Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2476334663\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.46410 | 1.54919 | 0.774597 | − | 0.632456i | \(-0.217953\pi\) | ||||
0.774597 | + | 0.632456i | \(0.217953\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.46410 | −0.931343 | −0.465671 | − | 0.884958i | \(-0.654187\pi\) | ||||
−0.465671 | + | 0.884958i | \(0.654187\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.46410 | −1.09545 | ||||||||
\(11\) | −1.26795 | −0.382301 | −0.191151 | − | 0.981561i | \(-0.561222\pi\) | ||||
−0.191151 | + | 0.981561i | \(0.561222\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.46410 | 1.51547 | 0.757735 | − | 0.652563i | \(-0.226306\pi\) | ||||
0.757735 | + | 0.652563i | \(0.226306\pi\) | |||||||
\(14\) | 2.46410 | 0.658559 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.73205 | 1.63276 | 0.816381 | − | 0.577514i | \(-0.195977\pi\) | ||||
0.816381 | + | 0.577514i | \(0.195977\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.46410 | −1.25355 | −0.626775 | − | 0.779200i | \(-0.715626\pi\) | ||||
−0.626775 | + | 0.779200i | \(0.715626\pi\) | |||||||
\(20\) | 3.46410 | 0.774597 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.26795 | 0.270328 | ||||||||
\(23\) | 4.26795 | 0.889929 | 0.444964 | − | 0.895548i | \(-0.353216\pi\) | ||||
0.444964 | + | 0.895548i | \(0.353216\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.00000 | 1.40000 | ||||||||
\(26\) | −5.46410 | −1.07160 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.46410 | −0.465671 | ||||||||
\(29\) | −1.73205 | −0.321634 | −0.160817 | − | 0.986984i | \(-0.551413\pi\) | ||||
−0.160817 | + | 0.986984i | \(0.551413\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | 0.179605 | 0.0898027 | − | 0.995960i | \(-0.471376\pi\) | ||||
0.0898027 | + | 0.995960i | \(0.471376\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.73205 | −1.15454 | ||||||||
\(35\) | −8.53590 | −1.44283 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.73205 | 0.449146 | 0.224573 | − | 0.974457i | \(-0.427901\pi\) | ||||
0.224573 | + | 0.974457i | \(0.427901\pi\) | |||||||
\(38\) | 5.46410 | 0.886394 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.46410 | −0.547723 | ||||||||
\(41\) | 1.19615 | 0.186808 | 0.0934038 | − | 0.995628i | \(-0.470225\pi\) | ||||
0.0934038 | + | 0.995628i | \(0.470225\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.92820 | 1.36154 | 0.680769 | − | 0.732498i | \(-0.261646\pi\) | ||||
0.680769 | + | 0.732498i | \(0.261646\pi\) | |||||||
\(44\) | −1.26795 | −0.191151 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.26795 | −0.629275 | ||||||||
\(47\) | 7.46410 | 1.08875 | 0.544376 | − | 0.838842i | \(-0.316767\pi\) | ||||
0.544376 | + | 0.838842i | \(0.316767\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.928203 | −0.132600 | ||||||||
\(50\) | −7.00000 | −0.989949 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.46410 | 0.757735 | ||||||||
\(53\) | 6.26795 | 0.860969 | 0.430485 | − | 0.902598i | \(-0.358343\pi\) | ||||
0.430485 | + | 0.902598i | \(0.358343\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.39230 | −0.592258 | ||||||||
\(56\) | 2.46410 | 0.329279 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.73205 | 0.227429 | ||||||||
\(59\) | −3.26795 | −0.425451 | −0.212725 | − | 0.977112i | \(-0.568234\pi\) | ||||
−0.212725 | + | 0.977112i | \(0.568234\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.73205 | 0.349803 | 0.174902 | − | 0.984586i | \(-0.444039\pi\) | ||||
0.174902 | + | 0.984586i | \(0.444039\pi\) | |||||||
\(62\) | −1.00000 | −0.127000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 18.9282 | 2.34775 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.19615 | −0.756980 | −0.378490 | − | 0.925605i | \(-0.623557\pi\) | ||||
−0.378490 | + | 0.925605i | \(0.623557\pi\) | |||||||
\(68\) | 6.73205 | 0.816381 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 8.53590 | 1.02023 | ||||||||
\(71\) | −14.1244 | −1.67625 | −0.838126 | − | 0.545476i | \(-0.816349\pi\) | ||||
−0.838126 | + | 0.545476i | \(0.816349\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.46410 | 0.171360 | 0.0856801 | − | 0.996323i | \(-0.472694\pi\) | ||||
0.0856801 | + | 0.996323i | \(0.472694\pi\) | |||||||
\(74\) | −2.73205 | −0.317594 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.46410 | −0.626775 | ||||||||
\(77\) | 3.12436 | 0.356053 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.7321 | −1.43247 | −0.716234 | − | 0.697860i | \(-0.754136\pi\) | ||||
−0.716234 | + | 0.697860i | \(0.754136\pi\) | |||||||
\(80\) | 3.46410 | 0.387298 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.19615 | −0.132093 | ||||||||
\(83\) | −1.80385 | −0.197998 | −0.0989990 | − | 0.995088i | \(-0.531564\pi\) | ||||
−0.0989990 | + | 0.995088i | \(0.531564\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 23.3205 | 2.52946 | ||||||||
\(86\) | −8.92820 | −0.962753 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.26795 | 0.135164 | ||||||||
\(89\) | −4.26795 | −0.452402 | −0.226201 | − | 0.974081i | \(-0.572631\pi\) | ||||
−0.226201 | + | 0.974081i | \(0.572631\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.4641 | −1.41142 | ||||||||
\(92\) | 4.26795 | 0.444964 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.46410 | −0.769863 | ||||||||
\(95\) | −18.9282 | −1.94199 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.7321 | 1.08967 | 0.544837 | − | 0.838542i | \(-0.316591\pi\) | ||||
0.544837 | + | 0.838542i | \(0.316591\pi\) | |||||||
\(98\) | 0.928203 | 0.0937627 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.00000 | 0.700000 | ||||||||
\(101\) | 6.39230 | 0.636058 | 0.318029 | − | 0.948081i | \(-0.396979\pi\) | ||||
0.318029 | + | 0.948081i | \(0.396979\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.9282 | 1.56945 | 0.784726 | − | 0.619842i | \(-0.212804\pi\) | ||||
0.784726 | + | 0.619842i | \(0.212804\pi\) | |||||||
\(104\) | −5.46410 | −0.535799 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.26795 | −0.608797 | ||||||||
\(107\) | 4.53590 | 0.438502 | 0.219251 | − | 0.975669i | \(-0.429639\pi\) | ||||
0.219251 | + | 0.975669i | \(0.429639\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.92820 | −0.567819 | −0.283909 | − | 0.958851i | \(-0.591632\pi\) | ||||
−0.283909 | + | 0.958851i | \(0.591632\pi\) | |||||||
\(110\) | 4.39230 | 0.418790 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.46410 | −0.232836 | ||||||||
\(113\) | −16.1962 | −1.52361 | −0.761803 | − | 0.647809i | \(-0.775686\pi\) | ||||
−0.761803 | + | 0.647809i | \(0.775686\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.7846 | 1.37867 | ||||||||
\(116\) | −1.73205 | −0.160817 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.26795 | 0.300839 | ||||||||
\(119\) | −16.5885 | −1.52066 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.39230 | −0.853846 | ||||||||
\(122\) | −2.73205 | −0.247348 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.00000 | 0.0898027 | ||||||||
\(125\) | 6.92820 | 0.619677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.0000 | 1.24230 | 0.621150 | − | 0.783692i | \(-0.286666\pi\) | ||||
0.621150 | + | 0.783692i | \(0.286666\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −18.9282 | −1.66011 | ||||||||
\(131\) | −9.46410 | −0.826882 | −0.413441 | − | 0.910531i | \(-0.635673\pi\) | ||||
−0.413441 | + | 0.910531i | \(0.635673\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.4641 | 1.16749 | ||||||||
\(134\) | 6.19615 | 0.535266 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.73205 | −0.577269 | ||||||||
\(137\) | −1.19615 | −0.102194 | −0.0510971 | − | 0.998694i | \(-0.516272\pi\) | ||||
−0.0510971 | + | 0.998694i | \(0.516272\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.00000 | −0.593732 | −0.296866 | − | 0.954919i | \(-0.595942\pi\) | ||||
−0.296866 | + | 0.954919i | \(0.595942\pi\) | |||||||
\(140\) | −8.53590 | −0.721415 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 14.1244 | 1.18529 | ||||||||
\(143\) | −6.92820 | −0.579365 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.00000 | −0.498273 | ||||||||
\(146\) | −1.46410 | −0.121170 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.73205 | 0.224573 | ||||||||
\(149\) | −1.00000 | −0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.1244 | 1.71908 | 0.859538 | − | 0.511072i | \(-0.170751\pi\) | ||||
0.859538 | + | 0.511072i | \(0.170751\pi\) | |||||||
\(152\) | 5.46410 | 0.443197 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.12436 | −0.251768 | ||||||||
\(155\) | 3.46410 | 0.278243 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.53590 | 0.282195 | 0.141098 | − | 0.989996i | \(-0.454937\pi\) | ||||
0.141098 | + | 0.989996i | \(0.454937\pi\) | |||||||
\(158\) | 12.7321 | 1.01291 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.46410 | −0.273861 | ||||||||
\(161\) | −10.5167 | −0.828829 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.92820 | 0.777637 | 0.388818 | − | 0.921314i | \(-0.372883\pi\) | ||||
0.388818 | + | 0.921314i | \(0.372883\pi\) | |||||||
\(164\) | 1.19615 | 0.0934038 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.80385 | 0.140006 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.8564 | 1.29665 | ||||||||
\(170\) | −23.3205 | −1.78860 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.92820 | 0.680769 | ||||||||
\(173\) | 14.2679 | 1.08477 | 0.542386 | − | 0.840129i | \(-0.317521\pi\) | ||||
0.542386 | + | 0.840129i | \(0.317521\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −17.2487 | −1.30388 | ||||||||
\(176\) | −1.26795 | −0.0955753 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.26795 | 0.319896 | ||||||||
\(179\) | −9.58846 | −0.716675 | −0.358337 | − | 0.933592i | \(-0.616656\pi\) | ||||
−0.358337 | + | 0.933592i | \(0.616656\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.4641 | −1.37243 | −0.686213 | − | 0.727401i | \(-0.740728\pi\) | ||||
−0.686213 | + | 0.727401i | \(0.740728\pi\) | |||||||
\(182\) | 13.4641 | 0.998026 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.26795 | −0.314637 | ||||||||
\(185\) | 9.46410 | 0.695815 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.53590 | −0.624207 | ||||||||
\(188\) | 7.46410 | 0.544376 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 18.9282 | 1.37320 | ||||||||
\(191\) | 21.1244 | 1.52850 | 0.764252 | − | 0.644917i | \(-0.223108\pi\) | ||||
0.764252 | + | 0.644917i | \(0.223108\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.5885 | 1.62595 | 0.812976 | − | 0.582297i | \(-0.197846\pi\) | ||||
0.812976 | + | 0.582297i | \(0.197846\pi\) | |||||||
\(194\) | −10.7321 | −0.770516 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.928203 | −0.0663002 | ||||||||
\(197\) | −3.12436 | −0.222601 | −0.111301 | − | 0.993787i | \(-0.535502\pi\) | ||||
−0.111301 | + | 0.993787i | \(0.535502\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.2679 | 1.08232 | 0.541158 | − | 0.840921i | \(-0.317986\pi\) | ||||
0.541158 | + | 0.840921i | \(0.317986\pi\) | |||||||
\(200\) | −7.00000 | −0.494975 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.39230 | −0.449761 | ||||||||
\(203\) | 4.26795 | 0.299551 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.14359 | 0.289401 | ||||||||
\(206\) | −15.9282 | −1.10977 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.46410 | 0.378867 | ||||||||
\(209\) | 6.92820 | 0.479234 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.7846 | 1.08666 | 0.543329 | − | 0.839520i | \(-0.317164\pi\) | ||||
0.543329 | + | 0.839520i | \(0.317164\pi\) | |||||||
\(212\) | 6.26795 | 0.430485 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.53590 | −0.310068 | ||||||||
\(215\) | 30.9282 | 2.10929 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.46410 | −0.167274 | ||||||||
\(218\) | 5.92820 | 0.401509 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.39230 | −0.296129 | ||||||||
\(221\) | 36.7846 | 2.47440 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.26795 | −0.0849082 | −0.0424541 | − | 0.999098i | \(-0.513518\pi\) | ||||
−0.0424541 | + | 0.999098i | \(0.513518\pi\) | |||||||
\(224\) | 2.46410 | 0.164640 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.1962 | 1.07735 | ||||||||
\(227\) | −7.46410 | −0.495410 | −0.247705 | − | 0.968836i | \(-0.579676\pi\) | ||||
−0.247705 | + | 0.968836i | \(0.579676\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.19615 | 0.541617 | 0.270808 | − | 0.962633i | \(-0.412709\pi\) | ||||
0.270808 | + | 0.962633i | \(0.412709\pi\) | |||||||
\(230\) | −14.7846 | −0.974868 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.73205 | 0.113715 | ||||||||
\(233\) | −25.9808 | −1.70206 | −0.851028 | − | 0.525120i | \(-0.824020\pi\) | ||||
−0.851028 | + | 0.525120i | \(0.824020\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 25.8564 | 1.68669 | ||||||||
\(236\) | −3.26795 | −0.212725 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 16.5885 | 1.07527 | ||||||||
\(239\) | −6.12436 | −0.396152 | −0.198076 | − | 0.980187i | \(-0.563469\pi\) | ||||
−0.198076 | + | 0.980187i | \(0.563469\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.53590 | 0.549846 | 0.274923 | − | 0.961466i | \(-0.411348\pi\) | ||||
0.274923 | + | 0.961466i | \(0.411348\pi\) | |||||||
\(242\) | 9.39230 | 0.603760 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.73205 | 0.174902 | ||||||||
\(245\) | −3.21539 | −0.205424 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −29.8564 | −1.89972 | ||||||||
\(248\) | −1.00000 | −0.0635001 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.92820 | −0.438178 | ||||||||
\(251\) | −3.73205 | −0.235565 | −0.117782 | − | 0.993039i | \(-0.537579\pi\) | ||||
−0.117782 | + | 0.993039i | \(0.537579\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.41154 | −0.340221 | ||||||||
\(254\) | −14.0000 | −0.878438 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 21.1962 | 1.32218 | 0.661090 | − | 0.750307i | \(-0.270094\pi\) | ||||
0.661090 | + | 0.750307i | \(0.270094\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.73205 | −0.418309 | ||||||||
\(260\) | 18.9282 | 1.17388 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.46410 | 0.584694 | ||||||||
\(263\) | −14.7846 | −0.911658 | −0.455829 | − | 0.890067i | \(-0.650657\pi\) | ||||
−0.455829 | + | 0.890067i | \(0.650657\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 21.7128 | 1.33381 | ||||||||
\(266\) | −13.4641 | −0.825537 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.19615 | −0.378490 | ||||||||
\(269\) | −15.3397 | −0.935281 | −0.467640 | − | 0.883919i | \(-0.654896\pi\) | ||||
−0.467640 | + | 0.883919i | \(0.654896\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.7846 | 1.74854 | 0.874270 | − | 0.485440i | \(-0.161340\pi\) | ||||
0.874270 | + | 0.485440i | \(0.161340\pi\) | |||||||
\(272\) | 6.73205 | 0.408191 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.19615 | 0.0722622 | ||||||||
\(275\) | −8.87564 | −0.535221 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.00000 | 0.300421 | 0.150210 | − | 0.988654i | \(-0.452005\pi\) | ||||
0.150210 | + | 0.988654i | \(0.452005\pi\) | |||||||
\(278\) | 7.00000 | 0.419832 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.53590 | 0.510117 | ||||||||
\(281\) | 24.0526 | 1.43486 | 0.717428 | − | 0.696633i | \(-0.245319\pi\) | ||||
0.717428 | + | 0.696633i | \(0.245319\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.53590 | 0.0912997 | 0.0456498 | − | 0.998958i | \(-0.485464\pi\) | ||||
0.0456498 | + | 0.998958i | \(0.485464\pi\) | |||||||
\(284\) | −14.1244 | −0.838126 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.92820 | 0.409673 | ||||||||
\(287\) | −2.94744 | −0.173982 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 28.3205 | 1.66591 | ||||||||
\(290\) | 6.00000 | 0.352332 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.46410 | 0.0856801 | ||||||||
\(293\) | 12.1244 | 0.708312 | 0.354156 | − | 0.935186i | \(-0.384768\pi\) | ||||
0.354156 | + | 0.935186i | \(0.384768\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.3205 | −0.659105 | ||||||||
\(296\) | −2.73205 | −0.158797 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.00000 | 0.0579284 | ||||||||
\(299\) | 23.3205 | 1.34866 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.0000 | −1.26806 | ||||||||
\(302\) | −21.1244 | −1.21557 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.46410 | −0.313388 | ||||||||
\(305\) | 9.46410 | 0.541913 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.3205 | −1.67341 | −0.836705 | − | 0.547654i | \(-0.815521\pi\) | ||||
−0.836705 | + | 0.547654i | \(0.815521\pi\) | |||||||
\(308\) | 3.12436 | 0.178027 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.46410 | −0.196748 | ||||||||
\(311\) | −28.1244 | −1.59479 | −0.797393 | − | 0.603460i | \(-0.793788\pi\) | ||||
−0.797393 | + | 0.603460i | \(0.793788\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.5359 | −1.27380 | −0.636902 | − | 0.770945i | \(-0.719784\pi\) | ||||
−0.636902 | + | 0.770945i | \(0.719784\pi\) | |||||||
\(314\) | −3.53590 | −0.199542 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.7321 | −0.716234 | ||||||||
\(317\) | −3.85641 | −0.216597 | −0.108299 | − | 0.994118i | \(-0.534540\pi\) | ||||
−0.108299 | + | 0.994118i | \(0.534540\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.19615 | 0.122961 | ||||||||
\(320\) | 3.46410 | 0.193649 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10.5167 | 0.586071 | ||||||||
\(323\) | −36.7846 | −2.04675 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 38.2487 | 2.12166 | ||||||||
\(326\) | −9.92820 | −0.549872 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.19615 | −0.0660465 | ||||||||
\(329\) | −18.3923 | −1.01400 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.80385 | 0.0991484 | 0.0495742 | − | 0.998770i | \(-0.484214\pi\) | ||||
0.0495742 | + | 0.998770i | \(0.484214\pi\) | |||||||
\(332\) | −1.80385 | −0.0989990 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −21.4641 | −1.17271 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.0000 | 1.03500 | 0.517498 | − | 0.855684i | \(-0.326864\pi\) | ||||
0.517498 | + | 0.855684i | \(0.326864\pi\) | |||||||
\(338\) | −16.8564 | −0.916868 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 23.3205 | 1.26473 | ||||||||
\(341\) | −1.26795 | −0.0686633 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.5359 | 1.05484 | ||||||||
\(344\) | −8.92820 | −0.481376 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.2679 | −0.767050 | ||||||||
\(347\) | 13.7321 | 0.737175 | 0.368588 | − | 0.929593i | \(-0.379841\pi\) | ||||
0.368588 | + | 0.929593i | \(0.379841\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.320508 | −0.0171564 | −0.00857820 | − | 0.999963i | \(-0.502731\pi\) | ||||
−0.00857820 | + | 0.999963i | \(0.502731\pi\) | |||||||
\(350\) | 17.2487 | 0.921982 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.26795 | 0.0675819 | ||||||||
\(353\) | −6.92820 | −0.368751 | −0.184376 | − | 0.982856i | \(-0.559026\pi\) | ||||
−0.184376 | + | 0.982856i | \(0.559026\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −48.9282 | −2.59684 | ||||||||
\(356\) | −4.26795 | −0.226201 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.58846 | 0.506766 | ||||||||
\(359\) | −3.60770 | −0.190407 | −0.0952034 | − | 0.995458i | \(-0.530350\pi\) | ||||
−0.0952034 | + | 0.995458i | \(0.530350\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.8564 | 0.571390 | ||||||||
\(362\) | 18.4641 | 0.970452 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −13.4641 | −0.705711 | ||||||||
\(365\) | 5.07180 | 0.265470 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.14359 | 0.372893 | 0.186446 | − | 0.982465i | \(-0.440303\pi\) | ||||
0.186446 | + | 0.982465i | \(0.440303\pi\) | |||||||
\(368\) | 4.26795 | 0.222482 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −9.46410 | −0.492015 | ||||||||
\(371\) | −15.4449 | −0.801857 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.0717968 | 0.00371750 | 0.00185875 | − | 0.999998i | \(-0.499408\pi\) | ||||
0.00185875 | + | 0.999998i | \(0.499408\pi\) | |||||||
\(374\) | 8.53590 | 0.441381 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.46410 | −0.384932 | ||||||||
\(377\) | −9.46410 | −0.487426 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.14359 | 0.418308 | 0.209154 | − | 0.977883i | \(-0.432929\pi\) | ||||
0.209154 | + | 0.977883i | \(0.432929\pi\) | |||||||
\(380\) | −18.9282 | −0.970996 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −21.1244 | −1.08082 | ||||||||
\(383\) | 2.33975 | 0.119555 | 0.0597777 | − | 0.998212i | \(-0.480961\pi\) | ||||
0.0597777 | + | 0.998212i | \(0.480961\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.8231 | 0.551596 | ||||||||
\(386\) | −22.5885 | −1.14972 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.7321 | 0.544837 | ||||||||
\(389\) | −16.5359 | −0.838403 | −0.419202 | − | 0.907893i | \(-0.637690\pi\) | ||||
−0.419202 | + | 0.907893i | \(0.637690\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.7321 | 1.45304 | ||||||||
\(392\) | 0.928203 | 0.0468813 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.12436 | 0.157403 | ||||||||
\(395\) | −44.1051 | −2.21917 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.78461 | 0.340510 | 0.170255 | − | 0.985400i | \(-0.445541\pi\) | ||||
0.170255 | + | 0.985400i | \(0.445541\pi\) | |||||||
\(398\) | −15.2679 | −0.765313 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.00000 | 0.350000 | ||||||||
\(401\) | 19.1244 | 0.955025 | 0.477512 | − | 0.878625i | \(-0.341539\pi\) | ||||
0.477512 | + | 0.878625i | \(0.341539\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.46410 | 0.272186 | ||||||||
\(404\) | 6.39230 | 0.318029 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.26795 | −0.211815 | ||||||||
\(407\) | −3.46410 | −0.171709 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.3923 | 0.909441 | 0.454720 | − | 0.890634i | \(-0.349739\pi\) | ||||
0.454720 | + | 0.890634i | \(0.349739\pi\) | |||||||
\(410\) | −4.14359 | −0.204637 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 15.9282 | 0.784726 | ||||||||
\(413\) | 8.05256 | 0.396241 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.24871 | −0.306737 | ||||||||
\(416\) | −5.46410 | −0.267900 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.92820 | −0.338869 | ||||||||
\(419\) | 27.5885 | 1.34778 | 0.673892 | − | 0.738830i | \(-0.264621\pi\) | ||||
0.673892 | + | 0.738830i | \(0.264621\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.3923 | 1.09133 | 0.545667 | − | 0.838002i | \(-0.316276\pi\) | ||||
0.545667 | + | 0.838002i | \(0.316276\pi\) | |||||||
\(422\) | −15.7846 | −0.768383 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.26795 | −0.304399 | ||||||||
\(425\) | 47.1244 | 2.28587 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.73205 | −0.325787 | ||||||||
\(428\) | 4.53590 | 0.219251 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −30.9282 | −1.49149 | ||||||||
\(431\) | −36.2487 | −1.74604 | −0.873019 | − | 0.487685i | \(-0.837841\pi\) | ||||
−0.873019 | + | 0.487685i | \(0.837841\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.9808 | 1.77718 | 0.888591 | − | 0.458700i | \(-0.151685\pi\) | ||||
0.888591 | + | 0.458700i | \(0.151685\pi\) | |||||||
\(434\) | 2.46410 | 0.118281 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.92820 | −0.283909 | ||||||||
\(437\) | −23.3205 | −1.11557 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.8038 | 0.754276 | 0.377138 | − | 0.926157i | \(-0.376908\pi\) | ||||
0.377138 | + | 0.926157i | \(0.376908\pi\) | |||||||
\(440\) | 4.39230 | 0.209395 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −36.7846 | −1.74967 | ||||||||
\(443\) | −2.66025 | −0.126392 | −0.0631962 | − | 0.998001i | \(-0.520129\pi\) | ||||
−0.0631962 | + | 0.998001i | \(0.520129\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.7846 | −0.700858 | ||||||||
\(446\) | 1.26795 | 0.0600391 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.46410 | −0.116418 | ||||||||
\(449\) | −42.1244 | −1.98797 | −0.993986 | − | 0.109511i | \(-0.965072\pi\) | ||||
−0.993986 | + | 0.109511i | \(0.965072\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.51666 | −0.0714168 | ||||||||
\(452\) | −16.1962 | −0.761803 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.46410 | 0.350308 | ||||||||
\(455\) | −46.6410 | −2.18656 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −36.9282 | −1.72743 | −0.863714 | − | 0.503982i | \(-0.831868\pi\) | ||||
−0.863714 | + | 0.503982i | \(0.831868\pi\) | |||||||
\(458\) | −8.19615 | −0.382981 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 14.7846 | 0.689336 | ||||||||
\(461\) | 29.3205 | 1.36559 | 0.682796 | − | 0.730609i | \(-0.260764\pi\) | ||||
0.682796 | + | 0.730609i | \(0.260764\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −37.6410 | −1.74933 | −0.874663 | − | 0.484731i | \(-0.838917\pi\) | ||||
−0.874663 | + | 0.484731i | \(0.838917\pi\) | |||||||
\(464\) | −1.73205 | −0.0804084 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 25.9808 | 1.20354 | ||||||||
\(467\) | −40.1051 | −1.85584 | −0.927922 | − | 0.372775i | \(-0.878406\pi\) | ||||
−0.927922 | + | 0.372775i | \(0.878406\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.2679 | 0.705008 | ||||||||
\(470\) | −25.8564 | −1.19267 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.26795 | 0.150420 | ||||||||
\(473\) | −11.3205 | −0.520518 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −38.2487 | −1.75497 | ||||||||
\(476\) | −16.5885 | −0.760331 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.12436 | 0.280122 | ||||||||
\(479\) | 11.7321 | 0.536051 | 0.268026 | − | 0.963412i | \(-0.413629\pi\) | ||||
0.268026 | + | 0.963412i | \(0.413629\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.9282 | 0.680667 | ||||||||
\(482\) | −8.53590 | −0.388800 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.39230 | −0.426923 | ||||||||
\(485\) | 37.1769 | 1.68812 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.392305 | −0.0177770 | −0.00888851 | − | 0.999960i | \(-0.502829\pi\) | ||||
−0.00888851 | + | 0.999960i | \(0.502829\pi\) | |||||||
\(488\) | −2.73205 | −0.123674 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.21539 | 0.145257 | ||||||||
\(491\) | −24.0000 | −1.08310 | −0.541552 | − | 0.840667i | \(-0.682163\pi\) | ||||
−0.541552 | + | 0.840667i | \(0.682163\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.6603 | −0.525151 | ||||||||
\(494\) | 29.8564 | 1.34330 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.00000 | 0.0449013 | ||||||||
\(497\) | 34.8038 | 1.56117 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.3923 | −0.599522 | −0.299761 | − | 0.954014i | \(-0.596907\pi\) | ||||
−0.299761 | + | 0.954014i | \(0.596907\pi\) | |||||||
\(500\) | 6.92820 | 0.309839 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.73205 | 0.166570 | ||||||||
\(503\) | 14.5359 | 0.648124 | 0.324062 | − | 0.946036i | \(-0.394951\pi\) | ||||
0.324062 | + | 0.946036i | \(0.394951\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.1436 | 0.985377 | ||||||||
\(506\) | 5.41154 | 0.240572 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14.0000 | 0.621150 | ||||||||
\(509\) | −14.9808 | −0.664011 | −0.332005 | − | 0.943278i | \(-0.607725\pi\) | ||||
−0.332005 | + | 0.943278i | \(0.607725\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.60770 | −0.159595 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −21.1962 | −0.934922 | ||||||||
\(515\) | 55.1769 | 2.43139 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.46410 | −0.416231 | ||||||||
\(518\) | 6.73205 | 0.295789 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −18.9282 | −0.830057 | ||||||||
\(521\) | 13.3205 | 0.583582 | 0.291791 | − | 0.956482i | \(-0.405749\pi\) | ||||
0.291791 | + | 0.956482i | \(0.405749\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.928203 | −0.0405875 | −0.0202937 | − | 0.999794i | \(-0.506460\pi\) | ||||
−0.0202937 | + | 0.999794i | \(0.506460\pi\) | |||||||
\(524\) | −9.46410 | −0.413441 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.7846 | 0.644640 | ||||||||
\(527\) | 6.73205 | 0.293253 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.78461 | −0.208027 | ||||||||
\(530\) | −21.7128 | −0.943144 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 13.4641 | 0.583743 | ||||||||
\(533\) | 6.53590 | 0.283101 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.7128 | 0.679324 | ||||||||
\(536\) | 6.19615 | 0.267633 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15.3397 | 0.661343 | ||||||||
\(539\) | 1.17691 | 0.0506933 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.4641 | 1.26676 | 0.633380 | − | 0.773841i | \(-0.281667\pi\) | ||||
0.633380 | + | 0.773841i | \(0.281667\pi\) | |||||||
\(542\) | −28.7846 | −1.23640 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.73205 | −0.288634 | ||||||||
\(545\) | −20.5359 | −0.879661 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.4641 | −0.490170 | −0.245085 | − | 0.969502i | \(-0.578816\pi\) | ||||
−0.245085 | + | 0.969502i | \(0.578816\pi\) | |||||||
\(548\) | −1.19615 | −0.0510971 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 8.87564 | 0.378459 | ||||||||
\(551\) | 9.46410 | 0.403184 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 31.3731 | 1.33412 | ||||||||
\(554\) | −5.00000 | −0.212430 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.00000 | −0.296866 | ||||||||
\(557\) | 28.1244 | 1.19167 | 0.595834 | − | 0.803108i | \(-0.296822\pi\) | ||||
0.595834 | + | 0.803108i | \(0.296822\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 48.7846 | 2.06337 | ||||||||
\(560\) | −8.53590 | −0.360708 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −24.0526 | −1.01460 | ||||||||
\(563\) | 30.6603 | 1.29218 | 0.646088 | − | 0.763263i | \(-0.276404\pi\) | ||||
0.646088 | + | 0.763263i | \(0.276404\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −56.1051 | −2.36036 | ||||||||
\(566\) | −1.53590 | −0.0645586 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14.1244 | 0.592645 | ||||||||
\(569\) | 12.1244 | 0.508279 | 0.254140 | − | 0.967168i | \(-0.418208\pi\) | ||||
0.254140 | + | 0.967168i | \(0.418208\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.07180 | −0.0448533 | −0.0224266 | − | 0.999748i | \(-0.507139\pi\) | ||||
−0.0224266 | + | 0.999748i | \(0.507139\pi\) | |||||||
\(572\) | −6.92820 | −0.289683 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.94744 | 0.123024 | ||||||||
\(575\) | 29.8756 | 1.24590 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −43.7846 | −1.82278 | −0.911389 | − | 0.411547i | \(-0.864989\pi\) | ||||
−0.911389 | + | 0.411547i | \(0.864989\pi\) | |||||||
\(578\) | −28.3205 | −1.17798 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.00000 | −0.249136 | ||||||||
\(581\) | 4.44486 | 0.184404 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.94744 | −0.329149 | ||||||||
\(584\) | −1.46410 | −0.0605850 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.1244 | −0.500853 | ||||||||
\(587\) | 25.6077 | 1.05694 | 0.528471 | − | 0.848951i | \(-0.322765\pi\) | ||||
0.528471 | + | 0.848951i | \(0.322765\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.46410 | −0.225144 | ||||||||
\(590\) | 11.3205 | 0.466058 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.73205 | 0.112287 | ||||||||
\(593\) | 14.4115 | 0.591811 | 0.295906 | − | 0.955217i | \(-0.404379\pi\) | ||||
0.295906 | + | 0.955217i | \(0.404379\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −57.4641 | −2.35580 | ||||||||
\(596\) | −1.00000 | −0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −23.3205 | −0.953646 | ||||||||
\(599\) | −21.8564 | −0.893029 | −0.446514 | − | 0.894777i | \(-0.647335\pi\) | ||||
−0.446514 | + | 0.894777i | \(0.647335\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.60770 | 0.351115 | 0.175558 | − | 0.984469i | \(-0.443827\pi\) | ||||
0.175558 | + | 0.984469i | \(0.443827\pi\) | |||||||
\(602\) | 22.0000 | 0.896653 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 21.1244 | 0.859538 | ||||||||
\(605\) | −32.5359 | −1.32277 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.80385 | 0.316748 | 0.158374 | − | 0.987379i | \(-0.449375\pi\) | ||||
0.158374 | + | 0.987379i | \(0.449375\pi\) | |||||||
\(608\) | 5.46410 | 0.221599 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.46410 | −0.383190 | ||||||||
\(611\) | 40.7846 | 1.64997 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.2487 | −1.06018 | −0.530088 | − | 0.847943i | \(-0.677841\pi\) | ||||
−0.530088 | + | 0.847943i | \(0.677841\pi\) | |||||||
\(614\) | 29.3205 | 1.18328 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.12436 | −0.125884 | ||||||||
\(617\) | 20.2487 | 0.815182 | 0.407591 | − | 0.913165i | \(-0.366369\pi\) | ||||
0.407591 | + | 0.913165i | \(0.366369\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.5359 | −0.503860 | −0.251930 | − | 0.967745i | \(-0.581065\pi\) | ||||
−0.251930 | + | 0.967745i | \(0.581065\pi\) | |||||||
\(620\) | 3.46410 | 0.139122 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 28.1244 | 1.12768 | ||||||||
\(623\) | 10.5167 | 0.421341 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 22.5359 | 0.900716 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.53590 | 0.141098 | ||||||||
\(629\) | 18.3923 | 0.733349 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.1436 | 0.403810 | 0.201905 | − | 0.979405i | \(-0.435287\pi\) | ||||
0.201905 | + | 0.979405i | \(0.435287\pi\) | |||||||
\(632\) | 12.7321 | 0.506454 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.85641 | 0.153157 | ||||||||
\(635\) | 48.4974 | 1.92456 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.07180 | −0.200952 | ||||||||
\(638\) | −2.19615 | −0.0869465 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.46410 | −0.136931 | ||||||||
\(641\) | 25.1244 | 0.992352 | 0.496176 | − | 0.868222i | \(-0.334737\pi\) | ||||
0.496176 | + | 0.868222i | \(0.334737\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.94744 | −0.234544 | −0.117272 | − | 0.993100i | \(-0.537415\pi\) | ||||
−0.117272 | + | 0.993100i | \(0.537415\pi\) | |||||||
\(644\) | −10.5167 | −0.414414 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 36.7846 | 1.44727 | ||||||||
\(647\) | 36.5167 | 1.43562 | 0.717809 | − | 0.696240i | \(-0.245145\pi\) | ||||
0.717809 | + | 0.696240i | \(0.245145\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.14359 | 0.162650 | ||||||||
\(650\) | −38.2487 | −1.50024 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.92820 | 0.388818 | ||||||||
\(653\) | −25.8564 | −1.01184 | −0.505920 | − | 0.862581i | \(-0.668847\pi\) | ||||
−0.505920 | + | 0.862581i | \(0.668847\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −32.7846 | −1.28100 | ||||||||
\(656\) | 1.19615 | 0.0467019 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 18.3923 | 0.717007 | ||||||||
\(659\) | 1.48334 | 0.0577827 | 0.0288914 | − | 0.999583i | \(-0.490802\pi\) | ||||
0.0288914 | + | 0.999583i | \(0.490802\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.2487 | 0.437524 | 0.218762 | − | 0.975778i | \(-0.429798\pi\) | ||||
0.218762 | + | 0.975778i | \(0.429798\pi\) | |||||||
\(662\) | −1.80385 | −0.0701085 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.80385 | 0.0700029 | ||||||||
\(665\) | 46.6410 | 1.80866 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.39230 | −0.286231 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 21.4641 | 0.829231 | ||||||||
\(671\) | −3.46410 | −0.133730 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.4115 | 0.439883 | 0.219941 | − | 0.975513i | \(-0.429413\pi\) | ||||
0.219941 | + | 0.975513i | \(0.429413\pi\) | |||||||
\(674\) | −19.0000 | −0.731853 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.8564 | 0.648323 | ||||||||
\(677\) | −18.3923 | −0.706874 | −0.353437 | − | 0.935458i | \(-0.614987\pi\) | ||||
−0.353437 | + | 0.935458i | \(0.614987\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −26.4449 | −1.01486 | ||||||||
\(680\) | −23.3205 | −0.894301 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.26795 | 0.0485523 | ||||||||
\(683\) | −36.3923 | −1.39251 | −0.696256 | − | 0.717793i | \(-0.745152\pi\) | ||||
−0.696256 | + | 0.717793i | \(0.745152\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.14359 | −0.158319 | ||||||||
\(686\) | −19.5359 | −0.745884 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.92820 | 0.340385 | ||||||||
\(689\) | 34.2487 | 1.30477 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −51.5167 | −1.95979 | −0.979893 | − | 0.199523i | \(-0.936061\pi\) | ||||
−0.979893 | + | 0.199523i | \(0.936061\pi\) | |||||||
\(692\) | 14.2679 | 0.542386 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13.7321 | −0.521262 | ||||||||
\(695\) | −24.2487 | −0.919806 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.05256 | 0.305012 | ||||||||
\(698\) | 0.320508 | 0.0121314 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −17.2487 | −0.651940 | ||||||||
\(701\) | 4.33975 | 0.163910 | 0.0819550 | − | 0.996636i | \(-0.473884\pi\) | ||||
0.0819550 | + | 0.996636i | \(0.473884\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.9282 | −0.563028 | ||||||||
\(704\) | −1.26795 | −0.0477876 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.92820 | 0.260746 | ||||||||
\(707\) | −15.7513 | −0.592388 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.3923 | 0.390291 | 0.195146 | − | 0.980774i | \(-0.437482\pi\) | ||||
0.195146 | + | 0.980774i | \(0.437482\pi\) | |||||||
\(710\) | 48.9282 | 1.83624 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.26795 | 0.159948 | ||||||||
\(713\) | 4.26795 | 0.159836 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.0000 | −0.897549 | ||||||||
\(716\) | −9.58846 | −0.358337 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.60770 | 0.134638 | ||||||||
\(719\) | 44.1962 | 1.64824 | 0.824119 | − | 0.566416i | \(-0.191671\pi\) | ||||
0.824119 | + | 0.566416i | \(0.191671\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −39.2487 | −1.46170 | ||||||||
\(722\) | −10.8564 | −0.404034 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −18.4641 | −0.686213 | ||||||||
\(725\) | −12.1244 | −0.450287 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.5167 | −0.872185 | −0.436092 | − | 0.899902i | \(-0.643638\pi\) | ||||
−0.436092 | + | 0.899902i | \(0.643638\pi\) | |||||||
\(728\) | 13.4641 | 0.499013 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.07180 | −0.187716 | ||||||||
\(731\) | 60.1051 | 2.22307 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.4641 | 1.27296 | 0.636480 | − | 0.771293i | \(-0.280390\pi\) | ||||
0.636480 | + | 0.771293i | \(0.280390\pi\) | |||||||
\(734\) | −7.14359 | −0.263675 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.26795 | −0.157319 | ||||||||
\(737\) | 7.85641 | 0.289394 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.4115 | −0.493352 | −0.246676 | − | 0.969098i | \(-0.579338\pi\) | ||||
−0.246676 | + | 0.969098i | \(0.579338\pi\) | |||||||
\(740\) | 9.46410 | 0.347907 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 15.4449 | 0.566999 | ||||||||
\(743\) | 42.3731 | 1.55452 | 0.777259 | − | 0.629181i | \(-0.216610\pi\) | ||||
0.777259 | + | 0.629181i | \(0.216610\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.46410 | −0.126915 | ||||||||
\(746\) | −0.0717968 | −0.00262867 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.53590 | −0.312103 | ||||||||
\(749\) | −11.1769 | −0.408396 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.9282 | 1.09210 | 0.546048 | − | 0.837754i | \(-0.316132\pi\) | ||||
0.546048 | + | 0.837754i | \(0.316132\pi\) | |||||||
\(752\) | 7.46410 | 0.272188 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9.46410 | 0.344662 | ||||||||
\(755\) | 73.1769 | 2.66318 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.0000 | 1.41748 | 0.708740 | − | 0.705470i | \(-0.249264\pi\) | ||||
0.708740 | + | 0.705470i | \(0.249264\pi\) | |||||||
\(758\) | −8.14359 | −0.295789 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 18.9282 | 0.686598 | ||||||||
\(761\) | −26.3923 | −0.956720 | −0.478360 | − | 0.878164i | \(-0.658769\pi\) | ||||
−0.478360 | + | 0.878164i | \(0.658769\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.6077 | 0.528834 | ||||||||
\(764\) | 21.1244 | 0.764252 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.33975 | −0.0845385 | ||||||||
\(767\) | −17.8564 | −0.644757 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −50.9282 | −1.83652 | −0.918259 | − | 0.395980i | \(-0.870405\pi\) | ||||
−0.918259 | + | 0.395980i | \(0.870405\pi\) | |||||||
\(770\) | −10.8231 | −0.390037 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 22.5885 | 0.812976 | ||||||||
\(773\) | −33.7321 | −1.21326 | −0.606629 | − | 0.794985i | \(-0.707479\pi\) | ||||
−0.606629 | + | 0.794985i | \(0.707479\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.00000 | 0.251447 | ||||||||
\(776\) | −10.7321 | −0.385258 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 16.5359 | 0.592841 | ||||||||
\(779\) | −6.53590 | −0.234173 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.9090 | 0.640833 | ||||||||
\(782\) | −28.7321 | −1.02746 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.928203 | −0.0331501 | ||||||||
\(785\) | 12.2487 | 0.437175 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.1244 | 0.539125 | 0.269563 | − | 0.962983i | \(-0.413121\pi\) | ||||
0.269563 | + | 0.962983i | \(0.413121\pi\) | |||||||
\(788\) | −3.12436 | −0.111301 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 44.1051 | 1.56919 | ||||||||
\(791\) | 39.9090 | 1.41900 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.9282 | 0.530116 | ||||||||
\(794\) | −6.78461 | −0.240777 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15.2679 | 0.541158 | ||||||||
\(797\) | 6.67949 | 0.236600 | 0.118300 | − | 0.992978i | \(-0.462256\pi\) | ||||
0.118300 | + | 0.992978i | \(0.462256\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 50.2487 | 1.77767 | ||||||||
\(800\) | −7.00000 | −0.247487 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −19.1244 | −0.675304 | ||||||||
\(803\) | −1.85641 | −0.0655112 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −36.4308 | −1.28402 | ||||||||
\(806\) | −5.46410 | −0.192465 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.39230 | −0.224880 | ||||||||
\(809\) | −45.0333 | −1.58329 | −0.791644 | − | 0.610983i | \(-0.790774\pi\) | ||||
−0.791644 | + | 0.610983i | \(0.790774\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.6077 | 0.618290 | 0.309145 | − | 0.951015i | \(-0.399957\pi\) | ||||
0.309145 | + | 0.951015i | \(0.399957\pi\) | |||||||
\(812\) | 4.26795 | 0.149776 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.46410 | 0.121417 | ||||||||
\(815\) | 34.3923 | 1.20471 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −48.7846 | −1.70676 | ||||||||
\(818\) | −18.3923 | −0.643072 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.14359 | 0.144701 | ||||||||
\(821\) | 4.94744 | 0.172667 | 0.0863334 | − | 0.996266i | \(-0.472485\pi\) | ||||
0.0863334 | + | 0.996266i | \(0.472485\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 50.9282 | 1.77525 | 0.887623 | − | 0.460571i | \(-0.152355\pi\) | ||||
0.887623 | + | 0.460571i | \(0.152355\pi\) | |||||||
\(824\) | −15.9282 | −0.554885 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.05256 | −0.280184 | ||||||||
\(827\) | 44.3923 | 1.54367 | 0.771836 | − | 0.635822i | \(-0.219339\pi\) | ||||
0.771836 | + | 0.635822i | \(0.219339\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −56.1769 | −1.95110 | −0.975552 | − | 0.219767i | \(-0.929470\pi\) | ||||
−0.975552 | + | 0.219767i | \(0.929470\pi\) | |||||||
\(830\) | 6.24871 | 0.216896 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.46410 | 0.189434 | ||||||||
\(833\) | −6.24871 | −0.216505 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.92820 | 0.239617 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −27.5885 | −0.953027 | ||||||||
\(839\) | 28.5167 | 0.984504 | 0.492252 | − | 0.870453i | \(-0.336174\pi\) | ||||
0.492252 | + | 0.870453i | \(0.336174\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0000 | −0.896552 | ||||||||
\(842\) | −22.3923 | −0.771690 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15.7846 | 0.543329 | ||||||||
\(845\) | 58.3923 | 2.00876 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.1436 | 0.795223 | ||||||||
\(848\) | 6.26795 | 0.215242 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −47.1244 | −1.61635 | ||||||||
\(851\) | 11.6603 | 0.399708 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.6410 | 0.432820 | 0.216410 | − | 0.976303i | \(-0.430565\pi\) | ||||
0.216410 | + | 0.976303i | \(0.430565\pi\) | |||||||
\(854\) | 6.73205 | 0.230366 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.53590 | −0.155034 | ||||||||
\(857\) | 24.1962 | 0.826525 | 0.413262 | − | 0.910612i | \(-0.364389\pi\) | ||||
0.413262 | + | 0.910612i | \(0.364389\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.9474 | 0.612359 | 0.306179 | − | 0.951974i | \(-0.400949\pi\) | ||||
0.306179 | + | 0.951974i | \(0.400949\pi\) | |||||||
\(860\) | 30.9282 | 1.05464 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 36.2487 | 1.23464 | ||||||||
\(863\) | 53.2295 | 1.81195 | 0.905976 | − | 0.423329i | \(-0.139138\pi\) | ||||
0.905976 | + | 0.423329i | \(0.139138\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 49.4256 | 1.68052 | ||||||||
\(866\) | −36.9808 | −1.25666 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.46410 | −0.0836371 | ||||||||
\(869\) | 16.1436 | 0.547634 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −33.8564 | −1.14718 | ||||||||
\(872\) | 5.92820 | 0.200754 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 23.3205 | 0.788828 | ||||||||
\(875\) | −17.0718 | −0.577132 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.9282 | 1.51712 | 0.758559 | − | 0.651605i | \(-0.225904\pi\) | ||||
0.758559 | + | 0.651605i | \(0.225904\pi\) | |||||||
\(878\) | −15.8038 | −0.533354 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.39230 | −0.148065 | ||||||||
\(881\) | −20.9090 | −0.704441 | −0.352220 | − | 0.935917i | \(-0.614573\pi\) | ||||
−0.352220 | + | 0.935917i | \(0.614573\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.248711 | −0.00836980 | −0.00418490 | − | 0.999991i | \(-0.501332\pi\) | ||||
−0.00418490 | + | 0.999991i | \(0.501332\pi\) | |||||||
\(884\) | 36.7846 | 1.23720 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.66025 | 0.0893730 | ||||||||
\(887\) | 29.9090 | 1.00424 | 0.502122 | − | 0.864797i | \(-0.332553\pi\) | ||||
0.502122 | + | 0.864797i | \(0.332553\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −34.4974 | −1.15701 | ||||||||
\(890\) | 14.7846 | 0.495581 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.26795 | −0.0424541 | ||||||||
\(893\) | −40.7846 | −1.36480 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −33.2154 | −1.11027 | ||||||||
\(896\) | 2.46410 | 0.0823199 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 42.1244 | 1.40571 | ||||||||
\(899\) | −1.73205 | −0.0577671 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 42.1962 | 1.40576 | ||||||||
\(902\) | 1.51666 | 0.0504993 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16.1962 | 0.538676 | ||||||||
\(905\) | −63.9615 | −2.12615 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.2487 | 1.60207 | 0.801036 | − | 0.598616i | \(-0.204282\pi\) | ||||
0.801036 | + | 0.598616i | \(0.204282\pi\) | |||||||
\(908\) | −7.46410 | −0.247705 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 46.6410 | 1.54613 | ||||||||
\(911\) | 11.7128 | 0.388063 | 0.194031 | − | 0.980995i | \(-0.437844\pi\) | ||||
0.194031 | + | 0.980995i | \(0.437844\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.28719 | 0.0756948 | ||||||||
\(914\) | 36.9282 | 1.22148 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.19615 | 0.270808 | ||||||||
\(917\) | 23.3205 | 0.770111 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.7846 | 1.11445 | 0.557226 | − | 0.830361i | \(-0.311866\pi\) | ||||
0.557226 | + | 0.830361i | \(0.311866\pi\) | |||||||
\(920\) | −14.7846 | −0.487434 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −29.3205 | −0.965620 | ||||||||
\(923\) | −77.1769 | −2.54031 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.1244 | 0.628805 | ||||||||
\(926\) | 37.6410 | 1.23696 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.73205 | 0.0568574 | ||||||||
\(929\) | 1.60770 | 0.0527468 | 0.0263734 | − | 0.999652i | \(-0.491604\pi\) | ||||
0.0263734 | + | 0.999652i | \(0.491604\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.07180 | 0.166221 | ||||||||
\(932\) | −25.9808 | −0.851028 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 40.1051 | 1.31228 | ||||||||
\(935\) | −29.5692 | −0.967017 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.4833 | 0.473150 | 0.236575 | − | 0.971613i | \(-0.423975\pi\) | ||||
0.236575 | + | 0.971613i | \(0.423975\pi\) | |||||||
\(938\) | −15.2679 | −0.498516 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 25.8564 | 0.843343 | ||||||||
\(941\) | −11.9808 | −0.390562 | −0.195281 | − | 0.980747i | \(-0.562562\pi\) | ||||
−0.195281 | + | 0.980747i | \(0.562562\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.10512 | 0.166246 | ||||||||
\(944\) | −3.26795 | −0.106363 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.3205 | 0.368061 | ||||||||
\(947\) | 33.9808 | 1.10423 | 0.552113 | − | 0.833769i | \(-0.313822\pi\) | ||||
0.552113 | + | 0.833769i | \(0.313822\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.00000 | 0.259691 | ||||||||
\(950\) | 38.2487 | 1.24095 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 16.5885 | 0.537635 | ||||||||
\(953\) | −0.124356 | −0.00402827 | −0.00201414 | − | 0.999998i | \(-0.500641\pi\) | ||||
−0.00201414 | + | 0.999998i | \(0.500641\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 73.1769 | 2.36795 | ||||||||
\(956\) | −6.12436 | −0.198076 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −11.7321 | −0.379045 | ||||||||
\(959\) | 2.94744 | 0.0951778 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0000 | −0.967742 | ||||||||
\(962\) | −14.9282 | −0.481305 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.53590 | 0.274923 | ||||||||
\(965\) | 78.2487 | 2.51892 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.0718 | −0.356045 | −0.178022 | − | 0.984026i | \(-0.556970\pi\) | ||||
−0.178022 | + | 0.984026i | \(0.556970\pi\) | |||||||
\(968\) | 9.39230 | 0.301880 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −37.1769 | −1.19368 | ||||||||
\(971\) | −46.0526 | −1.47790 | −0.738948 | − | 0.673762i | \(-0.764677\pi\) | ||||
−0.738948 | + | 0.673762i | \(0.764677\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.2487 | 0.552968 | ||||||||
\(974\) | 0.392305 | 0.0125703 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.73205 | 0.0874508 | ||||||||
\(977\) | 36.0000 | 1.15174 | 0.575871 | − | 0.817541i | \(-0.304663\pi\) | ||||
0.575871 | + | 0.817541i | \(0.304663\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.41154 | 0.172954 | ||||||||
\(980\) | −3.21539 | −0.102712 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 24.0000 | 0.765871 | ||||||||
\(983\) | −17.0526 | −0.543892 | −0.271946 | − | 0.962312i | \(-0.587667\pi\) | ||||
−0.271946 | + | 0.962312i | \(0.587667\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.8231 | −0.344852 | ||||||||
\(986\) | 11.6603 | 0.371338 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −29.8564 | −0.949859 | ||||||||
\(989\) | 38.1051 | 1.21167 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.5692 | 1.00283 | 0.501415 | − | 0.865207i | \(-0.332813\pi\) | ||||
0.501415 | + | 0.865207i | \(0.332813\pi\) | |||||||
\(992\) | −1.00000 | −0.0317500 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −34.8038 | −1.10391 | ||||||||
\(995\) | 52.8897 | 1.67672 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.0526 | 0.825093 | 0.412546 | − | 0.910937i | \(-0.364639\pi\) | ||||
0.412546 | + | 0.910937i | \(0.364639\pi\) | |||||||
\(998\) | 13.3923 | 0.423926 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8046.2.a.c.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 8046.2.a.d.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.c.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
8046.2.a.d.1.1 | yes | 2 | 3.2 | odd | 2 |