Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2178,2,Mod(1,2178)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2178, 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("2178.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2178 = 2 \cdot 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2178.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: | \(17.3914175602\) |
Analytic rank: | \(0\) |
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: | no (minimal twist has level 242) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2178.1 |
$q$-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 | ||||||||
\(7\) | 4.73205 | 1.78855 | 0.894274 | − | 0.447521i | \(-0.147693\pi\) | ||||
0.894274 | + | 0.447521i | \(0.147693\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.73205 | −0.547723 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00000 | 0.832050 | 0.416025 | − | 0.909353i | \(-0.363423\pi\) | ||||
0.416025 | + | 0.909353i | \(0.363423\pi\) | |||||||
\(14\) | −4.73205 | −1.26469 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.19615 | 1.26025 | 0.630126 | − | 0.776493i | \(-0.283003\pi\) | ||||
0.630126 | + | 0.776493i | \(0.283003\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.26795 | 0.290887 | 0.145444 | − | 0.989367i | \(-0.453539\pi\) | ||||
0.145444 | + | 0.989367i | \(0.453539\pi\) | |||||||
\(20\) | 1.73205 | 0.387298 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.26795 | 0.264386 | 0.132193 | − | 0.991224i | \(-0.457798\pi\) | ||||
0.132193 | + | 0.991224i | \(0.457798\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | −0.400000 | ||||||||
\(26\) | −3.00000 | −0.588348 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.73205 | 0.894274 | ||||||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.196152 | 0.0352300 | 0.0176150 | − | 0.999845i | \(-0.494393\pi\) | ||||
0.0176150 | + | 0.999845i | \(0.494393\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.19615 | −0.891133 | ||||||||
\(35\) | 8.19615 | 1.38540 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.19615 | −1.18304 | −0.591520 | − | 0.806290i | \(-0.701472\pi\) | ||||
−0.591520 | + | 0.806290i | \(0.701472\pi\) | |||||||
\(38\) | −1.26795 | −0.205689 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.73205 | −0.273861 | ||||||||
\(41\) | 0.803848 | 0.125540 | 0.0627700 | − | 0.998028i | \(-0.480007\pi\) | ||||
0.0627700 | + | 0.998028i | \(0.480007\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.26795 | −0.186949 | ||||||||
\(47\) | 8.19615 | 1.19553 | 0.597766 | − | 0.801671i | \(-0.296055\pi\) | ||||
0.597766 | + | 0.801671i | \(0.296055\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.3923 | 2.19890 | ||||||||
\(50\) | 2.00000 | 0.282843 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.00000 | 0.416025 | ||||||||
\(53\) | −11.1962 | −1.53791 | −0.768955 | − | 0.639303i | \(-0.779223\pi\) | ||||
−0.768955 | + | 0.639303i | \(0.779223\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.73205 | −0.632347 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.00000 | −0.393919 | ||||||||
\(59\) | −9.46410 | −1.23212 | −0.616061 | − | 0.787699i | \(-0.711272\pi\) | ||||
−0.616061 | + | 0.787699i | \(0.711272\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.53590 | 0.324689 | 0.162344 | − | 0.986734i | \(-0.448094\pi\) | ||||
0.162344 | + | 0.986734i | \(0.448094\pi\) | |||||||
\(62\) | −0.196152 | −0.0249114 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.19615 | 0.644503 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.1962 | −1.24566 | −0.622829 | − | 0.782358i | \(-0.714017\pi\) | ||||
−0.622829 | + | 0.782358i | \(0.714017\pi\) | |||||||
\(68\) | 5.19615 | 0.630126 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8.19615 | −0.979628 | ||||||||
\(71\) | 9.46410 | 1.12318 | 0.561591 | − | 0.827415i | \(-0.310189\pi\) | ||||
0.561591 | + | 0.827415i | \(0.310189\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.928203 | −0.108638 | −0.0543190 | − | 0.998524i | \(-0.517299\pi\) | ||||
−0.0543190 | + | 0.998524i | \(0.517299\pi\) | |||||||
\(74\) | 7.19615 | 0.836536 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.26795 | 0.145444 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.73205 | −0.532397 | −0.266199 | − | 0.963918i | \(-0.585768\pi\) | ||||
−0.266199 | + | 0.963918i | \(0.585768\pi\) | |||||||
\(80\) | 1.73205 | 0.193649 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.803848 | −0.0887701 | ||||||||
\(83\) | −8.19615 | −0.899645 | −0.449822 | − | 0.893118i | \(-0.648513\pi\) | ||||
−0.449822 | + | 0.893118i | \(0.648513\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.00000 | 0.976187 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.46410 | −0.685193 | −0.342597 | − | 0.939483i | \(-0.611306\pi\) | ||||
−0.342597 | + | 0.939483i | \(0.611306\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.1962 | 1.48816 | ||||||||
\(92\) | 1.26795 | 0.132193 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.19615 | −0.845369 | ||||||||
\(95\) | 2.19615 | 0.225320 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.00000 | −0.101535 | −0.0507673 | − | 0.998711i | \(-0.516167\pi\) | ||||
−0.0507673 | + | 0.998711i | \(0.516167\pi\) | |||||||
\(98\) | −15.3923 | −1.55486 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.00000 | −0.200000 | ||||||||
\(101\) | −16.3923 | −1.63110 | −0.815548 | − | 0.578690i | \(-0.803564\pi\) | ||||
−0.815548 | + | 0.578690i | \(0.803564\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.39230 | −0.826918 | −0.413459 | − | 0.910523i | \(-0.635680\pi\) | ||||
−0.413459 | + | 0.910523i | \(0.635680\pi\) | |||||||
\(104\) | −3.00000 | −0.294174 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.1962 | 1.08747 | ||||||||
\(107\) | −12.5885 | −1.21697 | −0.608486 | − | 0.793565i | \(-0.708223\pi\) | ||||
−0.608486 | + | 0.793565i | \(0.708223\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.07180 | −0.198442 | −0.0992211 | − | 0.995065i | \(-0.531635\pi\) | ||||
−0.0992211 | + | 0.995065i | \(0.531635\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.73205 | 0.447137 | ||||||||
\(113\) | −10.8564 | −1.02128 | −0.510642 | − | 0.859793i | \(-0.670592\pi\) | ||||
−0.510642 | + | 0.859793i | \(0.670592\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.19615 | 0.204792 | ||||||||
\(116\) | 3.00000 | 0.278543 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.46410 | 0.871241 | ||||||||
\(119\) | 24.5885 | 2.25402 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −2.53590 | −0.229589 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.196152 | 0.0176150 | ||||||||
\(125\) | −12.1244 | −1.08444 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.8564 | 1.22956 | 0.614779 | − | 0.788700i | \(-0.289245\pi\) | ||||
0.614779 | + | 0.788700i | \(0.289245\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.19615 | −0.455733 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.00000 | 0.520266 | ||||||||
\(134\) | 10.1962 | 0.880813 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.19615 | −0.445566 | ||||||||
\(137\) | 9.46410 | 0.808573 | 0.404286 | − | 0.914632i | \(-0.367520\pi\) | ||||
0.404286 | + | 0.914632i | \(0.367520\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.1962 | 1.71302 | 0.856508 | − | 0.516134i | \(-0.172629\pi\) | ||||
0.856508 | + | 0.516134i | \(0.172629\pi\) | |||||||
\(140\) | 8.19615 | 0.692701 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.46410 | −0.794210 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.19615 | 0.431517 | ||||||||
\(146\) | 0.928203 | 0.0768186 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.19615 | −0.591520 | ||||||||
\(149\) | 15.0000 | 1.22885 | 0.614424 | − | 0.788976i | \(-0.289388\pi\) | ||||
0.614424 | + | 0.788976i | \(0.289388\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.39230 | −0.357441 | −0.178720 | − | 0.983900i | \(-0.557196\pi\) | ||||
−0.178720 | + | 0.983900i | \(0.557196\pi\) | |||||||
\(152\) | −1.26795 | −0.102844 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.339746 | 0.0272891 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.00000 | 0.319235 | 0.159617 | − | 0.987179i | \(-0.448974\pi\) | ||||
0.159617 | + | 0.987179i | \(0.448974\pi\) | |||||||
\(158\) | 4.73205 | 0.376462 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.73205 | −0.136931 | ||||||||
\(161\) | 6.00000 | 0.472866 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.1962 | 1.73854 | 0.869268 | − | 0.494340i | \(-0.164590\pi\) | ||||
0.869268 | + | 0.494340i | \(0.164590\pi\) | |||||||
\(164\) | 0.803848 | 0.0627700 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.19615 | 0.636145 | ||||||||
\(167\) | −16.3923 | −1.26847 | −0.634237 | − | 0.773138i | \(-0.718686\pi\) | ||||
−0.634237 | + | 0.773138i | \(0.718686\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.00000 | −0.307692 | ||||||||
\(170\) | −9.00000 | −0.690268 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.39230 | 0.333941 | 0.166970 | − | 0.985962i | \(-0.446602\pi\) | ||||
0.166970 | + | 0.985962i | \(0.446602\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.46410 | −0.715419 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.46410 | 0.484505 | ||||||||
\(179\) | 13.8564 | 1.03568 | 0.517838 | − | 0.855479i | \(-0.326737\pi\) | ||||
0.517838 | + | 0.855479i | \(0.326737\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.19615 | 0.534886 | 0.267443 | − | 0.963574i | \(-0.413821\pi\) | ||||
0.267443 | + | 0.963574i | \(0.413821\pi\) | |||||||
\(182\) | −14.1962 | −1.05229 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.26795 | −0.0934745 | ||||||||
\(185\) | −12.4641 | −0.916379 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 8.19615 | 0.597766 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.19615 | −0.159326 | ||||||||
\(191\) | 21.4641 | 1.55309 | 0.776544 | − | 0.630063i | \(-0.216971\pi\) | ||||
0.776544 | + | 0.630063i | \(0.216971\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.2679 | 0.739103 | 0.369552 | − | 0.929210i | \(-0.379511\pi\) | ||||
0.369552 | + | 0.929210i | \(0.379511\pi\) | |||||||
\(194\) | 1.00000 | 0.0717958 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 15.3923 | 1.09945 | ||||||||
\(197\) | 13.3923 | 0.954162 | 0.477081 | − | 0.878859i | \(-0.341695\pi\) | ||||
0.477081 | + | 0.878859i | \(0.341695\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.392305 | −0.0278098 | −0.0139049 | − | 0.999903i | \(-0.504426\pi\) | ||||
−0.0139049 | + | 0.999903i | \(0.504426\pi\) | |||||||
\(200\) | 2.00000 | 0.141421 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 16.3923 | 1.15336 | ||||||||
\(203\) | 14.1962 | 0.996375 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.39230 | 0.0972428 | ||||||||
\(206\) | 8.39230 | 0.584720 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.00000 | 0.208013 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.8564 | −1.78003 | −0.890014 | − | 0.455933i | \(-0.849306\pi\) | ||||
−0.890014 | + | 0.455933i | \(0.849306\pi\) | |||||||
\(212\) | −11.1962 | −0.768955 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 12.5885 | 0.860529 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.928203 | 0.0630105 | ||||||||
\(218\) | 2.07180 | 0.140320 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.5885 | 1.04859 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.3923 | −1.36557 | −0.682785 | − | 0.730619i | \(-0.739231\pi\) | ||||
−0.682785 | + | 0.730619i | \(0.739231\pi\) | |||||||
\(224\) | −4.73205 | −0.316173 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.8564 | 0.722157 | ||||||||
\(227\) | 16.3923 | 1.08800 | 0.543998 | − | 0.839087i | \(-0.316910\pi\) | ||||
0.543998 | + | 0.839087i | \(0.316910\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.1962 | −0.872026 | −0.436013 | − | 0.899940i | \(-0.643610\pi\) | ||||
−0.436013 | + | 0.899940i | \(0.643610\pi\) | |||||||
\(230\) | −2.19615 | −0.144810 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.00000 | −0.196960 | ||||||||
\(233\) | 6.80385 | 0.445735 | 0.222867 | − | 0.974849i | \(-0.428458\pi\) | ||||
0.222867 | + | 0.974849i | \(0.428458\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.1962 | 0.926055 | ||||||||
\(236\) | −9.46410 | −0.616061 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −24.5885 | −1.59383 | ||||||||
\(239\) | 14.1962 | 0.918273 | 0.459136 | − | 0.888366i | \(-0.348159\pi\) | ||||
0.459136 | + | 0.888366i | \(0.348159\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.7846 | 1.72535 | 0.862674 | − | 0.505760i | \(-0.168788\pi\) | ||||
0.862674 | + | 0.505760i | \(0.168788\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.53590 | 0.162344 | ||||||||
\(245\) | 26.6603 | 1.70326 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.80385 | 0.242033 | ||||||||
\(248\) | −0.196152 | −0.0124557 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12.1244 | 0.766812 | ||||||||
\(251\) | −9.12436 | −0.575924 | −0.287962 | − | 0.957642i | \(-0.592978\pi\) | ||||
−0.287962 | + | 0.957642i | \(0.592978\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −13.8564 | −0.869428 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 19.3923 | 1.20966 | 0.604829 | − | 0.796355i | \(-0.293241\pi\) | ||||
0.604829 | + | 0.796355i | \(0.293241\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −34.0526 | −2.11592 | ||||||||
\(260\) | 5.19615 | 0.322252 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.80385 | −0.604531 | −0.302266 | − | 0.953224i | \(-0.597743\pi\) | ||||
−0.302266 | + | 0.953224i | \(0.597743\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −19.3923 | −1.19126 | ||||||||
\(266\) | −6.00000 | −0.367884 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.1962 | −0.622829 | ||||||||
\(269\) | −9.58846 | −0.584619 | −0.292309 | − | 0.956324i | \(-0.594424\pi\) | ||||
−0.292309 | + | 0.956324i | \(0.594424\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.3923 | −0.995762 | −0.497881 | − | 0.867245i | \(-0.665888\pi\) | ||||
−0.497881 | + | 0.867245i | \(0.665888\pi\) | |||||||
\(272\) | 5.19615 | 0.315063 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.46410 | −0.571747 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.32051 | −0.499931 | −0.249965 | − | 0.968255i | \(-0.580419\pi\) | ||||
−0.249965 | + | 0.968255i | \(0.580419\pi\) | |||||||
\(278\) | −20.1962 | −1.21128 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.19615 | −0.489814 | ||||||||
\(281\) | −18.0000 | −1.07379 | −0.536895 | − | 0.843649i | \(-0.680403\pi\) | ||||
−0.536895 | + | 0.843649i | \(0.680403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.92820 | 0.411839 | 0.205919 | − | 0.978569i | \(-0.433982\pi\) | ||||
0.205919 | + | 0.978569i | \(0.433982\pi\) | |||||||
\(284\) | 9.46410 | 0.561591 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.80385 | 0.224534 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.0000 | 0.588235 | ||||||||
\(290\) | −5.19615 | −0.305129 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.928203 | −0.0543190 | ||||||||
\(293\) | −23.7846 | −1.38951 | −0.694756 | − | 0.719246i | \(-0.744488\pi\) | ||||
−0.694756 | + | 0.719246i | \(0.744488\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.3923 | −0.954397 | ||||||||
\(296\) | 7.19615 | 0.418268 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −15.0000 | −0.868927 | ||||||||
\(299\) | 3.80385 | 0.219982 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4.39230 | 0.252749 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.26795 | 0.0727219 | ||||||||
\(305\) | 4.39230 | 0.251503 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.2679 | 1.44212 | 0.721059 | − | 0.692874i | \(-0.243656\pi\) | ||||
0.721059 | + | 0.692874i | \(0.243656\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.339746 | −0.0192963 | ||||||||
\(311\) | −8.78461 | −0.498130 | −0.249065 | − | 0.968487i | \(-0.580123\pi\) | ||||
−0.249065 | + | 0.968487i | \(0.580123\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −31.7846 | −1.79657 | −0.898286 | − | 0.439411i | \(-0.855187\pi\) | ||||
−0.898286 | + | 0.439411i | \(0.855187\pi\) | |||||||
\(314\) | −4.00000 | −0.225733 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.73205 | −0.266199 | ||||||||
\(317\) | 7.85641 | 0.441260 | 0.220630 | − | 0.975358i | \(-0.429189\pi\) | ||||
0.220630 | + | 0.975358i | \(0.429189\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.73205 | 0.0968246 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.00000 | −0.334367 | ||||||||
\(323\) | 6.58846 | 0.366592 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.00000 | −0.332820 | ||||||||
\(326\) | −22.1962 | −1.22933 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.803848 | −0.0443851 | ||||||||
\(329\) | 38.7846 | 2.13826 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.7846 | 1.58215 | 0.791073 | − | 0.611722i | \(-0.209523\pi\) | ||||
0.791073 | + | 0.611722i | \(0.209523\pi\) | |||||||
\(332\) | −8.19615 | −0.449822 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 16.3923 | 0.896947 | ||||||||
\(335\) | −17.6603 | −0.964883 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.66025 | 0.144913 | 0.0724566 | − | 0.997372i | \(-0.476916\pi\) | ||||
0.0724566 | + | 0.997372i | \(0.476916\pi\) | |||||||
\(338\) | 4.00000 | 0.217571 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9.00000 | 0.488094 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 39.7128 | 2.14429 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.39230 | −0.236132 | ||||||||
\(347\) | 28.3923 | 1.52418 | 0.762089 | − | 0.647472i | \(-0.224174\pi\) | ||||
0.762089 | + | 0.647472i | \(0.224174\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.9282 | −1.17379 | −0.586895 | − | 0.809663i | \(-0.699650\pi\) | ||||
−0.586895 | + | 0.809663i | \(0.699650\pi\) | |||||||
\(350\) | 9.46410 | 0.505878 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.9282 | −1.16712 | −0.583560 | − | 0.812070i | \(-0.698341\pi\) | ||||
−0.583560 | + | 0.812070i | \(0.698341\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.3923 | 0.870013 | ||||||||
\(356\) | −6.46410 | −0.342597 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.8564 | −0.732334 | ||||||||
\(359\) | 6.58846 | 0.347725 | 0.173863 | − | 0.984770i | \(-0.444375\pi\) | ||||
0.173863 | + | 0.984770i | \(0.444375\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.3923 | −0.915384 | ||||||||
\(362\) | −7.19615 | −0.378221 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 14.1962 | 0.744081 | ||||||||
\(365\) | −1.60770 | −0.0841506 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.58846 | 0.448314 | 0.224157 | − | 0.974553i | \(-0.428037\pi\) | ||||
0.224157 | + | 0.974553i | \(0.428037\pi\) | |||||||
\(368\) | 1.26795 | 0.0660964 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 12.4641 | 0.647978 | ||||||||
\(371\) | −52.9808 | −2.75062 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.3205 | −0.586154 | −0.293077 | − | 0.956089i | \(-0.594679\pi\) | ||||
−0.293077 | + | 0.956089i | \(0.594679\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.19615 | −0.422684 | ||||||||
\(377\) | 9.00000 | 0.463524 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.60770 | 0.185315 | 0.0926574 | − | 0.995698i | \(-0.470464\pi\) | ||||
0.0926574 | + | 0.995698i | \(0.470464\pi\) | |||||||
\(380\) | 2.19615 | 0.112660 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −21.4641 | −1.09820 | ||||||||
\(383\) | 0.679492 | 0.0347204 | 0.0173602 | − | 0.999849i | \(-0.494474\pi\) | ||||
0.0173602 | + | 0.999849i | \(0.494474\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.2679 | −0.522625 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.00000 | −0.0507673 | ||||||||
\(389\) | −32.6603 | −1.65594 | −0.827970 | − | 0.560772i | \(-0.810504\pi\) | ||||
−0.827970 | + | 0.560772i | \(0.810504\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.58846 | 0.333193 | ||||||||
\(392\) | −15.3923 | −0.777429 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −13.3923 | −0.674695 | ||||||||
\(395\) | −8.19615 | −0.412393 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.58846 | 0.280477 | 0.140238 | − | 0.990118i | \(-0.455213\pi\) | ||||
0.140238 | + | 0.990118i | \(0.455213\pi\) | |||||||
\(398\) | 0.392305 | 0.0196645 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.00000 | −0.100000 | ||||||||
\(401\) | 7.39230 | 0.369154 | 0.184577 | − | 0.982818i | \(-0.440908\pi\) | ||||
0.184577 | + | 0.982818i | \(0.440908\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.588457 | 0.0293131 | ||||||||
\(404\) | −16.3923 | −0.815548 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −14.1962 | −0.704543 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.66025 | −0.131541 | −0.0657705 | − | 0.997835i | \(-0.520951\pi\) | ||||
−0.0657705 | + | 0.997835i | \(0.520951\pi\) | |||||||
\(410\) | −1.39230 | −0.0687610 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.39230 | −0.413459 | ||||||||
\(413\) | −44.7846 | −2.20371 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.1962 | −0.696862 | ||||||||
\(416\) | −3.00000 | −0.147087 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 39.3731 | 1.92350 | 0.961750 | − | 0.273928i | \(-0.0883231\pi\) | ||||
0.961750 | + | 0.273928i | \(0.0883231\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.58846 | 0.369839 | 0.184919 | − | 0.982754i | \(-0.440798\pi\) | ||||
0.184919 | + | 0.982754i | \(0.440798\pi\) | |||||||
\(422\) | 25.8564 | 1.25867 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.1962 | 0.543733 | ||||||||
\(425\) | −10.3923 | −0.504101 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.0000 | 0.580721 | ||||||||
\(428\) | −12.5885 | −0.608486 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.3923 | −0.789590 | −0.394795 | − | 0.918769i | \(-0.629184\pi\) | ||||
−0.394795 | + | 0.918769i | \(0.629184\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.7846 | 1.52747 | 0.763735 | − | 0.645529i | \(-0.223363\pi\) | ||||
0.763735 | + | 0.645529i | \(0.223363\pi\) | |||||||
\(434\) | −0.928203 | −0.0445552 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.07180 | −0.0992211 | ||||||||
\(437\) | 1.60770 | 0.0769065 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.1244 | −1.00821 | −0.504105 | − | 0.863642i | \(-0.668178\pi\) | ||||
−0.504105 | + | 0.863642i | \(0.668178\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −15.5885 | −0.741467 | ||||||||
\(443\) | −17.0718 | −0.811106 | −0.405553 | − | 0.914072i | \(-0.632921\pi\) | ||||
−0.405553 | + | 0.914072i | \(0.632921\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.1962 | −0.530749 | ||||||||
\(446\) | 20.3923 | 0.965604 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.73205 | 0.223568 | ||||||||
\(449\) | 9.92820 | 0.468541 | 0.234270 | − | 0.972171i | \(-0.424730\pi\) | ||||
0.234270 | + | 0.972171i | \(0.424730\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −10.8564 | −0.510642 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −16.3923 | −0.769329 | ||||||||
\(455\) | 24.5885 | 1.15272 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.19615 | −0.243066 | −0.121533 | − | 0.992587i | \(-0.538781\pi\) | ||||
−0.121533 | + | 0.992587i | \(0.538781\pi\) | |||||||
\(458\) | 13.1962 | 0.616616 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.19615 | 0.102396 | ||||||||
\(461\) | −33.0000 | −1.53696 | −0.768482 | − | 0.639872i | \(-0.778987\pi\) | ||||
−0.768482 | + | 0.639872i | \(0.778987\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.7846 | 1.33773 | 0.668867 | − | 0.743382i | \(-0.266780\pi\) | ||||
0.668867 | + | 0.743382i | \(0.266780\pi\) | |||||||
\(464\) | 3.00000 | 0.139272 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.80385 | −0.315182 | ||||||||
\(467\) | −21.4641 | −0.993240 | −0.496620 | − | 0.867968i | \(-0.665426\pi\) | ||||
−0.496620 | + | 0.867968i | \(0.665426\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −48.2487 | −2.22792 | ||||||||
\(470\) | −14.1962 | −0.654820 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9.46410 | 0.435621 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.53590 | −0.116355 | ||||||||
\(476\) | 24.5885 | 1.12701 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −14.1962 | −0.649317 | ||||||||
\(479\) | 8.78461 | 0.401379 | 0.200690 | − | 0.979655i | \(-0.435682\pi\) | ||||
0.200690 | + | 0.979655i | \(0.435682\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21.5885 | −0.984349 | ||||||||
\(482\) | −26.7846 | −1.22001 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.73205 | −0.0786484 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.9808 | −0.588214 | −0.294107 | − | 0.955772i | \(-0.595022\pi\) | ||||
−0.294107 | + | 0.955772i | \(0.595022\pi\) | |||||||
\(488\) | −2.53590 | −0.114795 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −26.6603 | −1.20439 | ||||||||
\(491\) | 33.3731 | 1.50611 | 0.753053 | − | 0.657960i | \(-0.228581\pi\) | ||||
0.753053 | + | 0.657960i | \(0.228581\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.5885 | 0.702069 | ||||||||
\(494\) | −3.80385 | −0.171143 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.196152 | 0.00880750 | ||||||||
\(497\) | 44.7846 | 2.00886 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.0000 | 0.716258 | 0.358129 | − | 0.933672i | \(-0.383415\pi\) | ||||
0.358129 | + | 0.933672i | \(0.383415\pi\) | |||||||
\(500\) | −12.1244 | −0.542218 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.12436 | 0.407240 | ||||||||
\(503\) | 14.1962 | 0.632975 | 0.316488 | − | 0.948597i | \(-0.397496\pi\) | ||||
0.316488 | + | 0.948597i | \(0.397496\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −28.3923 | −1.26344 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.8564 | 0.614779 | ||||||||
\(509\) | −12.9282 | −0.573033 | −0.286516 | − | 0.958075i | \(-0.592497\pi\) | ||||
−0.286516 | + | 0.958075i | \(0.592497\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.39230 | −0.194304 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −19.3923 | −0.855358 | ||||||||
\(515\) | −14.5359 | −0.640528 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 34.0526 | 1.49618 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.19615 | −0.227866 | ||||||||
\(521\) | −9.46410 | −0.414630 | −0.207315 | − | 0.978274i | \(-0.566472\pi\) | ||||
−0.207315 | + | 0.978274i | \(0.566472\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.53590 | 0.110887 | 0.0554435 | − | 0.998462i | \(-0.482343\pi\) | ||||
0.0554435 | + | 0.998462i | \(0.482343\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.80385 | 0.427468 | ||||||||
\(527\) | 1.01924 | 0.0443987 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.3923 | −0.930100 | ||||||||
\(530\) | 19.3923 | 0.842348 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.00000 | 0.260133 | ||||||||
\(533\) | 2.41154 | 0.104456 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −21.8038 | −0.942663 | ||||||||
\(536\) | 10.1962 | 0.440407 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9.58846 | 0.413388 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.0000 | −1.28980 | −0.644900 | − | 0.764267i | \(-0.723101\pi\) | ||||
−0.644900 | + | 0.764267i | \(0.723101\pi\) | |||||||
\(542\) | 16.3923 | 0.704110 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.19615 | −0.222783 | ||||||||
\(545\) | −3.58846 | −0.153713 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.0000 | −1.02617 | −0.513083 | − | 0.858339i | \(-0.671497\pi\) | ||||
−0.513083 | + | 0.858339i | \(0.671497\pi\) | |||||||
\(548\) | 9.46410 | 0.404286 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.80385 | 0.162049 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22.3923 | −0.952218 | ||||||||
\(554\) | 8.32051 | 0.353505 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 20.1962 | 0.856508 | ||||||||
\(557\) | −37.1769 | −1.57524 | −0.787618 | − | 0.616164i | \(-0.788686\pi\) | ||||
−0.787618 | + | 0.616164i | \(0.788686\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 8.19615 | 0.346351 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.0000 | 0.759284 | ||||||||
\(563\) | 0.588457 | 0.0248005 | 0.0124003 | − | 0.999923i | \(-0.496053\pi\) | ||||
0.0124003 | + | 0.999923i | \(0.496053\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.8038 | −0.791084 | ||||||||
\(566\) | −6.92820 | −0.291214 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.46410 | −0.397105 | ||||||||
\(569\) | −42.0000 | −1.76073 | −0.880366 | − | 0.474295i | \(-0.842703\pi\) | ||||
−0.880366 | + | 0.474295i | \(0.842703\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.66025 | 0.236874 | 0.118437 | − | 0.992962i | \(-0.462212\pi\) | ||||
0.118437 | + | 0.992962i | \(0.462212\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.80385 | −0.158770 | ||||||||
\(575\) | −2.53590 | −0.105754 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.6077 | 0.608126 | 0.304063 | − | 0.952652i | \(-0.401657\pi\) | ||||
0.304063 | + | 0.952652i | \(0.401657\pi\) | |||||||
\(578\) | −10.0000 | −0.415945 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.19615 | 0.215758 | ||||||||
\(581\) | −38.7846 | −1.60906 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0.928203 | 0.0384093 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 23.7846 | 0.982533 | ||||||||
\(587\) | −30.5885 | −1.26252 | −0.631260 | − | 0.775571i | \(-0.717462\pi\) | ||||
−0.631260 | + | 0.775571i | \(0.717462\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.248711 | 0.0102480 | ||||||||
\(590\) | 16.3923 | 0.674861 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.19615 | −0.295760 | ||||||||
\(593\) | 23.1962 | 0.952552 | 0.476276 | − | 0.879296i | \(-0.341986\pi\) | ||||
0.476276 | + | 0.879296i | \(0.341986\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 42.5885 | 1.74596 | ||||||||
\(596\) | 15.0000 | 0.614424 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.80385 | −0.155551 | ||||||||
\(599\) | 3.80385 | 0.155421 | 0.0777105 | − | 0.996976i | \(-0.475239\pi\) | ||||
0.0777105 | + | 0.996976i | \(0.475239\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.66025 | −0.353259 | −0.176630 | − | 0.984277i | \(-0.556519\pi\) | ||||
−0.176630 | + | 0.984277i | \(0.556519\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.39230 | −0.178720 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.1962 | 1.06327 | 0.531635 | − | 0.846974i | \(-0.321578\pi\) | ||||
0.531635 | + | 0.846974i | \(0.321578\pi\) | |||||||
\(608\) | −1.26795 | −0.0514221 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.39230 | −0.177839 | ||||||||
\(611\) | 24.5885 | 0.994743 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.3205 | 0.820738 | 0.410369 | − | 0.911920i | \(-0.365400\pi\) | ||||
0.410369 | + | 0.911920i | \(0.365400\pi\) | |||||||
\(614\) | −25.2679 | −1.01973 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.6077 | −0.427050 | −0.213525 | − | 0.976938i | \(-0.568494\pi\) | ||||
−0.213525 | + | 0.976938i | \(0.568494\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.1962 | −1.21369 | −0.606843 | − | 0.794822i | \(-0.707564\pi\) | ||||
−0.606843 | + | 0.794822i | \(0.707564\pi\) | |||||||
\(620\) | 0.339746 | 0.0136445 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.78461 | 0.352231 | ||||||||
\(623\) | −30.5885 | −1.22550 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 31.7846 | 1.27037 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.00000 | 0.159617 | ||||||||
\(629\) | −37.3923 | −1.49093 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.5885 | −0.819614 | −0.409807 | − | 0.912172i | \(-0.634404\pi\) | ||||
−0.409807 | + | 0.912172i | \(0.634404\pi\) | |||||||
\(632\) | 4.73205 | 0.188231 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.85641 | −0.312018 | ||||||||
\(635\) | 24.0000 | 0.952411 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 46.1769 | 1.82960 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.73205 | −0.0684653 | ||||||||
\(641\) | −3.67949 | −0.145331 | −0.0726656 | − | 0.997356i | \(-0.523151\pi\) | ||||
−0.0726656 | + | 0.997356i | \(0.523151\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.8038 | −1.01760 | −0.508802 | − | 0.860883i | \(-0.669912\pi\) | ||||
−0.508802 | + | 0.860883i | \(0.669912\pi\) | |||||||
\(644\) | 6.00000 | 0.236433 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.58846 | −0.259219 | ||||||||
\(647\) | 23.3205 | 0.916824 | 0.458412 | − | 0.888740i | \(-0.348418\pi\) | ||||
0.458412 | + | 0.888740i | \(0.348418\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 6.00000 | 0.235339 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 22.1962 | 0.869268 | ||||||||
\(653\) | 1.85641 | 0.0726468 | 0.0363234 | − | 0.999340i | \(-0.488435\pi\) | ||||
0.0363234 | + | 0.999340i | \(0.488435\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.803848 | 0.0313850 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −38.7846 | −1.51198 | ||||||||
\(659\) | −16.9808 | −0.661477 | −0.330738 | − | 0.943723i | \(-0.607298\pi\) | ||||
−0.330738 | + | 0.943723i | \(0.607298\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.4115 | −0.638335 | −0.319168 | − | 0.947698i | \(-0.603403\pi\) | ||||
−0.319168 | + | 0.947698i | \(0.603403\pi\) | |||||||
\(662\) | −28.7846 | −1.11875 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.19615 | 0.318072 | ||||||||
\(665\) | 10.3923 | 0.402996 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.80385 | 0.147286 | ||||||||
\(668\) | −16.3923 | −0.634237 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 17.6603 | 0.682275 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.928203 | 0.0357796 | 0.0178898 | − | 0.999840i | \(-0.494305\pi\) | ||||
0.0178898 | + | 0.999840i | \(0.494305\pi\) | |||||||
\(674\) | −2.66025 | −0.102469 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.00000 | −0.153846 | ||||||||
\(677\) | −4.60770 | −0.177088 | −0.0885441 | − | 0.996072i | \(-0.528221\pi\) | ||||
−0.0885441 | + | 0.996072i | \(0.528221\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.73205 | −0.181599 | ||||||||
\(680\) | −9.00000 | −0.345134 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.41154 | 0.207067 | 0.103533 | − | 0.994626i | \(-0.466985\pi\) | ||||
0.103533 | + | 0.994626i | \(0.466985\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.3923 | 0.626318 | ||||||||
\(686\) | −39.7128 | −1.51624 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −33.5885 | −1.27962 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −41.1769 | −1.56644 | −0.783222 | − | 0.621742i | \(-0.786425\pi\) | ||||
−0.783222 | + | 0.621742i | \(0.786425\pi\) | |||||||
\(692\) | 4.39230 | 0.166970 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28.3923 | −1.07776 | ||||||||
\(695\) | 34.9808 | 1.32690 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.17691 | 0.158212 | ||||||||
\(698\) | 21.9282 | 0.829995 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −9.46410 | −0.357709 | ||||||||
\(701\) | 17.7846 | 0.671715 | 0.335858 | − | 0.941913i | \(-0.390974\pi\) | ||||
0.335858 | + | 0.941913i | \(0.390974\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.12436 | −0.344132 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.9282 | 0.825279 | ||||||||
\(707\) | −77.5692 | −2.91729 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −38.0000 | −1.42712 | −0.713560 | − | 0.700594i | \(-0.752918\pi\) | ||||
−0.713560 | + | 0.700594i | \(0.752918\pi\) | |||||||
\(710\) | −16.3923 | −0.615192 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.46410 | 0.242252 | ||||||||
\(713\) | 0.248711 | 0.00931431 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 13.8564 | 0.517838 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.58846 | −0.245879 | ||||||||
\(719\) | 46.7321 | 1.74281 | 0.871406 | − | 0.490563i | \(-0.163209\pi\) | ||||
0.871406 | + | 0.490563i | \(0.163209\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −39.7128 | −1.47898 | ||||||||
\(722\) | 17.3923 | 0.647275 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.19615 | 0.267443 | ||||||||
\(725\) | −6.00000 | −0.222834 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.9808 | −1.37154 | −0.685770 | − | 0.727818i | \(-0.740535\pi\) | ||||
−0.685770 | + | 0.727818i | \(0.740535\pi\) | |||||||
\(728\) | −14.1962 | −0.526144 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.60770 | 0.0595035 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.6077 | 0.613419 | 0.306710 | − | 0.951803i | \(-0.400772\pi\) | ||||
0.306710 | + | 0.951803i | \(0.400772\pi\) | |||||||
\(734\) | −8.58846 | −0.317006 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.26795 | −0.0467372 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.7321 | 0.394785 | 0.197392 | − | 0.980325i | \(-0.436753\pi\) | ||||
0.197392 | + | 0.980325i | \(0.436753\pi\) | |||||||
\(740\) | −12.4641 | −0.458189 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 52.9808 | 1.94498 | ||||||||
\(743\) | 38.1962 | 1.40128 | 0.700640 | − | 0.713514i | \(-0.252898\pi\) | ||||
0.700640 | + | 0.713514i | \(0.252898\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 25.9808 | 0.951861 | ||||||||
\(746\) | 11.3205 | 0.414473 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −59.5692 | −2.17661 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.00000 | 0.145962 | 0.0729810 | − | 0.997333i | \(-0.476749\pi\) | ||||
0.0729810 | + | 0.997333i | \(0.476749\pi\) | |||||||
\(752\) | 8.19615 | 0.298883 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −9.00000 | −0.327761 | ||||||||
\(755\) | −7.60770 | −0.276872 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.1962 | −0.479622 | −0.239811 | − | 0.970820i | \(-0.577086\pi\) | ||||
−0.239811 | + | 0.970820i | \(0.577086\pi\) | |||||||
\(758\) | −3.60770 | −0.131037 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.19615 | −0.0796628 | ||||||||
\(761\) | −19.9808 | −0.724302 | −0.362151 | − | 0.932119i | \(-0.617958\pi\) | ||||
−0.362151 | + | 0.932119i | \(0.617958\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.80385 | −0.354923 | ||||||||
\(764\) | 21.4641 | 0.776544 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.679492 | −0.0245510 | ||||||||
\(767\) | −28.3923 | −1.02519 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.5167 | 1.24470 | 0.622351 | − | 0.782738i | \(-0.286178\pi\) | ||||
0.622351 | + | 0.782738i | \(0.286178\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 10.2679 | 0.369552 | ||||||||
\(773\) | 18.0000 | 0.647415 | 0.323708 | − | 0.946157i | \(-0.395071\pi\) | ||||
0.323708 | + | 0.946157i | \(0.395071\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.392305 | −0.0140920 | ||||||||
\(776\) | 1.00000 | 0.0358979 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 32.6603 | 1.17093 | ||||||||
\(779\) | 1.01924 | 0.0365180 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −6.58846 | −0.235603 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 15.3923 | 0.549725 | ||||||||
\(785\) | 6.92820 | 0.247278 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 44.7846 | 1.59640 | 0.798199 | − | 0.602393i | \(-0.205786\pi\) | ||||
0.798199 | + | 0.602393i | \(0.205786\pi\) | |||||||
\(788\) | 13.3923 | 0.477081 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.19615 | 0.291606 | ||||||||
\(791\) | −51.3731 | −1.82662 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.60770 | 0.270157 | ||||||||
\(794\) | −5.58846 | −0.198327 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.392305 | −0.0139049 | ||||||||
\(797\) | −36.9282 | −1.30806 | −0.654032 | − | 0.756467i | \(-0.726924\pi\) | ||||
−0.654032 | + | 0.756467i | \(0.726924\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 42.5885 | 1.50667 | ||||||||
\(800\) | 2.00000 | 0.0707107 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.39230 | −0.261031 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.3923 | 0.366281 | ||||||||
\(806\) | −0.588457 | −0.0207275 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 16.3923 | 0.576679 | ||||||||
\(809\) | −18.0000 | −0.632846 | −0.316423 | − | 0.948618i | \(-0.602482\pi\) | ||||
−0.316423 | + | 0.948618i | \(0.602482\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.92820 | 0.243282 | 0.121641 | − | 0.992574i | \(-0.461184\pi\) | ||||
0.121641 | + | 0.992574i | \(0.461184\pi\) | |||||||
\(812\) | 14.1962 | 0.498187 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 38.4449 | 1.34666 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 2.66025 | 0.0930136 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.39230 | 0.0486214 | ||||||||
\(821\) | 16.3923 | 0.572095 | 0.286048 | − | 0.958215i | \(-0.407658\pi\) | ||||
0.286048 | + | 0.958215i | \(0.407658\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.0000 | 1.11545 | 0.557725 | − | 0.830026i | \(-0.311674\pi\) | ||||
0.557725 | + | 0.830026i | \(0.311674\pi\) | |||||||
\(824\) | 8.39230 | 0.292360 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 44.7846 | 1.55826 | ||||||||
\(827\) | 20.1962 | 0.702289 | 0.351145 | − | 0.936321i | \(-0.385793\pi\) | ||||
0.351145 | + | 0.936321i | \(0.385793\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.8038 | 0.514159 | 0.257079 | − | 0.966390i | \(-0.417240\pi\) | ||||
0.257079 | + | 0.966390i | \(0.417240\pi\) | |||||||
\(830\) | 14.1962 | 0.492756 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.00000 | 0.104006 | ||||||||
\(833\) | 79.9808 | 2.77117 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28.3923 | −0.982556 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −39.3731 | −1.36012 | ||||||||
\(839\) | 50.4449 | 1.74155 | 0.870775 | − | 0.491682i | \(-0.163618\pi\) | ||||
0.870775 | + | 0.491682i | \(0.163618\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | −7.58846 | −0.261516 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −25.8564 | −0.890014 | ||||||||
\(845\) | −6.92820 | −0.238337 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −11.1962 | −0.384477 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 10.3923 | 0.356453 | ||||||||
\(851\) | −9.12436 | −0.312779 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.8564 | −0.371716 | −0.185858 | − | 0.982577i | \(-0.559506\pi\) | ||||
−0.185858 | + | 0.982577i | \(0.559506\pi\) | |||||||
\(854\) | −12.0000 | −0.410632 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.5885 | 0.430265 | ||||||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.7846 | −0.845640 | −0.422820 | − | 0.906214i | \(-0.638960\pi\) | ||||
−0.422820 | + | 0.906214i | \(0.638960\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.3923 | 0.558324 | ||||||||
\(863\) | 3.80385 | 0.129484 | 0.0647422 | − | 0.997902i | \(-0.479377\pi\) | ||||
0.0647422 | + | 0.997902i | \(0.479377\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.60770 | 0.258669 | ||||||||
\(866\) | −31.7846 | −1.08009 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.928203 | 0.0315053 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.5885 | −1.03645 | ||||||||
\(872\) | 2.07180 | 0.0701599 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.60770 | −0.0543811 | ||||||||
\(875\) | −57.3731 | −1.93956 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.46410 | −0.218277 | −0.109139 | − | 0.994027i | \(-0.534809\pi\) | ||||
−0.109139 | + | 0.994027i | \(0.534809\pi\) | |||||||
\(878\) | 21.1244 | 0.712912 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41.5359 | −1.39938 | −0.699690 | − | 0.714447i | \(-0.746679\pi\) | ||||
−0.699690 | + | 0.714447i | \(0.746679\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.6077 | −0.525241 | −0.262620 | − | 0.964899i | \(-0.584587\pi\) | ||||
−0.262620 | + | 0.964899i | \(0.584587\pi\) | |||||||
\(884\) | 15.5885 | 0.524297 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 17.0718 | 0.573538 | ||||||||
\(887\) | 45.8038 | 1.53794 | 0.768971 | − | 0.639283i | \(-0.220769\pi\) | ||||
0.768971 | + | 0.639283i | \(0.220769\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 65.5692 | 2.19912 | ||||||||
\(890\) | 11.1962 | 0.375296 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −20.3923 | −0.682785 | ||||||||
\(893\) | 10.3923 | 0.347765 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.0000 | 0.802232 | ||||||||
\(896\) | −4.73205 | −0.158087 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.92820 | −0.331308 | ||||||||
\(899\) | 0.588457 | 0.0196261 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −58.1769 | −1.93815 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.8564 | 0.361079 | ||||||||
\(905\) | 12.4641 | 0.414321 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.5692 | 1.24747 | 0.623733 | − | 0.781638i | \(-0.285615\pi\) | ||||
0.623733 | + | 0.781638i | \(0.285615\pi\) | |||||||
\(908\) | 16.3923 | 0.543998 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −24.5885 | −0.815099 | ||||||||
\(911\) | 31.6077 | 1.04721 | 0.523605 | − | 0.851961i | \(-0.324587\pi\) | ||||
0.523605 | + | 0.851961i | \(0.324587\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 5.19615 | 0.171873 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.1962 | −0.436013 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.1436 | 0.730450 | 0.365225 | − | 0.930919i | \(-0.380992\pi\) | ||||
0.365225 | + | 0.930919i | \(0.380992\pi\) | |||||||
\(920\) | −2.19615 | −0.0724050 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 33.0000 | 1.08680 | ||||||||
\(923\) | 28.3923 | 0.934544 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.3923 | 0.473216 | ||||||||
\(926\) | −28.7846 | −0.945921 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.00000 | −0.0984798 | ||||||||
\(929\) | −39.0000 | −1.27955 | −0.639774 | − | 0.768563i | \(-0.720972\pi\) | ||||
−0.639774 | + | 0.768563i | \(0.720972\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.5167 | 0.639633 | ||||||||
\(932\) | 6.80385 | 0.222867 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 21.4641 | 0.702327 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.4449 | 1.15793 | 0.578967 | − | 0.815351i | \(-0.303456\pi\) | ||||
0.578967 | + | 0.815351i | \(0.303456\pi\) | |||||||
\(938\) | 48.2487 | 1.57538 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 14.1962 | 0.463027 | ||||||||
\(941\) | 34.6077 | 1.12818 | 0.564089 | − | 0.825714i | \(-0.309227\pi\) | ||||
0.564089 | + | 0.825714i | \(0.309227\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.01924 | 0.0331910 | ||||||||
\(944\) | −9.46410 | −0.308030 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.90897 | −0.192016 | −0.0960078 | − | 0.995381i | \(-0.530607\pi\) | ||||
−0.0960078 | + | 0.995381i | \(0.530607\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.78461 | −0.0903923 | ||||||||
\(950\) | 2.53590 | 0.0822754 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −24.5885 | −0.796916 | ||||||||
\(953\) | 39.5885 | 1.28240 | 0.641198 | − | 0.767376i | \(-0.278438\pi\) | ||||
0.641198 | + | 0.767376i | \(0.278438\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 37.1769 | 1.20302 | ||||||||
\(956\) | 14.1962 | 0.459136 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.78461 | −0.283818 | ||||||||
\(959\) | 44.7846 | 1.44617 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9615 | −0.998759 | ||||||||
\(962\) | 21.5885 | 0.696040 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 26.7846 | 0.862674 | ||||||||
\(965\) | 17.7846 | 0.572507 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.4449 | −1.04336 | −0.521678 | − | 0.853142i | \(-0.674694\pi\) | ||||
−0.521678 | + | 0.853142i | \(0.674694\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.73205 | 0.0556128 | ||||||||
\(971\) | 4.05256 | 0.130053 | 0.0650264 | − | 0.997884i | \(-0.479287\pi\) | ||||
0.0650264 | + | 0.997884i | \(0.479287\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 95.5692 | 3.06381 | ||||||||
\(974\) | 12.9808 | 0.415930 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.53590 | 0.0811721 | ||||||||
\(977\) | −32.3205 | −1.03402 | −0.517012 | − | 0.855978i | \(-0.672956\pi\) | ||||
−0.517012 | + | 0.855978i | \(0.672956\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 26.6603 | 0.851631 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −33.3731 | −1.06498 | ||||||||
\(983\) | −32.1051 | −1.02399 | −0.511997 | − | 0.858987i | \(-0.671094\pi\) | ||||
−0.511997 | + | 0.858987i | \(0.671094\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.1962 | 0.739091 | ||||||||
\(986\) | −15.5885 | −0.496438 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.80385 | 0.121017 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.0000 | −0.635321 | −0.317660 | − | 0.948205i | \(-0.602897\pi\) | ||||
−0.317660 | + | 0.948205i | \(0.602897\pi\) | |||||||
\(992\) | −0.196152 | −0.00622785 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −44.7846 | −1.42048 | ||||||||
\(995\) | −0.679492 | −0.0215413 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.4641 | 0.394742 | 0.197371 | − | 0.980329i | \(-0.436760\pi\) | ||||
0.197371 | + | 0.980329i | \(0.436760\pi\) | |||||||
\(998\) | −16.0000 | −0.506471 | ||||||||
\(999\) | 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 | 2178.2.a.s.1.2 | 2 | ||
3.2 | odd | 2 | 242.2.a.e.1.2 | yes | 2 | ||
11.10 | odd | 2 | 2178.2.a.y.1.2 | 2 | |||
12.11 | even | 2 | 1936.2.a.v.1.1 | 2 | |||
15.14 | odd | 2 | 6050.2.a.cc.1.1 | 2 | |||
24.5 | odd | 2 | 7744.2.a.cv.1.1 | 2 | |||
24.11 | even | 2 | 7744.2.a.bq.1.2 | 2 | |||
33.2 | even | 10 | 242.2.c.g.81.2 | 8 | |||
33.5 | odd | 10 | 242.2.c.f.3.2 | 8 | |||
33.8 | even | 10 | 242.2.c.g.9.1 | 8 | |||
33.14 | odd | 10 | 242.2.c.f.9.1 | 8 | |||
33.17 | even | 10 | 242.2.c.g.3.2 | 8 | |||
33.20 | odd | 10 | 242.2.c.f.81.2 | 8 | |||
33.26 | odd | 10 | 242.2.c.f.27.1 | 8 | |||
33.29 | even | 10 | 242.2.c.g.27.1 | 8 | |||
33.32 | even | 2 | 242.2.a.c.1.2 | ✓ | 2 | ||
132.131 | odd | 2 | 1936.2.a.y.1.1 | 2 | |||
165.164 | even | 2 | 6050.2.a.cv.1.1 | 2 | |||
264.131 | odd | 2 | 7744.2.a.bt.1.2 | 2 | |||
264.197 | even | 2 | 7744.2.a.cs.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
242.2.a.c.1.2 | ✓ | 2 | 33.32 | even | 2 | ||
242.2.a.e.1.2 | yes | 2 | 3.2 | odd | 2 | ||
242.2.c.f.3.2 | 8 | 33.5 | odd | 10 | |||
242.2.c.f.9.1 | 8 | 33.14 | odd | 10 | |||
242.2.c.f.27.1 | 8 | 33.26 | odd | 10 | |||
242.2.c.f.81.2 | 8 | 33.20 | odd | 10 | |||
242.2.c.g.3.2 | 8 | 33.17 | even | 10 | |||
242.2.c.g.9.1 | 8 | 33.8 | even | 10 | |||
242.2.c.g.27.1 | 8 | 33.29 | even | 10 | |||
242.2.c.g.81.2 | 8 | 33.2 | even | 10 | |||
1936.2.a.v.1.1 | 2 | 12.11 | even | 2 | |||
1936.2.a.y.1.1 | 2 | 132.131 | odd | 2 | |||
2178.2.a.s.1.2 | 2 | 1.1 | even | 1 | trivial | ||
2178.2.a.y.1.2 | 2 | 11.10 | odd | 2 | |||
6050.2.a.cc.1.1 | 2 | 15.14 | odd | 2 | |||
6050.2.a.cv.1.1 | 2 | 165.164 | even | 2 | |||
7744.2.a.bq.1.2 | 2 | 24.11 | even | 2 | |||
7744.2.a.bt.1.2 | 2 | 264.131 | odd | 2 | |||
7744.2.a.cs.1.1 | 2 | 264.197 | even | 2 | |||
7744.2.a.cv.1.1 | 2 | 24.5 | odd | 2 |