Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3200,2,Mod(1,3200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3200.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3200 = 2^{7} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3200.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: | \(25.5521286468\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 640) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3200.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.70928 | −0.986851 | −0.493425 | − | 0.869788i | \(-0.664255\pi\) | ||||
−0.493425 | + | 0.869788i | \(0.664255\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.63090 | −0.994386 | −0.497193 | − | 0.867640i | \(-0.665636\pi\) | ||||
−0.497193 | + | 0.867640i | \(0.665636\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.0783777 | −0.0261259 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.41855 | −1.63375 | −0.816877 | − | 0.576812i | \(-0.804297\pi\) | ||||
−0.816877 | + | 0.576812i | \(0.804297\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.34017 | 1.75845 | 0.879224 | − | 0.476409i | \(-0.158062\pi\) | ||||
0.879224 | + | 0.476409i | \(0.158062\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.41855 | −0.829120 | −0.414560 | − | 0.910022i | \(-0.636065\pi\) | ||||
−0.414560 | + | 0.910022i | \(0.636065\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.26180 | −0.748307 | −0.374154 | − | 0.927367i | \(-0.622067\pi\) | ||||
−0.374154 | + | 0.927367i | \(0.622067\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.49693 | 0.981310 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.36910 | −0.285478 | −0.142739 | − | 0.989760i | \(-0.545591\pi\) | ||||
−0.142739 | + | 0.989760i | \(0.545591\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.26180 | 1.01263 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.68035 | −0.840615 | −0.420307 | − | 0.907382i | \(-0.638078\pi\) | ||||
−0.420307 | + | 0.907382i | \(0.638078\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.26180 | 1.61227 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.75872 | −0.946728 | −0.473364 | − | 0.880867i | \(-0.656961\pi\) | ||||
−0.473364 | + | 0.880867i | \(0.656961\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.8371 | −1.73533 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.75872 | −1.21171 | −0.605855 | − | 0.795575i | \(-0.707169\pi\) | ||||
−0.605855 | + | 0.795575i | \(0.707169\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.44748 | 0.678234 | 0.339117 | − | 0.940744i | \(-0.389872\pi\) | ||||
0.339117 | + | 0.940744i | \(0.389872\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.78765 | −0.698351 | −0.349175 | − | 0.937057i | \(-0.613538\pi\) | ||||
−0.349175 | + | 0.937057i | \(0.613538\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.0783777 | −0.0111968 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.84324 | 0.818218 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.65983 | 0.227995 | 0.113997 | − | 0.993481i | \(-0.463634\pi\) | ||||
0.113997 | + | 0.993481i | \(0.463634\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.57531 | 0.738467 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.26180 | 0.424650 | 0.212325 | − | 0.977199i | \(-0.431897\pi\) | ||||
0.212325 | + | 0.977199i | \(0.431897\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.49693 | 0.319699 | 0.159849 | − | 0.987141i | \(-0.448899\pi\) | ||||
0.159849 | + | 0.987141i | \(0.448899\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.206204 | 0.0259792 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.86603 | 0.960989 | 0.480494 | − | 0.876998i | \(-0.340457\pi\) | ||||
0.480494 | + | 0.876998i | \(0.340457\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.34017 | 0.281724 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.15676 | −0.730672 | −0.365336 | − | 0.930876i | \(-0.619046\pi\) | ||||
−0.365336 | + | 0.930876i | \(0.619046\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.5753 | 1.58887 | 0.794435 | − | 0.607350i | \(-0.207767\pi\) | ||||
0.794435 | + | 0.607350i | \(0.207767\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14.2557 | 1.62458 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.6803 | 1.42665 | 0.713325 | − | 0.700833i | \(-0.247188\pi\) | ||||
0.713325 | + | 0.700833i | \(0.247188\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.75872 | −0.973192 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.9711 | 1.64329 | 0.821644 | − | 0.570001i | \(-0.193057\pi\) | ||||
0.821644 | + | 0.570001i | \(0.193057\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.41855 | 0.366507 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.52359 | −0.903499 | −0.451749 | − | 0.892145i | \(-0.649200\pi\) | ||||
−0.451749 | + | 0.892145i | \(0.649200\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16.6803 | −1.74858 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.00000 | 0.829561 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.58145 | 0.465176 | 0.232588 | − | 0.972575i | \(-0.425281\pi\) | ||||
0.232588 | + | 0.972575i | \(0.425281\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.424694 | 0.0426833 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.31351 | −0.230203 | −0.115101 | − | 0.993354i | \(-0.536719\pi\) | ||||
−0.115101 | + | 0.993354i | \(0.536719\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.2062 | −1.59684 | −0.798422 | − | 0.602098i | \(-0.794332\pi\) | ||||
−0.798422 | + | 0.602098i | \(0.794332\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.6514 | −1.51308 | −0.756540 | − | 0.653948i | \(-0.773112\pi\) | ||||
−0.756540 | + | 0.653948i | \(0.773112\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.3402 | 1.18197 | 0.590987 | − | 0.806681i | \(-0.298738\pi\) | ||||
0.590987 | + | 0.806681i | \(0.298738\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.84324 | 0.934279 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.36069 | −0.880580 | −0.440290 | − | 0.897856i | \(-0.645124\pi\) | ||||
−0.440290 | + | 0.897856i | \(0.645124\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.496928 | −0.0459411 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.99386 | 0.824466 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.3607 | 1.66915 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.2618 | 1.19578 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.95055 | −0.173083 | −0.0865417 | − | 0.996248i | \(-0.527582\pi\) | ||||
−0.0865417 | + | 0.996248i | \(0.527582\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.60197 | −0.669316 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.5753 | 1.36082 | 0.680410 | − | 0.732831i | \(-0.261802\pi\) | ||||
0.680410 | + | 0.732831i | \(0.261802\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.58145 | 0.744106 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.2039 | 1.29896 | 0.649480 | − | 0.760379i | \(-0.274987\pi\) | ||||
0.649480 | + | 0.760379i | \(0.274987\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.58145 | −0.218956 | −0.109478 | − | 0.993989i | \(-0.534918\pi\) | ||||
−0.109478 | + | 0.993989i | \(0.534918\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.18342 | 0.689168 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −34.3545 | −2.87287 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.133969 | 0.0110496 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.81658 | 0.148820 | 0.0744101 | − | 0.997228i | \(-0.476293\pi\) | ||||
0.0744101 | + | 0.997228i | \(0.476293\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.16290 | −0.420151 | −0.210075 | − | 0.977685i | \(-0.567371\pi\) | ||||
−0.210075 | + | 0.977685i | \(0.567371\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.267938 | 0.0216615 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.7587 | 1.09807 | 0.549033 | − | 0.835801i | \(-0.314996\pi\) | ||||
0.549033 | + | 0.835801i | \(0.314996\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.83710 | −0.224997 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.60197 | 0.283875 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.29072 | 0.492728 | 0.246364 | − | 0.969177i | \(-0.420764\pi\) | ||||
0.246364 | + | 0.969177i | \(0.420764\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.89269 | 0.301226 | 0.150613 | − | 0.988593i | \(-0.451875\pi\) | ||||
0.150613 | + | 0.988593i | \(0.451875\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27.1978 | 2.09214 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.255652 | 0.0195502 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.44521 | −0.109877 | −0.0549387 | − | 0.998490i | \(-0.517496\pi\) | ||||
−0.0549387 | + | 0.998490i | \(0.517496\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.57531 | −0.419066 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.9421 | 0.892598 | 0.446299 | − | 0.894884i | \(-0.352742\pi\) | ||||
0.446299 | + | 0.894884i | \(0.352742\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.3607 | −1.14175 | −0.570876 | − | 0.821037i | \(-0.693396\pi\) | ||||
−0.570876 | + | 0.821037i | \(0.693396\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.26794 | −0.315495 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.5236 | 1.35458 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.8432 | −1.00695 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.3607 | 1.83504 | 0.917518 | − | 0.397695i | \(-0.130190\pi\) | ||||
0.917518 | + | 0.397695i | \(0.130190\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.58145 | 0.329780 | 0.164890 | − | 0.986312i | \(-0.447273\pi\) | ||||
0.164890 | + | 0.986312i | \(0.447273\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.8638 | 1.20149 | 0.600747 | − | 0.799439i | \(-0.294870\pi\) | ||||
0.600747 | + | 0.799439i | \(0.294870\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.84324 | −0.697769 | −0.348885 | − | 0.937166i | \(-0.613439\pi\) | ||||
−0.348885 | + | 0.937166i | \(0.613439\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.4452 | −0.948352 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.26180 | 0.369306 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.107307 | 0.00745836 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 17.6742 | 1.22255 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.5753 | 1.07225 | 0.536124 | − | 0.844139i | \(-0.319888\pi\) | ||||
0.536124 | + | 0.844139i | \(0.319888\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.5236 | 0.721065 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.3135 | 0.835896 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −23.2039 | −1.56798 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.6742 | −1.45796 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.9854 | 1.13743 | 0.568715 | − | 0.822535i | \(-0.307441\pi\) | ||||
0.568715 | + | 0.822535i | \(0.307441\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.9649 | −1.32512 | −0.662559 | − | 0.749009i | \(-0.730530\pi\) | ||||
−0.662559 | + | 0.749009i | \(0.730530\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.6742 | −1.56444 | −0.782218 | − | 0.623005i | \(-0.785912\pi\) | ||||
−0.782218 | + | 0.623005i | \(0.785912\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −24.3668 | −1.60322 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.5753 | 0.889348 | 0.444674 | − | 0.895693i | \(-0.353320\pi\) | ||||
0.444674 | + | 0.895693i | \(0.353320\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −21.6742 | −1.40789 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.36683 | −0.541206 | −0.270603 | − | 0.962691i | \(-0.587223\pi\) | ||||
−0.270603 | + | 0.962691i | \(0.587223\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.91548 | 0.638712 | 0.319356 | − | 0.947635i | \(-0.396533\pi\) | ||||
0.319356 | + | 0.947635i | \(0.396533\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.814315 | −0.0522383 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.6803 | −1.31586 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −25.5897 | −1.62168 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.6163 | 1.11193 | 0.555967 | − | 0.831204i | \(-0.312348\pi\) | ||||
0.555967 | + | 0.831204i | \(0.312348\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.41855 | 0.466400 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.68649 | −0.229957 | −0.114978 | − | 0.993368i | \(-0.536680\pi\) | ||||
−0.114978 | + | 0.993368i | \(0.536680\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.1506 | 0.941413 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.156755 | 0.00970292 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.107307 | 0.00661684 | 0.00330842 | − | 0.999995i | \(-0.498947\pi\) | ||||
0.00330842 | + | 0.999995i | \(0.498947\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.5692 | 0.891618 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.85762 | −0.235203 | −0.117602 | − | 0.993061i | \(-0.537521\pi\) | ||||
−0.117602 | + | 0.993061i | \(0.537521\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.3074 | 1.29433 | 0.647165 | − | 0.762350i | \(-0.275954\pi\) | ||||
0.647165 | + | 0.762350i | \(0.275954\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 28.5113 | 1.72558 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.44521 | −0.0868344 | −0.0434172 | − | 0.999057i | \(-0.513824\pi\) | ||||
−0.0434172 | + | 0.999057i | \(0.513824\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.366835 | 0.0219618 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.4391 | 0.742053 | 0.371026 | − | 0.928622i | \(-0.379006\pi\) | ||||
0.371026 | + | 0.928622i | \(0.379006\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.29072 | 0.373945 | 0.186972 | − | 0.982365i | \(-0.440133\pi\) | ||||
0.186972 | + | 0.982365i | \(0.440133\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.4124 | 1.20491 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.31351 | −0.312559 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.83096 | −0.459059 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.07838 | −0.0629995 | −0.0314998 | − | 0.999504i | \(-0.510028\pi\) | ||||
−0.0314998 | + | 0.999504i | \(0.510028\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −28.5113 | −1.65439 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.68035 | −0.501997 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.7009 | −0.674427 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.95443 | 0.227176 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.2267 | 1.43977 | 0.719883 | − | 0.694096i | \(-0.244196\pi\) | ||||
0.719883 | + | 0.694096i | \(0.244196\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 27.7009 | 1.57585 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.8371 | −1.06815 | −0.534077 | − | 0.845436i | \(-0.679341\pi\) | ||||
−0.534077 | + | 0.845436i | \(0.679341\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.2039 | 0.859377 | 0.429689 | − | 0.902977i | \(-0.358623\pi\) | ||||
0.429689 | + | 0.902977i | \(0.358623\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.8638 | −0.947163 | −0.473582 | − | 0.880750i | \(-0.657039\pi\) | ||||
−0.473582 | + | 0.880750i | \(0.657039\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.8371 | 0.606761 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 26.7526 | 1.49318 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.1506 | 0.620437 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −21.0928 | −1.16643 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.5958 | 0.694430 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.5753 | −1.29582 | −0.647908 | − | 0.761719i | \(-0.724356\pi\) | ||||
−0.647908 | + | 0.761719i | \(0.724356\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.451356 | 0.0247341 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.8371 | 0.808228 | 0.404114 | − | 0.914709i | \(-0.367580\pi\) | ||||
0.404114 | + | 0.914709i | \(0.367580\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.0000 | 0.869001 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.3607 | 1.37336 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.6225 | 1.00552 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.133969 | −0.00719184 | −0.00359592 | − | 0.999994i | \(-0.501145\pi\) | ||||
−0.00359592 | + | 0.999994i | \(0.501145\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.3135 | −1.19441 | −0.597207 | − | 0.802087i | \(-0.703723\pi\) | ||||
−0.597207 | + | 0.802087i | \(0.703723\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 33.3607 | 1.78066 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.8371 | −1.21550 | −0.607748 | − | 0.794130i | \(-0.707927\pi\) | ||||
−0.607748 | + | 0.794130i | \(0.707927\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −15.3730 | −0.813624 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 31.8843 | 1.68279 | 0.841394 | − | 0.540422i | \(-0.181735\pi\) | ||||
0.841394 | + | 0.540422i | \(0.181735\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.36069 | −0.440036 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −31.3835 | −1.64721 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.4619 | −1.59010 | −0.795048 | − | 0.606547i | \(-0.792554\pi\) | ||||
−0.795048 | + | 0.606547i | \(0.792554\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.608111 | 0.0316570 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.36683 | −0.226715 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0722 | 0.521521 | 0.260760 | − | 0.965404i | \(-0.416027\pi\) | ||||
0.260760 | + | 0.965404i | \(0.416027\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.6803 | −0.653071 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.7792 | 0.759159 | 0.379579 | − | 0.925159i | \(-0.376069\pi\) | ||||
0.379579 | + | 0.925159i | \(0.376069\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.33403 | 0.170808 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.4619 | 0.738966 | 0.369483 | − | 0.929237i | \(-0.379535\pi\) | ||||
0.369483 | + | 0.929237i | \(0.379535\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.348583 | −0.0177195 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.17727 | 0.161094 | 0.0805471 | − | 0.996751i | \(-0.474333\pi\) | ||||
0.0805471 | + | 0.996751i | \(0.474333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.68035 | 0.236695 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −26.6225 | −1.34293 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.8227 | 0.543177 | 0.271589 | − | 0.962413i | \(-0.412451\pi\) | ||||
0.271589 | + | 0.962413i | \(0.412451\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −14.6681 | −0.734321 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.5236 | −0.625398 | −0.312699 | − | 0.949852i | \(-0.601233\pi\) | ||||
−0.312699 | + | 0.949852i | \(0.601233\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −29.6742 | −1.47818 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 31.2039 | 1.54672 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.2885 | −0.657072 | −0.328536 | − | 0.944491i | \(-0.606555\pi\) | ||||
−0.328536 | + | 0.944491i | \(0.606555\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −25.9877 | −1.28188 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.58145 | −0.422266 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.41241 | 0.216077 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.255652 | 0.0124894 | 0.00624471 | − | 0.999981i | \(-0.498012\pi\) | ||||
0.00624471 | + | 0.999981i | \(0.498012\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.49693 | 0.121693 | 0.0608464 | − | 0.998147i | \(-0.480620\pi\) | ||||
0.0608464 | + | 0.998147i | \(0.480620\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.375245 | 0.0182451 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.56916 | −0.317904 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 58.7214 | 2.83510 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.993857 | −0.0478724 | −0.0239362 | − | 0.999713i | \(-0.507620\pi\) | ||||
−0.0239362 | + | 0.999713i | \(0.507620\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.6286 | 0.847178 | 0.423589 | − | 0.905855i | \(-0.360770\pi\) | ||||
0.423589 | + | 0.905855i | \(0.360770\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.46573 | 0.213625 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −40.5113 | −1.93350 | −0.966750 | − | 0.255725i | \(-0.917686\pi\) | ||||
−0.966750 | + | 0.255725i | \(0.917686\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.00614307 | 0.000292527 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.7093 | −0.841393 | −0.420697 | − | 0.907201i | \(-0.638214\pi\) | ||||
−0.420697 | + | 0.907201i | \(0.638214\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.10504 | −0.146863 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.28846 | −0.0608061 | −0.0304030 | − | 0.999538i | \(-0.509679\pi\) | ||||
−0.0304030 | + | 0.999538i | \(0.509679\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 42.0410 | 1.97964 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.82482 | 0.414626 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.3545 | −1.23281 | −0.616407 | − | 0.787428i | \(-0.711412\pi\) | ||||
−0.616407 | + | 0.787428i | \(0.711412\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −17.9877 | −0.839595 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 41.0349 | 1.91119 | 0.955593 | − | 0.294690i | \(-0.0952165\pi\) | ||||
0.955593 | + | 0.294690i | \(0.0952165\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.7708 | −1.33709 | −0.668547 | − | 0.743670i | \(-0.733083\pi\) | ||||
−0.668547 | + | 0.743670i | \(0.733083\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.12783 | −0.237287 | −0.118644 | − | 0.992937i | \(-0.537855\pi\) | ||||
−0.118644 | + | 0.992937i | \(0.537855\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −20.6947 | −0.955593 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.5174 | −1.08363 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −24.0989 | −1.10807 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.130094 | −0.00595657 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.6742 | 0.624790 | 0.312395 | − | 0.949952i | \(-0.398869\pi\) | ||||
0.312395 | + | 0.949952i | \(0.398869\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −36.5113 | −1.66477 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.15676 | −0.280142 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.51971 | 0.386065 | 0.193033 | − | 0.981192i | \(-0.438168\pi\) | ||||
0.193033 | + | 0.981192i | \(0.438168\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.7526 | −0.486249 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.73820 | 0.213832 | 0.106916 | − | 0.994268i | \(-0.465902\pi\) | ||||
0.106916 | + | 0.994268i | \(0.465902\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.83710 | 0.307928 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.1978 | 0.726570 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.0928 | −0.496580 | −0.248290 | − | 0.968686i | \(-0.579869\pi\) | ||||
−0.248290 | + | 0.968686i | \(0.579869\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.65368 | −0.297265 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.42082 | 0.375466 | 0.187733 | − | 0.982220i | \(-0.439886\pi\) | ||||
0.187733 | + | 0.982220i | \(0.439886\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −46.4885 | −2.06463 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −26.0000 | −1.15243 | −0.576215 | − | 0.817298i | \(-0.695471\pi\) | ||||
−0.576215 | + | 0.817298i | \(0.695471\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −35.7152 | −1.57995 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −17.1629 | −0.757760 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.9421 | 1.14093 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.47027 | 0.108433 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.3135 | −0.451843 | −0.225922 | − | 0.974145i | \(-0.572539\pi\) | ||||
−0.225922 | + | 0.974145i | \(0.572539\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.2784 | 0.711806 | 0.355903 | − | 0.934523i | \(-0.384173\pi\) | ||||
0.355903 | + | 0.934523i | \(0.384173\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.0000 | 0.696971 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.1256 | −0.918503 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.255652 | −0.0110944 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −49.1917 | −2.13073 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −20.4124 | −0.880860 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.424694 | 0.0182929 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.36069 | 0.144487 | 0.0722437 | − | 0.997387i | \(-0.476984\pi\) | ||||
0.0722437 | + | 0.997387i | \(0.476984\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 26.2557 | 1.12674 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.51148 | 0.0646263 | 0.0323132 | − | 0.999478i | \(-0.489713\pi\) | ||||
0.0323132 | + | 0.999478i | \(0.489713\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.195704 | −0.00835243 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.52359 | 0.277914 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −33.3607 | −1.41864 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −36.2290 | −1.53507 | −0.767536 | − | 0.641006i | \(-0.778517\pi\) | ||||
−0.767536 | + | 0.641006i | \(0.778517\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 28.1978 | 1.19264 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −31.6619 | −1.33677 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.17501 | 0.0916656 | 0.0458328 | − | 0.998949i | \(-0.485406\pi\) | ||||
0.0458328 | + | 0.998949i | \(0.485406\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.0433 | 0.967728 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.1194 | 1.38844 | 0.694219 | − | 0.719764i | \(-0.255750\pi\) | ||||
0.694219 | + | 0.719764i | \(0.255750\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.4657 | −0.772767 | −0.386383 | − | 0.922338i | \(-0.626276\pi\) | ||||
−0.386383 | + | 0.922338i | \(0.626276\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −43.3484 | −1.81091 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.2101 | 0.591573 | 0.295787 | − | 0.955254i | \(-0.404418\pi\) | ||||
0.295787 | + | 0.955254i | \(0.404418\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.83096 | −0.325444 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −39.3874 | −1.63406 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.99386 | −0.372487 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.7503 | 0.484987 | 0.242494 | − | 0.970153i | \(-0.422035\pi\) | ||||
0.242494 | + | 0.970153i | \(0.422035\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.2663 | 0.629038 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −28.8248 | −1.18569 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.00000 | −0.328521 | −0.164260 | − | 0.986417i | \(-0.552524\pi\) | ||||
−0.164260 | + | 0.986417i | \(0.552524\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.8248 | 0.688594 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.5646 | −0.840248 | −0.420124 | − | 0.907467i | \(-0.638013\pi\) | ||||
−0.420124 | + | 0.907467i | \(0.638013\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.60811 | −0.351132 | −0.175566 | − | 0.984468i | \(-0.556176\pi\) | ||||
−0.175566 | + | 0.984468i | \(0.556176\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.616522 | −0.0251067 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.259528 | 0.0105339 | 0.00526695 | − | 0.999986i | \(-0.498323\pi\) | ||||
0.00526695 | + | 0.999986i | \(0.498323\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.99386 | −0.364449 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −30.3545 | −1.22801 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −47.1650 | −1.90498 | −0.952488 | − | 0.304576i | \(-0.901485\pi\) | ||||
−0.952488 | + | 0.304576i | \(0.901485\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 40.2967 | 1.62228 | 0.811142 | − | 0.584849i | \(-0.198846\pi\) | ||||
0.811142 | + | 0.584849i | \(0.198846\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.6102 | 1.23033 | 0.615164 | − | 0.788399i | \(-0.289090\pi\) | ||||
0.615164 | + | 0.788399i | \(0.289090\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.20394 | −0.289084 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22.4247 | 0.898426 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −30.2101 | −1.20647 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.6865 | 0.784952 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.21008 | 0.0879819 | 0.0439909 | − | 0.999032i | \(-0.485993\pi\) | ||||
0.0439909 | + | 0.999032i | \(0.485993\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −26.6225 | −1.05815 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.496928 | −0.0196890 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.482553 | 0.0190895 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.92777 | 0.313128 | 0.156564 | − | 0.987668i | \(-0.449958\pi\) | ||||
0.156564 | + | 0.987668i | \(0.449958\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.18115 | 0.204325 | 0.102162 | − | 0.994768i | \(-0.467424\pi\) | ||||
0.102162 | + | 0.994768i | \(0.467424\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.2062 | 0.479875 | 0.239938 | − | 0.970788i | \(-0.422873\pi\) | ||||
0.239938 | + | 0.970788i | \(0.422873\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.6742 | −0.693773 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21.0472 | −0.824904 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −32.4969 | −1.27170 | −0.635852 | − | 0.771811i | \(-0.719351\pi\) | ||||
−0.635852 | + | 0.771811i | \(0.719351\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.06400 | −0.0415107 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.4186 | −1.14598 | −0.572992 | − | 0.819561i | \(-0.694217\pi\) | ||||
−0.572992 | + | 0.819561i | \(0.694217\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.0677 | 1.01392 | 0.506958 | − | 0.861971i | \(-0.330770\pi\) | ||||
0.506958 | + | 0.861971i | \(0.330770\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 37.0472 | 1.43879 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.73820 | 0.106024 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −29.0328 | −1.12247 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.5297 | −0.522310 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.62863 | −0.371156 | −0.185578 | − | 0.982629i | \(-0.559416\pi\) | ||||
−0.185578 | + | 0.982629i | \(0.559416\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.0205 | −0.731018 | −0.365509 | − | 0.930808i | \(-0.619105\pi\) | ||||
−0.365509 | + | 0.930808i | \(0.619105\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.0533 | −0.462564 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 34.1256 | 1.30769 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.4947 | 0.669415 | 0.334707 | − | 0.942322i | \(-0.391363\pi\) | ||||
0.334707 | + | 0.942322i | \(0.391363\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 40.4657 | 1.54386 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.5236 | 0.400917 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.3090 | 0.620423 | 0.310211 | − | 0.950668i | \(-0.399600\pi\) | ||||
0.310211 | + | 0.950668i | \(0.399600\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.11733 | −0.0424437 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 26.5236 | 1.00465 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.2039 | −0.877653 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.9672 | −0.489764 | −0.244882 | − | 0.969553i | \(-0.578749\pi\) | ||||
−0.244882 | + | 0.969553i | \(0.578749\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.7838 | 0.708444 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.08661 | 0.228911 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.36069 | 0.276437 | 0.138218 | − | 0.990402i | \(-0.455862\pi\) | ||||
0.138218 | + | 0.990402i | \(0.455862\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.993857 | −0.0372725 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.40787 | 0.239977 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.3012 | 0.534089 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.3197 | −0.720502 | −0.360251 | − | 0.932856i | \(-0.617309\pi\) | ||||
−0.360251 | + | 0.932856i | \(0.617309\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 42.6369 | 1.58788 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16.9483 | −0.630313 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.1545 | −0.784577 | −0.392288 | − | 0.919842i | \(-0.628316\pi\) | ||||
−0.392288 | + | 0.919842i | \(0.628316\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.6681 | 1.02474 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.2039 | −0.562338 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.7526 | 0.840386 | 0.420193 | − | 0.907435i | \(-0.361962\pi\) | ||||
0.420193 | + | 0.907435i | \(0.361962\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −42.6225 | −1.57002 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.4534 | −1.04668 | −0.523338 | − | 0.852125i | \(-0.675314\pi\) | ||||
−0.523338 | + | 0.852125i | \(0.675314\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 35.3484 | 1.29856 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.79380 | 0.139181 | 0.0695904 | − | 0.997576i | \(-0.477831\pi\) | ||||
0.0695904 | + | 0.997576i | \(0.477831\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.17340 | −0.0429324 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 41.1773 | 1.50458 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.3607 | 0.633501 | 0.316750 | − | 0.948509i | \(-0.397408\pi\) | ||||
0.316750 | + | 0.948509i | \(0.397408\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −30.1112 | −1.09731 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.76487 | 0.173182 | 0.0865910 | − | 0.996244i | \(-0.472403\pi\) | ||||
0.0865910 | + | 0.996244i | \(0.472403\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.6803 | −0.460267 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.1978 | −0.514670 | −0.257335 | − | 0.966322i | \(-0.582844\pi\) | ||||
−0.257335 | + | 0.966322i | \(0.582844\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −32.4657 | −1.17534 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.6803 | 0.746724 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 54.7091 | 1.97286 | 0.986430 | − | 0.164181i | \(-0.0524981\pi\) | ||||
0.986430 | + | 0.164181i | \(0.0524981\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.30122 | 0.226933 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.0205 | 0.396381 | 0.198190 | − | 0.980164i | \(-0.436494\pi\) | ||||
0.198190 | + | 0.980164i | \(0.436494\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −25.8966 | −0.929034 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.3074 | 0.906731 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 33.3607 | 1.19374 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.5236 | −0.376082 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.6925 | −1.20101 | −0.600503 | − | 0.799622i | \(-0.705033\pi\) | ||||
−0.600503 | + | 0.799622i | \(0.705033\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.183417 | −0.00652984 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.6270 | 0.875636 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.8310 | 0.562174 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.7009 | −0.839528 | −0.419764 | − | 0.907633i | \(-0.637887\pi\) | ||||
−0.419764 | + | 0.907633i | \(0.637887\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.3668 | 0.579017 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.668060 | 0.0236047 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −73.5585 | −2.59582 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.59374 | 0.232110 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −33.0349 | −1.16145 | −0.580723 | − | 0.814102i | \(-0.697230\pi\) | ||||
−0.580723 | + | 0.814102i | \(0.697230\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.26794 | 0.220097 | 0.110049 | − | 0.993926i | \(-0.464899\pi\) | ||||
0.110049 | + | 0.993926i | \(0.464899\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −36.4202 | −1.27731 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.5068 | −0.507528 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.30737 | 0.0456831 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.0616 | −0.525652 | −0.262826 | − | 0.964843i | \(-0.584655\pi\) | ||||
−0.262826 | + | 0.964843i | \(0.584655\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.5669 | −1.17007 | −0.585034 | − | 0.811009i | \(-0.698919\pi\) | ||||
−0.585034 | + | 0.811009i | \(0.698919\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.6576 | −0.370600 | −0.185300 | − | 0.982682i | \(-0.559326\pi\) | ||||
−0.185300 | + | 0.982682i | \(0.559326\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −52.4846 | −1.82287 | −0.911433 | − | 0.411447i | \(-0.865023\pi\) | ||||
−0.911433 | + | 0.411447i | \(0.865023\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.47027 | 0.0856926 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.267938 | 0.00928351 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −24.6270 | −0.851234 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.2101 | 0.628682 | 0.314341 | − | 0.949310i | \(-0.398217\pi\) | ||||
0.314341 | + | 0.949310i | \(0.398217\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −21.2618 | −0.732295 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −48.3051 | −1.65978 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.7526 | −0.369028 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.88428 | 0.270270 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.7542 | 0.676371 | 0.338185 | − | 0.941080i | \(-0.390187\pi\) | ||||
0.338185 | + | 0.941080i | \(0.390187\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −48.9939 | −1.67360 | −0.836799 | − | 0.547510i | \(-0.815576\pi\) | ||||
−0.836799 | + | 0.547510i | \(0.815576\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.3090 | 0.829412 | 0.414706 | − | 0.909956i | \(-0.363885\pi\) | ||||
0.414706 | + | 0.909956i | \(0.363885\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −34.8904 | −1.18906 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.3584 | 1.50998 | 0.754989 | − | 0.655737i | \(-0.227642\pi\) | ||||
0.754989 | + | 0.655737i | \(0.227642\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.08225 | 0.308449 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −68.7091 | −2.33080 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 49.8720 | 1.68985 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.359084 | −0.0121531 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.9565 | 1.28170 | 0.640850 | − | 0.767666i | \(-0.278582\pi\) | ||||
0.640850 | + | 0.767666i | \(0.278582\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.84324 | 0.0621711 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.0661 | 0.844498 | 0.422249 | − | 0.906480i | \(-0.361241\pi\) | ||||
0.422249 | + | 0.906480i | \(0.361241\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.1278 | 0.711008 | 0.355504 | − | 0.934675i | \(-0.384309\pi\) | ||||
0.355504 | + | 0.934675i | \(0.384309\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.1894 | −1.21512 | −0.607560 | − | 0.794274i | \(-0.707852\pi\) | ||||
−0.607560 | + | 0.794274i | \(0.707852\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.13170 | 0.172112 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 47.4596 | 1.58996 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.6163 | 0.522581 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.8371 | 0.495396 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.36069 | 0.312197 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.67420 | −0.189035 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.0000 | 0.665558 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.2678 | 1.17105 | 0.585523 | − | 0.810656i | \(-0.300889\pi\) | ||||
0.585523 | + | 0.810656i | \(0.300889\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.181328 | 0.00601426 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.0061 | −0.497176 | −0.248588 | − | 0.968609i | \(-0.579966\pi\) | ||||
−0.248588 | + | 0.968609i | \(0.579966\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −81.1215 | −2.68473 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −40.9770 | −1.35318 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.8781 | 1.08455 | 0.542275 | − | 0.840201i | \(-0.317563\pi\) | ||||
0.542275 | + | 0.840201i | \(0.317563\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −43.1194 | −1.42083 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −39.0349 | −1.28485 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.27021 | 0.0417190 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30.2290 | −0.991781 | −0.495890 | − | 0.868385i | \(-0.665158\pi\) | ||||
−0.495890 | + | 0.868385i | \(0.665158\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.255652 | 0.00837866 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 32.1978 | 1.05411 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.4124 | 0.928193 | 0.464096 | − | 0.885785i | \(-0.346379\pi\) | ||||
0.464096 | + | 0.885785i | \(0.346379\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.9877 | −0.848077 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.0821 | −1.37184 | −0.685918 | − | 0.727679i | \(-0.740599\pi\) | ||||
−0.685918 | + | 0.727679i | \(0.740599\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.6225 | 0.345916 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.2739 | 0.723805 | 0.361902 | − | 0.932216i | \(-0.382127\pi\) | ||||
0.361902 | + | 0.932216i | \(0.382127\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 86.0698 | 2.79394 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28.8248 | 0.934709 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.6681 | 0.475145 | 0.237573 | − | 0.971370i | \(-0.423648\pi\) | ||||
0.237573 | + | 0.971370i | \(0.423648\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −18.5236 | −0.598783 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −40.0000 | −1.29167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.09436 | −0.293367 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.22672 | 0.0395306 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.403997 | 0.0129917 | 0.00649584 | − | 0.999979i | \(-0.497932\pi\) | ||||
0.00649584 | + | 0.999979i | \(0.497932\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −19.0595 | −0.612278 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 46.8326 | 1.50293 | 0.751464 | − | 0.659774i | \(-0.229348\pi\) | ||||
0.751464 | + | 0.659774i | \(0.229348\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.79153 | 0.217726 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −53.6041 | −1.71495 | −0.857473 | − | 0.514529i | \(-0.827967\pi\) | ||||
−0.857473 | + | 0.514529i | \(0.827967\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 46.1855 | 1.47610 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.967195 | −0.0308802 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.9916 | 0.637633 | 0.318816 | − | 0.947817i | \(-0.396715\pi\) | ||||
0.318816 | + | 0.947817i | \(0.396715\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −21.5297 | −0.685299 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.08906 | −0.193621 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.6270 | −0.782303 | −0.391152 | − | 0.920326i | \(-0.627923\pi\) | ||||
−0.391152 | + | 0.920326i | \(0.627923\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 40.2967 | 1.27878 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.9795 | 0.664427 | 0.332213 | − | 0.943204i | \(-0.392205\pi\) | ||||
0.332213 | + | 0.943204i | \(0.392205\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −30.3012 | −0.958688 |
(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 | 3200.2.a.bs.1.1 | 3 | ||
4.3 | odd | 2 | 3200.2.a.br.1.3 | 3 | |||
5.2 | odd | 4 | 640.2.c.a.129.5 | yes | 6 | ||
5.3 | odd | 4 | 640.2.c.a.129.2 | ✓ | 6 | ||
5.4 | even | 2 | 3200.2.a.bq.1.3 | 3 | |||
8.3 | odd | 2 | 3200.2.a.bu.1.1 | 3 | |||
8.5 | even | 2 | 3200.2.a.bp.1.3 | 3 | |||
20.3 | even | 4 | 640.2.c.b.129.5 | yes | 6 | ||
20.7 | even | 4 | 640.2.c.b.129.2 | yes | 6 | ||
20.19 | odd | 2 | 3200.2.a.bt.1.1 | 3 | |||
40.3 | even | 4 | 640.2.c.c.129.2 | yes | 6 | ||
40.13 | odd | 4 | 640.2.c.d.129.5 | yes | 6 | ||
40.19 | odd | 2 | 3200.2.a.bo.1.3 | 3 | |||
40.27 | even | 4 | 640.2.c.c.129.5 | yes | 6 | ||
40.29 | even | 2 | 3200.2.a.bv.1.1 | 3 | |||
40.37 | odd | 4 | 640.2.c.d.129.2 | yes | 6 | ||
80.3 | even | 4 | 1280.2.f.k.129.2 | 6 | |||
80.13 | odd | 4 | 1280.2.f.i.129.6 | 6 | |||
80.27 | even | 4 | 1280.2.f.k.129.1 | 6 | |||
80.37 | odd | 4 | 1280.2.f.i.129.5 | 6 | |||
80.43 | even | 4 | 1280.2.f.j.129.5 | 6 | |||
80.53 | odd | 4 | 1280.2.f.l.129.1 | 6 | |||
80.67 | even | 4 | 1280.2.f.j.129.6 | 6 | |||
80.77 | odd | 4 | 1280.2.f.l.129.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
640.2.c.a.129.2 | ✓ | 6 | 5.3 | odd | 4 | ||
640.2.c.a.129.5 | yes | 6 | 5.2 | odd | 4 | ||
640.2.c.b.129.2 | yes | 6 | 20.7 | even | 4 | ||
640.2.c.b.129.5 | yes | 6 | 20.3 | even | 4 | ||
640.2.c.c.129.2 | yes | 6 | 40.3 | even | 4 | ||
640.2.c.c.129.5 | yes | 6 | 40.27 | even | 4 | ||
640.2.c.d.129.2 | yes | 6 | 40.37 | odd | 4 | ||
640.2.c.d.129.5 | yes | 6 | 40.13 | odd | 4 | ||
1280.2.f.i.129.5 | 6 | 80.37 | odd | 4 | |||
1280.2.f.i.129.6 | 6 | 80.13 | odd | 4 | |||
1280.2.f.j.129.5 | 6 | 80.43 | even | 4 | |||
1280.2.f.j.129.6 | 6 | 80.67 | even | 4 | |||
1280.2.f.k.129.1 | 6 | 80.27 | even | 4 | |||
1280.2.f.k.129.2 | 6 | 80.3 | even | 4 | |||
1280.2.f.l.129.1 | 6 | 80.53 | odd | 4 | |||
1280.2.f.l.129.2 | 6 | 80.77 | odd | 4 | |||
3200.2.a.bo.1.3 | 3 | 40.19 | odd | 2 | |||
3200.2.a.bp.1.3 | 3 | 8.5 | even | 2 | |||
3200.2.a.bq.1.3 | 3 | 5.4 | even | 2 | |||
3200.2.a.br.1.3 | 3 | 4.3 | odd | 2 | |||
3200.2.a.bs.1.1 | 3 | 1.1 | even | 1 | trivial | ||
3200.2.a.bt.1.1 | 3 | 20.19 | odd | 2 | |||
3200.2.a.bu.1.1 | 3 | 8.3 | odd | 2 | |||
3200.2.a.bv.1.1 | 3 | 40.29 | even | 2 |