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: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 46 x^{14} + 192 x^{13} + 752 x^{12} - 3378 x^{11} - 5277 x^{10} + 27132 x^{9} + \cdots - 4260 \) |
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 | 1.14 | ||
Root | \(3.23488\) 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 | ||||||||
\(5\) | 3.23488 | 1.44668 | 0.723341 | − | 0.690491i | \(-0.242605\pi\) | ||||
0.723341 | + | 0.690491i | \(0.242605\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.87212 | −0.707594 | −0.353797 | − | 0.935322i | \(-0.615110\pi\) | ||||
−0.353797 | + | 0.935322i | \(0.615110\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.23488 | 1.02296 | ||||||||
\(11\) | 4.66557 | 1.40672 | 0.703361 | − | 0.710833i | \(-0.251682\pi\) | ||||
0.703361 | + | 0.710833i | \(0.251682\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.77562 | 1.04717 | 0.523584 | − | 0.851974i | \(-0.324595\pi\) | ||||
0.523584 | + | 0.851974i | \(0.324595\pi\) | |||||||
\(14\) | −1.87212 | −0.500345 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.68172 | 1.13548 | 0.567742 | − | 0.823207i | \(-0.307817\pi\) | ||||
0.567742 | + | 0.823207i | \(0.307817\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.83250 | 0.649821 | 0.324910 | − | 0.945745i | \(-0.394666\pi\) | ||||
0.324910 | + | 0.945745i | \(0.394666\pi\) | |||||||
\(20\) | 3.23488 | 0.723341 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.66557 | 0.994703 | ||||||||
\(23\) | 4.42544 | 0.922767 | 0.461384 | − | 0.887201i | \(-0.347353\pi\) | ||||
0.461384 | + | 0.887201i | \(0.347353\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.46445 | 1.09289 | ||||||||
\(26\) | 3.77562 | 0.740459 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.87212 | −0.353797 | ||||||||
\(29\) | −7.42347 | −1.37850 | −0.689251 | − | 0.724522i | \(-0.742060\pi\) | ||||
−0.689251 | + | 0.724522i | \(0.742060\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.38774 | 1.50648 | 0.753241 | − | 0.657744i | \(-0.228489\pi\) | ||||
0.753241 | + | 0.657744i | \(0.228489\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.68172 | 0.802908 | ||||||||
\(35\) | −6.05608 | −1.02366 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.87734 | −0.966228 | −0.483114 | − | 0.875557i | \(-0.660494\pi\) | ||||
−0.483114 | + | 0.875557i | \(0.660494\pi\) | |||||||
\(38\) | 2.83250 | 0.459493 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.23488 | 0.511479 | ||||||||
\(41\) | 7.57269 | 1.18266 | 0.591328 | − | 0.806431i | \(-0.298604\pi\) | ||||
0.591328 | + | 0.806431i | \(0.298604\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.17859 | −1.24722 | −0.623612 | − | 0.781734i | \(-0.714335\pi\) | ||||
−0.623612 | + | 0.781734i | \(0.714335\pi\) | |||||||
\(44\) | 4.66557 | 0.703361 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.42544 | 0.652495 | ||||||||
\(47\) | −1.31778 | −0.192218 | −0.0961088 | − | 0.995371i | \(-0.530640\pi\) | ||||
−0.0961088 | + | 0.995371i | \(0.530640\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.49517 | −0.499310 | ||||||||
\(50\) | 5.46445 | 0.772790 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.77562 | 0.523584 | ||||||||
\(53\) | 7.98570 | 1.09692 | 0.548460 | − | 0.836177i | \(-0.315214\pi\) | ||||
0.548460 | + | 0.836177i | \(0.315214\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.0926 | 2.03508 | ||||||||
\(56\) | −1.87212 | −0.250172 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.42347 | −0.974749 | ||||||||
\(59\) | 0.0111878 | 0.00145653 | 0.000728263 | − | 1.00000i | \(-0.499768\pi\) | ||||
0.000728263 | 1.00000i | \(0.499768\pi\) | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.5308 | −1.73244 | −0.866221 | − | 0.499660i | \(-0.833458\pi\) | ||||
−0.866221 | + | 0.499660i | \(0.833458\pi\) | |||||||
\(62\) | 8.38774 | 1.06524 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 12.2137 | 1.51492 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.8561 | −1.81496 | −0.907481 | − | 0.420093i | \(-0.861997\pi\) | ||||
−0.907481 | + | 0.420093i | \(0.861997\pi\) | |||||||
\(68\) | 4.68172 | 0.567742 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.05608 | −0.723840 | ||||||||
\(71\) | −8.49039 | −1.00762 | −0.503812 | − | 0.863814i | \(-0.668069\pi\) | ||||
−0.503812 | + | 0.863814i | \(0.668069\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −16.8516 | −1.97233 | −0.986167 | − | 0.165753i | \(-0.946995\pi\) | ||||
−0.986167 | + | 0.165753i | \(0.946995\pi\) | |||||||
\(74\) | −5.87734 | −0.683227 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.83250 | 0.324910 | ||||||||
\(77\) | −8.73450 | −0.995389 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.48279 | −0.504354 | −0.252177 | − | 0.967681i | \(-0.581146\pi\) | ||||
−0.252177 | + | 0.967681i | \(0.581146\pi\) | |||||||
\(80\) | 3.23488 | 0.361671 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.57269 | 0.836264 | ||||||||
\(83\) | 11.1948 | 1.22879 | 0.614394 | − | 0.789000i | \(-0.289401\pi\) | ||||
0.614394 | + | 0.789000i | \(0.289401\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 15.1448 | 1.64268 | ||||||||
\(86\) | −8.17859 | −0.881920 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.66557 | 0.497351 | ||||||||
\(89\) | 7.32113 | 0.776039 | 0.388019 | − | 0.921651i | \(-0.373159\pi\) | ||||
0.388019 | + | 0.921651i | \(0.373159\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.06840 | −0.740970 | ||||||||
\(92\) | 4.42544 | 0.461384 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.31778 | −0.135918 | ||||||||
\(95\) | 9.16281 | 0.940085 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.4460 | −1.26370 | −0.631850 | − | 0.775091i | \(-0.717704\pi\) | ||||
−0.631850 | + | 0.775091i | \(0.717704\pi\) | |||||||
\(98\) | −3.49517 | −0.353066 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.46445 | 0.546445 | ||||||||
\(101\) | −3.51868 | −0.350121 | −0.175061 | − | 0.984558i | \(-0.556012\pi\) | ||||
−0.175061 | + | 0.984558i | \(0.556012\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.14904 | 0.605883 | 0.302941 | − | 0.953009i | \(-0.402031\pi\) | ||||
0.302941 | + | 0.953009i | \(0.402031\pi\) | |||||||
\(104\) | 3.77562 | 0.370230 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.98570 | 0.775640 | ||||||||
\(107\) | 0.862074 | 0.0833398 | 0.0416699 | − | 0.999131i | \(-0.486732\pi\) | ||||
0.0416699 | + | 0.999131i | \(0.486732\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.0784 | 1.06112 | 0.530560 | − | 0.847647i | \(-0.321982\pi\) | ||||
0.530560 | + | 0.847647i | \(0.321982\pi\) | |||||||
\(110\) | 15.0926 | 1.43902 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.87212 | −0.176899 | ||||||||
\(113\) | −16.0867 | −1.51331 | −0.756654 | − | 0.653815i | \(-0.773167\pi\) | ||||
−0.756654 | + | 0.653815i | \(0.773167\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.3158 | 1.33495 | ||||||||
\(116\) | −7.42347 | −0.689251 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.0111878 | 0.00102992 | ||||||||
\(119\) | −8.76473 | −0.803462 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.7675 | 0.978868 | ||||||||
\(122\) | −13.5308 | −1.22502 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.38774 | 0.753241 | ||||||||
\(125\) | 1.50243 | 0.134382 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.16232 | 0.458082 | 0.229041 | − | 0.973417i | \(-0.426441\pi\) | ||||
0.229041 | + | 0.973417i | \(0.426441\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 12.2137 | 1.07121 | ||||||||
\(131\) | 3.81504 | 0.333322 | 0.166661 | − | 0.986014i | \(-0.446701\pi\) | ||||
0.166661 | + | 0.986014i | \(0.446701\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.30278 | −0.459810 | ||||||||
\(134\) | −14.8561 | −1.28337 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.68172 | 0.401454 | ||||||||
\(137\) | 8.93528 | 0.763392 | 0.381696 | − | 0.924288i | \(-0.375340\pi\) | ||||
0.381696 | + | 0.924288i | \(0.375340\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.9035 | 1.00964 | 0.504819 | − | 0.863225i | \(-0.331559\pi\) | ||||
0.504819 | + | 0.863225i | \(0.331559\pi\) | |||||||
\(140\) | −6.05608 | −0.511832 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.49039 | −0.712497 | ||||||||
\(143\) | 17.6154 | 1.47307 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −24.0140 | −1.99426 | ||||||||
\(146\) | −16.8516 | −1.39465 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.87734 | −0.483114 | ||||||||
\(149\) | −1.00000 | −0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.5730 | −1.59283 | −0.796413 | − | 0.604752i | \(-0.793272\pi\) | ||||
−0.796413 | + | 0.604752i | \(0.793272\pi\) | |||||||
\(152\) | 2.83250 | 0.229746 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.73450 | −0.703846 | ||||||||
\(155\) | 27.1333 | 2.17940 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.16484 | 0.651625 | 0.325812 | − | 0.945434i | \(-0.394362\pi\) | ||||
0.325812 | + | 0.945434i | \(0.394362\pi\) | |||||||
\(158\) | −4.48279 | −0.356632 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.23488 | 0.255740 | ||||||||
\(161\) | −8.28494 | −0.652945 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.7237 | −1.15325 | −0.576623 | − | 0.817010i | \(-0.695630\pi\) | ||||
−0.576623 | + | 0.817010i | \(0.695630\pi\) | |||||||
\(164\) | 7.57269 | 0.591328 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.1948 | 0.868884 | ||||||||
\(167\) | 3.40133 | 0.263203 | 0.131601 | − | 0.991303i | \(-0.457988\pi\) | ||||
0.131601 | + | 0.991303i | \(0.457988\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.25528 | 0.0965597 | ||||||||
\(170\) | 15.1448 | 1.16155 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.17859 | −0.623612 | ||||||||
\(173\) | −12.3853 | −0.941635 | −0.470817 | − | 0.882231i | \(-0.656041\pi\) | ||||
−0.470817 | + | 0.882231i | \(0.656041\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.2301 | −0.773322 | ||||||||
\(176\) | 4.66557 | 0.351681 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.32113 | 0.548742 | ||||||||
\(179\) | 4.42416 | 0.330677 | 0.165339 | − | 0.986237i | \(-0.447128\pi\) | ||||
0.165339 | + | 0.986237i | \(0.447128\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.56556 | 0.413685 | 0.206842 | − | 0.978374i | \(-0.433681\pi\) | ||||
0.206842 | + | 0.978374i | \(0.433681\pi\) | |||||||
\(182\) | −7.06840 | −0.523945 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.42544 | 0.326247 | ||||||||
\(185\) | −19.0125 | −1.39783 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 21.8429 | 1.59731 | ||||||||
\(188\) | −1.31778 | −0.0961088 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.16281 | 0.664740 | ||||||||
\(191\) | −19.4431 | −1.40685 | −0.703427 | − | 0.710768i | \(-0.748348\pi\) | ||||
−0.703427 | + | 0.710768i | \(0.748348\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.1823 | 1.30879 | 0.654397 | − | 0.756151i | \(-0.272922\pi\) | ||||
0.654397 | + | 0.756151i | \(0.272922\pi\) | |||||||
\(194\) | −12.4460 | −0.893571 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.49517 | −0.249655 | ||||||||
\(197\) | 3.60218 | 0.256645 | 0.128323 | − | 0.991732i | \(-0.459041\pi\) | ||||
0.128323 | + | 0.991732i | \(0.459041\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.7345 | 0.760948 | 0.380474 | − | 0.924792i | \(-0.375761\pi\) | ||||
0.380474 | + | 0.924792i | \(0.375761\pi\) | |||||||
\(200\) | 5.46445 | 0.386395 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.51868 | −0.247573 | ||||||||
\(203\) | 13.8976 | 0.975421 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 24.4967 | 1.71093 | ||||||||
\(206\) | 6.14904 | 0.428424 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.77562 | 0.261792 | ||||||||
\(209\) | 13.2152 | 0.914118 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.4045 | 1.33586 | 0.667929 | − | 0.744225i | \(-0.267181\pi\) | ||||
0.667929 | + | 0.744225i | \(0.267181\pi\) | |||||||
\(212\) | 7.98570 | 0.548460 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.862074 | 0.0589302 | ||||||||
\(215\) | −26.4568 | −1.80434 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.7028 | −1.06598 | ||||||||
\(218\) | 11.0784 | 0.750325 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 15.0926 | 1.01754 | ||||||||
\(221\) | 17.6764 | 1.18904 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.0723012 | 0.00484164 | 0.00242082 | − | 0.999997i | \(-0.499229\pi\) | ||||
0.00242082 | + | 0.999997i | \(0.499229\pi\) | |||||||
\(224\) | −1.87212 | −0.125086 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −16.0867 | −1.07007 | ||||||||
\(227\) | −11.1563 | −0.740471 | −0.370236 | − | 0.928938i | \(-0.620723\pi\) | ||||
−0.370236 | + | 0.928938i | \(0.620723\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.4325 | 1.21806 | 0.609028 | − | 0.793149i | \(-0.291560\pi\) | ||||
0.609028 | + | 0.793149i | \(0.291560\pi\) | |||||||
\(230\) | 14.3158 | 0.943953 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.42347 | −0.487374 | ||||||||
\(233\) | 15.3706 | 1.00696 | 0.503481 | − | 0.864006i | \(-0.332052\pi\) | ||||
0.503481 | + | 0.864006i | \(0.332052\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.26285 | −0.278078 | ||||||||
\(236\) | 0.0111878 | 0.000728263 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.76473 | −0.568133 | ||||||||
\(239\) | −10.1084 | −0.653858 | −0.326929 | − | 0.945049i | \(-0.606014\pi\) | ||||
−0.326929 | + | 0.945049i | \(0.606014\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.3305 | 0.665447 | 0.332724 | − | 0.943024i | \(-0.392032\pi\) | ||||
0.332724 | + | 0.943024i | \(0.392032\pi\) | |||||||
\(242\) | 10.7675 | 0.692164 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −13.5308 | −0.866221 | ||||||||
\(245\) | −11.3065 | −0.722343 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.6944 | 0.680471 | ||||||||
\(248\) | 8.38774 | 0.532622 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.50243 | 0.0950222 | ||||||||
\(251\) | 29.1816 | 1.84193 | 0.920964 | − | 0.389647i | \(-0.127403\pi\) | ||||
0.920964 | + | 0.389647i | \(0.127403\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.6472 | 1.29808 | ||||||||
\(254\) | 5.16232 | 0.323913 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −16.6147 | −1.03639 | −0.518197 | − | 0.855261i | \(-0.673397\pi\) | ||||
−0.518197 | + | 0.855261i | \(0.673397\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.0031 | 0.683698 | ||||||||
\(260\) | 12.2137 | 0.757459 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.81504 | 0.235694 | ||||||||
\(263\) | 24.8311 | 1.53115 | 0.765575 | − | 0.643346i | \(-0.222454\pi\) | ||||
0.765575 | + | 0.643346i | \(0.222454\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.8328 | 1.58690 | ||||||||
\(266\) | −5.30278 | −0.325134 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −14.8561 | −0.907481 | ||||||||
\(269\) | 7.21483 | 0.439896 | 0.219948 | − | 0.975512i | \(-0.429411\pi\) | ||||
0.219948 | + | 0.975512i | \(0.429411\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0375 | −0.974207 | −0.487103 | − | 0.873344i | \(-0.661946\pi\) | ||||
−0.487103 | + | 0.873344i | \(0.661946\pi\) | |||||||
\(272\) | 4.68172 | 0.283871 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.93528 | 0.539800 | ||||||||
\(275\) | 25.4948 | 1.53739 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.3652 | −1.22363 | −0.611813 | − | 0.791003i | \(-0.709559\pi\) | ||||
−0.611813 | + | 0.791003i | \(0.709559\pi\) | |||||||
\(278\) | 11.9035 | 0.713922 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.05608 | −0.361920 | ||||||||
\(281\) | −32.1042 | −1.91518 | −0.957588 | − | 0.288139i | \(-0.906963\pi\) | ||||
−0.957588 | + | 0.288139i | \(0.906963\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.53278 | −0.566665 | −0.283332 | − | 0.959022i | \(-0.591440\pi\) | ||||
−0.283332 | + | 0.959022i | \(0.591440\pi\) | |||||||
\(284\) | −8.49039 | −0.503812 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 17.6154 | 1.04162 | ||||||||
\(287\) | −14.1770 | −0.836840 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.91849 | 0.289323 | ||||||||
\(290\) | −24.0140 | −1.41015 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −16.8516 | −0.986167 | ||||||||
\(293\) | −19.7079 | −1.15135 | −0.575673 | − | 0.817680i | \(-0.695260\pi\) | ||||
−0.575673 | + | 0.817680i | \(0.695260\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.0361912 | 0.00210713 | ||||||||
\(296\) | −5.87734 | −0.341613 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.00000 | −0.0579284 | ||||||||
\(299\) | 16.7087 | 0.966292 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.3113 | 0.882528 | ||||||||
\(302\) | −19.5730 | −1.12630 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.83250 | 0.162455 | ||||||||
\(305\) | −43.7706 | −2.50629 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.3057 | 1.84379 | 0.921893 | − | 0.387444i | \(-0.126642\pi\) | ||||
0.921893 | + | 0.387444i | \(0.126642\pi\) | |||||||
\(308\) | −8.73450 | −0.497694 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 27.1333 | 1.54107 | ||||||||
\(311\) | 10.6783 | 0.605514 | 0.302757 | − | 0.953068i | \(-0.402093\pi\) | ||||
0.302757 | + | 0.953068i | \(0.402093\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.11853 | −0.0632229 | −0.0316115 | − | 0.999500i | \(-0.510064\pi\) | ||||
−0.0316115 | + | 0.999500i | \(0.510064\pi\) | |||||||
\(314\) | 8.16484 | 0.460768 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.48279 | −0.252177 | ||||||||
\(317\) | −16.0206 | −0.899808 | −0.449904 | − | 0.893077i | \(-0.648542\pi\) | ||||
−0.449904 | + | 0.893077i | \(0.648542\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −34.6347 | −1.93917 | ||||||||
\(320\) | 3.23488 | 0.180835 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.28494 | −0.461702 | ||||||||
\(323\) | 13.2610 | 0.737861 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.6317 | 1.14444 | ||||||||
\(326\) | −14.7237 | −0.815468 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.57269 | 0.418132 | ||||||||
\(329\) | 2.46703 | 0.136012 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.490745 | −0.0269738 | −0.0134869 | − | 0.999909i | \(-0.504293\pi\) | ||||
−0.0134869 | + | 0.999909i | \(0.504293\pi\) | |||||||
\(332\) | 11.1948 | 0.614394 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.40133 | 0.186113 | ||||||||
\(335\) | −48.0577 | −2.62567 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.6204 | 0.578532 | 0.289266 | − | 0.957249i | \(-0.406589\pi\) | ||||
0.289266 | + | 0.957249i | \(0.406589\pi\) | |||||||
\(338\) | 1.25528 | 0.0682780 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 15.1448 | 0.821342 | ||||||||
\(341\) | 39.1336 | 2.11920 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.6482 | 1.06090 | ||||||||
\(344\) | −8.17859 | −0.440960 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.3853 | −0.665836 | ||||||||
\(347\) | −18.6395 | −1.00062 | −0.500312 | − | 0.865845i | \(-0.666781\pi\) | ||||
−0.500312 | + | 0.865845i | \(0.666781\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.5174 | 1.36591 | 0.682957 | − | 0.730459i | \(-0.260694\pi\) | ||||
0.682957 | + | 0.730459i | \(0.260694\pi\) | |||||||
\(350\) | −10.2301 | −0.546822 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.66557 | 0.248676 | ||||||||
\(353\) | 4.63419 | 0.246653 | 0.123327 | − | 0.992366i | \(-0.460644\pi\) | ||||
0.123327 | + | 0.992366i | \(0.460644\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −27.4654 | −1.45771 | ||||||||
\(356\) | 7.32113 | 0.388019 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.42416 | 0.233824 | ||||||||
\(359\) | 4.43020 | 0.233817 | 0.116908 | − | 0.993143i | \(-0.462702\pi\) | ||||
0.116908 | + | 0.993143i | \(0.462702\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.9769 | −0.577733 | ||||||||
\(362\) | 5.56556 | 0.292519 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.06840 | −0.370485 | ||||||||
\(365\) | −54.5130 | −2.85334 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.04147 | −0.106564 | −0.0532821 | − | 0.998580i | \(-0.516968\pi\) | ||||
−0.0532821 | + | 0.998580i | \(0.516968\pi\) | |||||||
\(368\) | 4.42544 | 0.230692 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −19.0125 | −0.988412 | ||||||||
\(371\) | −14.9502 | −0.776175 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.59725 | −0.393371 | −0.196685 | − | 0.980467i | \(-0.563018\pi\) | ||||
−0.196685 | + | 0.980467i | \(0.563018\pi\) | |||||||
\(374\) | 21.8429 | 1.12947 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.31778 | −0.0679592 | ||||||||
\(377\) | −28.0282 | −1.44352 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.5108 | −0.796735 | −0.398368 | − | 0.917226i | \(-0.630423\pi\) | ||||
−0.398368 | + | 0.917226i | \(0.630423\pi\) | |||||||
\(380\) | 9.16281 | 0.470042 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −19.4431 | −0.994796 | ||||||||
\(383\) | 18.4202 | 0.941227 | 0.470614 | − | 0.882339i | \(-0.344033\pi\) | ||||
0.470614 | + | 0.882339i | \(0.344033\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −28.2551 | −1.44001 | ||||||||
\(386\) | 18.1823 | 0.925457 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12.4460 | −0.631850 | ||||||||
\(389\) | −1.57147 | −0.0796766 | −0.0398383 | − | 0.999206i | \(-0.512684\pi\) | ||||
−0.0398383 | + | 0.999206i | \(0.512684\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.7186 | 1.04779 | ||||||||
\(392\) | −3.49517 | −0.176533 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.60218 | 0.181475 | ||||||||
\(395\) | −14.5013 | −0.729640 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.4991 | −0.727689 | −0.363844 | − | 0.931460i | \(-0.618536\pi\) | ||||
−0.363844 | + | 0.931460i | \(0.618536\pi\) | |||||||
\(398\) | 10.7345 | 0.538072 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.46445 | 0.273222 | ||||||||
\(401\) | −30.5872 | −1.52745 | −0.763726 | − | 0.645540i | \(-0.776632\pi\) | ||||
−0.763726 | + | 0.645540i | \(0.776632\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 31.6689 | 1.57754 | ||||||||
\(404\) | −3.51868 | −0.175061 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 13.8976 | 0.689727 | ||||||||
\(407\) | −27.4211 | −1.35922 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.58789 | −0.375197 | −0.187599 | − | 0.982246i | \(-0.560070\pi\) | ||||
−0.187599 | + | 0.982246i | \(0.560070\pi\) | |||||||
\(410\) | 24.4967 | 1.20981 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.14904 | 0.302941 | ||||||||
\(413\) | −0.0209449 | −0.00103063 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 36.2138 | 1.77767 | ||||||||
\(416\) | 3.77562 | 0.185115 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 13.2152 | 0.646379 | ||||||||
\(419\) | 34.4523 | 1.68310 | 0.841551 | − | 0.540177i | \(-0.181643\pi\) | ||||
0.841551 | + | 0.540177i | \(0.181643\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.9298 | −1.31248 | −0.656240 | − | 0.754552i | \(-0.727854\pi\) | ||||
−0.656240 | + | 0.754552i | \(0.727854\pi\) | |||||||
\(422\) | 19.4045 | 0.944594 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.98570 | 0.387820 | ||||||||
\(425\) | 25.5830 | 1.24096 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 25.3313 | 1.22587 | ||||||||
\(428\) | 0.862074 | 0.0416699 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −26.4568 | −1.27586 | ||||||||
\(431\) | 11.5963 | 0.558576 | 0.279288 | − | 0.960207i | \(-0.409902\pi\) | ||||
0.279288 | + | 0.960207i | \(0.409902\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 39.6098 | 1.90352 | 0.951762 | − | 0.306837i | \(-0.0992706\pi\) | ||||
0.951762 | + | 0.306837i | \(0.0992706\pi\) | |||||||
\(434\) | −15.7028 | −0.753761 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.0784 | 0.530560 | ||||||||
\(437\) | 12.5351 | 0.599633 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.9278 | 0.998828 | 0.499414 | − | 0.866363i | \(-0.333549\pi\) | ||||
0.499414 | + | 0.866363i | \(0.333549\pi\) | |||||||
\(440\) | 15.0926 | 0.719509 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 17.6764 | 0.840779 | ||||||||
\(443\) | 6.11587 | 0.290574 | 0.145287 | − | 0.989390i | \(-0.453589\pi\) | ||||
0.145287 | + | 0.989390i | \(0.453589\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23.6830 | 1.12268 | ||||||||
\(446\) | 0.0723012 | 0.00342356 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.87212 | −0.0884493 | ||||||||
\(449\) | −15.0463 | −0.710079 | −0.355040 | − | 0.934851i | \(-0.615533\pi\) | ||||
−0.355040 | + | 0.934851i | \(0.615533\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 35.3309 | 1.66367 | ||||||||
\(452\) | −16.0867 | −0.756654 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11.1563 | −0.523592 | ||||||||
\(455\) | −22.8654 | −1.07195 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.2281 | −0.946229 | −0.473114 | − | 0.881001i | \(-0.656870\pi\) | ||||
−0.473114 | + | 0.881001i | \(0.656870\pi\) | |||||||
\(458\) | 18.4325 | 0.861295 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 14.3158 | 0.667475 | ||||||||
\(461\) | −5.16604 | −0.240606 | −0.120303 | − | 0.992737i | \(-0.538387\pi\) | ||||
−0.120303 | + | 0.992737i | \(0.538387\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.7033 | −1.14806 | −0.574030 | − | 0.818834i | \(-0.694621\pi\) | ||||
−0.574030 | + | 0.818834i | \(0.694621\pi\) | |||||||
\(464\) | −7.42347 | −0.344626 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15.3706 | 0.712029 | ||||||||
\(467\) | −41.0322 | −1.89875 | −0.949373 | − | 0.314151i | \(-0.898280\pi\) | ||||
−0.949373 | + | 0.314151i | \(0.898280\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 27.8124 | 1.28426 | ||||||||
\(470\) | −4.26285 | −0.196631 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.0111878 | 0.000514960 0 | ||||||||
\(473\) | −38.1578 | −1.75450 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.4781 | 0.710183 | ||||||||
\(476\) | −8.76473 | −0.401731 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −10.1084 | −0.462347 | ||||||||
\(479\) | 9.10686 | 0.416103 | 0.208052 | − | 0.978118i | \(-0.433288\pi\) | ||||
0.208052 | + | 0.978118i | \(0.433288\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.1906 | −1.01180 | ||||||||
\(482\) | 10.3305 | 0.470542 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.7675 | 0.489434 | ||||||||
\(485\) | −40.2613 | −1.82817 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.5260 | 0.839495 | 0.419747 | − | 0.907641i | \(-0.362119\pi\) | ||||
0.419747 | + | 0.907641i | \(0.362119\pi\) | |||||||
\(488\) | −13.5308 | −0.612511 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −11.3065 | −0.510774 | ||||||||
\(491\) | −31.1935 | −1.40774 | −0.703871 | − | 0.710328i | \(-0.748547\pi\) | ||||
−0.703871 | + | 0.710328i | \(0.748547\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −34.7546 | −1.56527 | ||||||||
\(494\) | 10.6944 | 0.481166 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.38774 | 0.376621 | ||||||||
\(497\) | 15.8950 | 0.712989 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.12704 | −0.139985 | −0.0699927 | − | 0.997548i | \(-0.522298\pi\) | ||||
−0.0699927 | + | 0.997548i | \(0.522298\pi\) | |||||||
\(500\) | 1.50243 | 0.0671909 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 29.1816 | 1.30244 | ||||||||
\(503\) | 40.7902 | 1.81874 | 0.909372 | − | 0.415984i | \(-0.136563\pi\) | ||||
0.909372 | + | 0.415984i | \(0.136563\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.3825 | −0.506514 | ||||||||
\(506\) | 20.6472 | 0.917879 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.16232 | 0.229041 | ||||||||
\(509\) | 27.4998 | 1.21891 | 0.609455 | − | 0.792821i | \(-0.291388\pi\) | ||||
0.609455 | + | 0.792821i | \(0.291388\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 31.5483 | 1.39561 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −16.6147 | −0.732841 | ||||||||
\(515\) | 19.8914 | 0.876520 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.14818 | −0.270397 | ||||||||
\(518\) | 11.0031 | 0.483447 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 12.2137 | 0.535605 | ||||||||
\(521\) | −23.3356 | −1.02235 | −0.511175 | − | 0.859476i | \(-0.670790\pi\) | ||||
−0.511175 | + | 0.859476i | \(0.670790\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.0766 | −1.18398 | −0.591989 | − | 0.805946i | \(-0.701657\pi\) | ||||
−0.591989 | + | 0.805946i | \(0.701657\pi\) | |||||||
\(524\) | 3.81504 | 0.166661 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.8311 | 1.08269 | ||||||||
\(527\) | 39.2690 | 1.71059 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.41552 | −0.148501 | ||||||||
\(530\) | 25.8328 | 1.12210 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.30278 | −0.229905 | ||||||||
\(533\) | 28.5916 | 1.23844 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.78871 | 0.120566 | ||||||||
\(536\) | −14.8561 | −0.641686 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.21483 | 0.311054 | ||||||||
\(539\) | −16.3070 | −0.702391 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.3614 | −1.39132 | −0.695662 | − | 0.718369i | \(-0.744889\pi\) | ||||
−0.695662 | + | 0.718369i | \(0.744889\pi\) | |||||||
\(542\) | −16.0375 | −0.688868 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.68172 | 0.200727 | ||||||||
\(545\) | 35.8374 | 1.53510 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.0227 | −1.32644 | −0.663218 | − | 0.748426i | \(-0.730810\pi\) | ||||
−0.663218 | + | 0.748426i | \(0.730810\pi\) | |||||||
\(548\) | 8.93528 | 0.381696 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 25.4948 | 1.08710 | ||||||||
\(551\) | −21.0270 | −0.895780 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.39232 | 0.356878 | ||||||||
\(554\) | −20.3652 | −0.865234 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11.9035 | 0.504819 | ||||||||
\(557\) | 3.24463 | 0.137479 | 0.0687397 | − | 0.997635i | \(-0.478102\pi\) | ||||
0.0687397 | + | 0.997635i | \(0.478102\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −30.8792 | −1.30605 | ||||||||
\(560\) | −6.05608 | −0.255916 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −32.1042 | −1.35423 | ||||||||
\(563\) | −24.0563 | −1.01385 | −0.506925 | − | 0.861990i | \(-0.669218\pi\) | ||||
−0.506925 | + | 0.861990i | \(0.669218\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −52.0385 | −2.18928 | ||||||||
\(566\) | −9.53278 | −0.400693 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.49039 | −0.356249 | ||||||||
\(569\) | −22.6225 | −0.948384 | −0.474192 | − | 0.880421i | \(-0.657260\pi\) | ||||
−0.474192 | + | 0.880421i | \(0.657260\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0927 | −0.422367 | −0.211184 | − | 0.977446i | \(-0.567732\pi\) | ||||
−0.211184 | + | 0.977446i | \(0.567732\pi\) | |||||||
\(572\) | 17.6154 | 0.736537 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −14.1770 | −0.591736 | ||||||||
\(575\) | 24.1826 | 1.00848 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.9585 | −1.41371 | −0.706856 | − | 0.707358i | \(-0.749887\pi\) | ||||
−0.706856 | + | 0.707358i | \(0.749887\pi\) | |||||||
\(578\) | 4.91849 | 0.204582 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −24.0140 | −0.997128 | ||||||||
\(581\) | −20.9580 | −0.869483 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 37.2578 | 1.54306 | ||||||||
\(584\) | −16.8516 | −0.697326 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −19.7079 | −0.814124 | ||||||||
\(587\) | 12.2053 | 0.503767 | 0.251883 | − | 0.967758i | \(-0.418950\pi\) | ||||
0.251883 | + | 0.967758i | \(0.418950\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.7583 | 0.978944 | ||||||||
\(590\) | 0.0361912 | 0.00148997 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.87734 | −0.241557 | ||||||||
\(593\) | 17.2868 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −28.3529 | −1.16235 | ||||||||
\(596\) | −1.00000 | −0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 16.7087 | 0.683271 | ||||||||
\(599\) | 32.9099 | 1.34466 | 0.672331 | − | 0.740251i | \(-0.265293\pi\) | ||||
0.672331 | + | 0.740251i | \(0.265293\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.5213 | 1.53053 | 0.765263 | − | 0.643718i | \(-0.222609\pi\) | ||||
0.765263 | + | 0.643718i | \(0.222609\pi\) | |||||||
\(602\) | 15.3113 | 0.624042 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −19.5730 | −0.796413 | ||||||||
\(605\) | 34.8317 | 1.41611 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.3048 | 1.39239 | 0.696194 | − | 0.717854i | \(-0.254875\pi\) | ||||
0.696194 | + | 0.717854i | \(0.254875\pi\) | |||||||
\(608\) | 2.83250 | 0.114873 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −43.7706 | −1.77222 | ||||||||
\(611\) | −4.97542 | −0.201284 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −46.8061 | −1.89048 | −0.945241 | − | 0.326373i | \(-0.894174\pi\) | ||||
−0.945241 | + | 0.326373i | \(0.894174\pi\) | |||||||
\(614\) | 32.3057 | 1.30375 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.73450 | −0.351923 | ||||||||
\(617\) | −28.3845 | −1.14272 | −0.571359 | − | 0.820700i | \(-0.693583\pi\) | ||||
−0.571359 | + | 0.820700i | \(0.693583\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.0578 | 0.725803 | 0.362901 | − | 0.931828i | \(-0.381786\pi\) | ||||
0.362901 | + | 0.931828i | \(0.381786\pi\) | |||||||
\(620\) | 27.1333 | 1.08970 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.6783 | 0.428163 | ||||||||
\(623\) | −13.7060 | −0.549120 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.4620 | −0.898482 | ||||||||
\(626\) | −1.11853 | −0.0447054 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.16484 | 0.325812 | ||||||||
\(629\) | −27.5160 | −1.09714 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.5705 | −1.53547 | −0.767734 | − | 0.640769i | \(-0.778616\pi\) | ||||
−0.767734 | + | 0.640769i | \(0.778616\pi\) | |||||||
\(632\) | −4.48279 | −0.178316 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −16.0206 | −0.636261 | ||||||||
\(635\) | 16.6995 | 0.662699 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.1964 | −0.522862 | ||||||||
\(638\) | −34.6347 | −1.37120 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.23488 | 0.127870 | ||||||||
\(641\) | −32.2745 | −1.27477 | −0.637383 | − | 0.770547i | \(-0.719983\pi\) | ||||
−0.637383 | + | 0.770547i | \(0.719983\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.0476 | 0.475111 | 0.237556 | − | 0.971374i | \(-0.423654\pi\) | ||||
0.237556 | + | 0.971374i | \(0.423654\pi\) | |||||||
\(644\) | −8.28494 | −0.326472 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13.2610 | 0.521747 | ||||||||
\(647\) | −3.15117 | −0.123885 | −0.0619427 | − | 0.998080i | \(-0.519730\pi\) | ||||
−0.0619427 | + | 0.998080i | \(0.519730\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.0521974 | 0.00204893 | ||||||||
\(650\) | 20.6317 | 0.809240 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.7237 | −0.576623 | ||||||||
\(653\) | 31.4558 | 1.23096 | 0.615480 | − | 0.788152i | \(-0.288962\pi\) | ||||
0.615480 | + | 0.788152i | \(0.288962\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.3412 | 0.482211 | ||||||||
\(656\) | 7.57269 | 0.295664 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.46703 | 0.0961750 | ||||||||
\(659\) | 29.5585 | 1.15144 | 0.575718 | − | 0.817648i | \(-0.304723\pi\) | ||||
0.575718 | + | 0.817648i | \(0.304723\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.95740 | 0.192820 | 0.0964102 | − | 0.995342i | \(-0.469264\pi\) | ||||
0.0964102 | + | 0.995342i | \(0.469264\pi\) | |||||||
\(662\) | −0.490745 | −0.0190734 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.1948 | 0.434442 | ||||||||
\(665\) | −17.1539 | −0.665198 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −32.8521 | −1.27204 | ||||||||
\(668\) | 3.40133 | 0.131601 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −48.0577 | −1.85663 | ||||||||
\(671\) | −63.1289 | −2.43707 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.5689 | 1.56381 | 0.781907 | − | 0.623395i | \(-0.214247\pi\) | ||||
0.781907 | + | 0.623395i | \(0.214247\pi\) | |||||||
\(674\) | 10.6204 | 0.409084 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.25528 | 0.0482799 | ||||||||
\(677\) | −3.47343 | −0.133495 | −0.0667473 | − | 0.997770i | \(-0.521262\pi\) | ||||
−0.0667473 | + | 0.997770i | \(0.521262\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 23.3004 | 0.894187 | ||||||||
\(680\) | 15.1448 | 0.580777 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 39.1336 | 1.49850 | ||||||||
\(683\) | −25.7397 | −0.984904 | −0.492452 | − | 0.870340i | \(-0.663899\pi\) | ||||
−0.492452 | + | 0.870340i | \(0.663899\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.9046 | 1.10439 | ||||||||
\(686\) | 19.6482 | 0.750172 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8.17859 | −0.311806 | ||||||||
\(689\) | 30.1509 | 1.14866 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.3628 | 0.736595 | 0.368298 | − | 0.929708i | \(-0.379941\pi\) | ||||
0.368298 | + | 0.929708i | \(0.379941\pi\) | |||||||
\(692\) | −12.3853 | −0.470817 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.6395 | −0.707547 | ||||||||
\(695\) | 38.5063 | 1.46063 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 35.4532 | 1.34289 | ||||||||
\(698\) | 25.5174 | 0.965846 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −10.2301 | −0.386661 | ||||||||
\(701\) | 21.6490 | 0.817673 | 0.408837 | − | 0.912608i | \(-0.365935\pi\) | ||||
0.408837 | + | 0.912608i | \(0.365935\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.6476 | −0.627876 | ||||||||
\(704\) | 4.66557 | 0.175840 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.63419 | 0.174410 | ||||||||
\(707\) | 6.58738 | 0.247744 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.2314 | 1.39825 | 0.699127 | − | 0.714998i | \(-0.253572\pi\) | ||||
0.699127 | + | 0.714998i | \(0.253572\pi\) | |||||||
\(710\) | −27.4654 | −1.03076 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.32113 | 0.274371 | ||||||||
\(713\) | 37.1194 | 1.39013 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 56.9837 | 2.13107 | ||||||||
\(716\) | 4.42416 | 0.165339 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.43020 | 0.165333 | ||||||||
\(719\) | −1.16406 | −0.0434119 | −0.0217060 | − | 0.999764i | \(-0.506910\pi\) | ||||
−0.0217060 | + | 0.999764i | \(0.506910\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.5117 | −0.428719 | ||||||||
\(722\) | −10.9769 | −0.408519 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.56556 | 0.206842 | ||||||||
\(725\) | −40.5651 | −1.50655 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.1336 | −0.375836 | −0.187918 | − | 0.982185i | \(-0.560174\pi\) | ||||
−0.187918 | + | 0.982185i | \(0.560174\pi\) | |||||||
\(728\) | −7.06840 | −0.261972 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −54.5130 | −2.01762 | ||||||||
\(731\) | −38.2899 | −1.41620 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 53.0744 | 1.96035 | 0.980173 | − | 0.198144i | \(-0.0634912\pi\) | ||||
0.980173 | + | 0.198144i | \(0.0634912\pi\) | |||||||
\(734\) | −2.04147 | −0.0753522 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.42544 | 0.163124 | ||||||||
\(737\) | −69.3122 | −2.55315 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.42744 | 0.0892947 | 0.0446473 | − | 0.999003i | \(-0.485784\pi\) | ||||
0.0446473 | + | 0.999003i | \(0.485784\pi\) | |||||||
\(740\) | −19.0125 | −0.698913 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −14.9502 | −0.548838 | ||||||||
\(743\) | −26.3368 | −0.966205 | −0.483103 | − | 0.875564i | \(-0.660490\pi\) | ||||
−0.483103 | + | 0.875564i | \(0.660490\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.23488 | −0.118517 | ||||||||
\(746\) | −7.59725 | −0.278155 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 21.8429 | 0.798655 | ||||||||
\(749\) | −1.61390 | −0.0589708 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.9669 | 0.838074 | 0.419037 | − | 0.907969i | \(-0.362368\pi\) | ||||
0.419037 | + | 0.907969i | \(0.362368\pi\) | |||||||
\(752\) | −1.31778 | −0.0480544 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −28.0282 | −1.02073 | ||||||||
\(755\) | −63.3163 | −2.30431 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.6173 | 0.494930 | 0.247465 | − | 0.968897i | \(-0.420402\pi\) | ||||
0.247465 | + | 0.968897i | \(0.420402\pi\) | |||||||
\(758\) | −15.5108 | −0.563377 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9.16281 | 0.332370 | ||||||||
\(761\) | −9.75835 | −0.353740 | −0.176870 | − | 0.984234i | \(-0.556597\pi\) | ||||
−0.176870 | + | 0.984234i | \(0.556597\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.7401 | −0.750842 | ||||||||
\(764\) | −19.4431 | −0.703427 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.4202 | 0.665548 | ||||||||
\(767\) | 0.0422408 | 0.00152523 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.0007 | −0.613061 | −0.306531 | − | 0.951861i | \(-0.599168\pi\) | ||||
−0.306531 | + | 0.951861i | \(0.599168\pi\) | |||||||
\(770\) | −28.2551 | −1.01824 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 18.1823 | 0.654397 | ||||||||
\(773\) | −3.43559 | −0.123570 | −0.0617849 | − | 0.998089i | \(-0.519679\pi\) | ||||
−0.0617849 | + | 0.998089i | \(0.519679\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 45.8344 | 1.64642 | ||||||||
\(776\) | −12.4460 | −0.446785 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.57147 | −0.0563398 | ||||||||
\(779\) | 21.4497 | 0.768515 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −39.6125 | −1.41745 | ||||||||
\(782\) | 20.7186 | 0.740897 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.49517 | −0.124828 | ||||||||
\(785\) | 26.4123 | 0.942694 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 42.5941 | 1.51832 | 0.759158 | − | 0.650906i | \(-0.225611\pi\) | ||||
0.759158 | + | 0.650906i | \(0.225611\pi\) | |||||||
\(788\) | 3.60218 | 0.128323 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −14.5013 | −0.515933 | ||||||||
\(791\) | 30.1162 | 1.07081 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −51.0871 | −1.81416 | ||||||||
\(794\) | −14.4991 | −0.514553 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.7345 | 0.380474 | ||||||||
\(797\) | −21.1891 | −0.750558 | −0.375279 | − | 0.926912i | \(-0.622453\pi\) | ||||
−0.375279 | + | 0.926912i | \(0.622453\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.16946 | −0.218260 | ||||||||
\(800\) | 5.46445 | 0.193197 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −30.5872 | −1.08007 | ||||||||
\(803\) | −78.6225 | −2.77453 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −26.8008 | −0.944604 | ||||||||
\(806\) | 31.6689 | 1.11549 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.51868 | −0.123787 | ||||||||
\(809\) | 30.0685 | 1.05715 | 0.528577 | − | 0.848885i | \(-0.322726\pi\) | ||||
0.528577 | + | 0.848885i | \(0.322726\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.7888 | 0.835337 | 0.417669 | − | 0.908599i | \(-0.362847\pi\) | ||||
0.417669 | + | 0.908599i | \(0.362847\pi\) | |||||||
\(812\) | 13.8976 | 0.487710 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −27.4211 | −0.961110 | ||||||||
\(815\) | −47.6293 | −1.66838 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23.1659 | −0.810472 | ||||||||
\(818\) | −7.58789 | −0.265304 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 24.4967 | 0.855464 | ||||||||
\(821\) | 14.5095 | 0.506385 | 0.253193 | − | 0.967416i | \(-0.418519\pi\) | ||||
0.253193 | + | 0.967416i | \(0.418519\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.563994 | −0.0196596 | −0.00982980 | − | 0.999952i | \(-0.503129\pi\) | ||||
−0.00982980 | + | 0.999952i | \(0.503129\pi\) | |||||||
\(824\) | 6.14904 | 0.214212 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.0209449 | −0.000728765 0 | ||||||||
\(827\) | 7.59775 | 0.264200 | 0.132100 | − | 0.991236i | \(-0.457828\pi\) | ||||
0.132100 | + | 0.991236i | \(0.457828\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.7016 | −0.614803 | −0.307401 | − | 0.951580i | \(-0.599459\pi\) | ||||
−0.307401 | + | 0.951580i | \(0.599459\pi\) | |||||||
\(830\) | 36.2138 | 1.25700 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.77562 | 0.130896 | ||||||||
\(833\) | −16.3634 | −0.566959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.0029 | 0.380771 | ||||||||
\(836\) | 13.2152 | 0.457059 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 34.4523 | 1.19013 | ||||||||
\(839\) | 52.2507 | 1.80389 | 0.901947 | − | 0.431846i | \(-0.142138\pi\) | ||||
0.901947 | + | 0.431846i | \(0.142138\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.1078 | 0.900270 | ||||||||
\(842\) | −26.9298 | −0.928063 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 19.4045 | 0.667929 | ||||||||
\(845\) | 4.06067 | 0.139691 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.1581 | −0.692641 | ||||||||
\(848\) | 7.98570 | 0.274230 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 25.5830 | 0.877490 | ||||||||
\(851\) | −26.0098 | −0.891604 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −50.6035 | −1.73263 | −0.866315 | − | 0.499497i | \(-0.833518\pi\) | ||||
−0.866315 | + | 0.499497i | \(0.833518\pi\) | |||||||
\(854\) | 25.3313 | 0.866819 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.862074 | 0.0294651 | ||||||||
\(857\) | −21.6346 | −0.739023 | −0.369511 | − | 0.929226i | \(-0.620475\pi\) | ||||
−0.369511 | + | 0.929226i | \(0.620475\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.1183 | −0.857025 | −0.428513 | − | 0.903536i | \(-0.640962\pi\) | ||||
−0.428513 | + | 0.903536i | \(0.640962\pi\) | |||||||
\(860\) | −26.4568 | −0.902168 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 11.5963 | 0.394973 | ||||||||
\(863\) | 16.4271 | 0.559185 | 0.279593 | − | 0.960119i | \(-0.409801\pi\) | ||||
0.279593 | + | 0.960119i | \(0.409801\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −40.0649 | −1.36225 | ||||||||
\(866\) | 39.6098 | 1.34599 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −15.7028 | −0.532989 | ||||||||
\(869\) | −20.9148 | −0.709486 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −56.0910 | −1.90057 | ||||||||
\(872\) | 11.0784 | 0.375163 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 12.5351 | 0.424005 | ||||||||
\(875\) | −2.81273 | −0.0950877 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32.2537 | −1.08913 | −0.544565 | − | 0.838719i | \(-0.683305\pi\) | ||||
−0.544565 | + | 0.838719i | \(0.683305\pi\) | |||||||
\(878\) | 20.9278 | 0.706278 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 15.0926 | 0.508770 | ||||||||
\(881\) | −12.5362 | −0.422355 | −0.211177 | − | 0.977448i | \(-0.567730\pi\) | ||||
−0.211177 | + | 0.977448i | \(0.567730\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 53.2761 | 1.79288 | 0.896441 | − | 0.443162i | \(-0.146143\pi\) | ||||
0.896441 | + | 0.443162i | \(0.146143\pi\) | |||||||
\(884\) | 17.6764 | 0.594521 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.11587 | 0.205467 | ||||||||
\(887\) | −28.0539 | −0.941957 | −0.470979 | − | 0.882145i | \(-0.656099\pi\) | ||||
−0.470979 | + | 0.882145i | \(0.656099\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.66447 | −0.324136 | ||||||||
\(890\) | 23.6830 | 0.793855 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.0723012 | 0.00242082 | ||||||||
\(893\) | −3.73261 | −0.124907 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.3116 | 0.478385 | ||||||||
\(896\) | −1.87212 | −0.0625431 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15.0463 | −0.502102 | ||||||||
\(899\) | −62.2661 | −2.07669 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.3868 | 1.24554 | ||||||||
\(902\) | 35.3309 | 1.17639 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −16.0867 | −0.535035 | ||||||||
\(905\) | 18.0039 | 0.598471 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 46.8565 | 1.55585 | 0.777923 | − | 0.628360i | \(-0.216273\pi\) | ||||
0.777923 | + | 0.628360i | \(0.216273\pi\) | |||||||
\(908\) | −11.1563 | −0.370236 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −22.8654 | −0.757981 | ||||||||
\(911\) | 33.7262 | 1.11740 | 0.558699 | − | 0.829371i | \(-0.311301\pi\) | ||||
0.558699 | + | 0.829371i | \(0.311301\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 52.2301 | 1.72856 | ||||||||
\(914\) | −20.2281 | −0.669085 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.4325 | 0.609028 | ||||||||
\(917\) | −7.14221 | −0.235857 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.8406 | 0.423572 | 0.211786 | − | 0.977316i | \(-0.432072\pi\) | ||||
0.211786 | + | 0.977316i | \(0.432072\pi\) | |||||||
\(920\) | 14.3158 | 0.471976 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.16604 | −0.170134 | ||||||||
\(923\) | −32.0564 | −1.05515 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32.1164 | −1.05598 | ||||||||
\(926\) | −24.7033 | −0.811801 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.42347 | −0.243687 | ||||||||
\(929\) | −52.1975 | −1.71254 | −0.856272 | − | 0.516526i | \(-0.827225\pi\) | ||||
−0.856272 | + | 0.516526i | \(0.827225\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.90009 | −0.324462 | ||||||||
\(932\) | 15.3706 | 0.503481 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −41.0322 | −1.34262 | ||||||||
\(935\) | 70.6591 | 2.31080 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.26863 | 0.270124 | 0.135062 | − | 0.990837i | \(-0.456877\pi\) | ||||
0.135062 | + | 0.990837i | \(0.456877\pi\) | |||||||
\(938\) | 27.8124 | 0.908107 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.26285 | −0.139039 | ||||||||
\(941\) | 3.85862 | 0.125787 | 0.0628937 | − | 0.998020i | \(-0.479967\pi\) | ||||
0.0628937 | + | 0.998020i | \(0.479967\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 33.5125 | 1.09132 | ||||||||
\(944\) | 0.0111878 | 0.000364132 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −38.1578 | −1.24062 | ||||||||
\(947\) | 48.1525 | 1.56475 | 0.782373 | − | 0.622810i | \(-0.214009\pi\) | ||||
0.782373 | + | 0.622810i | \(0.214009\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −63.6253 | −2.06536 | ||||||||
\(950\) | 15.4781 | 0.502175 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.76473 | −0.284067 | ||||||||
\(953\) | −37.1054 | −1.20196 | −0.600981 | − | 0.799263i | \(-0.705223\pi\) | ||||
−0.600981 | + | 0.799263i | \(0.705223\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −62.8961 | −2.03527 | ||||||||
\(956\) | −10.1084 | −0.326929 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.10686 | 0.294229 | ||||||||
\(959\) | −16.7279 | −0.540172 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 39.3542 | 1.26949 | ||||||||
\(962\) | −22.1906 | −0.715453 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.3305 | 0.332724 | ||||||||
\(965\) | 58.8177 | 1.89341 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.85309 | 0.123907 | 0.0619536 | − | 0.998079i | \(-0.480267\pi\) | ||||
0.0619536 | + | 0.998079i | \(0.480267\pi\) | |||||||
\(968\) | 10.7675 | 0.346082 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −40.2613 | −1.29271 | ||||||||
\(971\) | −18.2980 | −0.587211 | −0.293605 | − | 0.955927i | \(-0.594855\pi\) | ||||
−0.293605 | + | 0.955927i | \(0.594855\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.2847 | −0.714415 | ||||||||
\(974\) | 18.5260 | 0.593613 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.5308 | −0.433111 | ||||||||
\(977\) | 45.3303 | 1.45024 | 0.725122 | − | 0.688621i | \(-0.241783\pi\) | ||||
0.725122 | + | 0.688621i | \(0.241783\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 34.1573 | 1.09167 | ||||||||
\(980\) | −11.3065 | −0.361172 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −31.1935 | −0.995424 | ||||||||
\(983\) | 59.1676 | 1.88715 | 0.943577 | − | 0.331154i | \(-0.107438\pi\) | ||||
0.943577 | + | 0.331154i | \(0.107438\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.6526 | 0.371284 | ||||||||
\(986\) | −34.7546 | −1.10681 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.6944 | 0.340236 | ||||||||
\(989\) | −36.1938 | −1.15090 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.4592 | 0.395780 | 0.197890 | − | 0.980224i | \(-0.436591\pi\) | ||||
0.197890 | + | 0.980224i | \(0.436591\pi\) | |||||||
\(992\) | 8.38774 | 0.266311 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 15.8950 | 0.504159 | ||||||||
\(995\) | 34.7248 | 1.10085 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.2829 | 0.389003 | 0.194502 | − | 0.980902i | \(-0.437691\pi\) | ||||
0.194502 | + | 0.980902i | \(0.437691\pi\) | |||||||
\(998\) | −3.12704 | −0.0989847 | ||||||||
\(999\) | 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.t.1.14 | yes | 16 | |
3.2 | odd | 2 | 8046.2.a.s.1.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.s.1.3 | ✓ | 16 | 3.2 | odd | 2 | ||
8046.2.a.t.1.14 | yes | 16 | 1.1 | even | 1 | trivial |