Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, 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("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2476334663\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
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 | \(\chi\) | \(=\) | 8046.1 |
$q$-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 | ||||||||
\(5\) | 3.46410 | 1.54919 | 0.774597 | − | 0.632456i | \(-0.217953\pi\) | ||||
0.774597 | + | 0.632456i | \(0.217953\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.46410 | 1.68727 | 0.843636 | − | 0.536916i | \(-0.180411\pi\) | ||||
0.843636 | + | 0.536916i | \(0.180411\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.46410 | 1.09545 | ||||||||
\(11\) | 4.73205 | 1.42677 | 0.713384 | − | 0.700774i | \(-0.247162\pi\) | ||||
0.713384 | + | 0.700774i | \(0.247162\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.46410 | −0.406069 | −0.203034 | − | 0.979172i | \(-0.565080\pi\) | ||||
−0.203034 | + | 0.979172i | \(0.565080\pi\) | |||||||
\(14\) | 4.46410 | 1.19308 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.26795 | −0.792594 | −0.396297 | − | 0.918122i | \(-0.629705\pi\) | ||||
−0.396297 | + | 0.918122i | \(0.629705\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.46410 | 0.335888 | 0.167944 | − | 0.985797i | \(-0.446287\pi\) | ||||
0.167944 | + | 0.985797i | \(0.446287\pi\) | |||||||
\(20\) | 3.46410 | 0.774597 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.73205 | 1.00888 | ||||||||
\(23\) | −7.73205 | −1.61224 | −0.806122 | − | 0.591749i | \(-0.798438\pi\) | ||||
−0.806122 | + | 0.591749i | \(0.798438\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.00000 | 1.40000 | ||||||||
\(26\) | −1.46410 | −0.287134 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.46410 | 0.843636 | ||||||||
\(29\) | −1.73205 | −0.321634 | −0.160817 | − | 0.986984i | \(-0.551413\pi\) | ||||
−0.160817 | + | 0.986984i | \(0.551413\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | 0.179605 | 0.0898027 | − | 0.995960i | \(-0.471376\pi\) | ||||
0.0898027 | + | 0.995960i | \(0.471376\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.26795 | −0.560449 | ||||||||
\(35\) | 15.4641 | 2.61391 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.732051 | −0.120348 | −0.0601742 | − | 0.998188i | \(-0.519166\pi\) | ||||
−0.0601742 | + | 0.998188i | \(0.519166\pi\) | |||||||
\(38\) | 1.46410 | 0.237509 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.46410 | 0.547723 | ||||||||
\(41\) | 9.19615 | 1.43620 | 0.718099 | − | 0.695941i | \(-0.245013\pi\) | ||||
0.718099 | + | 0.695941i | \(0.245013\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.92820 | −0.751544 | −0.375772 | − | 0.926712i | \(-0.622622\pi\) | ||||
−0.375772 | + | 0.926712i | \(0.622622\pi\) | |||||||
\(44\) | 4.73205 | 0.713384 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.73205 | −1.14003 | ||||||||
\(47\) | −0.535898 | −0.0781688 | −0.0390844 | − | 0.999236i | \(-0.512444\pi\) | ||||
−0.0390844 | + | 0.999236i | \(0.512444\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.9282 | 1.84689 | ||||||||
\(50\) | 7.00000 | 0.989949 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.46410 | −0.203034 | ||||||||
\(53\) | −9.73205 | −1.33680 | −0.668400 | − | 0.743802i | \(-0.733021\pi\) | ||||
−0.668400 | + | 0.743802i | \(0.733021\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16.3923 | 2.21034 | ||||||||
\(56\) | 4.46410 | 0.596541 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.73205 | −0.227429 | ||||||||
\(59\) | 6.73205 | 0.876438 | 0.438219 | − | 0.898868i | \(-0.355609\pi\) | ||||
0.438219 | + | 0.898868i | \(0.355609\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.732051 | −0.0937295 | −0.0468648 | − | 0.998901i | \(-0.514923\pi\) | ||||
−0.0468648 | + | 0.998901i | \(0.514923\pi\) | |||||||
\(62\) | 1.00000 | 0.127000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.07180 | −0.629079 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.19615 | 0.512642 | 0.256321 | − | 0.966592i | \(-0.417490\pi\) | ||||
0.256321 | + | 0.966592i | \(0.417490\pi\) | |||||||
\(68\) | −3.26795 | −0.396297 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 15.4641 | 1.84831 | ||||||||
\(71\) | −10.1244 | −1.20154 | −0.600770 | − | 0.799422i | \(-0.705139\pi\) | ||||
−0.600770 | + | 0.799422i | \(0.705139\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.46410 | −0.639525 | −0.319762 | − | 0.947498i | \(-0.603603\pi\) | ||||
−0.319762 | + | 0.947498i | \(0.603603\pi\) | |||||||
\(74\) | −0.732051 | −0.0850992 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.46410 | 0.167944 | ||||||||
\(77\) | 21.1244 | 2.40734 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.26795 | −1.04273 | −0.521363 | − | 0.853335i | \(-0.674576\pi\) | ||||
−0.521363 | + | 0.853335i | \(0.674576\pi\) | |||||||
\(80\) | 3.46410 | 0.387298 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.19615 | 1.01555 | ||||||||
\(83\) | 12.1962 | 1.33870 | 0.669351 | − | 0.742946i | \(-0.266572\pi\) | ||||
0.669351 | + | 0.742946i | \(0.266572\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.3205 | −1.22788 | ||||||||
\(86\) | −4.92820 | −0.531422 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.73205 | 0.504438 | ||||||||
\(89\) | 7.73205 | 0.819596 | 0.409798 | − | 0.912176i | \(-0.365599\pi\) | ||||
0.409798 | + | 0.912176i | \(0.365599\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.53590 | −0.685148 | ||||||||
\(92\) | −7.73205 | −0.806122 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.535898 | −0.0552737 | ||||||||
\(95\) | 5.07180 | 0.520355 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.26795 | 0.737948 | 0.368974 | − | 0.929440i | \(-0.379709\pi\) | ||||
0.368974 | + | 0.929440i | \(0.379709\pi\) | |||||||
\(98\) | 12.9282 | 1.30595 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.00000 | 0.700000 | ||||||||
\(101\) | 14.3923 | 1.43209 | 0.716044 | − | 0.698055i | \(-0.245951\pi\) | ||||
0.716044 | + | 0.698055i | \(0.245951\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.07180 | 0.204140 | 0.102070 | − | 0.994777i | \(-0.467453\pi\) | ||||
0.102070 | + | 0.994777i | \(0.467453\pi\) | |||||||
\(104\) | −1.46410 | −0.143567 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.73205 | −0.945260 | ||||||||
\(107\) | −11.4641 | −1.10828 | −0.554138 | − | 0.832425i | \(-0.686952\pi\) | ||||
−0.554138 | + | 0.832425i | \(0.686952\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.92820 | 0.759384 | 0.379692 | − | 0.925113i | \(-0.376030\pi\) | ||||
0.379692 | + | 0.925113i | \(0.376030\pi\) | |||||||
\(110\) | 16.3923 | 1.56294 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.46410 | 0.421818 | ||||||||
\(113\) | 5.80385 | 0.545980 | 0.272990 | − | 0.962017i | \(-0.411987\pi\) | ||||
0.272990 | + | 0.962017i | \(0.411987\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −26.7846 | −2.49768 | ||||||||
\(116\) | −1.73205 | −0.160817 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.73205 | 0.619736 | ||||||||
\(119\) | −14.5885 | −1.33732 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.3923 | 1.03566 | ||||||||
\(122\) | −0.732051 | −0.0662768 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.00000 | 0.0898027 | ||||||||
\(125\) | 6.92820 | 0.619677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.0000 | 1.24230 | 0.621150 | − | 0.783692i | \(-0.286666\pi\) | ||||
0.621150 | + | 0.783692i | \(0.286666\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.07180 | −0.444826 | ||||||||
\(131\) | 2.53590 | 0.221562 | 0.110781 | − | 0.993845i | \(-0.464665\pi\) | ||||
0.110781 | + | 0.993845i | \(0.464665\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.53590 | 0.566734 | ||||||||
\(134\) | 4.19615 | 0.362492 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.26795 | −0.280224 | ||||||||
\(137\) | −9.19615 | −0.785680 | −0.392840 | − | 0.919607i | \(-0.628507\pi\) | ||||
−0.392840 | + | 0.919607i | \(0.628507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.00000 | −0.593732 | −0.296866 | − | 0.954919i | \(-0.595942\pi\) | ||||
−0.296866 | + | 0.954919i | \(0.595942\pi\) | |||||||
\(140\) | 15.4641 | 1.30696 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.1244 | −0.849617 | ||||||||
\(143\) | −6.92820 | −0.579365 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.00000 | −0.498273 | ||||||||
\(146\) | −5.46410 | −0.452212 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.732051 | −0.0601742 | ||||||||
\(149\) | 1.00000 | 0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.12436 | −0.254256 | −0.127128 | − | 0.991886i | \(-0.540576\pi\) | ||||
−0.127128 | + | 0.991886i | \(0.540576\pi\) | |||||||
\(152\) | 1.46410 | 0.118754 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 21.1244 | 1.70225 | ||||||||
\(155\) | 3.46410 | 0.278243 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.4641 | 0.835126 | 0.417563 | − | 0.908648i | \(-0.362884\pi\) | ||||
0.417563 | + | 0.908648i | \(0.362884\pi\) | |||||||
\(158\) | −9.26795 | −0.737318 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.46410 | 0.273861 | ||||||||
\(161\) | −34.5167 | −2.72029 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.92820 | −0.307681 | −0.153840 | − | 0.988096i | \(-0.549164\pi\) | ||||
−0.153840 | + | 0.988096i | \(0.549164\pi\) | |||||||
\(164\) | 9.19615 | 0.718099 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.1962 | 0.946605 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.8564 | −0.835108 | ||||||||
\(170\) | −11.3205 | −0.868243 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.92820 | −0.375772 | ||||||||
\(173\) | −17.7321 | −1.34814 | −0.674071 | − | 0.738666i | \(-0.735456\pi\) | ||||
−0.674071 | + | 0.738666i | \(0.735456\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 31.2487 | 2.36218 | ||||||||
\(176\) | 4.73205 | 0.356692 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.73205 | 0.579542 | ||||||||
\(179\) | −21.5885 | −1.61360 | −0.806799 | − | 0.590827i | \(-0.798802\pi\) | ||||
−0.806799 | + | 0.590827i | \(0.798802\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.5359 | −0.857457 | −0.428728 | − | 0.903433i | \(-0.641038\pi\) | ||||
−0.428728 | + | 0.903433i | \(0.641038\pi\) | |||||||
\(182\) | −6.53590 | −0.484473 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.73205 | −0.570014 | ||||||||
\(185\) | −2.53590 | −0.186443 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.4641 | −1.13085 | ||||||||
\(188\) | −0.535898 | −0.0390844 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.07180 | 0.367947 | ||||||||
\(191\) | 3.12436 | 0.226070 | 0.113035 | − | 0.993591i | \(-0.463943\pi\) | ||||
0.113035 | + | 0.993591i | \(0.463943\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.58846 | −0.618211 | −0.309105 | − | 0.951028i | \(-0.600030\pi\) | ||||
−0.309105 | + | 0.951028i | \(0.600030\pi\) | |||||||
\(194\) | 7.26795 | 0.521808 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.9282 | 0.923443 | ||||||||
\(197\) | −21.1244 | −1.50505 | −0.752524 | − | 0.658565i | \(-0.771164\pi\) | ||||
−0.752524 | + | 0.658565i | \(0.771164\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.7321 | 1.32788 | 0.663940 | − | 0.747786i | \(-0.268883\pi\) | ||||
0.663940 | + | 0.747786i | \(0.268883\pi\) | |||||||
\(200\) | 7.00000 | 0.494975 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 14.3923 | 1.01264 | ||||||||
\(203\) | −7.73205 | −0.542684 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 31.8564 | 2.22495 | ||||||||
\(206\) | 2.07180 | 0.144349 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.46410 | −0.101517 | ||||||||
\(209\) | 6.92820 | 0.479234 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.7846 | −1.77509 | −0.887543 | − | 0.460725i | \(-0.847589\pi\) | ||||
−0.887543 | + | 0.460725i | \(0.847589\pi\) | |||||||
\(212\) | −9.73205 | −0.668400 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −11.4641 | −0.783670 | ||||||||
\(215\) | −17.0718 | −1.16429 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.46410 | 0.303043 | ||||||||
\(218\) | 7.92820 | 0.536966 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 16.3923 | 1.10517 | ||||||||
\(221\) | 4.78461 | 0.321848 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.73205 | −0.316882 | −0.158441 | − | 0.987368i | \(-0.550647\pi\) | ||||
−0.158441 | + | 0.987368i | \(0.550647\pi\) | |||||||
\(224\) | 4.46410 | 0.298270 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.80385 | 0.386066 | ||||||||
\(227\) | 0.535898 | 0.0355688 | 0.0177844 | − | 0.999842i | \(-0.494339\pi\) | ||||
0.0177844 | + | 0.999842i | \(0.494339\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.19615 | −0.145126 | −0.0725629 | − | 0.997364i | \(-0.523118\pi\) | ||||
−0.0725629 | + | 0.997364i | \(0.523118\pi\) | |||||||
\(230\) | −26.7846 | −1.76612 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.73205 | −0.113715 | ||||||||
\(233\) | −25.9808 | −1.70206 | −0.851028 | − | 0.525120i | \(-0.824020\pi\) | ||||
−0.851028 | + | 0.525120i | \(0.824020\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.85641 | −0.121099 | ||||||||
\(236\) | 6.73205 | 0.438219 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −14.5885 | −0.945629 | ||||||||
\(239\) | −18.1244 | −1.17237 | −0.586184 | − | 0.810178i | \(-0.699370\pi\) | ||||
−0.586184 | + | 0.810178i | \(0.699370\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.4641 | 0.996130 | 0.498065 | − | 0.867140i | \(-0.334044\pi\) | ||||
0.498065 | + | 0.867140i | \(0.334044\pi\) | |||||||
\(242\) | 11.3923 | 0.732325 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.732051 | −0.0468648 | ||||||||
\(245\) | 44.7846 | 2.86118 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.14359 | −0.136394 | ||||||||
\(248\) | 1.00000 | 0.0635001 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.92820 | 0.438178 | ||||||||
\(251\) | 0.267949 | 0.0169128 | 0.00845640 | − | 0.999964i | \(-0.497308\pi\) | ||||
0.00845640 | + | 0.999964i | \(0.497308\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −36.5885 | −2.30030 | ||||||||
\(254\) | 14.0000 | 0.878438 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.8038 | −0.673925 | −0.336963 | − | 0.941518i | \(-0.609400\pi\) | ||||
−0.336963 | + | 0.941518i | \(0.609400\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.26795 | −0.203060 | ||||||||
\(260\) | −5.07180 | −0.314539 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.53590 | 0.156668 | ||||||||
\(263\) | −26.7846 | −1.65161 | −0.825805 | − | 0.563956i | \(-0.809279\pi\) | ||||
−0.825805 | + | 0.563956i | \(0.809279\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −33.7128 | −2.07096 | ||||||||
\(266\) | 6.53590 | 0.400742 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.19615 | 0.256321 | ||||||||
\(269\) | 32.6603 | 1.99133 | 0.995665 | − | 0.0930074i | \(-0.0296480\pi\) | ||||
0.995665 | + | 0.0930074i | \(0.0296480\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.7846 | −0.776610 | −0.388305 | − | 0.921531i | \(-0.626939\pi\) | ||||
−0.388305 | + | 0.921531i | \(0.626939\pi\) | |||||||
\(272\) | −3.26795 | −0.198149 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.19615 | −0.555560 | ||||||||
\(275\) | 33.1244 | 1.99747 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.00000 | 0.300421 | 0.150210 | − | 0.988654i | \(-0.452005\pi\) | ||||
0.150210 | + | 0.988654i | \(0.452005\pi\) | |||||||
\(278\) | −7.00000 | −0.419832 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 15.4641 | 0.924157 | ||||||||
\(281\) | 14.0526 | 0.838305 | 0.419153 | − | 0.907916i | \(-0.362327\pi\) | ||||
0.419153 | + | 0.907916i | \(0.362327\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.46410 | 0.503139 | 0.251569 | − | 0.967839i | \(-0.419053\pi\) | ||||
0.251569 | + | 0.967839i | \(0.419053\pi\) | |||||||
\(284\) | −10.1244 | −0.600770 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.92820 | −0.409673 | ||||||||
\(287\) | 41.0526 | 2.42326 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.32051 | −0.371795 | ||||||||
\(290\) | −6.00000 | −0.352332 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.46410 | −0.319762 | ||||||||
\(293\) | 12.1244 | 0.708312 | 0.354156 | − | 0.935186i | \(-0.384768\pi\) | ||||
0.354156 | + | 0.935186i | \(0.384768\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 23.3205 | 1.35777 | ||||||||
\(296\) | −0.732051 | −0.0425496 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.00000 | 0.0579284 | ||||||||
\(299\) | 11.3205 | 0.654682 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.0000 | −1.26806 | ||||||||
\(302\) | −3.12436 | −0.179786 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.46410 | 0.0839720 | ||||||||
\(305\) | −2.53590 | −0.145205 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.32051 | 0.303657 | 0.151829 | − | 0.988407i | \(-0.451484\pi\) | ||||
0.151829 | + | 0.988407i | \(0.451484\pi\) | |||||||
\(308\) | 21.1244 | 1.20367 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.46410 | 0.196748 | ||||||||
\(311\) | 3.87564 | 0.219768 | 0.109884 | − | 0.993944i | \(-0.464952\pi\) | ||||
0.109884 | + | 0.993944i | \(0.464952\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −29.4641 | −1.66541 | −0.832705 | − | 0.553717i | \(-0.813209\pi\) | ||||
−0.832705 | + | 0.553717i | \(0.813209\pi\) | |||||||
\(314\) | 10.4641 | 0.590523 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.26795 | −0.521363 | ||||||||
\(317\) | −23.8564 | −1.33991 | −0.669955 | − | 0.742402i | \(-0.733686\pi\) | ||||
−0.669955 | + | 0.742402i | \(0.733686\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.19615 | −0.458896 | ||||||||
\(320\) | 3.46410 | 0.193649 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −34.5167 | −1.92354 | ||||||||
\(323\) | −4.78461 | −0.266223 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.2487 | −0.568496 | ||||||||
\(326\) | −3.92820 | −0.217563 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.19615 | 0.507773 | ||||||||
\(329\) | −2.39230 | −0.131892 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.1962 | 0.670361 | 0.335181 | − | 0.942154i | \(-0.391203\pi\) | ||||
0.335181 | + | 0.942154i | \(0.391203\pi\) | |||||||
\(332\) | 12.1962 | 0.669351 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.5359 | 0.794181 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.0000 | 1.03500 | 0.517498 | − | 0.855684i | \(-0.326864\pi\) | ||||
0.517498 | + | 0.855684i | \(0.326864\pi\) | |||||||
\(338\) | −10.8564 | −0.590511 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −11.3205 | −0.613941 | ||||||||
\(341\) | 4.73205 | 0.256255 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 26.4641 | 1.42893 | ||||||||
\(344\) | −4.92820 | −0.265711 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.7321 | −0.953281 | ||||||||
\(347\) | −10.2679 | −0.551212 | −0.275606 | − | 0.961271i | \(-0.588879\pi\) | ||||
−0.275606 | + | 0.961271i | \(0.588879\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.3205 | 1.83713 | 0.918567 | − | 0.395265i | \(-0.129347\pi\) | ||||
0.918567 | + | 0.395265i | \(0.129347\pi\) | |||||||
\(350\) | 31.2487 | 1.67031 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.73205 | 0.252219 | ||||||||
\(353\) | −6.92820 | −0.368751 | −0.184376 | − | 0.982856i | \(-0.559026\pi\) | ||||
−0.184376 | + | 0.982856i | \(0.559026\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −35.0718 | −1.86142 | ||||||||
\(356\) | 7.73205 | 0.409798 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −21.5885 | −1.14099 | ||||||||
\(359\) | 24.3923 | 1.28738 | 0.643688 | − | 0.765288i | \(-0.277403\pi\) | ||||
0.643688 | + | 0.765288i | \(0.277403\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.8564 | −0.887179 | ||||||||
\(362\) | −11.5359 | −0.606313 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.53590 | −0.342574 | ||||||||
\(365\) | −18.9282 | −0.990747 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.8564 | 1.81949 | 0.909745 | − | 0.415168i | \(-0.136277\pi\) | ||||
0.909745 | + | 0.415168i | \(0.136277\pi\) | |||||||
\(368\) | −7.73205 | −0.403061 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.53590 | −0.131835 | ||||||||
\(371\) | −43.4449 | −2.25554 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.9282 | 0.721175 | 0.360588 | − | 0.932725i | \(-0.382576\pi\) | ||||
0.360588 | + | 0.932725i | \(0.382576\pi\) | |||||||
\(374\) | −15.4641 | −0.799630 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.535898 | −0.0276368 | ||||||||
\(377\) | 2.53590 | 0.130605 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 35.8564 | 1.84182 | 0.920910 | − | 0.389775i | \(-0.127447\pi\) | ||||
0.920910 | + | 0.389775i | \(0.127447\pi\) | |||||||
\(380\) | 5.07180 | 0.260178 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.12436 | 0.159856 | ||||||||
\(383\) | −19.6603 | −1.00459 | −0.502296 | − | 0.864696i | \(-0.667511\pi\) | ||||
−0.502296 | + | 0.864696i | \(0.667511\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 73.1769 | 3.72944 | ||||||||
\(386\) | −8.58846 | −0.437141 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.26795 | 0.368974 | ||||||||
\(389\) | 23.4641 | 1.18968 | 0.594839 | − | 0.803845i | \(-0.297216\pi\) | ||||
0.594839 | + | 0.803845i | \(0.297216\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.2679 | 1.27786 | ||||||||
\(392\) | 12.9282 | 0.652973 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −21.1244 | −1.06423 | ||||||||
\(395\) | −32.1051 | −1.61538 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.7846 | −1.74579 | −0.872895 | − | 0.487909i | \(-0.837760\pi\) | ||||
−0.872895 | + | 0.487909i | \(0.837760\pi\) | |||||||
\(398\) | 18.7321 | 0.938953 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.00000 | 0.350000 | ||||||||
\(401\) | 5.12436 | 0.255898 | 0.127949 | − | 0.991781i | \(-0.459161\pi\) | ||||
0.127949 | + | 0.991781i | \(0.459161\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.46410 | −0.0729321 | ||||||||
\(404\) | 14.3923 | 0.716044 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.73205 | −0.383735 | ||||||||
\(407\) | −3.46410 | −0.171709 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.39230 | −0.118292 | −0.0591459 | − | 0.998249i | \(-0.518838\pi\) | ||||
−0.0591459 | + | 0.998249i | \(0.518838\pi\) | |||||||
\(410\) | 31.8564 | 1.57328 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.07180 | 0.102070 | ||||||||
\(413\) | 30.0526 | 1.47879 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 42.2487 | 2.07391 | ||||||||
\(416\) | −1.46410 | −0.0717835 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.92820 | 0.338869 | ||||||||
\(419\) | 3.58846 | 0.175308 | 0.0876538 | − | 0.996151i | \(-0.472063\pi\) | ||||
0.0876538 | + | 0.996151i | \(0.472063\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.60770 | 0.0783543 | 0.0391771 | − | 0.999232i | \(-0.487526\pi\) | ||||
0.0391771 | + | 0.999232i | \(0.487526\pi\) | |||||||
\(422\) | −25.7846 | −1.25518 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.73205 | −0.472630 | ||||||||
\(425\) | −22.8756 | −1.10963 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.26795 | −0.158147 | ||||||||
\(428\) | −11.4641 | −0.554138 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −17.0718 | −0.823275 | ||||||||
\(431\) | −12.2487 | −0.590000 | −0.295000 | − | 0.955497i | \(-0.595320\pi\) | ||||
−0.295000 | + | 0.955497i | \(0.595320\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.9808 | −0.719929 | −0.359965 | − | 0.932966i | \(-0.617211\pi\) | ||||
−0.359965 | + | 0.932966i | \(0.617211\pi\) | |||||||
\(434\) | 4.46410 | 0.214284 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.92820 | 0.379692 | ||||||||
\(437\) | −11.3205 | −0.541533 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.1962 | 1.25027 | 0.625137 | − | 0.780515i | \(-0.285043\pi\) | ||||
0.625137 | + | 0.780515i | \(0.285043\pi\) | |||||||
\(440\) | 16.3923 | 0.781472 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.78461 | 0.227581 | ||||||||
\(443\) | −14.6603 | −0.696530 | −0.348265 | − | 0.937396i | \(-0.613229\pi\) | ||||
−0.348265 | + | 0.937396i | \(0.613229\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.7846 | 1.26971 | ||||||||
\(446\) | −4.73205 | −0.224069 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.46410 | 0.210909 | ||||||||
\(449\) | 17.8756 | 0.843604 | 0.421802 | − | 0.906688i | \(-0.361398\pi\) | ||||
0.421802 | + | 0.906688i | \(0.361398\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 43.5167 | 2.04912 | ||||||||
\(452\) | 5.80385 | 0.272990 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.535898 | 0.0251510 | ||||||||
\(455\) | −22.6410 | −1.06143 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.0718 | −1.07925 | −0.539627 | − | 0.841904i | \(-0.681435\pi\) | ||||
−0.539627 | + | 0.841904i | \(0.681435\pi\) | |||||||
\(458\) | −2.19615 | −0.102619 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −26.7846 | −1.24884 | ||||||||
\(461\) | 5.32051 | 0.247801 | 0.123900 | − | 0.992295i | \(-0.460460\pi\) | ||||
0.123900 | + | 0.992295i | \(0.460460\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.6410 | 1.47048 | 0.735241 | − | 0.677805i | \(-0.237069\pi\) | ||||
0.735241 | + | 0.677805i | \(0.237069\pi\) | |||||||
\(464\) | −1.73205 | −0.0804084 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −25.9808 | −1.20354 | ||||||||
\(467\) | −36.1051 | −1.67075 | −0.835373 | − | 0.549684i | \(-0.814748\pi\) | ||||
−0.835373 | + | 0.549684i | \(0.814748\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.7321 | 0.864966 | ||||||||
\(470\) | −1.85641 | −0.0856296 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.73205 | 0.309868 | ||||||||
\(473\) | −23.3205 | −1.07228 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.2487 | 0.470243 | ||||||||
\(476\) | −14.5885 | −0.668661 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −18.1244 | −0.828989 | ||||||||
\(479\) | −8.26795 | −0.377772 | −0.188886 | − | 0.981999i | \(-0.560488\pi\) | ||||
−0.188886 | + | 0.981999i | \(0.560488\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.07180 | 0.0488697 | ||||||||
\(482\) | 15.4641 | 0.704371 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.3923 | 0.517832 | ||||||||
\(485\) | 25.1769 | 1.14322 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.3923 | 0.924064 | 0.462032 | − | 0.886863i | \(-0.347121\pi\) | ||||
0.462032 | + | 0.886863i | \(0.347121\pi\) | |||||||
\(488\) | −0.732051 | −0.0331384 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 44.7846 | 2.02316 | ||||||||
\(491\) | 24.0000 | 1.08310 | 0.541552 | − | 0.840667i | \(-0.317837\pi\) | ||||
0.541552 | + | 0.840667i | \(0.317837\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.66025 | 0.254925 | ||||||||
\(494\) | −2.14359 | −0.0964448 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.00000 | 0.0449013 | ||||||||
\(497\) | −45.1962 | −2.02732 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.39230 | 0.330925 | 0.165463 | − | 0.986216i | \(-0.447088\pi\) | ||||
0.165463 | + | 0.986216i | \(0.447088\pi\) | |||||||
\(500\) | 6.92820 | 0.309839 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.267949 | 0.0119592 | ||||||||
\(503\) | −21.4641 | −0.957037 | −0.478518 | − | 0.878077i | \(-0.658826\pi\) | ||||
−0.478518 | + | 0.878077i | \(0.658826\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 49.8564 | 2.21858 | ||||||||
\(506\) | −36.5885 | −1.62656 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14.0000 | 0.621150 | ||||||||
\(509\) | −36.9808 | −1.63914 | −0.819572 | − | 0.572977i | \(-0.805789\pi\) | ||||
−0.819572 | + | 0.572977i | \(0.805789\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.3923 | −1.07905 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10.8038 | −0.476537 | ||||||||
\(515\) | 7.17691 | 0.316253 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.53590 | −0.111529 | ||||||||
\(518\) | −3.26795 | −0.143585 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.07180 | −0.222413 | ||||||||
\(521\) | 21.3205 | 0.934068 | 0.467034 | − | 0.884239i | \(-0.345322\pi\) | ||||
0.467034 | + | 0.884239i | \(0.345322\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.9282 | 0.565311 | 0.282655 | − | 0.959222i | \(-0.408785\pi\) | ||||
0.282655 | + | 0.959222i | \(0.408785\pi\) | |||||||
\(524\) | 2.53590 | 0.110781 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −26.7846 | −1.16786 | ||||||||
\(527\) | −3.26795 | −0.142354 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 36.7846 | 1.59933 | ||||||||
\(530\) | −33.7128 | −1.46439 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.53590 | 0.283367 | ||||||||
\(533\) | −13.4641 | −0.583195 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −39.7128 | −1.71693 | ||||||||
\(536\) | 4.19615 | 0.181246 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 32.6603 | 1.40808 | ||||||||
\(539\) | 61.1769 | 2.63508 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.5359 | 0.968894 | 0.484447 | − | 0.874821i | \(-0.339021\pi\) | ||||
0.484447 | + | 0.874821i | \(0.339021\pi\) | |||||||
\(542\) | −12.7846 | −0.549146 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.26795 | −0.140112 | ||||||||
\(545\) | 27.4641 | 1.17643 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.53590 | −0.193941 | −0.0969705 | − | 0.995287i | \(-0.530915\pi\) | ||||
−0.0969705 | + | 0.995287i | \(0.530915\pi\) | |||||||
\(548\) | −9.19615 | −0.392840 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 33.1244 | 1.41243 | ||||||||
\(551\) | −2.53590 | −0.108033 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −41.3731 | −1.75936 | ||||||||
\(554\) | 5.00000 | 0.212430 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.00000 | −0.296866 | ||||||||
\(557\) | −3.87564 | −0.164216 | −0.0821082 | − | 0.996623i | \(-0.526165\pi\) | ||||
−0.0821082 | + | 0.996623i | \(0.526165\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.21539 | 0.305178 | ||||||||
\(560\) | 15.4641 | 0.653478 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.0526 | 0.592771 | ||||||||
\(563\) | −13.3397 | −0.562203 | −0.281102 | − | 0.959678i | \(-0.590700\pi\) | ||||
−0.281102 | + | 0.959678i | \(0.590700\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.1051 | 0.845829 | ||||||||
\(566\) | 8.46410 | 0.355773 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.1244 | −0.424809 | ||||||||
\(569\) | 12.1244 | 0.508279 | 0.254140 | − | 0.967168i | \(-0.418208\pi\) | ||||
0.254140 | + | 0.967168i | \(0.418208\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.9282 | −0.624726 | −0.312363 | − | 0.949963i | \(-0.601120\pi\) | ||||
−0.312363 | + | 0.949963i | \(0.601120\pi\) | |||||||
\(572\) | −6.92820 | −0.289683 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 41.0526 | 1.71350 | ||||||||
\(575\) | −54.1244 | −2.25714 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.21539 | −0.0922279 | −0.0461140 | − | 0.998936i | \(-0.514684\pi\) | ||||
−0.0461140 | + | 0.998936i | \(0.514684\pi\) | |||||||
\(578\) | −6.32051 | −0.262898 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.00000 | −0.249136 | ||||||||
\(581\) | 54.4449 | 2.25875 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −46.0526 | −1.90730 | ||||||||
\(584\) | −5.46410 | −0.226106 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.1244 | 0.500853 | ||||||||
\(587\) | −46.3923 | −1.91482 | −0.957408 | − | 0.288740i | \(-0.906764\pi\) | ||||
−0.957408 | + | 0.288740i | \(0.906764\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.46410 | 0.0603273 | ||||||||
\(590\) | 23.3205 | 0.960090 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.732051 | −0.0300871 | ||||||||
\(593\) | −45.5885 | −1.87209 | −0.936047 | − | 0.351876i | \(-0.885544\pi\) | ||||
−0.936047 | + | 0.351876i | \(0.885544\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −50.5359 | −2.07177 | ||||||||
\(596\) | 1.00000 | 0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 11.3205 | 0.462930 | ||||||||
\(599\) | −5.85641 | −0.239286 | −0.119643 | − | 0.992817i | \(-0.538175\pi\) | ||||
−0.119643 | + | 0.992817i | \(0.538175\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.3923 | 1.19894 | 0.599469 | − | 0.800398i | \(-0.295379\pi\) | ||||
0.599469 | + | 0.800398i | \(0.295379\pi\) | |||||||
\(602\) | −22.0000 | −0.896653 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.12436 | −0.127128 | ||||||||
\(605\) | 39.4641 | 1.60444 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.1962 | 0.738559 | 0.369280 | − | 0.929318i | \(-0.379604\pi\) | ||||
0.369280 | + | 0.929318i | \(0.379604\pi\) | |||||||
\(608\) | 1.46410 | 0.0593772 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.53590 | −0.102676 | ||||||||
\(611\) | 0.784610 | 0.0317419 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.2487 | 0.898617 | 0.449308 | − | 0.893377i | \(-0.351670\pi\) | ||||
0.449308 | + | 0.893377i | \(0.351670\pi\) | |||||||
\(614\) | 5.32051 | 0.214718 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 21.1244 | 0.851125 | ||||||||
\(617\) | 28.2487 | 1.13725 | 0.568625 | − | 0.822597i | \(-0.307476\pi\) | ||||
0.568625 | + | 0.822597i | \(0.307476\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.4641 | −0.782328 | −0.391164 | − | 0.920321i | \(-0.627928\pi\) | ||||
−0.391164 | + | 0.920321i | \(0.627928\pi\) | |||||||
\(620\) | 3.46410 | 0.139122 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.87564 | 0.155399 | ||||||||
\(623\) | 34.5167 | 1.38288 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | −29.4641 | −1.17762 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.4641 | 0.417563 | ||||||||
\(629\) | 2.39230 | 0.0953874 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.8564 | 1.50704 | 0.753520 | − | 0.657425i | \(-0.228354\pi\) | ||||
0.753520 | + | 0.657425i | \(0.228354\pi\) | |||||||
\(632\) | −9.26795 | −0.368659 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −23.8564 | −0.947459 | ||||||||
\(635\) | 48.4974 | 1.92456 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.9282 | −0.749963 | ||||||||
\(638\) | −8.19615 | −0.324489 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.46410 | 0.136931 | ||||||||
\(641\) | −0.875644 | −0.0345859 | −0.0172929 | − | 0.999850i | \(-0.505505\pi\) | ||||
−0.0172929 | + | 0.999850i | \(0.505505\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −44.0526 | −1.73726 | −0.868632 | − | 0.495458i | \(-0.835000\pi\) | ||||
−0.868632 | + | 0.495458i | \(0.835000\pi\) | |||||||
\(644\) | −34.5167 | −1.36015 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.78461 | −0.188248 | ||||||||
\(647\) | 8.51666 | 0.334824 | 0.167412 | − | 0.985887i | \(-0.446459\pi\) | ||||
0.167412 | + | 0.985887i | \(0.446459\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31.8564 | 1.25047 | ||||||||
\(650\) | −10.2487 | −0.401988 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.92820 | −0.153840 | ||||||||
\(653\) | −1.85641 | −0.0726468 | −0.0363234 | − | 0.999340i | \(-0.511565\pi\) | ||||
−0.0363234 | + | 0.999340i | \(0.511565\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.78461 | 0.343243 | ||||||||
\(656\) | 9.19615 | 0.359049 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.39230 | −0.0932618 | ||||||||
\(659\) | −46.5167 | −1.81203 | −0.906016 | − | 0.423244i | \(-0.860891\pi\) | ||||
−0.906016 | + | 0.423244i | \(0.860891\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.2487 | −1.44881 | −0.724403 | − | 0.689376i | \(-0.757885\pi\) | ||||
−0.724403 | + | 0.689376i | \(0.757885\pi\) | |||||||
\(662\) | 12.1962 | 0.474017 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.1962 | 0.473303 | ||||||||
\(665\) | 22.6410 | 0.877981 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.3923 | 0.518552 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 14.5359 | 0.561571 | ||||||||
\(671\) | −3.46410 | −0.133730 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 42.5885 | 1.64166 | 0.820832 | − | 0.571169i | \(-0.193510\pi\) | ||||
0.820832 | + | 0.571169i | \(0.193510\pi\) | |||||||
\(674\) | 19.0000 | 0.731853 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.8564 | −0.417554 | ||||||||
\(677\) | −2.39230 | −0.0919437 | −0.0459719 | − | 0.998943i | \(-0.514638\pi\) | ||||
−0.0459719 | + | 0.998943i | \(0.514638\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32.4449 | 1.24512 | ||||||||
\(680\) | −11.3205 | −0.434122 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.73205 | 0.181200 | ||||||||
\(683\) | 15.6077 | 0.597212 | 0.298606 | − | 0.954376i | \(-0.403478\pi\) | ||||
0.298606 | + | 0.954376i | \(0.403478\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −31.8564 | −1.21717 | ||||||||
\(686\) | 26.4641 | 1.01040 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.92820 | −0.187886 | ||||||||
\(689\) | 14.2487 | 0.542833 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.48334 | −0.246638 | −0.123319 | − | 0.992367i | \(-0.539354\pi\) | ||||
−0.123319 | + | 0.992367i | \(0.539354\pi\) | |||||||
\(692\) | −17.7321 | −0.674071 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.2679 | −0.389766 | ||||||||
\(695\) | −24.2487 | −0.919806 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.0526 | −1.13832 | ||||||||
\(698\) | 34.3205 | 1.29905 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 31.2487 | 1.18109 | ||||||||
\(701\) | −21.6603 | −0.818097 | −0.409048 | − | 0.912513i | \(-0.634139\pi\) | ||||
−0.409048 | + | 0.912513i | \(0.634139\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.07180 | −0.0404236 | ||||||||
\(704\) | 4.73205 | 0.178346 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.92820 | −0.260746 | ||||||||
\(707\) | 64.2487 | 2.41632 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.3923 | −0.390291 | −0.195146 | − | 0.980774i | \(-0.562518\pi\) | ||||
−0.195146 | + | 0.980774i | \(0.562518\pi\) | |||||||
\(710\) | −35.0718 | −1.31622 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.73205 | 0.289771 | ||||||||
\(713\) | −7.73205 | −0.289568 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.0000 | −0.897549 | ||||||||
\(716\) | −21.5885 | −0.806799 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 24.3923 | 0.910313 | ||||||||
\(719\) | −33.8038 | −1.26067 | −0.630335 | − | 0.776323i | \(-0.717083\pi\) | ||||
−0.630335 | + | 0.776323i | \(0.717083\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.24871 | 0.344440 | ||||||||
\(722\) | −16.8564 | −0.627330 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −11.5359 | −0.428728 | ||||||||
\(725\) | −12.1244 | −0.450287 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.5167 | 0.798009 | 0.399004 | − | 0.916949i | \(-0.369356\pi\) | ||||
0.399004 | + | 0.916949i | \(0.369356\pi\) | |||||||
\(728\) | −6.53590 | −0.242237 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −18.9282 | −0.700564 | ||||||||
\(731\) | 16.1051 | 0.595669 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.5359 | 1.01706 | 0.508531 | − | 0.861044i | \(-0.330189\pi\) | ||||
0.508531 | + | 0.861044i | \(0.330189\pi\) | |||||||
\(734\) | 34.8564 | 1.28657 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.73205 | −0.285007 | ||||||||
\(737\) | 19.8564 | 0.731420 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.5885 | −1.64021 | −0.820106 | − | 0.572211i | \(-0.806086\pi\) | ||||
−0.820106 | + | 0.572211i | \(0.806086\pi\) | |||||||
\(740\) | −2.53590 | −0.0932215 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −43.4449 | −1.59491 | ||||||||
\(743\) | 30.3731 | 1.11428 | 0.557140 | − | 0.830419i | \(-0.311899\pi\) | ||||
0.557140 | + | 0.830419i | \(0.311899\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.46410 | 0.126915 | ||||||||
\(746\) | 13.9282 | 0.509948 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −15.4641 | −0.565424 | ||||||||
\(749\) | −51.1769 | −1.86996 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.0718 | 0.586468 | 0.293234 | − | 0.956041i | \(-0.405268\pi\) | ||||
0.293234 | + | 0.956041i | \(0.405268\pi\) | |||||||
\(752\) | −0.535898 | −0.0195422 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.53590 | 0.0923520 | ||||||||
\(755\) | −10.8231 | −0.393892 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.0000 | 1.41748 | 0.708740 | − | 0.705470i | \(-0.249264\pi\) | ||||
0.708740 | + | 0.705470i | \(0.249264\pi\) | |||||||
\(758\) | 35.8564 | 1.30236 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.07180 | 0.183973 | ||||||||
\(761\) | 5.60770 | 0.203279 | 0.101639 | − | 0.994821i | \(-0.467591\pi\) | ||||
0.101639 | + | 0.994821i | \(0.467591\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 35.3923 | 1.28129 | ||||||||
\(764\) | 3.12436 | 0.113035 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19.6603 | −0.710354 | ||||||||
\(767\) | −9.85641 | −0.355894 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37.0718 | −1.33684 | −0.668422 | − | 0.743783i | \(-0.733030\pi\) | ||||
−0.668422 | + | 0.743783i | \(0.733030\pi\) | |||||||
\(770\) | 73.1769 | 2.63711 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.58846 | −0.309105 | ||||||||
\(773\) | 30.2679 | 1.08866 | 0.544331 | − | 0.838870i | \(-0.316783\pi\) | ||||
0.544331 | + | 0.838870i | \(0.316783\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.00000 | 0.251447 | ||||||||
\(776\) | 7.26795 | 0.260904 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 23.4641 | 0.841229 | ||||||||
\(779\) | 13.4641 | 0.482402 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −47.9090 | −1.71432 | ||||||||
\(782\) | 25.2679 | 0.903580 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 12.9282 | 0.461722 | ||||||||
\(785\) | 36.2487 | 1.29377 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.12436 | −0.325248 | −0.162624 | − | 0.986688i | \(-0.551996\pi\) | ||||
−0.162624 | + | 0.986688i | \(0.551996\pi\) | |||||||
\(788\) | −21.1244 | −0.752524 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −32.1051 | −1.14225 | ||||||||
\(791\) | 25.9090 | 0.921217 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.07180 | 0.0380606 | ||||||||
\(794\) | −34.7846 | −1.23446 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.7321 | 0.663940 | ||||||||
\(797\) | −41.3205 | −1.46365 | −0.731824 | − | 0.681494i | \(-0.761331\pi\) | ||||
−0.731824 | + | 0.681494i | \(0.761331\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.75129 | 0.0619561 | ||||||||
\(800\) | 7.00000 | 0.247487 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.12436 | 0.180947 | ||||||||
\(803\) | −25.8564 | −0.912453 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −119.569 | −4.21426 | ||||||||
\(806\) | −1.46410 | −0.0515708 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 14.3923 | 0.506320 | ||||||||
\(809\) | −45.0333 | −1.58329 | −0.791644 | − | 0.610983i | \(-0.790774\pi\) | ||||
−0.791644 | + | 0.610983i | \(0.790774\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.3923 | 1.34814 | 0.674068 | − | 0.738669i | \(-0.264545\pi\) | ||||
0.674068 | + | 0.738669i | \(0.264545\pi\) | |||||||
\(812\) | −7.73205 | −0.271342 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.46410 | −0.121417 | ||||||||
\(815\) | −13.6077 | −0.476657 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.21539 | −0.252435 | ||||||||
\(818\) | −2.39230 | −0.0836450 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 31.8564 | 1.11247 | ||||||||
\(821\) | −43.0526 | −1.50254 | −0.751272 | − | 0.659992i | \(-0.770560\pi\) | ||||
−0.751272 | + | 0.659992i | \(0.770560\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.0718 | 1.29224 | 0.646121 | − | 0.763235i | \(-0.276390\pi\) | ||||
0.646121 | + | 0.763235i | \(0.276390\pi\) | |||||||
\(824\) | 2.07180 | 0.0721745 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 30.0526 | 1.04566 | ||||||||
\(827\) | −23.6077 | −0.820920 | −0.410460 | − | 0.911879i | \(-0.634632\pi\) | ||||
−0.410460 | + | 0.911879i | \(0.634632\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.17691 | 0.214533 | 0.107267 | − | 0.994230i | \(-0.465790\pi\) | ||||
0.107267 | + | 0.994230i | \(0.465790\pi\) | |||||||
\(830\) | 42.2487 | 1.46647 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.46410 | −0.0507586 | ||||||||
\(833\) | −42.2487 | −1.46383 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.92820 | 0.239617 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.58846 | 0.123961 | ||||||||
\(839\) | 16.5167 | 0.570218 | 0.285109 | − | 0.958495i | \(-0.407970\pi\) | ||||
0.285109 | + | 0.958495i | \(0.407970\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0000 | −0.896552 | ||||||||
\(842\) | 1.60770 | 0.0554048 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −25.7846 | −0.887543 | ||||||||
\(845\) | −37.6077 | −1.29374 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 50.8564 | 1.74745 | ||||||||
\(848\) | −9.73205 | −0.334200 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −22.8756 | −0.784628 | ||||||||
\(851\) | 5.66025 | 0.194031 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −56.6410 | −1.93935 | −0.969676 | − | 0.244395i | \(-0.921411\pi\) | ||||
−0.969676 | + | 0.244395i | \(0.921411\pi\) | |||||||
\(854\) | −3.26795 | −0.111827 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11.4641 | −0.391835 | ||||||||
\(857\) | −13.8038 | −0.471530 | −0.235765 | − | 0.971810i | \(-0.575760\pi\) | ||||
−0.235765 | + | 0.971810i | \(0.575760\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 56.0526 | 1.91249 | 0.956244 | − | 0.292569i | \(-0.0945102\pi\) | ||||
0.956244 | + | 0.292569i | \(0.0945102\pi\) | |||||||
\(860\) | −17.0718 | −0.582143 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12.2487 | −0.417193 | ||||||||
\(863\) | 47.2295 | 1.60771 | 0.803855 | − | 0.594825i | \(-0.202779\pi\) | ||||
0.803855 | + | 0.594825i | \(0.202779\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −61.4256 | −2.08853 | ||||||||
\(866\) | −14.9808 | −0.509067 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.46410 | 0.151521 | ||||||||
\(869\) | −43.8564 | −1.48773 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.14359 | −0.208168 | ||||||||
\(872\) | 7.92820 | 0.268483 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −11.3205 | −0.382922 | ||||||||
\(875\) | 30.9282 | 1.04556 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.0718 | 1.04922 | 0.524610 | − | 0.851343i | \(-0.324211\pi\) | ||||
0.524610 | + | 0.851343i | \(0.324211\pi\) | |||||||
\(878\) | 26.1962 | 0.884077 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 16.3923 | 0.552584 | ||||||||
\(881\) | −44.9090 | −1.51302 | −0.756511 | − | 0.653981i | \(-0.773098\pi\) | ||||
−0.756511 | + | 0.653981i | \(0.773098\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48.2487 | 1.62370 | 0.811849 | − | 0.583867i | \(-0.198461\pi\) | ||||
0.811849 | + | 0.583867i | \(0.198461\pi\) | |||||||
\(884\) | 4.78461 | 0.160924 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14.6603 | −0.492521 | ||||||||
\(887\) | 35.9090 | 1.20571 | 0.602853 | − | 0.797853i | \(-0.294031\pi\) | ||||
0.602853 | + | 0.797853i | \(0.294031\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 62.4974 | 2.09610 | ||||||||
\(890\) | 26.7846 | 0.897822 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.73205 | −0.158441 | ||||||||
\(893\) | −0.784610 | −0.0262560 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −74.7846 | −2.49977 | ||||||||
\(896\) | 4.46410 | 0.149135 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 17.8756 | 0.596518 | ||||||||
\(899\) | −1.73205 | −0.0577671 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31.8038 | 1.05954 | ||||||||
\(902\) | 43.5167 | 1.44895 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.80385 | 0.193033 | ||||||||
\(905\) | −39.9615 | −1.32837 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.248711 | −0.00825832 | −0.00412916 | − | 0.999991i | \(-0.501314\pi\) | ||||
−0.00412916 | + | 0.999991i | \(0.501314\pi\) | |||||||
\(908\) | 0.535898 | 0.0177844 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −22.6410 | −0.750542 | ||||||||
\(911\) | 43.7128 | 1.44827 | 0.724135 | − | 0.689658i | \(-0.242239\pi\) | ||||
0.724135 | + | 0.689658i | \(0.242239\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 57.7128 | 1.91002 | ||||||||
\(914\) | −23.0718 | −0.763147 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.19615 | −0.0725629 | ||||||||
\(917\) | 11.3205 | 0.373836 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.78461 | −0.256791 | −0.128395 | − | 0.991723i | \(-0.540983\pi\) | ||||
−0.128395 | + | 0.991723i | \(0.540983\pi\) | |||||||
\(920\) | −26.7846 | −0.883062 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5.32051 | 0.175222 | ||||||||
\(923\) | 14.8231 | 0.487908 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.12436 | −0.168488 | ||||||||
\(926\) | 31.6410 | 1.03979 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.73205 | −0.0568574 | ||||||||
\(929\) | −22.3923 | −0.734668 | −0.367334 | − | 0.930089i | \(-0.619729\pi\) | ||||
−0.367334 | + | 0.930089i | \(0.619729\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.9282 | 0.620347 | ||||||||
\(932\) | −25.9808 | −0.851028 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −36.1051 | −1.18140 | ||||||||
\(935\) | −53.5692 | −1.75190 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 59.5167 | 1.94432 | 0.972162 | − | 0.234309i | \(-0.0752826\pi\) | ||||
0.972162 | + | 0.234309i | \(0.0752826\pi\) | |||||||
\(938\) | 18.7321 | 0.611623 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.85641 | −0.0605493 | ||||||||
\(941\) | −39.9808 | −1.30334 | −0.651668 | − | 0.758505i | \(-0.725930\pi\) | ||||
−0.651668 | + | 0.758505i | \(0.725930\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −71.1051 | −2.31550 | ||||||||
\(944\) | 6.73205 | 0.219110 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −23.3205 | −0.758215 | ||||||||
\(947\) | 17.9808 | 0.584296 | 0.292148 | − | 0.956373i | \(-0.405630\pi\) | ||||
0.292148 | + | 0.956373i | \(0.405630\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.00000 | 0.259691 | ||||||||
\(950\) | 10.2487 | 0.332512 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −14.5885 | −0.472815 | ||||||||
\(953\) | −24.1244 | −0.781465 | −0.390732 | − | 0.920504i | \(-0.627778\pi\) | ||||
−0.390732 | + | 0.920504i | \(0.627778\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.8231 | 0.350227 | ||||||||
\(956\) | −18.1244 | −0.586184 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.26795 | −0.267125 | ||||||||
\(959\) | −41.0526 | −1.32566 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0000 | −0.967742 | ||||||||
\(962\) | 1.07180 | 0.0345561 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 15.4641 | 0.498065 | ||||||||
\(965\) | −29.7513 | −0.957728 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.9282 | −0.801637 | −0.400818 | − | 0.916157i | \(-0.631274\pi\) | ||||
−0.400818 | + | 0.916157i | \(0.631274\pi\) | |||||||
\(968\) | 11.3923 | 0.366163 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 25.1769 | 0.808382 | ||||||||
\(971\) | 7.94744 | 0.255046 | 0.127523 | − | 0.991836i | \(-0.459297\pi\) | ||||
0.127523 | + | 0.991836i | \(0.459297\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −31.2487 | −1.00179 | ||||||||
\(974\) | 20.3923 | 0.653412 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.732051 | −0.0234324 | ||||||||
\(977\) | −36.0000 | −1.15174 | −0.575871 | − | 0.817541i | \(-0.695337\pi\) | ||||
−0.575871 | + | 0.817541i | \(0.695337\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.5885 | 1.16937 | ||||||||
\(980\) | 44.7846 | 1.43059 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 24.0000 | 0.765871 | ||||||||
\(983\) | −21.0526 | −0.671472 | −0.335736 | − | 0.941956i | \(-0.608985\pi\) | ||||
−0.335736 | + | 0.941956i | \(0.608985\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −73.1769 | −2.33161 | ||||||||
\(986\) | 5.66025 | 0.180259 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.14359 | −0.0681968 | ||||||||
\(989\) | 38.1051 | 1.21167 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −51.5692 | −1.63815 | −0.819075 | − | 0.573686i | \(-0.805513\pi\) | ||||
−0.819075 | + | 0.573686i | \(0.805513\pi\) | |||||||
\(992\) | 1.00000 | 0.0317500 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −45.1962 | −1.43353 | ||||||||
\(995\) | 64.8897 | 2.05714 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.0526 | −0.381708 | −0.190854 | − | 0.981618i | \(-0.561126\pi\) | ||||
−0.190854 | + | 0.981618i | \(0.561126\pi\) | |||||||
\(998\) | 7.39230 | 0.233999 | ||||||||
\(999\) | 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 | 8046.2.a.d.1.2 | yes | 2 | |
3.2 | odd | 2 | 8046.2.a.c.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.c.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
8046.2.a.d.1.2 | yes | 2 | 1.1 | even | 1 | trivial |