0.112189 | − | 0.993687i | \(-0.535786\pi\) | ||||
−0.112189 | + | 0.993687i | \(0.535786\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.37202 | −0.205870 | ||||||||
\(452\) | 4.99464 | 0.234928 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 25.0595 | 1.17610 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.9703 | −0.747059 | −0.373529 | − | 0.927618i | \(-0.621852\pi\) | ||||
−0.373529 | + | 0.927618i | \(0.621852\pi\) | |||||||
\(458\) | −33.3566 | −1.55865 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −39.7558 | −1.85161 | −0.925806 | − | 0.377998i | \(-0.876613\pi\) | ||||
−0.925806 | + | 0.377998i | \(0.876613\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.1209 | 1.21394 | 0.606971 | − | 0.794724i | \(-0.292384\pi\) | ||||
0.606971 | + | 0.794724i | \(0.292384\pi\) | |||||||
\(464\) | 36.2748 | 1.68402 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.7957 | −0.963343 | ||||||||
\(467\) | 3.85204 | 0.178251 | 0.0891256 | − | 0.996020i | \(-0.471593\pi\) | ||||
0.0891256 | + | 0.996020i | \(0.471593\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.45095 | 0.297877 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 27.8657 | 1.28262 | ||||||||
\(473\) | 18.8942 | 0.868756 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.18443 | 0.0542884 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 16.1857 | 0.740318 | ||||||||
\(479\) | 14.2698 | 0.652004 | 0.326002 | − | 0.945369i | \(-0.394298\pi\) | ||||
0.326002 | + | 0.945369i | \(0.394298\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.1590 | 0.599998 | ||||||||
\(482\) | 29.9377 | 1.36363 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.96662 | −0.0893919 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.8222 | 1.12480 | 0.562401 | − | 0.826865i | \(-0.309878\pi\) | ||||
0.562401 | + | 0.826865i | \(0.309878\pi\) | |||||||
\(488\) | 30.8187 | 1.39510 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.4893 | −0.518507 | −0.259253 | − | 0.965809i | \(-0.583476\pi\) | ||||
−0.259253 | + | 0.965809i | \(0.583476\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.3334 | 0.780656 | ||||||||
\(494\) | −11.8416 | −0.532777 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 16.9761 | 0.762250 | ||||||||
\(497\) | 8.64023 | 0.387567 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.17487 | −0.186893 | −0.0934465 | − | 0.995624i | \(-0.529788\pi\) | ||||
−0.0934465 | + | 0.995624i | \(0.529788\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 32.1824 | 1.43637 | ||||||||
\(503\) | −38.7163 | −1.72627 | −0.863137 | − | 0.504970i | \(-0.831503\pi\) | ||||
−0.863137 | + | 0.504970i | \(0.831503\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 31.8423 | 1.41556 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.07199 | −0.0919296 | ||||||||
\(509\) | −30.1797 | −1.33769 | −0.668845 | − | 0.743402i | \(-0.733211\pi\) | ||||
−0.668845 | + | 0.743402i | \(0.733211\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.3591 | 0.458258 | ||||||||
\(512\) | −13.8597 | −0.612519 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.56790 | −0.113265 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.6997 | 0.690471 | ||||||||
\(518\) | 22.4067 | 0.984496 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.4856 | 1.11654 | 0.558272 | − | 0.829658i | \(-0.311464\pi\) | ||||
0.558272 | + | 0.829658i | \(0.311464\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.89180 | −0.170176 | −0.0850882 | − | 0.996373i | \(-0.527117\pi\) | ||||
−0.0850882 | + | 0.996373i | \(0.527117\pi\) | |||||||
\(524\) | 1.57298 | 0.0687158 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.6112 | 0.506271 | ||||||||
\(527\) | 8.11178 | 0.353355 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 54.3522 | 2.36314 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.08285 | −0.133659 | ||||||||
\(533\) | 2.50400 | 0.108460 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 10.8635 | 0.469231 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 17.3386 | 0.747519 | ||||||||
\(539\) | −11.2240 | −0.483452 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.2148 | 1.72897 | 0.864484 | − | 0.502661i | \(-0.167646\pi\) | ||||
0.864484 | + | 0.502661i | \(0.167646\pi\) | |||||||
\(542\) | −16.8639 | −0.724367 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.42849 | 0.189870 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.37923 | −0.315513 | −0.157757 | − | 0.987478i | \(-0.550426\pi\) | ||||
−0.157757 | + | 0.987478i | \(0.550426\pi\) | |||||||
\(548\) | 0.712786 | 0.0304487 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −45.1154 | −1.92198 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.9550 | 0.678478 | ||||||||
\(554\) | 8.83686 | 0.375442 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.606114 | 0.0257050 | ||||||||
\(557\) | 1.52499 | 0.0646160 | 0.0323080 | − | 0.999478i | \(-0.489714\pi\) | ||||
0.0323080 | + | 0.999478i | \(0.489714\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.8213 | −0.457694 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.0601 | −0.550905 | ||||||||
\(563\) | 13.7955 | 0.581411 | 0.290706 | − | 0.956813i | \(-0.406110\pi\) | ||||
0.290706 | + | 0.956813i | \(0.406110\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 26.4667 | 1.11248 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14.5503 | 0.610516 | ||||||||
\(569\) | 8.49904 | 0.356298 | 0.178149 | − | 0.984004i | \(-0.442989\pi\) | ||||
0.178149 | + | 0.984004i | \(0.442989\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39.3230 | 1.64562 | 0.822809 | − | 0.568319i | \(-0.192406\pi\) | ||||
0.822809 | + | 0.568319i | \(0.192406\pi\) | |||||||
\(572\) | −1.14783 | −0.0479930 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.26374 | 0.177965 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.5832 | −1.02341 | −0.511707 | − | 0.859160i | \(-0.670987\pi\) | ||||
−0.511707 | + | 0.859160i | \(0.670987\pi\) | |||||||
\(578\) | −18.7246 | −0.778840 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.334995 | −0.0138980 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.82918 | 0.407083 | ||||||||
\(584\) | 17.4448 | 0.721871 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.4245 | 0.595872 | ||||||||
\(587\) | −9.24270 | −0.381487 | −0.190744 | − | 0.981640i | \(-0.561090\pi\) | ||||
−0.190744 | + | 0.981640i | \(0.561090\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.1134 | −0.869962 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 44.7730 | 1.84016 | ||||||||
\(593\) | −6.07888 | −0.249630 | −0.124815 | − | 0.992180i | \(-0.539834\pi\) | ||||
−0.124815 | + | 0.992180i | \(0.539834\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.66590 | 0.109199 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −18.2372 | −0.745773 | ||||||||
\(599\) | −6.40129 | −0.261550 | −0.130775 | − | 0.991412i | \(-0.541746\pi\) | ||||
−0.130775 | + | 0.991412i | \(0.541746\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −38.4675 | −1.56912 | −0.784560 | − | 0.620052i | \(-0.787111\pi\) | ||||
−0.784560 | + | 0.620052i | \(0.787111\pi\) | |||||||
\(602\) | −18.4263 | −0.750999 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.53825 | −0.0625906 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.22464 | −0.212062 | −0.106031 | − | 0.994363i | \(-0.533814\pi\) | ||||
−0.106031 | + | 0.994363i | \(0.533814\pi\) | |||||||
\(608\) | −11.5265 | −0.467462 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.99173 | −0.363766 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.8153 | −1.20423 | −0.602114 | − | 0.798410i | \(-0.705675\pi\) | ||||
−0.602114 | + | 0.798410i | \(0.705675\pi\) | |||||||
\(614\) | −16.3588 | −0.660189 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.87439 | 0.357559 | ||||||||
\(617\) | 23.3025 | 0.938124 | 0.469062 | − | 0.883165i | \(-0.344592\pi\) | ||||
0.469062 | + | 0.883165i | \(0.344592\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.236492 | −0.00950543 | −0.00475272 | − | 0.999989i | \(-0.501513\pi\) | ||||
−0.00475272 | + | 0.999989i | \(0.501513\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 42.0356 | 1.68547 | ||||||||
\(623\) | 0.641818 | 0.0257139 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3.06555 | 0.122524 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.79632 | −0.231298 | ||||||||
\(629\) | 21.3941 | 0.853039 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.8789 | −0.711748 | −0.355874 | − | 0.934534i | \(-0.615817\pi\) | ||||
−0.355874 | + | 0.934534i | \(0.615817\pi\) | |||||||
\(632\) | 26.8685 | 1.06877 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.2892 | 0.527782 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.42836 | 0.254701 | ||||||||
\(638\) | −28.6025 | −1.13239 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.8680 | −0.429259 | −0.214630 | − | 0.976695i | \(-0.568854\pi\) | ||||
−0.214630 | + | 0.976695i | \(0.568854\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.09039 | −0.121873 | −0.0609366 | − | 0.998142i | \(-0.519409\pi\) | ||||
−0.0609366 | + | 0.998142i | \(0.519409\pi\) | |||||||
\(644\) | −4.74789 | −0.187093 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −19.2522 | −0.757468 | ||||||||
\(647\) | −5.53705 | −0.217684 | −0.108842 | − | 0.994059i | \(-0.534714\pi\) | ||||
−0.108842 | + | 0.994059i | \(0.534714\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −26.0712 | −1.02338 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.04753 | 0.315166 | ||||||||
\(653\) | 38.8754 | 1.52131 | 0.760657 | − | 0.649154i | \(-0.224877\pi\) | ||||
0.760657 | + | 0.649154i | \(0.224877\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 8.51978 | 0.332642 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −15.3109 | −0.596879 | ||||||||
\(659\) | 20.5389 | 0.800082 | 0.400041 | − | 0.916497i | \(-0.368996\pi\) | ||||
0.400041 | + | 0.916497i | \(0.368996\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.4254 | 1.49457 | 0.747287 | − | 0.664502i | \(-0.231356\pi\) | ||||
0.747287 | + | 0.664502i | \(0.231356\pi\) | |||||||
\(662\) | −6.05907 | −0.235493 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.564137 | −0.0218928 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −69.4821 | −2.69036 | ||||||||
\(668\) | −2.33408 | −0.0903081 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.8340 | −1.11313 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.9819 | 0.500417 | 0.250208 | − | 0.968192i | \(-0.419501\pi\) | ||||
0.250208 | + | 0.968192i | \(0.419501\pi\) | |||||||
\(674\) | −6.07660 | −0.234062 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.03529 | −0.155204 | ||||||||
\(677\) | 7.23957 | 0.278239 | 0.139120 | − | 0.990276i | \(-0.455573\pi\) | ||||
0.139120 | + | 0.990276i | \(0.455573\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.6855 | 0.717086 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −13.3856 | −0.512561 | ||||||||
\(683\) | 24.8800 | 0.952005 | 0.476003 | − | 0.879444i | \(-0.342085\pi\) | ||||
0.476003 | + | 0.879444i | \(0.342085\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 27.0313 | 1.03206 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −36.8192 | −1.40372 | ||||||||
\(689\) | −5.62950 | −0.214467 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.2706 | −1.26567 | −0.632836 | − | 0.774286i | \(-0.718109\pi\) | ||||
−0.632836 | + | 0.774286i | \(0.718109\pi\) | |||||||
\(692\) | −4.26604 | −0.162170 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −15.3593 | −0.583029 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.07105 | 0.154202 | ||||||||
\(698\) | 28.3546 | 1.07324 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.2163 | 0.499173 | 0.249586 | − | 0.968353i | \(-0.419705\pi\) | ||||
0.249586 | + | 0.968353i | \(0.419705\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −55.6847 | −2.10019 | ||||||||
\(704\) | 14.3305 | 0.540103 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.3267 | 0.539194 | ||||||||
\(707\) | 12.2596 | 0.461069 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.25068 | 0.234749 | 0.117375 | − | 0.993088i | \(-0.462552\pi\) | ||||
0.117375 | + | 0.993088i | \(0.462552\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.08083 | 0.0405058 | ||||||||
\(713\) | −32.5167 | −1.21776 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.62205 | −0.210106 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −44.4735 | −1.65973 | ||||||||
\(719\) | −27.5016 | −1.02564 | −0.512818 | − | 0.858497i | \(-0.671398\pi\) | ||||
−0.512818 | + | 0.858497i | \(0.671398\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.73882 | 0.139241 | ||||||||
\(722\) | 20.9154 | 0.778390 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.26293 | −0.195595 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.0397 | 0.817406 | 0.408703 | − | 0.912668i | \(-0.365981\pi\) | ||||
0.408703 | + | 0.912668i | \(0.365981\pi\) | |||||||
\(728\) | −5.08266 | −0.188376 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.5935 | −0.650720 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.7134 | −1.28217 | −0.641085 | − | 0.767470i | \(-0.721515\pi\) | ||||
−0.641085 | + | 0.767470i | \(0.721515\pi\) | |||||||
\(734\) | 6.14417 | 0.226785 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −17.7519 | −0.654345 | ||||||||
\(737\) | −10.1639 | −0.374392 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.58593 | −0.279053 | −0.139526 | − | 0.990218i | \(-0.544558\pi\) | ||||
−0.139526 | + | 0.990218i | \(0.544558\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.58575 | −0.351904 | ||||||||
\(743\) | 27.5328 | 1.01008 | 0.505040 | − | 0.863096i | \(-0.331478\pi\) | ||||
0.505040 | + | 0.863096i | \(0.331478\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4.87484 | 0.178481 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.86615 | −0.0682334 | ||||||||
\(749\) | 2.70690 | 0.0989081 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.24930 | 0.155059 | 0.0775296 | − | 0.996990i | \(-0.475297\pi\) | ||||
0.0775296 | + | 0.996990i | \(0.475297\pi\) | |||||||
\(752\) | −30.5940 | −1.11565 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 16.3816 | 0.596584 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.6609 | 1.65957 | 0.829787 | − | 0.558081i | \(-0.188462\pi\) | ||||
0.829787 | + | 0.558081i | \(0.188462\pi\) | |||||||
\(758\) | 43.8232 | 1.59173 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.1268 | 1.45460 | 0.727298 | − | 0.686322i | \(-0.240776\pi\) | ||||
0.727298 | + | 0.686322i | \(0.240776\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.40839 | 0.159594 | ||||||||
\(764\) | 7.57631 | 0.274101 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17.6105 | −0.636295 | ||||||||
\(767\) | 14.9318 | 0.539157 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37.8350 | −1.36437 | −0.682183 | − | 0.731181i | \(-0.738969\pi\) | ||||
−0.682183 | + | 0.731181i | \(0.738969\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.19755 | −0.295036 | ||||||||
\(773\) | −26.2148 | −0.942881 | −0.471441 | − | 0.881898i | \(-0.656266\pi\) | ||||
−0.471441 | + | 0.881898i | \(0.656266\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 31.4667 | 1.12959 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −52.6211 | −1.88656 | ||||||||
\(779\) | −10.5962 | −0.379646 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.6133 | −0.487121 | ||||||||
\(782\) | −29.6503 | −1.06029 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 21.8723 | 0.781153 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.41254 | 0.0859977 | 0.0429988 | − | 0.999075i | \(-0.486309\pi\) | ||||
0.0429988 | + | 0.999075i | \(0.486309\pi\) | |||||||
\(788\) | 0.488551 | 0.0174039 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.6924 | −0.735737 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.5142 | 0.586437 | ||||||||
\(794\) | 30.7822 | 1.09242 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.23457 | −0.114646 | ||||||||
\(797\) | 8.11230 | 0.287353 | 0.143676 | − | 0.989625i | \(-0.454108\pi\) | ||||
0.143676 | + | 0.989625i | \(0.454108\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.6189 | −0.517180 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.65507 | −0.270310 | ||||||||
\(803\) | −16.3214 | −0.575970 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.66638 | 0.270037 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 20.6453 | 0.726299 | ||||||||
\(809\) | 40.7091 | 1.43125 | 0.715627 | − | 0.698482i | \(-0.246141\pi\) | ||||
0.715627 | + | 0.698482i | \(0.246141\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −49.4990 | −1.73814 | −0.869072 | − | 0.494685i | \(-0.835283\pi\) | ||||
−0.869072 | + | 0.494685i | \(0.835283\pi\) | |||||||
\(812\) | 4.26482 | 0.149666 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −35.3033 | −1.23738 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 45.7925 | 1.60208 | ||||||||
\(818\) | 36.6606 | 1.28181 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.2114 | −1.47319 | −0.736594 | − | 0.676335i | \(-0.763567\pi\) | ||||
−0.736594 | + | 0.676335i | \(0.763567\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 49.2349 | 1.71622 | 0.858111 | − | 0.513464i | \(-0.171638\pi\) | ||||
0.858111 | + | 0.513464i | \(0.171638\pi\) | |||||||
\(824\) | 6.29622 | 0.219339 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 25.4255 | 0.884666 | ||||||||
\(827\) | 51.0011 | 1.77348 | 0.886742 | − | 0.462266i | \(-0.152963\pi\) | ||||
0.886742 | + | 0.462266i | \(0.152963\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.2342 | −1.32793 | −0.663964 | − | 0.747764i | \(-0.731127\pi\) | ||||
−0.663964 | + | 0.747764i | \(0.731127\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.20758 | −0.284547 | ||||||||
\(833\) | 10.4513 | 0.362117 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.85724 | 0.167991 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.741461 | −0.0256133 | ||||||||
\(839\) | 16.7086 | 0.576845 | 0.288422 | − | 0.957503i | \(-0.406869\pi\) | ||||
0.288422 | + | 0.957503i | \(0.406869\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33.4127 | 1.15216 | ||||||||
\(842\) | −27.2250 | −0.938236 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.10804 | 0.0725618 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.14755 | 0.279953 | ||||||||
\(848\) | −19.1542 | −0.657757 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −85.7599 | −2.93981 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.2644 | 0.625361 | 0.312681 | − | 0.949858i | \(-0.398773\pi\) | ||||
0.312681 | + | 0.949858i | \(0.398773\pi\) | |||||||
\(854\) | 28.1199 | 0.962244 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.55846 | 0.155805 | ||||||||
\(857\) | −53.4773 | −1.82675 | −0.913375 | − | 0.407119i | \(-0.866534\pi\) | ||||
−0.913375 | + | 0.407119i | \(0.866534\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.7575 | −0.639998 | −0.319999 | − | 0.947418i | \(-0.603683\pi\) | ||||
−0.319999 | + | 0.947418i | \(0.603683\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −41.1889 | −1.40290 | ||||||||
\(863\) | −51.2363 | −1.74410 | −0.872051 | − | 0.489414i | \(-0.837211\pi\) | ||||
−0.872051 | + | 0.489414i | \(0.837211\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 14.1841 | 0.481995 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.99588 | 0.0677444 | ||||||||
\(869\) | −25.1383 | −0.852757 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.82121 | 0.197244 | ||||||||
\(872\) | 7.42378 | 0.251401 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 77.1739 | 2.61045 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.06306 | 0.204735 | 0.102368 | − | 0.994747i | \(-0.467358\pi\) | ||||
0.102368 | + | 0.994747i | \(0.467358\pi\) | |||||||
\(878\) | 1.54024 | 0.0519806 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.6698 | −0.763765 | −0.381883 | − | 0.924211i | \(-0.624724\pi\) | ||||
−0.381883 | + | 0.924211i | \(0.624724\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.53899 | 0.186402 | 0.0932009 | − | 0.995647i | \(-0.470290\pi\) | ||||
0.0932009 | + | 0.995647i | \(0.470290\pi\) | |||||||
\(884\) | 1.06881 | 0.0359480 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −40.3915 | −1.35698 | ||||||||
\(887\) | −10.9716 | −0.368390 | −0.184195 | − | 0.982890i | \(-0.558968\pi\) | ||||
−0.184195 | + | 0.982890i | \(0.558968\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.58408 | 0.287901 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.82319 | 0.0945272 | ||||||||
\(893\) | 38.0502 | 1.27330 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −20.0127 | −0.668577 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.30550 | −0.243788 | ||||||||
\(899\) | 29.2083 | 0.974151 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.15254 | −0.304915 | ||||||||
\(902\) | −6.71781 | −0.223679 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −34.8463 | −1.15897 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.3907 | 0.643856 | 0.321928 | − | 0.946764i | \(-0.395669\pi\) | ||||
0.321928 | + | 0.946764i | \(0.395669\pi\) | |||||||
\(908\) | 5.88715 | 0.195372 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.7190 | 0.454530 | 0.227265 | − | 0.973833i | \(-0.427022\pi\) | ||||
0.227265 | + | 0.973833i | \(0.427022\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.527808 | 0.0174679 | ||||||||
\(914\) | −24.5391 | −0.811681 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.83636 | −0.258920 | ||||||||
\(917\) | −6.51671 | −0.215201 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.4108 | −1.06913 | −0.534567 | − | 0.845126i | \(-0.679525\pi\) | ||||
−0.534567 | + | 0.845126i | \(0.679525\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −61.0867 | −2.01178 | ||||||||
\(923\) | 7.79678 | 0.256634 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 40.1360 | 1.31895 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 15.9458 | 0.523446 | ||||||||
\(929\) | 4.33444 | 0.142208 | 0.0711042 | − | 0.997469i | \(-0.477348\pi\) | ||||
0.0711042 | + | 0.997469i | \(0.477348\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.2028 | −0.891536 | ||||||||
\(932\) | −4.88548 | −0.160029 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.91884 | 0.193670 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 54.5925 | 1.78346 | 0.891730 | − | 0.452567i | \(-0.149492\pi\) | ||||
0.891730 | + | 0.452567i | \(0.149492\pi\) | |||||||
\(938\) | 9.91218 | 0.323644 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.23853 | −0.138172 | −0.0690861 | − | 0.997611i | \(-0.522008\pi\) | ||||
−0.0690861 | + | 0.997611i | \(0.522008\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.3191 | −0.531423 | ||||||||
\(944\) | 50.8051 | 1.65356 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 29.0318 | 0.943906 | ||||||||
\(947\) | −12.6069 | −0.409671 | −0.204835 | − | 0.978796i | \(-0.565666\pi\) | ||||
−0.204835 | + | 0.978796i | \(0.565666\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.34781 | 0.303443 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.26348 | −0.267821 | ||||||||
\(953\) | 31.1635 | 1.00948 | 0.504742 | − | 0.863270i | \(-0.331588\pi\) | ||||
0.504742 | + | 0.863270i | \(0.331588\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.80247 | 0.122981 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 21.9262 | 0.708405 | ||||||||
\(959\) | −2.95301 | −0.0953578 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.3309 | −0.559062 | ||||||||
\(962\) | 20.2194 | 0.651900 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7.03319 | 0.226524 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.55308 | 0.0499438 | 0.0249719 | − | 0.999688i | \(-0.492050\pi\) | ||||
0.0249719 | + | 0.999688i | \(0.492050\pi\) | |||||||
\(968\) | 13.7206 | 0.440997 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.2623 | 1.22790 | 0.613948 | − | 0.789347i | \(-0.289581\pi\) | ||||
0.613948 | + | 0.789347i | \(0.289581\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.51108 | −0.0805016 | ||||||||
\(974\) | 38.1405 | 1.22210 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 56.1890 | 1.79857 | ||||||||
\(977\) | 20.3661 | 0.651570 | 0.325785 | − | 0.945444i | \(-0.394371\pi\) | ||||
0.325785 | + | 0.945444i | \(0.394371\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.01123 | −0.0323190 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −17.6539 | −0.563359 | ||||||||
\(983\) | 13.2557 | 0.422791 | 0.211395 | − | 0.977401i | \(-0.432199\pi\) | ||||
0.211395 | + | 0.977401i | \(0.432199\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 26.6335 | 0.848185 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.78190 | −0.0885041 | ||||||||
\(989\) | 70.5249 | 2.24256 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.24081 | −0.0711816 | −0.0355908 | − | 0.999366i | \(-0.511331\pi\) | ||||
−0.0355908 | + | 0.999366i | \(0.511331\pi\) | |||||||
\(992\) | 7.46241 | 0.236932 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 13.2761 | 0.421093 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.0404 | −0.444663 | −0.222331 | − | 0.974971i | \(-0.571367\pi\) | ||||
−0.222331 | + | 0.974971i | \(0.571367\pi\) | |||||||
\(998\) | −6.41489 | −0.203060 | ||||||||
\(999\) | 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 | 5625.2.a.bd.1.6 | 8 | ||
3.2 | odd | 2 | 1875.2.a.m.1.3 | 8 | |||
5.4 | even | 2 | 5625.2.a.t.1.3 | 8 | |||
15.2 | even | 4 | 1875.2.b.h.1249.4 | 16 | |||
15.8 | even | 4 | 1875.2.b.h.1249.13 | 16 | |||
15.14 | odd | 2 | 1875.2.a.p.1.6 | 8 | |||
25.12 | odd | 20 | 225.2.m.b.19.1 | 16 | |||
25.23 | odd | 20 | 225.2.m.b.154.1 | 16 | |||
75.2 | even | 20 | 375.2.i.c.274.1 | 16 | |||
75.11 | odd | 10 | 375.2.g.e.226.2 | 16 | |||
75.14 | odd | 10 | 375.2.g.d.226.3 | 16 | |||
75.23 | even | 20 | 75.2.i.a.4.4 | ✓ | 16 | ||
75.38 | even | 20 | 375.2.i.c.349.1 | 16 | |||
75.41 | odd | 10 | 375.2.g.e.151.2 | 16 | |||
75.59 | odd | 10 | 375.2.g.d.151.3 | 16 | |||
75.62 | even | 20 | 75.2.i.a.19.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.i.a.4.4 | ✓ | 16 | 75.23 | even | 20 | ||
75.2.i.a.19.4 | yes | 16 | 75.62 | even | 20 | ||
225.2.m.b.19.1 | 16 | 25.12 | odd | 20 | |||
225.2.m.b.154.1 | 16 | 25.23 | odd | 20 | |||
375.2.g.d.151.3 | 16 | 75.59 | odd | 10 | |||
375.2.g.d.226.3 | 16 | 75.14 | odd | 10 | |||
375.2.g.e.151.2 | 16 | 75.41 | odd | 10 | |||
375.2.g.e.226.2 | 16 | 75.11 | odd | 10 | |||
375.2.i.c.274.1 | 16 | 75.2 | even | 20 | |||
375.2.i.c.349.1 | 16 | 75.38 | even | 20 | |||
1875.2.a.m.1.3 | 8 | 3.2 | odd | 2 | |||
1875.2.a.p.1.6 | 8 | 15.14 | odd | 2 | |||
1875.2.b.h.1249.4 | 16 | 15.2 | even | 4 | |||
1875.2.b.h.1249.13 | 16 | 15.8 | even | 4 | |||
5625.2.a.t.1.3 | 8 | 5.4 | even | 2 | |||
5625.2.a.bd.1.6 | 8 | 1.1 | even | 1 | trivial |