Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1024,2,Mod(1,1024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1024, 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("1024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1024 = 2^{10} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1024.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: | \(8.17668116698\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{24})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 256) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.93185\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.1 |
$q$-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 | ||||||||
\(3\) | −0.732051 | −0.422650 | −0.211325 | − | 0.977416i | \(-0.567778\pi\) | ||||
−0.211325 | + | 0.977416i | \(0.567778\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.44949 | −1.09545 | −0.547723 | − | 0.836660i | \(-0.684505\pi\) | ||||
−0.547723 | + | 0.836660i | \(0.684505\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.86370 | −1.46034 | −0.730171 | − | 0.683264i | \(-0.760560\pi\) | ||||
−0.730171 | + | 0.683264i | \(0.760560\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.46410 | −0.821367 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.73205 | 1.42677 | 0.713384 | − | 0.700774i | \(-0.247162\pi\) | ||||
0.713384 | + | 0.700774i | \(0.247162\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.378937 | −0.105098 | −0.0525492 | − | 0.998618i | \(-0.516735\pi\) | ||||
−0.0525492 | + | 0.998618i | \(0.516735\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.79315 | 0.462990 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.46410 | −0.840168 | −0.420084 | − | 0.907485i | \(-0.637999\pi\) | ||||
−0.420084 | + | 0.907485i | \(0.637999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.73205 | 1.08561 | 0.542803 | − | 0.839860i | \(-0.317363\pi\) | ||||
0.542803 | + | 0.839860i | \(0.317363\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.82843 | 0.617213 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.79315 | −0.373898 | −0.186949 | − | 0.982370i | \(-0.559860\pi\) | ||||
−0.186949 | + | 0.982370i | \(0.559860\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.44949 | 0.454859 | 0.227429 | − | 0.973795i | \(-0.426968\pi\) | ||||
0.227429 | + | 0.973795i | \(0.426968\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.65685 | 1.01600 | 0.508001 | − | 0.861357i | \(-0.330385\pi\) | ||||
0.508001 | + | 0.861357i | \(0.330385\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.46410 | −0.603023 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.46410 | 1.59973 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.27792 | 0.867684 | 0.433842 | − | 0.900989i | \(-0.357158\pi\) | ||||
0.433842 | + | 0.900989i | \(0.357158\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.277401 | 0.0444198 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.92820 | 1.08200 | 0.541002 | − | 0.841021i | \(-0.318045\pi\) | ||||
0.541002 | + | 0.841021i | \(0.318045\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.19615 | −0.334910 | −0.167455 | − | 0.985880i | \(-0.553555\pi\) | ||||
−0.167455 | + | 0.985880i | \(0.553555\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.03579 | 0.899763 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.79796 | 1.42918 | 0.714590 | − | 0.699544i | \(-0.246613\pi\) | ||||
0.714590 | + | 0.699544i | \(0.246613\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.92820 | 1.13260 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.53590 | 0.355097 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.9348 | −1.50201 | −0.751003 | − | 0.660299i | \(-0.770430\pi\) | ||||
−0.751003 | + | 0.660299i | \(0.770430\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.5911 | −1.56294 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.46410 | −0.458831 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.26795 | 0.946206 | 0.473103 | − | 0.881007i | \(-0.343134\pi\) | ||||
0.473103 | + | 0.881007i | \(0.343134\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.27792 | −0.675768 | −0.337884 | − | 0.941188i | \(-0.609711\pi\) | ||||
−0.337884 | + | 0.941188i | \(0.609711\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.52056 | 1.19948 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.928203 | 0.115129 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.19615 | 0.756980 | 0.378490 | − | 0.925605i | \(-0.376443\pi\) | ||||
0.378490 | + | 0.925605i | \(0.376443\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.31268 | 0.158028 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.79315 | 0.212808 | 0.106404 | − | 0.994323i | \(-0.466066\pi\) | ||||
0.106404 | + | 0.994323i | \(0.466066\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.53590 | −0.296804 | −0.148402 | − | 0.988927i | \(-0.547413\pi\) | ||||
−0.148402 | + | 0.988927i | \(0.547413\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.732051 | −0.0845299 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −18.2832 | −2.08357 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.14110 | −0.465911 | −0.232955 | − | 0.972487i | \(-0.574840\pi\) | ||||
−0.232955 | + | 0.972487i | \(0.574840\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.46410 | 0.496011 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.19615 | −0.241059 | −0.120530 | − | 0.992710i | \(-0.538459\pi\) | ||||
−0.120530 | + | 0.992710i | \(0.538459\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.48528 | 0.920358 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.79315 | −0.192246 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.53590 | −0.268805 | −0.134402 | − | 0.990927i | \(-0.542911\pi\) | ||||
−0.134402 | + | 0.990927i | \(0.542911\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.46410 | 0.153480 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.14110 | −0.429413 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11.5911 | −1.18922 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.46410 | 0.351726 | 0.175863 | − | 0.984415i | \(-0.443728\pi\) | ||||
0.175863 | + | 0.984415i | \(0.443728\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.6603 | −1.17190 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.13681 | 0.113117 | 0.0565585 | − | 0.998399i | \(-0.481987\pi\) | ||||
0.0565585 | + | 0.998399i | \(0.481987\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.52056 | −0.938088 | −0.469044 | − | 0.883175i | \(-0.655402\pi\) | ||||
−0.469044 | + | 0.883175i | \(0.655402\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.92820 | −0.676123 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.5885 | 1.79701 | 0.898507 | − | 0.438959i | \(-0.144653\pi\) | ||||
0.898507 | + | 0.438959i | \(0.144653\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.6622 | 1.78751 | 0.893756 | − | 0.448553i | \(-0.148060\pi\) | ||||
0.893756 | + | 0.448553i | \(0.148060\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.86370 | −0.366726 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.9282 | −1.21618 | −0.608092 | − | 0.793867i | \(-0.708065\pi\) | ||||
−0.608092 | + | 0.793867i | \(0.708065\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.39230 | 0.409585 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.933740 | 0.0863243 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.3843 | 1.22693 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.3923 | 1.03566 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.07180 | −0.457309 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.79796 | 0.876356 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.65685 | −0.501965 | −0.250982 | − | 0.967992i | \(-0.580754\pi\) | ||||
−0.250982 | + | 0.967992i | \(0.580754\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.60770 | 0.141550 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.339746 | 0.0296837 | 0.0148419 | − | 0.999890i | \(-0.495276\pi\) | ||||
0.0148419 | + | 0.999890i | \(0.495276\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.2832 | −1.58536 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.79796 | −0.843274 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.0000 | 1.02523 | 0.512615 | − | 0.858619i | \(-0.328677\pi\) | ||||
0.512615 | + | 0.858619i | \(0.328677\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.1962 | −0.864826 | −0.432413 | − | 0.901676i | \(-0.642338\pi\) | ||||
−0.432413 | + | 0.901676i | \(0.642338\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.17260 | −0.604042 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.79315 | −0.149951 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.00000 | −0.498273 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.80385 | −0.478693 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.4201 | 1.59095 | 0.795476 | − | 0.605985i | \(-0.207221\pi\) | ||||
0.795476 | + | 0.605985i | \(0.207221\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.52056 | 0.774772 | 0.387386 | − | 0.921918i | \(-0.373378\pi\) | ||||
0.387386 | + | 0.921918i | \(0.373378\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.53590 | 0.690086 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.8564 | −1.11297 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.1769 | 0.812205 | 0.406102 | − | 0.913828i | \(-0.366888\pi\) | ||||
0.406102 | + | 0.913828i | \(0.366888\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.00481 | 0.634823 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.92820 | 0.546019 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.7321 | −1.31056 | −0.655278 | − | 0.755388i | \(-0.727448\pi\) | ||||
−0.655278 | + | 0.755388i | \(0.727448\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.48528 | 0.660578 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.7637 | 1.45198 | 0.725990 | − | 0.687705i | \(-0.241382\pi\) | ||||
0.725990 | + | 0.687705i | \(0.241382\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8564 | −0.988954 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.6603 | −0.891682 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.9348 | 0.831355 | 0.415678 | − | 0.909512i | \(-0.363544\pi\) | ||||
0.415678 | + | 0.909512i | \(0.363544\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.86370 | −0.292069 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.32051 | −0.399914 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.19615 | −0.164148 | −0.0820741 | − | 0.996626i | \(-0.526154\pi\) | ||||
−0.0820741 | + | 0.996626i | \(0.526154\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.8033 | −1.69495 | −0.847477 | − | 0.530832i | \(-0.821880\pi\) | ||||
−0.847477 | + | 0.530832i | \(0.821880\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.86370 | 0.285613 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.9282 | −0.950500 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.3923 | −1.19872 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −15.4548 | −1.12417 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.9706 | −1.22795 | −0.613973 | − | 0.789327i | \(-0.710430\pi\) | ||||
−0.613973 | + | 0.789327i | \(0.710430\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.3923 | −1.32391 | −0.661954 | − | 0.749545i | \(-0.730272\pi\) | ||||
−0.661954 | + | 0.749545i | \(0.730272\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.679492 | −0.0486594 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.44949 | −0.174519 | −0.0872595 | − | 0.996186i | \(-0.527811\pi\) | ||||
−0.0872595 | + | 0.996186i | \(0.527811\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.7322 | 1.11523 | 0.557614 | − | 0.830101i | \(-0.311717\pi\) | ||||
0.557614 | + | 0.830101i | \(0.311717\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.53590 | −0.319938 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.46410 | −0.664250 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.9706 | −1.18528 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.41851 | 0.307107 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 22.3923 | 1.54891 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.1962 | −0.701932 | −0.350966 | − | 0.936388i | \(-0.614147\pi\) | ||||
−0.350966 | + | 0.936388i | \(0.614147\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.31268 | −0.0899432 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.37945 | 0.366876 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21.8564 | −1.48371 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.85641 | 0.125444 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.31268 | 0.0883003 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.65685 | 0.378811 | 0.189405 | − | 0.981899i | \(-0.439344\pi\) | ||||
0.189405 | + | 0.981899i | \(0.439344\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.46410 | −0.164273 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.1244 | 1.40207 | 0.701036 | − | 0.713126i | \(-0.252721\pi\) | ||||
0.701036 | + | 0.713126i | \(0.252721\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.0053 | 0.859416 | 0.429708 | − | 0.902968i | \(-0.358617\pi\) | ||||
0.429708 | + | 0.902968i | \(0.358617\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.3843 | 0.880620 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.53590 | −0.166132 | −0.0830661 | − | 0.996544i | \(-0.526471\pi\) | ||||
−0.0830661 | + | 0.996544i | \(0.526471\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.0000 | −1.56559 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.03150 | 0.196917 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.7685 | −1.73151 | −0.865756 | − | 0.500467i | \(-0.833162\pi\) | ||||
−0.865756 | + | 0.500467i | \(0.833162\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.39230 | 0.154102 | 0.0770510 | − | 0.997027i | \(-0.475450\pi\) | ||||
0.0770510 | + | 0.997027i | \(0.475450\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.2679 | −0.979439 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −19.4201 | −1.24070 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.79315 | −0.114095 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.60770 | 0.101884 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.1244 | 1.33336 | 0.666679 | − | 0.745345i | \(-0.267715\pi\) | ||||
0.666679 | + | 0.745345i | \(0.267715\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.48528 | −0.533465 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.21166 | −0.388989 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.9282 | 0.806439 | 0.403220 | − | 0.915103i | \(-0.367891\pi\) | ||||
0.403220 | + | 0.915103i | \(0.367891\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.3923 | −1.26712 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.03579 | −0.373606 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.3891 | 1.31891 | 0.659453 | − | 0.751746i | \(-0.270788\pi\) | ||||
0.659453 | + | 0.751746i | \(0.270788\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 26.7846 | 1.64537 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.85641 | 0.113610 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.34847 | 0.448044 | 0.224022 | − | 0.974584i | \(-0.428081\pi\) | ||||
0.224022 | + | 0.974584i | \(0.428081\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.51575 | −0.0920752 | −0.0460376 | − | 0.998940i | \(-0.514659\pi\) | ||||
−0.0460376 | + | 0.998940i | \(0.514659\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.07180 | −0.0648681 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.73205 | 0.285353 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.52004 | 0.271583 | 0.135792 | − | 0.990737i | \(-0.456642\pi\) | ||||
0.135792 | + | 0.990737i | \(0.456642\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −13.9391 | −0.834510 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.3923 | 0.977883 | 0.488941 | − | 0.872317i | \(-0.337383\pi\) | ||||
0.488941 | + | 0.872317i | \(0.337383\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.80385 | −0.107228 | −0.0536138 | − | 0.998562i | \(-0.517074\pi\) | ||||
−0.0536138 | + | 0.998562i | \(0.517074\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.48528 | 0.502625 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −26.7685 | −1.58010 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.53590 | −0.148657 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.1464 | 1.00171 | 0.500853 | − | 0.865533i | \(-0.333020\pi\) | ||||
0.500853 | + | 0.865533i | \(0.333020\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.8028 | −1.03652 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.9282 | 1.09833 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.679492 | 0.0392960 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.48528 | 0.489083 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.832204 | −0.0478089 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.9282 | 0.740267 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −30.9808 | −1.76817 | −0.884083 | − | 0.467330i | \(-0.845216\pi\) | ||||
−0.884083 | + | 0.467330i | \(0.845216\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.96953 | 0.396483 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.1774 | 0.860632 | 0.430316 | − | 0.902678i | \(-0.358402\pi\) | ||||
0.430316 | + | 0.902678i | \(0.358402\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.7846 | 0.722629 | 0.361314 | − | 0.932444i | \(-0.382328\pi\) | ||||
0.361314 | + | 0.932444i | \(0.382328\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −23.3205 | −1.31396 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.62209 | 0.540431 | 0.270215 | − | 0.962800i | \(-0.412905\pi\) | ||||
0.270215 | + | 0.962800i | \(0.412905\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.5911 | 0.648978 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.6077 | −0.759507 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.3923 | −0.912092 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.378937 | −0.0210197 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13.6617 | −0.755492 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −37.8564 | −2.08709 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.5885 | 1.46143 | 0.730717 | − | 0.682681i | \(-0.239186\pi\) | ||||
0.730717 | + | 0.682681i | \(0.239186\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −13.0053 | −0.712687 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15.1774 | −0.829231 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.7128 | −1.18277 | −0.591386 | − | 0.806389i | \(-0.701419\pi\) | ||||
−0.591386 | + | 0.806389i | \(0.701419\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.46410 | 0.514019 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26.7685 | 1.44960 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.58630 | −0.193642 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.21539 | −0.173111 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.26795 | 0.390164 | 0.195082 | − | 0.980787i | \(-0.437503\pi\) | ||||
0.195082 | + | 0.980787i | \(0.437503\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.83272 | −0.312218 | −0.156109 | − | 0.987740i | \(-0.549895\pi\) | ||||
−0.156109 | + | 0.987740i | \(0.549895\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.51575 | −0.0809047 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.928203 | −0.0494033 | −0.0247016 | − | 0.999695i | \(-0.507864\pi\) | ||||
−0.0247016 | + | 0.999695i | \(0.507864\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.39230 | −0.233119 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.79796 | −0.518563 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.8028 | −0.939594 | −0.469797 | − | 0.882774i | \(-0.655673\pi\) | ||||
−0.469797 | + | 0.882774i | \(0.655673\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.39230 | 0.178542 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.33975 | −0.437723 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.21166 | 0.325133 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 32.4254 | 1.69259 | 0.846295 | − | 0.532714i | \(-0.178828\pi\) | ||||
0.846295 | + | 0.532714i | \(0.178828\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −17.0718 | −0.888722 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 42.2487 | 2.19344 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.9749 | 1.03426 | 0.517129 | − | 0.855907i | \(-0.327001\pi\) | ||||
0.517129 | + | 0.855907i | \(0.327001\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.17260 | −0.370392 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.928203 | −0.0478049 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.87564 | −0.147712 | −0.0738560 | − | 0.997269i | \(-0.523531\pi\) | ||||
−0.0738560 | + | 0.997269i | \(0.523531\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.14110 | 0.212155 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.5959 | 1.00130 | 0.500652 | − | 0.865648i | \(-0.333094\pi\) | ||||
0.500652 | + | 0.865648i | \(0.333094\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 44.7846 | 2.28244 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.41154 | 0.275084 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.03579 | −0.306027 | −0.153013 | − | 0.988224i | \(-0.548898\pi\) | ||||
−0.153013 | + | 0.988224i | \(0.548898\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.21166 | 0.314137 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.248711 | −0.0125458 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.1436 | 0.510380 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.7023 | −1.39034 | −0.695168 | − | 0.718847i | \(-0.744670\pi\) | ||||
−0.695168 | + | 0.718847i | \(0.744670\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 13.3843 | 0.670051 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.6077 | −0.679536 | −0.339768 | − | 0.940509i | \(-0.610349\pi\) | ||||
−0.339768 | + | 0.940509i | \(0.610349\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.14359 | −0.106780 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10.9348 | −0.543353 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.9754 | 1.23798 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.0718 | 0.844146 | 0.422073 | − | 0.906562i | \(-0.361303\pi\) | ||||
0.422073 | + | 0.906562i | \(0.361303\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.78461 | −0.433313 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −28.0812 | −1.38179 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.37945 | 0.264067 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.46410 | 0.365519 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.1962 | 0.693527 | 0.346764 | − | 0.937953i | \(-0.387281\pi\) | ||||
0.346764 | + | 0.937953i | \(0.387281\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.1865 | −1.27625 | −0.638126 | − | 0.769932i | \(-0.720290\pi\) | ||||
−0.638126 | + | 0.769932i | \(0.720290\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −24.1432 | −1.17388 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.46410 | −0.168034 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.3923 | 0.986853 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.31268 | 0.0633767 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.7685 | −1.28939 | −0.644697 | − | 0.764438i | \(-0.723017\pi\) | ||||
−0.644697 | + | 0.764438i | \(0.723017\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.3923 | 1.65279 | 0.826394 | − | 0.563092i | \(-0.190388\pi\) | ||||
0.826394 | + | 0.563092i | \(0.190388\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.39230 | 0.210595 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.48528 | −0.405906 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.1459 | 0.579693 | 0.289846 | − | 0.957073i | \(-0.406396\pi\) | ||||
0.289846 | + | 0.957073i | \(0.406396\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.5359 | −0.930281 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.1962 | 0.674480 | 0.337240 | − | 0.941419i | \(-0.390507\pi\) | ||||
0.337240 | + | 0.941419i | \(0.390507\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.21166 | 0.294461 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.2165 | −0.672416 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.2487 | −1.14437 | −0.572184 | − | 0.820125i | \(-0.693904\pi\) | ||||
−0.572184 | + | 0.820125i | \(0.693904\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.7846 | 1.54377 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.96953 | −0.327457 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.58630 | −0.168128 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.7846 | −0.972263 | −0.486132 | − | 0.873886i | \(-0.661592\pi\) | ||||
−0.486132 | + | 0.873886i | \(0.661592\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13.8564 | −0.646762 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 34.1170 | 1.58899 | 0.794493 | − | 0.607273i | \(-0.207737\pi\) | ||||
0.794493 | + | 0.607273i | \(0.207737\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.0822 | 1.76983 | 0.884916 | − | 0.465751i | \(-0.154216\pi\) | ||||
0.884916 | + | 0.465751i | \(0.154216\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.1436 | 0.470398 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.7321 | 1.32956 | 0.664780 | − | 0.747039i | \(-0.268525\pi\) | ||||
0.664780 | + | 0.747039i | \(0.268525\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23.9401 | −1.10545 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.45001 | −0.343278 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.3923 | −0.477839 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.73205 | 0.217121 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 26.9444 | 1.23370 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 36.5665 | 1.67077 | 0.835383 | − | 0.549669i | \(-0.185246\pi\) | ||||
0.835383 | + | 0.549669i | \(0.185246\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00000 | −0.0911922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.07180 | −0.230775 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.48528 | −0.385297 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.0459 | 1.22557 | 0.612784 | − | 0.790251i | \(-0.290050\pi\) | ||||
0.612784 | + | 0.790251i | \(0.290050\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.2487 | 0.553906 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.8038 | 0.983994 | 0.491997 | − | 0.870597i | \(-0.336267\pi\) | ||||
0.491997 | + | 0.870597i | \(0.336267\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.48528 | −0.382158 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 28.5617 | 1.28375 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.92820 | −0.310772 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.80385 | 0.259816 | 0.129908 | − | 0.991526i | \(-0.458532\pi\) | ||||
0.129908 | + | 0.991526i | \(0.458532\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.7360 | −0.613679 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −40.9850 | −1.82743 | −0.913715 | − | 0.406355i | \(-0.866800\pi\) | ||||
−0.913715 | + | 0.406355i | \(0.866800\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.78461 | −0.123914 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.41154 | 0.417981 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.5601 | −0.601042 | −0.300521 | − | 0.953775i | \(-0.597161\pi\) | ||||
−0.300521 | + | 0.953775i | \(0.597161\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.79796 | 0.433436 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 18.9282 | 0.835701 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 23.3205 | 1.02762 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 46.3644 | 2.03911 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.00481 | −0.351372 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.0000 | 0.525730 | 0.262865 | − | 0.964833i | \(-0.415333\pi\) | ||||
0.262865 | + | 0.964833i | \(0.415333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.2679 | −0.842529 | −0.421264 | − | 0.906938i | \(-0.638414\pi\) | ||||
−0.421264 | + | 0.906938i | \(0.638414\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.82843 | 0.123443 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.5959 | −0.853612 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.7846 | −0.860200 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −17.9090 | −0.777183 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.62536 | −0.113717 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −45.5322 | −1.96853 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.60770 | 0.0693772 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 37.5167 | 1.61596 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.3180 | 0.615579 | 0.307789 | − | 0.951454i | \(-0.400411\pi\) | ||||
0.307789 | + | 0.951454i | \(0.400411\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.6932 | 0.716372 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −45.7128 | −1.95812 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.339746 | 0.0145265 | 0.00726324 | − | 0.999974i | \(-0.497688\pi\) | ||||
0.00726324 | + | 0.999974i | \(0.497688\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.0053 | 0.555054 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.5911 | 0.493798 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.0000 | 0.680389 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.46410 | 0.401729 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.8338 | −0.670898 | −0.335449 | − | 0.942058i | \(-0.608888\pi\) | ||||
−0.335449 | + | 0.942058i | \(0.608888\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.832204 | 0.0351985 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.0000 | 0.506640 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.8756 | 0.626934 | 0.313467 | − | 0.949599i | \(-0.398510\pi\) | ||||
0.313467 | + | 0.949599i | \(0.398510\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 31.6675 | 1.33226 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −17.2480 | −0.724346 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.0000 | 0.503066 | 0.251533 | − | 0.967849i | \(-0.419065\pi\) | ||||
0.251533 | + | 0.967849i | \(0.419065\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.1962 | 1.26367 | 0.631835 | − | 0.775103i | \(-0.282302\pi\) | ||||
0.631835 | + | 0.775103i | \(0.282302\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.4233 | 0.518991 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.79315 | −0.0747796 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −43.8564 | −1.82577 | −0.912883 | − | 0.408221i | \(-0.866149\pi\) | ||||
−0.912883 | + | 0.408221i | \(0.866149\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.4641 | 0.559549 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.48528 | 0.352029 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −51.7439 | −2.14301 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.28719 | −0.0945635 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.12436 | −0.376602 | −0.188301 | − | 0.982111i | \(-0.560298\pi\) | ||||
−0.188301 | + | 0.982111i | \(0.560298\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.7685 | 1.10298 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.79315 | 0.0737604 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.8564 | 0.815405 | 0.407702 | − | 0.913115i | \(-0.366330\pi\) | ||||
0.407702 | + | 0.913115i | \(0.366330\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −32.7846 | −1.34404 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.5168 | −0.471350 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.41851 | −0.180535 | −0.0902676 | − | 0.995918i | \(-0.528772\pi\) | ||||
−0.0902676 | + | 0.995918i | \(0.528772\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −40.3923 | −1.64764 | −0.823818 | − | 0.566854i | \(-0.808160\pi\) | ||||
−0.823818 | + | 0.566854i | \(0.808160\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.2679 | −0.621759 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −27.9053 | −1.13451 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.28221 | −0.336165 | −0.168082 | − | 0.985773i | \(-0.553757\pi\) | ||||
−0.168082 | + | 0.985773i | \(0.553757\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.92820 | 0.280745 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.71281 | −0.150204 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.2875 | 0.859795 | 0.429898 | − | 0.902878i | \(-0.358550\pi\) | ||||
0.429898 | + | 0.902878i | \(0.358550\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.4233 | 0.500956 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.3205 | −0.455746 | −0.227873 | − | 0.973691i | \(-0.573177\pi\) | ||||
−0.227873 | + | 0.973691i | \(0.573177\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.5885 | 1.06868 | 0.534340 | − | 0.845270i | \(-0.320560\pi\) | ||||
0.534340 | + | 0.845270i | \(0.320560\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.17260 | −0.287827 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.79796 | 0.392547 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.3923 | −0.654646 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.2832 | −0.729001 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.23835 | 0.0492979 | 0.0246489 | − | 0.999696i | \(-0.492153\pi\) | ||||
0.0246489 | + | 0.999696i | \(0.492153\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.46410 | 0.296671 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.8564 | 0.549875 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.00429 | −0.119034 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.41851 | −0.174793 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.6077 | 0.537472 | 0.268736 | − | 0.963214i | \(-0.413394\pi\) | ||||
0.268736 | + | 0.963214i | \(0.413394\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.80385 | −0.386626 | −0.193313 | − | 0.981137i | \(-0.561923\pi\) | ||||
−0.193313 | + | 0.981137i | \(0.561923\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.93803 | −0.155060 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.79315 | 0.0704960 | 0.0352480 | − | 0.999379i | \(-0.488778\pi\) | ||||
0.0352480 | + | 0.999379i | \(0.488778\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 34.3923 | 1.35002 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.0000 | 0.627089 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.6937 | 0.848939 | 0.424470 | − | 0.905442i | \(-0.360461\pi\) | ||||
0.424470 | + | 0.905442i | \(0.360461\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.832204 | −0.0325169 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.24871 | 0.243785 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.5167 | 0.993988 | 0.496994 | − | 0.867754i | \(-0.334437\pi\) | ||||
0.496994 | + | 0.867754i | \(0.334437\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.8348 | −1.00486 | −0.502428 | − | 0.864619i | \(-0.667560\pi\) | ||||
−0.502428 | + | 0.864619i | \(0.667560\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.960947 | −0.0373201 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 44.7846 | 1.73667 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.39230 | −0.170071 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.14110 | −0.160104 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.9754 | −0.964163 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 41.3205 | 1.59279 | 0.796394 | − | 0.604778i | \(-0.206738\pi\) | ||||
0.796394 | + | 0.604778i | \(0.206738\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.00000 | 0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −39.9769 | −1.53644 | −0.768219 | − | 0.640187i | \(-0.778857\pi\) | ||||
−0.768219 | + | 0.640187i | \(0.778857\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.3843 | −0.513641 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.4641 | −0.592586 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.3397 | −0.472167 | −0.236084 | − | 0.971733i | \(-0.575864\pi\) | ||||
−0.236084 | + | 0.971733i | \(0.575864\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −29.3939 | −1.12308 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.52056 | −0.363232 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.14359 | 0.157858 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.3731 | 1.49782 | 0.748911 | − | 0.662671i | \(-0.230577\pi\) | ||||
0.748911 | + | 0.662671i | \(0.230577\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 45.0518 | 1.71137 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 24.9754 | 0.947370 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.0000 | −0.909065 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.85641 | 0.0702157 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.2084 | 0.498874 | 0.249437 | − | 0.968391i | \(-0.419754\pi\) | ||||
0.249437 | + | 0.968391i | \(0.419754\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.9754 | 0.941964 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 17.5692 | 0.661695 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.39230 | −0.165190 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −41.0865 | −1.54304 | −0.771518 | − | 0.636207i | \(-0.780502\pi\) | ||||
−0.771518 | + | 0.636207i | \(0.780502\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.2041 | 0.382684 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.1436 | −0.379881 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.39230 | 0.164263 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.5959 | 0.731823 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.4233 | −0.463311 | −0.231656 | − | 0.972798i | \(-0.574414\pi\) | ||||
−0.231656 | + | 0.972798i | \(0.574414\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 36.7846 | 1.36993 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.75129 | −0.0651311 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.44949 | 0.0909718 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.4596 | 0.870069 | 0.435035 | − | 0.900414i | \(-0.356736\pi\) | ||||
0.435035 | + | 0.900414i | \(0.356736\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.21539 | −0.0820515 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.60770 | 0.281381 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.9358 | 0.773281 | 0.386641 | − | 0.922230i | \(-0.373635\pi\) | ||||
0.386641 | + | 0.922230i | \(0.373635\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 14.2165 | 0.524382 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 29.3205 | 1.08003 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.98076 | 0.109649 | 0.0548246 | − | 0.998496i | \(-0.482540\pi\) | ||||
0.0548246 | + | 0.998496i | \(0.482540\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.31268 | 0.0482224 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.1774 | −0.556805 | −0.278403 | − | 0.960464i | \(-0.589805\pi\) | ||||
−0.278403 | + | 0.960464i | \(0.589805\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −47.5692 | −1.74280 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.41154 | 0.197998 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −71.8203 | −2.62426 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.14110 | 0.151111 | 0.0755555 | − | 0.997142i | \(-0.475927\pi\) | ||||
0.0755555 | + | 0.997142i | \(0.475927\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.4641 | −0.563543 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −23.3205 | −0.848720 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.7338 | 1.11704 | 0.558519 | − | 0.829492i | \(-0.311370\pi\) | ||||
0.558519 | + | 0.829492i | \(0.311370\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.21166 | 0.225469 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.6410 | 1.25574 | 0.627868 | − | 0.778320i | \(-0.283928\pi\) | ||||
0.627868 | + | 0.778320i | \(0.283928\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −72.1051 | −2.61038 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −20.9086 | −0.755952 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.75410 | −0.0994447 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.39230 | −0.0862687 | −0.0431344 | − | 0.999069i | \(-0.513734\pi\) | ||||
−0.0431344 | + | 0.999069i | \(0.513734\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.46410 | −0.340841 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.7327 | 0.745704 | 0.372852 | − | 0.927891i | \(-0.378380\pi\) | ||||
0.372852 | + | 0.927891i | \(0.378380\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.65685 | 0.203200 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14.9282 | 0.535546 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 32.7846 | 1.17463 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.48528 | 0.303627 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.79796 | 0.350150 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −24.9282 | −0.889726 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.6603 | 1.27115 | 0.635575 | − | 0.772039i | \(-0.280763\pi\) | ||||
0.635575 | + | 0.772039i | \(0.280763\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.6579 | −0.557435 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 49.9507 | 1.77604 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.00000 | 0.0710221 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −19.6077 | −0.695413 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −47.5013 | −1.68258 | −0.841290 | − | 0.540584i | \(-0.818203\pi\) | ||||
−0.841290 | + | 0.540584i | \(0.818203\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −33.9411 | −1.20075 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.24871 | 0.220787 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.0000 | −0.423471 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.9706 | −0.598134 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.37945 | −0.189366 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.0718 | 0.600212 | 0.300106 | − | 0.953906i | \(-0.402978\pi\) | ||||
0.300106 | + | 0.953906i | \(0.402978\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −46.9808 | −1.64972 | −0.824859 | − | 0.565339i | \(-0.808745\pi\) | ||||
−0.824859 | + | 0.565339i | \(0.808745\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.10961 | 0.0389156 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 40.9850 | 1.43564 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.3923 | −0.363581 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.60770 | −0.126063 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.2571 | 0.986178 | 0.493089 | − | 0.869979i | \(-0.335868\pi\) | ||||
0.493089 | + | 0.869979i | \(0.335868\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.7322 | −0.548391 | −0.274195 | − | 0.961674i | \(-0.588411\pi\) | ||||
−0.274195 | + | 0.961674i | \(0.588411\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.46410 | −0.120605 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.6603 | −0.822748 | −0.411374 | − | 0.911467i | \(-0.634951\pi\) | ||||
−0.411374 | + | 0.911467i | \(0.634951\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.00429 | 0.104343 | 0.0521717 | − | 0.998638i | \(-0.483386\pi\) | ||||
0.0521717 | + | 0.998638i | \(0.483386\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.30890 | −0.114784 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −27.4641 | −0.951575 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −45.9615 | −1.59056 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 22.6274 | 0.782118 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 38.3596 | 1.32432 | 0.662161 | − | 0.749362i | \(-0.269640\pi\) | ||||
0.662161 | + | 0.749362i | \(0.269640\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.0000 | −0.793103 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.0000 | −0.413302 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 31.4916 | 1.08335 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −44.0165 | −1.51242 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.32051 | 0.0453197 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.46410 | −0.324425 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.9663 | −0.478196 | −0.239098 | − | 0.970995i | \(-0.576852\pi\) | ||||
−0.239098 | + | 0.970995i | \(0.576852\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 28.5617 | 0.976789 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.8564 | −0.883238 | −0.441619 | − | 0.897203i | \(-0.645596\pi\) | ||||
−0.441619 | + | 0.897203i | \(0.645596\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.4449 | −0.697570 | −0.348785 | − | 0.937203i | \(-0.613406\pi\) | ||||
−0.348785 | + | 0.937203i | \(0.613406\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 19.5959 | 0.667827 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.62536 | −0.0893681 | −0.0446841 | − | 0.999001i | \(-0.514228\pi\) | ||||
−0.0446841 | + | 0.999001i | \(0.514228\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26.7846 | −0.910704 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.66025 | 0.124309 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19.5959 | −0.664746 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.34795 | −0.0795574 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.53590 | −0.288896 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −37.8564 | −1.27978 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.8033 | 0.770012 | 0.385006 | − | 0.922914i | \(-0.374199\pi\) | ||||
0.385006 | + | 0.922914i | \(0.374199\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.5521 | −0.423370 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.8564 | −1.07327 | −0.536635 | − | 0.843815i | \(-0.680305\pi\) | ||||
−0.536635 | + | 0.843815i | \(0.680305\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −57.1244 | −1.92239 | −0.961194 | − | 0.275874i | \(-0.911033\pi\) | ||||
−0.961194 | + | 0.275874i | \(0.911033\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.0325 | 0.438084 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.1774 | 0.509608 | 0.254804 | − | 0.966993i | \(-0.417989\pi\) | ||||
0.254804 | + | 0.966993i | \(0.417989\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.8564 | 0.733040 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 21.1244 | 0.707693 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 46.3644 | 1.55153 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.37945 | 0.179815 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.497423 | −0.0166085 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.8564 | 0.462137 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.8792 | 1.26194 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.21166 | −0.206711 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 55.8564 | 1.85673 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.9090 | −0.993111 | −0.496555 | − | 0.868005i | \(-0.665402\pi\) | ||||
−0.496555 | + | 0.868005i | \(0.665402\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.80122 | −0.0929106 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.1432 | −0.799899 | −0.399949 | − | 0.916537i | \(-0.630972\pi\) | ||||
−0.399949 | + | 0.916537i | \(0.630972\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.3923 | −0.343935 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.46410 | −0.312874 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.31268 | −0.0433484 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.3576 | −0.605560 | −0.302780 | − | 0.953060i | \(-0.597915\pi\) | ||||
−0.302780 | + | 0.953060i | \(0.597915\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.6795 | 0.747315 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.679492 | −0.0223657 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.27792 | 0.173537 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 23.4596 | 0.770515 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.46410 | 0.113653 | 0.0568267 | − | 0.998384i | \(-0.481902\pi\) | ||||
0.0568267 | + | 0.998384i | \(0.481902\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 37.5167 | 1.22956 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −11.1106 | −0.363746 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 40.1528 | 1.31314 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.17691 | 0.299797 | 0.149898 | − | 0.988701i | \(-0.452105\pi\) | ||||
0.149898 | + | 0.988701i | \(0.452105\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.35898 | −0.305419 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.5927 | −0.866896 | −0.433448 | − | 0.901179i | \(-0.642703\pi\) | ||||
−0.433448 | + | 0.901179i | \(0.642703\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.4233 | −0.404559 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 37.8564 | 1.23147 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.2679 | −0.626124 | −0.313062 | − | 0.949733i | \(-0.601355\pi\) | ||||
−0.313062 | + | 0.949733i | \(0.601355\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.960947 | 0.0311936 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.04386 | −0.228413 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −53.5692 | −1.73528 | −0.867639 | − | 0.497195i | \(-0.834363\pi\) | ||||
−0.867639 | + | 0.497195i | \(0.834363\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 41.5692 | 1.34515 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.48528 | −0.274290 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −46.3644 | −1.49719 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −45.8038 | −1.47601 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 45.0518 | 1.45027 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.0459 | 0.869738 | 0.434869 | − | 0.900494i | \(-0.356795\pi\) | ||||
0.434869 | + | 0.900494i | \(0.356795\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.0000 | 0.385496 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39.3731 | 1.26354 | 0.631771 | − | 0.775155i | \(-0.282328\pi\) | ||||
0.631771 | + | 0.775155i | \(0.282328\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 39.3949 | 1.26294 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.277401 | 0.00888396 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 44.5359 | 1.42483 | 0.712415 | − | 0.701759i | \(-0.247601\pi\) | ||||
0.712415 | + | 0.701759i | \(0.247601\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.0000 | −0.383522 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −45.9855 | −1.46820 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −52.7048 | −1.68102 | −0.840512 | − | 0.541793i | \(-0.817745\pi\) | ||||
−0.840512 | + | 0.541793i | \(0.817745\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.00000 | 0.191176 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 27.7128 | 0.882109 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.93803 | 0.125222 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −61.8193 | −1.96375 | −0.981877 | − | 0.189521i | \(-0.939306\pi\) | ||||
−0.981877 | + | 0.189521i | \(0.939306\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −19.4641 | −0.617675 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −38.5359 | −1.22167 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.4906 | −0.680614 | −0.340307 | − | 0.940314i | \(-0.610531\pi\) | ||||
−0.340307 | + | 0.940314i | \(0.610531\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 21.1117 | 0.667944 |
(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 | 1024.2.a.j.1.1 | 4 | ||
3.2 | odd | 2 | 9216.2.a.bb.1.3 | 4 | |||
4.3 | odd | 2 | 1024.2.a.g.1.3 | 4 | |||
8.3 | odd | 2 | inner | 1024.2.a.j.1.2 | 4 | ||
8.5 | even | 2 | 1024.2.a.g.1.4 | 4 | |||
12.11 | even | 2 | 9216.2.a.bk.1.4 | 4 | |||
16.3 | odd | 4 | 1024.2.b.h.513.6 | 8 | |||
16.5 | even | 4 | 1024.2.b.h.513.5 | 8 | |||
16.11 | odd | 4 | 1024.2.b.h.513.3 | 8 | |||
16.13 | even | 4 | 1024.2.b.h.513.4 | 8 | |||
24.5 | odd | 2 | 9216.2.a.bk.1.1 | 4 | |||
24.11 | even | 2 | 9216.2.a.bb.1.2 | 4 | |||
32.3 | odd | 8 | 256.2.e.b.65.3 | yes | 8 | ||
32.5 | even | 8 | 256.2.e.a.193.3 | yes | 8 | ||
32.11 | odd | 8 | 256.2.e.b.193.3 | yes | 8 | ||
32.13 | even | 8 | 256.2.e.a.65.3 | yes | 8 | ||
32.19 | odd | 8 | 256.2.e.a.65.2 | ✓ | 8 | ||
32.21 | even | 8 | 256.2.e.b.193.2 | yes | 8 | ||
32.27 | odd | 8 | 256.2.e.a.193.2 | yes | 8 | ||
32.29 | even | 8 | 256.2.e.b.65.2 | yes | 8 | ||
96.5 | odd | 8 | 2304.2.k.f.1729.3 | 8 | |||
96.11 | even | 8 | 2304.2.k.k.1729.2 | 8 | |||
96.29 | odd | 8 | 2304.2.k.k.577.2 | 8 | |||
96.35 | even | 8 | 2304.2.k.k.577.1 | 8 | |||
96.53 | odd | 8 | 2304.2.k.k.1729.1 | 8 | |||
96.59 | even | 8 | 2304.2.k.f.1729.4 | 8 | |||
96.77 | odd | 8 | 2304.2.k.f.577.4 | 8 | |||
96.83 | even | 8 | 2304.2.k.f.577.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
256.2.e.a.65.2 | ✓ | 8 | 32.19 | odd | 8 | ||
256.2.e.a.65.3 | yes | 8 | 32.13 | even | 8 | ||
256.2.e.a.193.2 | yes | 8 | 32.27 | odd | 8 | ||
256.2.e.a.193.3 | yes | 8 | 32.5 | even | 8 | ||
256.2.e.b.65.2 | yes | 8 | 32.29 | even | 8 | ||
256.2.e.b.65.3 | yes | 8 | 32.3 | odd | 8 | ||
256.2.e.b.193.2 | yes | 8 | 32.21 | even | 8 | ||
256.2.e.b.193.3 | yes | 8 | 32.11 | odd | 8 | ||
1024.2.a.g.1.3 | 4 | 4.3 | odd | 2 | |||
1024.2.a.g.1.4 | 4 | 8.5 | even | 2 | |||
1024.2.a.j.1.1 | 4 | 1.1 | even | 1 | trivial | ||
1024.2.a.j.1.2 | 4 | 8.3 | odd | 2 | inner | ||
1024.2.b.h.513.3 | 8 | 16.11 | odd | 4 | |||
1024.2.b.h.513.4 | 8 | 16.13 | even | 4 | |||
1024.2.b.h.513.5 | 8 | 16.5 | even | 4 | |||
1024.2.b.h.513.6 | 8 | 16.3 | odd | 4 | |||
2304.2.k.f.577.3 | 8 | 96.83 | even | 8 | |||
2304.2.k.f.577.4 | 8 | 96.77 | odd | 8 | |||
2304.2.k.f.1729.3 | 8 | 96.5 | odd | 8 | |||
2304.2.k.f.1729.4 | 8 | 96.59 | even | 8 | |||
2304.2.k.k.577.1 | 8 | 96.35 | even | 8 | |||
2304.2.k.k.577.2 | 8 | 96.29 | odd | 8 | |||
2304.2.k.k.1729.1 | 8 | 96.53 | odd | 8 | |||
2304.2.k.k.1729.2 | 8 | 96.11 | even | 8 | |||
9216.2.a.bb.1.2 | 4 | 24.11 | even | 2 | |||
9216.2.a.bb.1.3 | 4 | 3.2 | odd | 2 | |||
9216.2.a.bk.1.1 | 4 | 24.5 | odd | 2 | |||
9216.2.a.bk.1.4 | 4 | 12.11 | even | 2 |