Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(1,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, 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("1134.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.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: | \(9.05503558921\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.73205 | 0.774597 | 0.387298 | − | 0.921954i | \(-0.373408\pi\) | ||||
0.387298 | + | 0.921954i | \(0.373408\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.73205 | −0.547723 | ||||||||
\(11\) | −4.73205 | −1.42677 | −0.713384 | − | 0.700774i | \(-0.752838\pi\) | ||||
−0.713384 | + | 0.700774i | \(0.752838\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | −0.138675 | − | 0.990338i | \(-0.544284\pi\) | ||||
−0.138675 | + | 0.990338i | \(0.544284\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.46410 | −1.56777 | −0.783887 | − | 0.620903i | \(-0.786766\pi\) | ||||
−0.783887 | + | 0.620903i | \(0.786766\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.19615 | −1.42149 | −0.710747 | − | 0.703447i | \(-0.751643\pi\) | ||||
−0.710747 | + | 0.703447i | \(0.751643\pi\) | |||||||
\(20\) | 1.73205 | 0.387298 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.73205 | 1.00888 | ||||||||
\(23\) | −1.26795 | −0.264386 | −0.132193 | − | 0.991224i | \(-0.542202\pi\) | ||||
−0.132193 | + | 0.991224i | \(0.542202\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | −0.400000 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −6.46410 | −1.20035 | −0.600177 | − | 0.799867i | \(-0.704903\pi\) | ||||
−0.600177 | + | 0.799867i | \(0.704903\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.19615 | 0.753651 | 0.376826 | − | 0.926284i | \(-0.377016\pi\) | ||||
0.376826 | + | 0.926284i | \(0.377016\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.46410 | 1.10858 | ||||||||
\(35\) | 1.73205 | 0.292770 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.19615 | −0.525444 | −0.262722 | − | 0.964872i | \(-0.584620\pi\) | ||||
−0.262722 | + | 0.964872i | \(0.584620\pi\) | |||||||
\(38\) | 6.19615 | 1.00515 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.73205 | −0.273861 | ||||||||
\(41\) | −2.53590 | −0.396041 | −0.198020 | − | 0.980198i | \(-0.563451\pi\) | ||||
−0.198020 | + | 0.980198i | \(0.563451\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.3923 | 1.88981 | 0.944904 | − | 0.327346i | \(-0.106154\pi\) | ||||
0.944904 | + | 0.327346i | \(0.106154\pi\) | |||||||
\(44\) | −4.73205 | −0.713384 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.26795 | 0.186949 | ||||||||
\(47\) | −2.19615 | −0.320342 | −0.160171 | − | 0.987089i | \(-0.551205\pi\) | ||||
−0.160171 | + | 0.987089i | \(0.551205\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.00000 | 0.282843 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | −9.46410 | −1.29999 | −0.649997 | − | 0.759937i | \(-0.725230\pi\) | ||||
−0.649997 | + | 0.759937i | \(0.725230\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.19615 | −1.10517 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.46410 | 0.848778 | ||||||||
\(59\) | 8.19615 | 1.06705 | 0.533524 | − | 0.845785i | \(-0.320867\pi\) | ||||
0.533524 | + | 0.845785i | \(0.320867\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.39230 | 1.20256 | 0.601281 | − | 0.799038i | \(-0.294657\pi\) | ||||
0.601281 | + | 0.799038i | \(0.294657\pi\) | |||||||
\(62\) | −4.19615 | −0.532912 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.73205 | −0.214834 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.19615 | 0.512642 | 0.256321 | − | 0.966592i | \(-0.417490\pi\) | ||||
0.256321 | + | 0.966592i | \(0.417490\pi\) | |||||||
\(68\) | −6.46410 | −0.783887 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.73205 | −0.207020 | ||||||||
\(71\) | 4.39230 | 0.521271 | 0.260635 | − | 0.965437i | \(-0.416068\pi\) | ||||
0.260635 | + | 0.965437i | \(0.416068\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.19615 | −1.07633 | −0.538164 | − | 0.842840i | \(-0.680882\pi\) | ||||
−0.538164 | + | 0.842840i | \(0.680882\pi\) | |||||||
\(74\) | 3.19615 | 0.371545 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.19615 | −0.710747 | ||||||||
\(77\) | −4.73205 | −0.539267 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.19615 | −0.697122 | −0.348561 | − | 0.937286i | \(-0.613330\pi\) | ||||
−0.348561 | + | 0.937286i | \(0.613330\pi\) | |||||||
\(80\) | 1.73205 | 0.193649 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.53590 | 0.280043 | ||||||||
\(83\) | −1.26795 | −0.139176 | −0.0695878 | − | 0.997576i | \(-0.522168\pi\) | ||||
−0.0695878 | + | 0.997576i | \(0.522168\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.1962 | −1.21439 | ||||||||
\(86\) | −12.3923 | −1.33630 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.73205 | 0.504438 | ||||||||
\(89\) | 12.4641 | 1.32119 | 0.660596 | − | 0.750742i | \(-0.270304\pi\) | ||||
0.660596 | + | 0.750742i | \(0.270304\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | −1.26795 | −0.132193 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.19615 | 0.226516 | ||||||||
\(95\) | −10.7321 | −1.10109 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.0000 | −1.62455 | −0.812277 | − | 0.583272i | \(-0.801772\pi\) | ||||
−0.812277 | + | 0.583272i | \(0.801772\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.00000 | −0.200000 | ||||||||
\(101\) | −12.9282 | −1.28640 | −0.643202 | − | 0.765696i | \(-0.722395\pi\) | ||||
−0.643202 | + | 0.765696i | \(0.722395\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.39230 | −0.826918 | −0.413459 | − | 0.910523i | \(-0.635680\pi\) | ||||
−0.413459 | + | 0.910523i | \(0.635680\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.46410 | 0.919235 | ||||||||
\(107\) | 13.8564 | 1.33955 | 0.669775 | − | 0.742564i | \(-0.266391\pi\) | ||||
0.669775 | + | 0.742564i | \(0.266391\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.80385 | −0.460125 | −0.230063 | − | 0.973176i | \(-0.573893\pi\) | ||||
−0.230063 | + | 0.973176i | \(0.573893\pi\) | |||||||
\(110\) | 8.19615 | 0.781472 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 10.2679 | 0.965927 | 0.482964 | − | 0.875640i | \(-0.339560\pi\) | ||||
0.482964 | + | 0.875640i | \(0.339560\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.19615 | −0.204792 | ||||||||
\(116\) | −6.46410 | −0.600177 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.19615 | −0.754517 | ||||||||
\(119\) | −6.46410 | −0.592563 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.3923 | 1.03566 | ||||||||
\(122\) | −9.39230 | −0.850339 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.19615 | 0.376826 | ||||||||
\(125\) | −12.1244 | −1.08444 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.00000 | −0.354943 | −0.177471 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177471 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.73205 | 0.151911 | ||||||||
\(131\) | 2.53590 | 0.221562 | 0.110781 | − | 0.993845i | \(-0.464665\pi\) | ||||
0.110781 | + | 0.993845i | \(0.464665\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.19615 | −0.537275 | ||||||||
\(134\) | −4.19615 | −0.362492 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.46410 | 0.554292 | ||||||||
\(137\) | 2.66025 | 0.227281 | 0.113640 | − | 0.993522i | \(-0.463749\pi\) | ||||
0.113640 | + | 0.993522i | \(0.463749\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.1962 | −1.54338 | −0.771689 | − | 0.636000i | \(-0.780588\pi\) | ||||
−0.771689 | + | 0.636000i | \(0.780588\pi\) | |||||||
\(140\) | 1.73205 | 0.146385 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.39230 | −0.368594 | ||||||||
\(143\) | 4.73205 | 0.395714 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.1962 | −0.929790 | ||||||||
\(146\) | 9.19615 | 0.761079 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.19615 | −0.262722 | ||||||||
\(149\) | 3.92820 | 0.321811 | 0.160905 | − | 0.986970i | \(-0.448559\pi\) | ||||
0.160905 | + | 0.986970i | \(0.448559\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.5885 | −1.83822 | −0.919111 | − | 0.393998i | \(-0.871092\pi\) | ||||
−0.919111 | + | 0.393998i | \(0.871092\pi\) | |||||||
\(152\) | 6.19615 | 0.502574 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.73205 | 0.381320 | ||||||||
\(155\) | 7.26795 | 0.583776 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.3923 | 1.22844 | 0.614220 | − | 0.789135i | \(-0.289471\pi\) | ||||
0.614220 | + | 0.789135i | \(0.289471\pi\) | |||||||
\(158\) | 6.19615 | 0.492939 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.73205 | −0.136931 | ||||||||
\(161\) | −1.26795 | −0.0999284 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24.3923 | 1.91055 | 0.955276 | − | 0.295714i | \(-0.0955577\pi\) | ||||
0.955276 | + | 0.295714i | \(0.0955577\pi\) | |||||||
\(164\) | −2.53590 | −0.198020 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.26795 | 0.0984119 | ||||||||
\(167\) | 7.26795 | 0.562411 | 0.281205 | − | 0.959648i | \(-0.409266\pi\) | ||||
0.281205 | + | 0.959648i | \(0.409266\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 11.1962 | 0.858706 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 12.3923 | 0.944904 | ||||||||
\(173\) | 12.8038 | 0.973459 | 0.486729 | − | 0.873553i | \(-0.338190\pi\) | ||||
0.486729 | + | 0.873553i | \(0.338190\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.00000 | −0.151186 | ||||||||
\(176\) | −4.73205 | −0.356692 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −12.4641 | −0.934224 | ||||||||
\(179\) | −7.26795 | −0.543232 | −0.271616 | − | 0.962406i | \(-0.587558\pi\) | ||||
−0.271616 | + | 0.962406i | \(0.587558\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.392305 | 0.0291598 | 0.0145799 | − | 0.999894i | \(-0.495359\pi\) | ||||
0.0145799 | + | 0.999894i | \(0.495359\pi\) | |||||||
\(182\) | 1.00000 | 0.0741249 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.26795 | 0.0934745 | ||||||||
\(185\) | −5.53590 | −0.407007 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 30.5885 | 2.23685 | ||||||||
\(188\) | −2.19615 | −0.160171 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.7321 | 0.778585 | ||||||||
\(191\) | −24.5885 | −1.77916 | −0.889579 | − | 0.456781i | \(-0.849002\pi\) | ||||
−0.889579 | + | 0.456781i | \(0.849002\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.0000 | −1.36765 | −0.683825 | − | 0.729646i | \(-0.739685\pi\) | ||||
−0.683825 | + | 0.729646i | \(0.739685\pi\) | |||||||
\(194\) | 16.0000 | 1.14873 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 15.0000 | 1.06871 | 0.534353 | − | 0.845262i | \(-0.320555\pi\) | ||||
0.534353 | + | 0.845262i | \(0.320555\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.5885 | 1.45948 | 0.729739 | − | 0.683726i | \(-0.239642\pi\) | ||||
0.729739 | + | 0.683726i | \(0.239642\pi\) | |||||||
\(200\) | 2.00000 | 0.141421 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.9282 | 0.909625 | ||||||||
\(203\) | −6.46410 | −0.453691 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.39230 | −0.306772 | ||||||||
\(206\) | 8.39230 | 0.584720 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 29.3205 | 2.02814 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.8038 | 0.812610 | 0.406305 | − | 0.913737i | \(-0.366817\pi\) | ||||
0.406305 | + | 0.913737i | \(0.366817\pi\) | |||||||
\(212\) | −9.46410 | −0.649997 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −13.8564 | −0.947204 | ||||||||
\(215\) | 21.4641 | 1.46384 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.19615 | 0.284853 | ||||||||
\(218\) | 4.80385 | 0.325358 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −8.19615 | −0.552584 | ||||||||
\(221\) | 6.46410 | 0.434823 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.3923 | 0.829850 | 0.414925 | − | 0.909856i | \(-0.363808\pi\) | ||||
0.414925 | + | 0.909856i | \(0.363808\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.2679 | −0.683014 | ||||||||
\(227\) | 5.07180 | 0.336627 | 0.168313 | − | 0.985734i | \(-0.446168\pi\) | ||||
0.168313 | + | 0.985734i | \(0.446168\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.7846 | −1.43957 | −0.719784 | − | 0.694198i | \(-0.755759\pi\) | ||||
−0.719784 | + | 0.694198i | \(0.755759\pi\) | |||||||
\(230\) | 2.19615 | 0.144810 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.46410 | 0.424389 | ||||||||
\(233\) | −13.7321 | −0.899617 | −0.449808 | − | 0.893125i | \(-0.648508\pi\) | ||||
−0.449808 | + | 0.893125i | \(0.648508\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.80385 | −0.248136 | ||||||||
\(236\) | 8.19615 | 0.533524 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.46410 | 0.419005 | ||||||||
\(239\) | −15.1244 | −0.978313 | −0.489157 | − | 0.872196i | \(-0.662695\pi\) | ||||
−0.489157 | + | 0.872196i | \(0.662695\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.5885 | −0.875309 | −0.437655 | − | 0.899143i | \(-0.644191\pi\) | ||||
−0.437655 | + | 0.899143i | \(0.644191\pi\) | |||||||
\(242\) | −11.3923 | −0.732325 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.39230 | 0.601281 | ||||||||
\(245\) | 1.73205 | 0.110657 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.19615 | 0.394252 | ||||||||
\(248\) | −4.19615 | −0.266456 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12.1244 | 0.766812 | ||||||||
\(251\) | 3.80385 | 0.240097 | 0.120048 | − | 0.992768i | \(-0.461695\pi\) | ||||
0.120048 | + | 0.992768i | \(0.461695\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00000 | 0.377217 | ||||||||
\(254\) | 4.00000 | 0.250982 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 27.9282 | 1.74211 | 0.871057 | − | 0.491182i | \(-0.163435\pi\) | ||||
0.871057 | + | 0.491182i | \(0.163435\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.19615 | −0.198599 | ||||||||
\(260\) | −1.73205 | −0.107417 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.53590 | −0.156668 | ||||||||
\(263\) | −15.1244 | −0.932608 | −0.466304 | − | 0.884625i | \(-0.654415\pi\) | ||||
−0.466304 | + | 0.884625i | \(0.654415\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.3923 | −1.00697 | ||||||||
\(266\) | 6.19615 | 0.379910 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.19615 | 0.256321 | ||||||||
\(269\) | −29.4449 | −1.79529 | −0.897643 | − | 0.440724i | \(-0.854722\pi\) | ||||
−0.897643 | + | 0.440724i | \(0.854722\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.1962 | 1.71279 | 0.856397 | − | 0.516318i | \(-0.172698\pi\) | ||||
0.856397 | + | 0.516318i | \(0.172698\pi\) | |||||||
\(272\) | −6.46410 | −0.391944 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.66025 | −0.160712 | ||||||||
\(275\) | 9.46410 | 0.570707 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.7846 | −1.12866 | −0.564329 | − | 0.825550i | \(-0.690865\pi\) | ||||
−0.564329 | + | 0.825550i | \(0.690865\pi\) | |||||||
\(278\) | 18.1962 | 1.09133 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.73205 | −0.103510 | ||||||||
\(281\) | 13.7321 | 0.819185 | 0.409593 | − | 0.912268i | \(-0.365671\pi\) | ||||
0.409593 | + | 0.912268i | \(0.365671\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.60770 | 0.214455 | 0.107228 | − | 0.994234i | \(-0.465803\pi\) | ||||
0.107228 | + | 0.994234i | \(0.465803\pi\) | |||||||
\(284\) | 4.39230 | 0.260635 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.73205 | −0.279812 | ||||||||
\(287\) | −2.53590 | −0.149689 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24.7846 | 1.45792 | ||||||||
\(290\) | 11.1962 | 0.657461 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.19615 | −0.538164 | ||||||||
\(293\) | 26.6603 | 1.55751 | 0.778754 | − | 0.627329i | \(-0.215852\pi\) | ||||
0.778754 | + | 0.627329i | \(0.215852\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.1962 | 0.826532 | ||||||||
\(296\) | 3.19615 | 0.185773 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.92820 | −0.227555 | ||||||||
\(299\) | 1.26795 | 0.0733274 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.3923 | 0.714281 | ||||||||
\(302\) | 22.5885 | 1.29982 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.19615 | −0.355374 | ||||||||
\(305\) | 16.2679 | 0.931500 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.00000 | 0.456584 | 0.228292 | − | 0.973593i | \(-0.426686\pi\) | ||||
0.228292 | + | 0.973593i | \(0.426686\pi\) | |||||||
\(308\) | −4.73205 | −0.269634 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.26795 | −0.412792 | ||||||||
\(311\) | 22.9808 | 1.30312 | 0.651560 | − | 0.758597i | \(-0.274115\pi\) | ||||
0.651560 | + | 0.758597i | \(0.274115\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.9808 | 1.24243 | 0.621213 | − | 0.783642i | \(-0.286640\pi\) | ||||
0.621213 | + | 0.783642i | \(0.286640\pi\) | |||||||
\(314\) | −15.3923 | −0.868638 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.19615 | −0.348561 | ||||||||
\(317\) | 1.39230 | 0.0781996 | 0.0390998 | − | 0.999235i | \(-0.487551\pi\) | ||||
0.0390998 | + | 0.999235i | \(0.487551\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 30.5885 | 1.71262 | ||||||||
\(320\) | 1.73205 | 0.0968246 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.26795 | 0.0706600 | ||||||||
\(323\) | 40.0526 | 2.22858 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.00000 | 0.110940 | ||||||||
\(326\) | −24.3923 | −1.35096 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.53590 | 0.140022 | ||||||||
\(329\) | −2.19615 | −0.121078 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.1769 | −1.60371 | −0.801854 | − | 0.597520i | \(-0.796153\pi\) | ||||
−0.801854 | + | 0.597520i | \(0.796153\pi\) | |||||||
\(332\) | −1.26795 | −0.0695878 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.26795 | −0.397684 | ||||||||
\(335\) | 7.26795 | 0.397090 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −32.3923 | −1.76452 | −0.882261 | − | 0.470761i | \(-0.843979\pi\) | ||||
−0.882261 | + | 0.470761i | \(0.843979\pi\) | |||||||
\(338\) | 12.0000 | 0.652714 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −11.1962 | −0.607197 | ||||||||
\(341\) | −19.8564 | −1.07528 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −12.3923 | −0.668148 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.8038 | −0.688339 | ||||||||
\(347\) | −16.3923 | −0.879985 | −0.439993 | − | 0.898001i | \(-0.645019\pi\) | ||||
−0.439993 | + | 0.898001i | \(0.645019\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.3923 | 0.663345 | 0.331672 | − | 0.943395i | \(-0.392387\pi\) | ||||
0.331672 | + | 0.943395i | \(0.392387\pi\) | |||||||
\(350\) | 2.00000 | 0.106904 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.73205 | 0.252219 | ||||||||
\(353\) | −4.14359 | −0.220541 | −0.110271 | − | 0.993902i | \(-0.535172\pi\) | ||||
−0.110271 | + | 0.993902i | \(0.535172\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.60770 | 0.403775 | ||||||||
\(356\) | 12.4641 | 0.660596 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.26795 | 0.384123 | ||||||||
\(359\) | −18.9282 | −0.998992 | −0.499496 | − | 0.866316i | \(-0.666482\pi\) | ||||
−0.499496 | + | 0.866316i | \(0.666482\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.3923 | 1.02065 | ||||||||
\(362\) | −0.392305 | −0.0206191 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.00000 | −0.0524142 | ||||||||
\(365\) | −15.9282 | −0.833720 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.58846 | −0.239516 | −0.119758 | − | 0.992803i | \(-0.538212\pi\) | ||||
−0.119758 | + | 0.992803i | \(0.538212\pi\) | |||||||
\(368\) | −1.26795 | −0.0660964 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.53590 | 0.287798 | ||||||||
\(371\) | −9.46410 | −0.491352 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.0000 | 1.03556 | 0.517780 | − | 0.855514i | \(-0.326758\pi\) | ||||
0.517780 | + | 0.855514i | \(0.326758\pi\) | |||||||
\(374\) | −30.5885 | −1.58169 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.19615 | 0.113258 | ||||||||
\(377\) | 6.46410 | 0.332918 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.5885 | −0.852092 | −0.426046 | − | 0.904702i | \(-0.640094\pi\) | ||||
−0.426046 | + | 0.904702i | \(0.640094\pi\) | |||||||
\(380\) | −10.7321 | −0.550543 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 24.5885 | 1.25805 | ||||||||
\(383\) | 10.1436 | 0.518313 | 0.259157 | − | 0.965835i | \(-0.416555\pi\) | ||||
0.259157 | + | 0.965835i | \(0.416555\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.19615 | −0.417715 | ||||||||
\(386\) | 19.0000 | 0.967075 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −16.0000 | −0.812277 | ||||||||
\(389\) | 30.2487 | 1.53367 | 0.766835 | − | 0.641844i | \(-0.221830\pi\) | ||||
0.766835 | + | 0.641844i | \(0.221830\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.19615 | 0.414497 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −15.0000 | −0.755689 | ||||||||
\(395\) | −10.7321 | −0.539988 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.3923 | −1.47516 | −0.737579 | − | 0.675261i | \(-0.764031\pi\) | ||||
−0.737579 | + | 0.675261i | \(0.764031\pi\) | |||||||
\(398\) | −20.5885 | −1.03201 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.00000 | −0.100000 | ||||||||
\(401\) | −22.2679 | −1.11201 | −0.556004 | − | 0.831180i | \(-0.687666\pi\) | ||||
−0.556004 | + | 0.831180i | \(0.687666\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.19615 | −0.209025 | ||||||||
\(404\) | −12.9282 | −0.643202 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.46410 | 0.320808 | ||||||||
\(407\) | 15.1244 | 0.749686 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.1962 | −1.04808 | −0.524041 | − | 0.851693i | \(-0.675576\pi\) | ||||
−0.524041 | + | 0.851693i | \(0.675576\pi\) | |||||||
\(410\) | 4.39230 | 0.216920 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.39230 | −0.413459 | ||||||||
\(413\) | 8.19615 | 0.403306 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.19615 | −0.107805 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −29.3205 | −1.43411 | ||||||||
\(419\) | −23.3205 | −1.13928 | −0.569641 | − | 0.821894i | \(-0.692918\pi\) | ||||
−0.569641 | + | 0.821894i | \(0.692918\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.1962 | 0.643141 | 0.321571 | − | 0.946886i | \(-0.395789\pi\) | ||||
0.321571 | + | 0.946886i | \(0.395789\pi\) | |||||||
\(422\) | −11.8038 | −0.574602 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.46410 | 0.459617 | ||||||||
\(425\) | 12.9282 | 0.627110 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.39230 | 0.454525 | ||||||||
\(428\) | 13.8564 | 0.669775 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −21.4641 | −1.03509 | ||||||||
\(431\) | −0.679492 | −0.0327300 | −0.0163650 | − | 0.999866i | \(-0.505209\pi\) | ||||
−0.0163650 | + | 0.999866i | \(0.505209\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.5885 | −1.51804 | −0.759022 | − | 0.651065i | \(-0.774323\pi\) | ||||
−0.759022 | + | 0.651065i | \(0.774323\pi\) | |||||||
\(434\) | −4.19615 | −0.201422 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.80385 | −0.230063 | ||||||||
\(437\) | 7.85641 | 0.375823 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.1769 | 1.01072 | 0.505359 | − | 0.862909i | \(-0.331360\pi\) | ||||
0.505359 | + | 0.862909i | \(0.331360\pi\) | |||||||
\(440\) | 8.19615 | 0.390736 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.46410 | −0.307466 | ||||||||
\(443\) | −2.19615 | −0.104342 | −0.0521712 | − | 0.998638i | \(-0.516614\pi\) | ||||
−0.0521712 | + | 0.998638i | \(0.516614\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.5885 | 1.02339 | ||||||||
\(446\) | −12.3923 | −0.586793 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −6.00000 | −0.283158 | −0.141579 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.0000 | 0.565058 | ||||||||
\(452\) | 10.2679 | 0.482964 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5.07180 | −0.238031 | ||||||||
\(455\) | −1.73205 | −0.0811998 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.00000 | −0.0467780 | −0.0233890 | − | 0.999726i | \(-0.507446\pi\) | ||||
−0.0233890 | + | 0.999726i | \(0.507446\pi\) | |||||||
\(458\) | 21.7846 | 1.01793 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.19615 | −0.102396 | ||||||||
\(461\) | −11.0718 | −0.515665 | −0.257832 | − | 0.966190i | \(-0.583008\pi\) | ||||
−0.257832 | + | 0.966190i | \(0.583008\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.80385 | 0.269728 | 0.134864 | − | 0.990864i | \(-0.456940\pi\) | ||||
0.134864 | + | 0.990864i | \(0.456940\pi\) | |||||||
\(464\) | −6.46410 | −0.300088 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 13.7321 | 0.636125 | ||||||||
\(467\) | 1.26795 | 0.0586737 | 0.0293368 | − | 0.999570i | \(-0.490660\pi\) | ||||
0.0293368 | + | 0.999570i | \(0.490660\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.19615 | 0.193760 | ||||||||
\(470\) | 3.80385 | 0.175458 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.19615 | −0.377258 | ||||||||
\(473\) | −58.6410 | −2.69632 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.3923 | 0.568598 | ||||||||
\(476\) | −6.46410 | −0.296282 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 15.1244 | 0.691772 | ||||||||
\(479\) | −16.7321 | −0.764507 | −0.382253 | − | 0.924058i | \(-0.624852\pi\) | ||||
−0.382253 | + | 0.924058i | \(0.624852\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.19615 | 0.145732 | ||||||||
\(482\) | 13.5885 | 0.618937 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.3923 | 0.517832 | ||||||||
\(485\) | −27.7128 | −1.25837 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.19615 | −0.280774 | −0.140387 | − | 0.990097i | \(-0.544835\pi\) | ||||
−0.140387 | + | 0.990097i | \(0.544835\pi\) | |||||||
\(488\) | −9.39230 | −0.425170 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.73205 | −0.0782461 | ||||||||
\(491\) | −11.3205 | −0.510887 | −0.255444 | − | 0.966824i | \(-0.582222\pi\) | ||||
−0.255444 | + | 0.966824i | \(0.582222\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 41.7846 | 1.88188 | ||||||||
\(494\) | −6.19615 | −0.278778 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.19615 | 0.188413 | ||||||||
\(497\) | 4.39230 | 0.197022 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.5885 | 0.921666 | 0.460833 | − | 0.887487i | \(-0.347551\pi\) | ||||
0.460833 | + | 0.887487i | \(0.347551\pi\) | |||||||
\(500\) | −12.1244 | −0.542218 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.80385 | −0.169774 | ||||||||
\(503\) | 22.9808 | 1.02466 | 0.512331 | − | 0.858788i | \(-0.328782\pi\) | ||||
0.512331 | + | 0.858788i | \(0.328782\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −22.3923 | −0.996444 | ||||||||
\(506\) | −6.00000 | −0.266733 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.00000 | −0.177471 | ||||||||
\(509\) | 21.7128 | 0.962404 | 0.481202 | − | 0.876610i | \(-0.340200\pi\) | ||||
0.481202 | + | 0.876610i | \(0.340200\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.19615 | −0.406814 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −27.9282 | −1.23186 | ||||||||
\(515\) | −14.5359 | −0.640528 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.3923 | 0.457053 | ||||||||
\(518\) | 3.19615 | 0.140431 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.73205 | 0.0759555 | ||||||||
\(521\) | −43.8564 | −1.92138 | −0.960692 | − | 0.277616i | \(-0.910456\pi\) | ||||
−0.960692 | + | 0.277616i | \(0.910456\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.6077 | 0.682477 | 0.341238 | − | 0.939977i | \(-0.389154\pi\) | ||||
0.341238 | + | 0.939977i | \(0.389154\pi\) | |||||||
\(524\) | 2.53590 | 0.110781 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.1244 | 0.659453 | ||||||||
\(527\) | −27.1244 | −1.18156 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.3923 | −0.930100 | ||||||||
\(530\) | 16.3923 | 0.712036 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.19615 | −0.268637 | ||||||||
\(533\) | 2.53590 | 0.109842 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.0000 | 1.03761 | ||||||||
\(536\) | −4.19615 | −0.181246 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 29.4449 | 1.26946 | ||||||||
\(539\) | −4.73205 | −0.203824 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.5885 | −1.35809 | −0.679047 | − | 0.734095i | \(-0.737607\pi\) | ||||
−0.679047 | + | 0.734095i | \(0.737607\pi\) | |||||||
\(542\) | −28.1962 | −1.21113 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.46410 | 0.277146 | ||||||||
\(545\) | −8.32051 | −0.356411 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.8038 | −0.846751 | −0.423376 | − | 0.905954i | \(-0.639155\pi\) | ||||
−0.423376 | + | 0.905954i | \(0.639155\pi\) | |||||||
\(548\) | 2.66025 | 0.113640 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −9.46410 | −0.403551 | ||||||||
\(551\) | 40.0526 | 1.70630 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.19615 | −0.263487 | ||||||||
\(554\) | 18.7846 | 0.798082 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −18.1962 | −0.771689 | ||||||||
\(557\) | −40.8564 | −1.73114 | −0.865571 | − | 0.500787i | \(-0.833044\pi\) | ||||
−0.865571 | + | 0.500787i | \(0.833044\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.3923 | −0.524139 | ||||||||
\(560\) | 1.73205 | 0.0731925 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.7321 | −0.579252 | ||||||||
\(563\) | −24.0000 | −1.01148 | −0.505740 | − | 0.862686i | \(-0.668780\pi\) | ||||
−0.505740 | + | 0.862686i | \(0.668780\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.7846 | 0.748204 | ||||||||
\(566\) | −3.60770 | −0.151643 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.39230 | −0.184297 | ||||||||
\(569\) | 7.98076 | 0.334571 | 0.167285 | − | 0.985908i | \(-0.446500\pi\) | ||||
0.167285 | + | 0.985908i | \(0.446500\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.8038 | −0.828765 | −0.414383 | − | 0.910103i | \(-0.636002\pi\) | ||||
−0.414383 | + | 0.910103i | \(0.636002\pi\) | |||||||
\(572\) | 4.73205 | 0.197857 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.53590 | 0.105846 | ||||||||
\(575\) | 2.53590 | 0.105754 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.1962 | 1.29871 | 0.649356 | − | 0.760484i | \(-0.275038\pi\) | ||||
0.649356 | + | 0.760484i | \(0.275038\pi\) | |||||||
\(578\) | −24.7846 | −1.03090 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −11.1962 | −0.464895 | ||||||||
\(581\) | −1.26795 | −0.0526034 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 44.7846 | 1.85479 | ||||||||
\(584\) | 9.19615 | 0.380539 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −26.6603 | −1.10132 | ||||||||
\(587\) | 10.7321 | 0.442959 | 0.221480 | − | 0.975165i | \(-0.428911\pi\) | ||||
0.221480 | + | 0.975165i | \(0.428911\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.0000 | −1.07131 | ||||||||
\(590\) | −14.1962 | −0.584446 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.19615 | −0.131361 | ||||||||
\(593\) | 40.8564 | 1.67777 | 0.838886 | − | 0.544308i | \(-0.183208\pi\) | ||||
0.838886 | + | 0.544308i | \(0.183208\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.1962 | −0.458997 | ||||||||
\(596\) | 3.92820 | 0.160905 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.26795 | −0.0518503 | ||||||||
\(599\) | 3.80385 | 0.155421 | 0.0777105 | − | 0.996976i | \(-0.475239\pi\) | ||||
0.0777105 | + | 0.996976i | \(0.475239\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.19615 | −0.375119 | −0.187559 | − | 0.982253i | \(-0.560058\pi\) | ||||
−0.187559 | + | 0.982253i | \(0.560058\pi\) | |||||||
\(602\) | −12.3923 | −0.505073 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −22.5885 | −0.919111 | ||||||||
\(605\) | 19.7321 | 0.802222 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.5885 | −1.16037 | −0.580185 | − | 0.814485i | \(-0.697020\pi\) | ||||
−0.580185 | + | 0.814485i | \(0.697020\pi\) | |||||||
\(608\) | 6.19615 | 0.251287 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −16.2679 | −0.658670 | ||||||||
\(611\) | 2.19615 | 0.0888468 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.78461 | −0.274028 | −0.137014 | − | 0.990569i | \(-0.543751\pi\) | ||||
−0.137014 | + | 0.990569i | \(0.543751\pi\) | |||||||
\(614\) | −8.00000 | −0.322854 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.73205 | 0.190660 | ||||||||
\(617\) | −16.5167 | −0.664936 | −0.332468 | − | 0.943115i | \(-0.607881\pi\) | ||||
−0.332468 | + | 0.943115i | \(0.607881\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.00000 | −0.160774 | −0.0803868 | − | 0.996764i | \(-0.525616\pi\) | ||||
−0.0803868 | + | 0.996764i | \(0.525616\pi\) | |||||||
\(620\) | 7.26795 | 0.291888 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −22.9808 | −0.921445 | ||||||||
\(623\) | 12.4641 | 0.499364 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | −21.9808 | −0.878528 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.3923 | 0.614220 | ||||||||
\(629\) | 20.6603 | 0.823778 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.5885 | −0.899232 | −0.449616 | − | 0.893222i | \(-0.648439\pi\) | ||||
−0.449616 | + | 0.893222i | \(0.648439\pi\) | |||||||
\(632\) | 6.19615 | 0.246470 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.39230 | −0.0552955 | ||||||||
\(635\) | −6.92820 | −0.274937 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | −30.5885 | −1.21101 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.73205 | −0.0684653 | ||||||||
\(641\) | −9.33975 | −0.368898 | −0.184449 | − | 0.982842i | \(-0.559050\pi\) | ||||
−0.184449 | + | 0.982842i | \(0.559050\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.8038 | 0.702115 | 0.351058 | − | 0.936354i | \(-0.385822\pi\) | ||||
0.351058 | + | 0.936354i | \(0.385822\pi\) | |||||||
\(644\) | −1.26795 | −0.0499642 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −40.0526 | −1.57585 | ||||||||
\(647\) | 23.3205 | 0.916824 | 0.458412 | − | 0.888740i | \(-0.348418\pi\) | ||||
0.458412 | + | 0.888740i | \(0.348418\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −38.7846 | −1.52243 | ||||||||
\(650\) | −2.00000 | −0.0784465 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 24.3923 | 0.955276 | ||||||||
\(653\) | 35.3205 | 1.38220 | 0.691099 | − | 0.722760i | \(-0.257127\pi\) | ||||
0.691099 | + | 0.722760i | \(0.257127\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.39230 | 0.171622 | ||||||||
\(656\) | −2.53590 | −0.0990102 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.19615 | 0.0856149 | ||||||||
\(659\) | −0.679492 | −0.0264692 | −0.0132346 | − | 0.999912i | \(-0.504213\pi\) | ||||
−0.0132346 | + | 0.999912i | \(0.504213\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.3923 | 1.29881 | 0.649405 | − | 0.760443i | \(-0.275018\pi\) | ||||
0.649405 | + | 0.760443i | \(0.275018\pi\) | |||||||
\(662\) | 29.1769 | 1.13399 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.26795 | 0.0492060 | ||||||||
\(665\) | −10.7321 | −0.416171 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.19615 | 0.317356 | ||||||||
\(668\) | 7.26795 | 0.281205 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.26795 | −0.280785 | ||||||||
\(671\) | −44.4449 | −1.71577 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.1769 | 0.700669 | 0.350334 | − | 0.936625i | \(-0.386068\pi\) | ||||
0.350334 | + | 0.936625i | \(0.386068\pi\) | |||||||
\(674\) | 32.3923 | 1.24770 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.0000 | −0.461538 | ||||||||
\(677\) | −44.7846 | −1.72121 | −0.860606 | − | 0.509271i | \(-0.829915\pi\) | ||||
−0.860606 | + | 0.509271i | \(0.829915\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.0000 | −0.614024 | ||||||||
\(680\) | 11.1962 | 0.429353 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 19.8564 | 0.760341 | ||||||||
\(683\) | 39.7128 | 1.51957 | 0.759784 | − | 0.650175i | \(-0.225305\pi\) | ||||
0.759784 | + | 0.650175i | \(0.225305\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.60770 | 0.176051 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 12.3923 | 0.472452 | ||||||||
\(689\) | 9.46410 | 0.360554 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.0000 | 1.67384 | 0.836919 | − | 0.547326i | \(-0.184354\pi\) | ||||
0.836919 | + | 0.547326i | \(0.184354\pi\) | |||||||
\(692\) | 12.8038 | 0.486729 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.3923 | 0.622243 | ||||||||
\(695\) | −31.5167 | −1.19550 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.3923 | 0.620903 | ||||||||
\(698\) | −12.3923 | −0.469056 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.00000 | −0.0755929 | ||||||||
\(701\) | −46.1769 | −1.74408 | −0.872039 | − | 0.489436i | \(-0.837203\pi\) | ||||
−0.872039 | + | 0.489436i | \(0.837203\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.8038 | 0.746916 | ||||||||
\(704\) | −4.73205 | −0.178346 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.14359 | 0.155946 | ||||||||
\(707\) | −12.9282 | −0.486215 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.58846 | −0.284990 | −0.142495 | − | 0.989795i | \(-0.545513\pi\) | ||||
−0.142495 | + | 0.989795i | \(0.545513\pi\) | |||||||
\(710\) | −7.60770 | −0.285512 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −12.4641 | −0.467112 | ||||||||
\(713\) | −5.32051 | −0.199255 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.19615 | 0.306519 | ||||||||
\(716\) | −7.26795 | −0.271616 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 18.9282 | 0.706394 | ||||||||
\(719\) | −23.3205 | −0.869708 | −0.434854 | − | 0.900501i | \(-0.643200\pi\) | ||||
−0.434854 | + | 0.900501i | \(0.643200\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.39230 | −0.312546 | ||||||||
\(722\) | −19.3923 | −0.721707 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.392305 | 0.0145799 | ||||||||
\(725\) | 12.9282 | 0.480141 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.6077 | 0.578857 | 0.289429 | − | 0.957200i | \(-0.406535\pi\) | ||||
0.289429 | + | 0.957200i | \(0.406535\pi\) | |||||||
\(728\) | 1.00000 | 0.0370625 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 15.9282 | 0.589529 | ||||||||
\(731\) | −80.1051 | −2.96279 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.1769 | −1.07767 | −0.538837 | − | 0.842410i | \(-0.681136\pi\) | ||||
−0.538837 | + | 0.842410i | \(0.681136\pi\) | |||||||
\(734\) | 4.58846 | 0.169363 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.26795 | 0.0467372 | ||||||||
\(737\) | −19.8564 | −0.731420 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.1962 | −0.890070 | −0.445035 | − | 0.895513i | \(-0.646809\pi\) | ||||
−0.445035 | + | 0.895513i | \(0.646809\pi\) | |||||||
\(740\) | −5.53590 | −0.203504 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.46410 | 0.347438 | ||||||||
\(743\) | 21.4641 | 0.787442 | 0.393721 | − | 0.919230i | \(-0.371188\pi\) | ||||
0.393721 | + | 0.919230i | \(0.371188\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.80385 | 0.249274 | ||||||||
\(746\) | −20.0000 | −0.732252 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 30.5885 | 1.11842 | ||||||||
\(749\) | 13.8564 | 0.506302 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.00000 | −0.145962 | −0.0729810 | − | 0.997333i | \(-0.523251\pi\) | ||||
−0.0729810 | + | 0.997333i | \(0.523251\pi\) | |||||||
\(752\) | −2.19615 | −0.0800854 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.46410 | −0.235409 | ||||||||
\(755\) | −39.1244 | −1.42388 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.78461 | 0.173900 | 0.0869498 | − | 0.996213i | \(-0.472288\pi\) | ||||
0.0869498 | + | 0.996213i | \(0.472288\pi\) | |||||||
\(758\) | 16.5885 | 0.602520 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.7321 | 0.389292 | ||||||||
\(761\) | 8.32051 | 0.301618 | 0.150809 | − | 0.988563i | \(-0.451812\pi\) | ||||
0.150809 | + | 0.988563i | \(0.451812\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.80385 | −0.173911 | ||||||||
\(764\) | −24.5885 | −0.889579 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.1436 | −0.366503 | ||||||||
\(767\) | −8.19615 | −0.295946 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.19615 | 0.259500 | 0.129750 | − | 0.991547i | \(-0.458583\pi\) | ||||
0.129750 | + | 0.991547i | \(0.458583\pi\) | |||||||
\(770\) | 8.19615 | 0.295369 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −19.0000 | −0.683825 | ||||||||
\(773\) | 21.3397 | 0.767537 | 0.383769 | − | 0.923429i | \(-0.374626\pi\) | ||||
0.383769 | + | 0.923429i | \(0.374626\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.39230 | −0.301460 | ||||||||
\(776\) | 16.0000 | 0.574367 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −30.2487 | −1.08447 | ||||||||
\(779\) | 15.7128 | 0.562970 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.7846 | −0.743732 | ||||||||
\(782\) | −8.19615 | −0.293094 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 26.6603 | 0.951545 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.1769 | 1.61038 | 0.805192 | − | 0.593015i | \(-0.202062\pi\) | ||||
0.805192 | + | 0.593015i | \(0.202062\pi\) | |||||||
\(788\) | 15.0000 | 0.534353 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 10.7321 | 0.381829 | ||||||||
\(791\) | 10.2679 | 0.365086 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.39230 | −0.333531 | ||||||||
\(794\) | 29.3923 | 1.04309 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.5885 | 0.729739 | ||||||||
\(797\) | −21.3397 | −0.755893 | −0.377946 | − | 0.925828i | \(-0.623370\pi\) | ||||
−0.377946 | + | 0.925828i | \(0.623370\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.1962 | 0.502224 | ||||||||
\(800\) | 2.00000 | 0.0707107 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 22.2679 | 0.786309 | ||||||||
\(803\) | 43.5167 | 1.53567 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.19615 | −0.0774042 | ||||||||
\(806\) | 4.19615 | 0.147803 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12.9282 | 0.454813 | ||||||||
\(809\) | 0.124356 | 0.00437211 | 0.00218606 | − | 0.999998i | \(-0.499304\pi\) | ||||
0.00218606 | + | 0.999998i | \(0.499304\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 54.9808 | 1.93064 | 0.965318 | − | 0.261078i | \(-0.0840778\pi\) | ||||
0.965318 | + | 0.261078i | \(0.0840778\pi\) | |||||||
\(812\) | −6.46410 | −0.226845 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −15.1244 | −0.530108 | ||||||||
\(815\) | 42.2487 | 1.47991 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −76.7846 | −2.68635 | ||||||||
\(818\) | 21.1962 | 0.741106 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.39230 | −0.153386 | ||||||||
\(821\) | 15.0000 | 0.523504 | 0.261752 | − | 0.965135i | \(-0.415700\pi\) | ||||
0.261752 | + | 0.965135i | \(0.415700\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.7846 | −0.863937 | −0.431969 | − | 0.901889i | \(-0.642181\pi\) | ||||
−0.431969 | + | 0.901889i | \(0.642181\pi\) | |||||||
\(824\) | 8.39230 | 0.292360 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.19615 | −0.285181 | ||||||||
\(827\) | −19.6077 | −0.681826 | −0.340913 | − | 0.940095i | \(-0.610736\pi\) | ||||
−0.340913 | + | 0.940095i | \(0.610736\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.0000 | 0.903017 | 0.451509 | − | 0.892267i | \(-0.350886\pi\) | ||||
0.451509 | + | 0.892267i | \(0.350886\pi\) | |||||||
\(830\) | 2.19615 | 0.0762296 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | −6.46410 | −0.223968 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.5885 | 0.435642 | ||||||||
\(836\) | 29.3205 | 1.01407 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 23.3205 | 0.805594 | ||||||||
\(839\) | −42.2487 | −1.45859 | −0.729294 | − | 0.684201i | \(-0.760151\pi\) | ||||
−0.729294 | + | 0.684201i | \(0.760151\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.7846 | 0.440849 | ||||||||
\(842\) | −13.1962 | −0.454769 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 11.8038 | 0.406305 | ||||||||
\(845\) | −20.7846 | −0.715012 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.3923 | 0.391444 | ||||||||
\(848\) | −9.46410 | −0.324999 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −12.9282 | −0.443434 | ||||||||
\(851\) | 4.05256 | 0.138920 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.00000 | 0.0684787 | 0.0342393 | − | 0.999414i | \(-0.489099\pi\) | ||||
0.0342393 | + | 0.999414i | \(0.489099\pi\) | |||||||
\(854\) | −9.39230 | −0.321398 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.8564 | −0.473602 | ||||||||
\(857\) | 18.4641 | 0.630722 | 0.315361 | − | 0.948972i | \(-0.397874\pi\) | ||||
0.315361 | + | 0.948972i | \(0.397874\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.392305 | 0.0133853 | 0.00669263 | − | 0.999978i | \(-0.497870\pi\) | ||||
0.00669263 | + | 0.999978i | \(0.497870\pi\) | |||||||
\(860\) | 21.4641 | 0.731920 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.679492 | 0.0231436 | ||||||||
\(863\) | −23.9090 | −0.813871 | −0.406935 | − | 0.913457i | \(-0.633403\pi\) | ||||
−0.406935 | + | 0.913457i | \(0.633403\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.1769 | 0.754038 | ||||||||
\(866\) | 31.5885 | 1.07342 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.19615 | 0.142427 | ||||||||
\(869\) | 29.3205 | 0.994630 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.19615 | −0.142181 | ||||||||
\(872\) | 4.80385 | 0.162679 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7.85641 | −0.265747 | ||||||||
\(875\) | −12.1244 | −0.409878 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.1962 | 1.05342 | 0.526710 | − | 0.850045i | \(-0.323426\pi\) | ||||
0.526710 | + | 0.850045i | \(0.323426\pi\) | |||||||
\(878\) | −21.1769 | −0.714686 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8.19615 | −0.276292 | ||||||||
\(881\) | 25.1769 | 0.848232 | 0.424116 | − | 0.905608i | \(-0.360585\pi\) | ||||
0.424116 | + | 0.905608i | \(0.360585\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.9808 | 0.436837 | 0.218419 | − | 0.975855i | \(-0.429910\pi\) | ||||
0.218419 | + | 0.975855i | \(0.429910\pi\) | |||||||
\(884\) | 6.46410 | 0.217411 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.19615 | 0.0737812 | ||||||||
\(887\) | −35.6603 | −1.19735 | −0.598677 | − | 0.800990i | \(-0.704307\pi\) | ||||
−0.598677 | + | 0.800990i | \(0.704307\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.00000 | −0.134156 | ||||||||
\(890\) | −21.5885 | −0.723647 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.3923 | 0.414925 | ||||||||
\(893\) | 13.6077 | 0.455364 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.5885 | −0.420786 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.00000 | 0.200223 | ||||||||
\(899\) | −27.1244 | −0.904648 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 61.1769 | 2.03810 | ||||||||
\(902\) | −12.0000 | −0.399556 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.2679 | −0.341507 | ||||||||
\(905\) | 0.679492 | 0.0225871 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.0000 | 0.664089 | 0.332045 | − | 0.943264i | \(-0.392262\pi\) | ||||
0.332045 | + | 0.943264i | \(0.392262\pi\) | |||||||
\(908\) | 5.07180 | 0.168313 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.73205 | 0.0574169 | ||||||||
\(911\) | 32.1051 | 1.06369 | 0.531845 | − | 0.846842i | \(-0.321499\pi\) | ||||
0.531845 | + | 0.846842i | \(0.321499\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.00000 | 0.198571 | ||||||||
\(914\) | 1.00000 | 0.0330771 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −21.7846 | −0.719784 | ||||||||
\(917\) | 2.53590 | 0.0837427 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.8038 | −1.24703 | −0.623517 | − | 0.781810i | \(-0.714297\pi\) | ||||
−0.623517 | + | 0.781810i | \(0.714297\pi\) | |||||||
\(920\) | 2.19615 | 0.0724050 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 11.0718 | 0.364630 | ||||||||
\(923\) | −4.39230 | −0.144574 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.39230 | 0.210178 | ||||||||
\(926\) | −5.80385 | −0.190726 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.46410 | 0.212195 | ||||||||
\(929\) | −7.39230 | −0.242534 | −0.121267 | − | 0.992620i | \(-0.538696\pi\) | ||||
−0.121267 | + | 0.992620i | \(0.538696\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.19615 | −0.203071 | ||||||||
\(932\) | −13.7321 | −0.449808 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.26795 | −0.0414886 | ||||||||
\(935\) | 52.9808 | 1.73266 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.8038 | −0.744969 | −0.372485 | − | 0.928038i | \(-0.621494\pi\) | ||||
−0.372485 | + | 0.928038i | \(0.621494\pi\) | |||||||
\(938\) | −4.19615 | −0.137009 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.80385 | −0.124068 | ||||||||
\(941\) | 46.7654 | 1.52451 | 0.762254 | − | 0.647278i | \(-0.224093\pi\) | ||||
0.762254 | + | 0.647278i | \(0.224093\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.21539 | 0.104708 | ||||||||
\(944\) | 8.19615 | 0.266762 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 58.6410 | 1.90658 | ||||||||
\(947\) | 7.60770 | 0.247217 | 0.123608 | − | 0.992331i | \(-0.460553\pi\) | ||||
0.123608 | + | 0.992331i | \(0.460553\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.19615 | 0.298520 | ||||||||
\(950\) | −12.3923 | −0.402059 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.46410 | 0.209503 | ||||||||
\(953\) | 55.9808 | 1.81339 | 0.906697 | − | 0.421782i | \(-0.138595\pi\) | ||||
0.906697 | + | 0.421782i | \(0.138595\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −42.5885 | −1.37813 | ||||||||
\(956\) | −15.1244 | −0.489157 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 16.7321 | 0.540588 | ||||||||
\(959\) | 2.66025 | 0.0859041 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.3923 | −0.432010 | ||||||||
\(962\) | −3.19615 | −0.103048 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −13.5885 | −0.437655 | ||||||||
\(965\) | −32.9090 | −1.05938 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.5885 | −0.726396 | −0.363198 | − | 0.931712i | \(-0.618315\pi\) | ||||
−0.363198 | + | 0.931712i | \(0.618315\pi\) | |||||||
\(968\) | −11.3923 | −0.366163 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 27.7128 | 0.889805 | ||||||||
\(971\) | −3.12436 | −0.100265 | −0.0501327 | − | 0.998743i | \(-0.515964\pi\) | ||||
−0.0501327 | + | 0.998743i | \(0.515964\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.1962 | −0.583342 | ||||||||
\(974\) | 6.19615 | 0.198538 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.39230 | 0.300640 | ||||||||
\(977\) | −35.5692 | −1.13796 | −0.568980 | − | 0.822351i | \(-0.692662\pi\) | ||||
−0.568980 | + | 0.822351i | \(0.692662\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −58.9808 | −1.88503 | ||||||||
\(980\) | 1.73205 | 0.0553283 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 11.3205 | 0.361252 | ||||||||
\(983\) | 41.0718 | 1.30999 | 0.654993 | − | 0.755635i | \(-0.272671\pi\) | ||||
0.654993 | + | 0.755635i | \(0.272671\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.9808 | 0.827816 | ||||||||
\(986\) | −41.7846 | −1.33069 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.19615 | 0.197126 | ||||||||
\(989\) | −15.7128 | −0.499638 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.9808 | 1.36533 | 0.682664 | − | 0.730732i | \(-0.260821\pi\) | ||||
0.682664 | + | 0.730732i | \(0.260821\pi\) | |||||||
\(992\) | −4.19615 | −0.133228 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.39230 | −0.139315 | ||||||||
\(995\) | 35.6603 | 1.13051 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.7846 | −0.689926 | −0.344963 | − | 0.938616i | \(-0.612108\pi\) | ||||
−0.344963 | + | 0.938616i | \(0.612108\pi\) | |||||||
\(998\) | −20.5885 | −0.651716 | ||||||||
\(999\) | 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 | 1134.2.a.j.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 1134.2.a.o.1.1 | yes | 2 | ||
4.3 | odd | 2 | 9072.2.a.bi.1.2 | 2 | |||
7.6 | odd | 2 | 7938.2.a.bi.1.1 | 2 | |||
9.2 | odd | 6 | 1134.2.f.q.757.2 | 4 | |||
9.4 | even | 3 | 1134.2.f.t.379.1 | 4 | |||
9.5 | odd | 6 | 1134.2.f.q.379.2 | 4 | |||
9.7 | even | 3 | 1134.2.f.t.757.1 | 4 | |||
12.11 | even | 2 | 9072.2.a.bf.1.1 | 2 | |||
21.20 | even | 2 | 7938.2.a.br.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1134.2.a.j.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1134.2.a.o.1.1 | yes | 2 | 3.2 | odd | 2 | ||
1134.2.f.q.379.2 | 4 | 9.5 | odd | 6 | |||
1134.2.f.q.757.2 | 4 | 9.2 | odd | 6 | |||
1134.2.f.t.379.1 | 4 | 9.4 | even | 3 | |||
1134.2.f.t.757.1 | 4 | 9.7 | even | 3 | |||
7938.2.a.bi.1.1 | 2 | 7.6 | odd | 2 | |||
7938.2.a.br.1.2 | 2 | 21.20 | even | 2 | |||
9072.2.a.bf.1.1 | 2 | 12.11 | even | 2 | |||
9072.2.a.bi.1.2 | 2 | 4.3 | odd | 2 |