Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7744,2,Mod(1,7744)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7744, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7744.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7744 = 2^{6} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7744.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: | \(61.8361513253\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.5225.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 8x^{2} + x + 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 88) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.88301\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7744.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.04678 | 1.75906 | 0.879528 | − | 0.475846i | \(-0.157858\pi\) | ||||
0.879528 | + | 0.475846i | \(0.157858\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.78180 | −0.796845 | −0.398422 | − | 0.917202i | \(-0.630442\pi\) | ||||
−0.398422 | + | 0.917202i | \(0.630442\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.353057 | 0.133443 | 0.0667215 | − | 0.997772i | \(-0.478746\pi\) | ||||
0.0667215 | + | 0.997772i | \(0.478746\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.28284 | 2.09428 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.54782 | −1.53869 | −0.769344 | − | 0.638834i | \(-0.779417\pi\) | ||||
−0.769344 | + | 0.638834i | \(0.779417\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.42874 | −1.40170 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.81280 | −0.924739 | −0.462370 | − | 0.886687i | \(-0.653001\pi\) | ||||
−0.462370 | + | 0.886687i | \(0.653001\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.61803 | −1.05945 | −0.529725 | − | 0.848170i | \(-0.677705\pi\) | ||||
−0.529725 | + | 0.848170i | \(0.677705\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.07569 | 0.234734 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.00209 | 1.46004 | 0.730018 | − | 0.683428i | \(-0.239511\pi\) | ||||
0.730018 | + | 0.683428i | \(0.239511\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.82519 | −0.365039 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 10.0021 | 1.92490 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.11908 | 0.393503 | 0.196752 | − | 0.980453i | \(-0.436961\pi\) | ||||
0.196752 | + | 0.980453i | \(0.436961\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.45427 | −0.620405 | −0.310203 | − | 0.950670i | \(-0.600397\pi\) | ||||
−0.310203 | + | 0.950670i | \(0.600397\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.629076 | −0.106333 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.74050 | 0.286136 | 0.143068 | − | 0.989713i | \(-0.454303\pi\) | ||||
0.143068 | + | 0.989713i | \(0.454303\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −16.9030 | −2.70664 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.48318 | 0.231634 | 0.115817 | − | 0.993271i | \(-0.463051\pi\) | ||||
0.115817 | + | 0.993271i | \(0.463051\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.92979 | 0.599287 | 0.299643 | − | 0.954051i | \(-0.403132\pi\) | ||||
0.299643 | + | 0.954051i | \(0.403132\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −11.1948 | −1.66882 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.21054 | 0.176576 | 0.0882878 | − | 0.996095i | \(-0.471860\pi\) | ||||
0.0882878 | + | 0.996095i | \(0.471860\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.87535 | −0.982193 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.6167 | −1.62667 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.92641 | −1.08878 | −0.544388 | − | 0.838834i | \(-0.683238\pi\) | ||||
−0.544388 | + | 0.838834i | \(0.683238\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −14.0701 | −1.86363 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.09017 | −0.402306 | −0.201153 | − | 0.979560i | \(-0.564469\pi\) | ||||
−0.201153 | + | 0.979560i | \(0.564469\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.60564 | −0.973802 | −0.486901 | − | 0.873457i | \(-0.661873\pi\) | ||||
−0.486901 | + | 0.873457i | \(0.661873\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.21820 | 0.279467 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.88510 | 1.22610 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.17352 | 0.143368 | 0.0716839 | − | 0.997427i | \(-0.477163\pi\) | ||||
0.0716839 | + | 0.997427i | \(0.477163\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 21.3338 | 2.56829 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.36957 | 0.281216 | 0.140608 | − | 0.990065i | \(-0.455094\pi\) | ||||
0.140608 | + | 0.990065i | \(0.455094\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.90426 | −0.456959 | −0.228480 | − | 0.973549i | \(-0.573375\pi\) | ||||
−0.228480 | + | 0.973549i | \(0.573375\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.56095 | −0.642124 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.10933 | 0.462336 | 0.231168 | − | 0.972914i | \(-0.425745\pi\) | ||||
0.231168 | + | 0.972914i | \(0.425745\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 11.6256 | 1.29173 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.818368 | −0.0898276 | −0.0449138 | − | 0.998991i | \(-0.514301\pi\) | ||||
−0.0449138 | + | 0.998991i | \(0.514301\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.79364 | 0.736874 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.45636 | 0.692194 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.92979 | −0.204557 | −0.102279 | − | 0.994756i | \(-0.532613\pi\) | ||||
−0.102279 | + | 0.994756i | \(0.532613\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.95870 | −0.205327 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.5244 | −1.09133 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.22841 | 0.844217 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.47761 | −0.962305 | −0.481153 | − | 0.876637i | \(-0.659782\pi\) | ||||
−0.481153 | + | 0.876637i | \(0.659782\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.4053 | −1.43338 | −0.716691 | − | 0.697391i | \(-0.754344\pi\) | ||||
−0.716691 | + | 0.697391i | \(0.754344\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.02553 | −0.790779 | −0.395389 | − | 0.918514i | \(-0.629390\pi\) | ||||
−0.395389 | + | 0.918514i | \(0.629390\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.91665 | −0.187046 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.57464 | −0.442247 | −0.221124 | − | 0.975246i | \(-0.570972\pi\) | ||||
−0.221124 | + | 0.975246i | \(0.570972\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −20.6592 | −1.97880 | −0.989398 | − | 0.145228i | \(-0.953608\pi\) | ||||
−0.989398 | + | 0.145228i | \(0.953608\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.30290 | 0.503329 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.80514 | 0.828318 | 0.414159 | − | 0.910205i | \(-0.364076\pi\) | ||||
0.414159 | + | 0.910205i | \(0.364076\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.4763 | −1.16342 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −34.8561 | −3.22245 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.34613 | −0.123400 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.51891 | 0.407457 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1611 | 1.08772 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.7927 | 1.57885 | 0.789425 | − | 0.613847i | \(-0.210379\pi\) | ||||
0.789425 | + | 0.613847i | \(0.210379\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.9732 | 1.05418 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.3585 | −1.60399 | −0.801996 | − | 0.597329i | \(-0.796229\pi\) | ||||
−0.801996 | + | 0.597329i | \(0.796229\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.63043 | −0.141376 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −17.8217 | −1.53385 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.4776 | −1.15147 | −0.575735 | − | 0.817636i | \(-0.695284\pi\) | ||||
−0.575735 | + | 0.817636i | \(0.695284\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.2704 | −1.21040 | −0.605202 | − | 0.796072i | \(-0.706908\pi\) | ||||
−0.605202 | + | 0.796072i | \(0.706908\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.68825 | 0.310606 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.77577 | −0.313561 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −20.9477 | −1.72773 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.2029 | −0.835853 | −0.417926 | − | 0.908481i | \(-0.637243\pi\) | ||||
−0.417926 | + | 0.908481i | \(0.637243\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.38879 | 0.357155 | 0.178577 | − | 0.983926i | \(-0.442851\pi\) | ||||
0.178577 | + | 0.983926i | \(0.442851\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −23.9552 | −1.93666 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.15481 | 0.494366 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.1811 | −1.77024 | −0.885121 | − | 0.465360i | \(-0.845925\pi\) | ||||
−0.885121 | + | 0.465360i | \(0.845925\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −24.1500 | −1.91522 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.47214 | 0.194832 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.7302 | 1.54539 | 0.772694 | − | 0.634779i | \(-0.218909\pi\) | ||||
0.772694 | + | 0.634779i | \(0.218909\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.988897 | −0.0765232 | −0.0382616 | − | 0.999268i | \(-0.512182\pi\) | ||||
−0.0382616 | + | 0.999268i | \(0.512182\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.7783 | 1.36756 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −29.0144 | −2.21879 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.4998 | −1.33048 | −0.665241 | − | 0.746629i | \(-0.731671\pi\) | ||||
−0.665241 | + | 0.746629i | \(0.731671\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.644397 | −0.0487118 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.41506 | −0.707679 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.85201 | −0.213169 | −0.106585 | − | 0.994304i | \(-0.533992\pi\) | ||||
−0.106585 | + | 0.994304i | \(0.533992\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.10256 | 0.156282 | 0.0781412 | − | 0.996942i | \(-0.475102\pi\) | ||||
0.0781412 | + | 0.996942i | \(0.475102\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −23.1727 | −1.71297 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.10121 | −0.228006 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.53131 | 0.256865 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.1212 | 1.23884 | 0.619422 | − | 0.785058i | \(-0.287367\pi\) | ||||
0.619422 | + | 0.785058i | \(0.287367\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.1288 | −1.44890 | −0.724452 | − | 0.689325i | \(-0.757907\pi\) | ||||
−0.724452 | + | 0.689325i | \(0.757907\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 30.1177 | 2.15677 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.5589 | 0.894786 | 0.447393 | − | 0.894337i | \(-0.352352\pi\) | ||||
0.447393 | + | 0.894337i | \(0.352352\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.32962 | 0.236031 | 0.118015 | − | 0.993012i | \(-0.462347\pi\) | ||||
0.118015 | + | 0.993012i | \(0.462347\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.57544 | 0.252192 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.748155 | 0.0525102 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.64273 | −0.184576 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 43.9930 | 3.05773 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.0944 | 1.65872 | 0.829362 | − | 0.558712i | \(-0.188704\pi\) | ||||
0.829362 | + | 0.558712i | \(0.188704\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.21955 | 0.494676 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.00209 | −0.477539 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.21955 | −0.0827887 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.8954 | −0.803817 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.1527 | 1.42289 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.529216 | −0.0354389 | −0.0177195 | − | 0.999843i | \(-0.505641\pi\) | ||||
−0.0177195 | + | 0.999843i | \(0.505641\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.4674 | −0.764493 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.6800 | 0.841603 | 0.420802 | − | 0.907153i | \(-0.361749\pi\) | ||||
0.420802 | + | 0.907153i | \(0.361749\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.10256 | 0.403269 | 0.201634 | − | 0.979461i | \(-0.435375\pi\) | ||||
0.201634 | + | 0.979461i | \(0.435375\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.49084 | 0.163180 | 0.0815901 | − | 0.996666i | \(-0.474000\pi\) | ||||
0.0815901 | + | 0.996666i | \(0.474000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.15694 | −0.140703 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.5202 | 0.813275 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.3682 | 1.44688 | 0.723439 | − | 0.690389i | \(-0.242560\pi\) | ||||
0.723439 | + | 0.690389i | \(0.242560\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.1025 | 1.55258 | 0.776288 | − | 0.630378i | \(-0.217100\pi\) | ||||
0.776288 | + | 0.630378i | \(0.217100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.41432 | 0.347329 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.2505 | 0.782655 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 25.6200 | 1.63016 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.49338 | −0.158012 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.93108 | −0.437486 | −0.218743 | − | 0.975783i | \(-0.570196\pi\) | ||||
−0.218743 | + | 0.975783i | \(0.570196\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 20.6987 | 1.29620 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.6529 | −0.914021 | −0.457011 | − | 0.889461i | \(-0.651080\pi\) | ||||
−0.457011 | + | 0.889461i | \(0.651080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.614494 | 0.0381828 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.3138 | 0.824106 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −22.9868 | −1.41742 | −0.708712 | − | 0.705497i | \(-0.750724\pi\) | ||||
−0.708712 | + | 0.705497i | \(0.750724\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.1233 | 0.867585 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.87963 | −0.359827 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.54782 | 0.338257 | 0.169128 | − | 0.985594i | \(-0.445905\pi\) | ||||
0.169128 | + | 0.985594i | \(0.445905\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.5355 | −0.822222 | −0.411111 | − | 0.911585i | \(-0.634859\pi\) | ||||
−0.411111 | + | 0.911585i | \(0.634859\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.96771 | −0.361182 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.96005 | −0.177852 | −0.0889260 | − | 0.996038i | \(-0.528343\pi\) | ||||
−0.0889260 | + | 0.996038i | \(0.528343\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −21.7026 | −1.29930 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.96297 | 0.534686 | 0.267343 | − | 0.963601i | \(-0.413854\pi\) | ||||
0.267343 | + | 0.963601i | \(0.413854\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.0407 | −1.07241 | −0.536203 | − | 0.844089i | \(-0.680142\pi\) | ||||
−0.536203 | + | 0.844089i | \(0.680142\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 25.0701 | 1.48503 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.523646 | 0.0309099 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.46257 | −0.144857 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −28.8761 | −1.69275 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.6400 | 1.61475 | 0.807373 | − | 0.590042i | \(-0.200889\pi\) | ||||
0.807373 | + | 0.590042i | \(0.200889\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.50606 | 0.320575 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −38.8463 | −2.24654 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.38744 | 0.0799706 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −43.8897 | −2.52140 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.5517 | 0.775969 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.662166 | −0.0377918 | −0.0188959 | − | 0.999821i | \(-0.506015\pi\) | ||||
−0.0188959 | + | 0.999821i | \(0.506015\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −24.4520 | −1.39102 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.0701 | 0.741138 | 0.370569 | − | 0.928805i | \(-0.379163\pi\) | ||||
0.370569 | + | 0.928805i | \(0.379163\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.8128 | 1.11989 | 0.559943 | − | 0.828531i | \(-0.310823\pi\) | ||||
0.559943 | + | 0.828531i | \(0.310823\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.95239 | −0.222692 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.7391 | 1.10866 | 0.554329 | − | 0.832297i | \(-0.312975\pi\) | ||||
0.554329 | + | 0.832297i | \(0.312975\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.9379 | −0.777938 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.6076 | 0.979715 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.1258 | 0.561681 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −62.9441 | −3.48082 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.427390 | 0.0235628 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.0860 | 1.15899 | 0.579494 | − | 0.814976i | \(-0.303250\pi\) | ||||
0.579494 | + | 0.814976i | \(0.303250\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.9353 | 0.599249 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.09097 | −0.114242 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.38615 | 0.0755082 | 0.0377541 | − | 0.999287i | \(-0.487980\pi\) | ||||
0.0377541 | + | 0.999287i | \(0.487980\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 26.8273 | 1.45706 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.89879 | −0.264510 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −38.0125 | −2.04653 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.1162 | −1.02621 | −0.513104 | − | 0.858326i | \(-0.671505\pi\) | ||||
−0.513104 | + | 0.858326i | \(0.671505\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.7163 | 1.10892 | 0.554460 | − | 0.832211i | \(-0.312925\pi\) | ||||
0.554460 | + | 0.832211i | \(0.312925\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −55.4898 | −2.96183 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.09091 | 0.270962 | 0.135481 | − | 0.990780i | \(-0.456742\pi\) | ||||
0.135481 | + | 0.990780i | \(0.456742\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.22210 | −0.224086 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.10137 | −0.217068 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.12437 | −0.217676 | −0.108838 | − | 0.994060i | \(-0.534713\pi\) | ||||
−0.108838 | + | 0.994060i | \(0.534713\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.32624 | 0.122434 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.95661 | 0.364125 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −36.5018 | −1.90538 | −0.952690 | − | 0.303943i | \(-0.901697\pi\) | ||||
−0.952690 | + | 0.303943i | \(0.901697\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.31858 | 0.485106 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.79847 | −0.145289 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.01741 | −0.259792 | −0.129896 | − | 0.991528i | \(-0.541464\pi\) | ||||
−0.129896 | + | 0.991528i | \(0.541464\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 37.0522 | 1.91337 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.7563 | −0.605479 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.2483 | 1.04009 | 0.520043 | − | 0.854140i | \(-0.325916\pi\) | ||||
0.520043 | + | 0.854140i | \(0.325916\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 54.2105 | 2.77729 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.40321 | 0.480482 | 0.240241 | − | 0.970713i | \(-0.422774\pi\) | ||||
0.240241 | + | 0.970713i | \(0.422774\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 24.6902 | 1.25508 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.76467 | −0.342982 | −0.171491 | − | 0.985186i | \(-0.554859\pi\) | ||||
−0.171491 | + | 0.985186i | \(0.554859\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −26.6976 | −1.35015 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −55.9343 | −2.82151 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.32200 | −0.368410 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.18919 | 0.260438 | 0.130219 | − | 0.991485i | \(-0.458432\pi\) | ||||
0.130219 | + | 0.991485i | \(0.458432\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.96755 | −0.248689 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.88922 | 0.294094 | 0.147047 | − | 0.989130i | \(-0.453023\pi\) | ||||
0.147047 | + | 0.989130i | \(0.453023\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.1637 | 0.954610 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −20.7145 | −1.02931 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.5388 | 1.70783 | 0.853916 | − | 0.520411i | \(-0.174221\pi\) | ||||
0.853916 | + | 0.520411i | \(0.174221\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −41.0633 | −2.02550 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.09101 | −0.0536849 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.45817 | 0.0715786 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −43.4789 | −2.12917 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.32141 | −0.357674 | −0.178837 | − | 0.983879i | \(-0.557233\pi\) | ||||
−0.178837 | + | 0.983879i | \(0.557233\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.8786 | −1.60241 | −0.801203 | − | 0.598392i | \(-0.795806\pi\) | ||||
−0.801203 | + | 0.598392i | \(0.795806\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.60564 | 0.369799 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.95909 | 0.337566 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.68522 | −0.129947 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.21611 | −0.251251 | −0.125626 | − | 0.992078i | \(-0.540094\pi\) | ||||
−0.125626 | + | 0.992078i | \(0.540094\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.0282 | 0.529980 | 0.264990 | − | 0.964251i | \(-0.414631\pi\) | ||||
0.264990 | + | 0.964251i | \(0.414631\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.5039 | −0.551571 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −32.3359 | −1.54684 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.5808 | 1.07772 | 0.538862 | − | 0.842394i | \(-0.318855\pi\) | ||||
0.538862 | + | 0.842394i | \(0.318855\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −43.1968 | −2.05699 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −35.3181 | −1.67801 | −0.839006 | − | 0.544122i | \(-0.816863\pi\) | ||||
−0.839006 | + | 0.544122i | \(0.816863\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.43849 | 0.163000 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −31.0859 | −1.47031 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 37.0598 | 1.74896 | 0.874480 | − | 0.485061i | \(-0.161203\pi\) | ||||
0.874480 | + | 0.485061i | \(0.161203\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.3717 | 0.628255 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.49000 | 0.163614 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.352996 | −0.0165125 | −0.00825624 | − | 0.999966i | \(-0.502628\pi\) | ||||
−0.00825624 | + | 0.999966i | \(0.502628\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −38.1360 | −1.78003 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.2449 | 0.570303 | 0.285151 | − | 0.958482i | \(-0.407956\pi\) | ||||
0.285151 | + | 0.958482i | \(0.407956\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.9578 | −0.973992 | −0.486996 | − | 0.873404i | \(-0.661907\pi\) | ||||
−0.486996 | + | 0.873404i | \(0.661907\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 18.7523 | 0.869619 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 29.5768 | 1.36865 | 0.684325 | − | 0.729177i | \(-0.260097\pi\) | ||||
0.684325 | + | 0.729177i | \(0.260097\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.414318 | 0.0191314 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −67.5808 | −3.11396 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.42880 | 0.386740 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −49.8004 | −2.28020 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.82609 | −0.266201 | −0.133100 | − | 0.991103i | \(-0.542493\pi\) | ||||
−0.133100 | + | 0.991103i | \(0.542493\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.65596 | −0.440274 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.53204 | 0.342720 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.8872 | 0.766808 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.9518 | −1.40256 | −0.701279 | − | 0.712887i | \(-0.747387\pi\) | ||||
−0.701279 | + | 0.712887i | \(0.747387\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 60.1135 | 2.71843 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.6930 | −0.482567 | −0.241284 | − | 0.970455i | \(-0.577568\pi\) | ||||
−0.241284 | + | 0.970455i | \(0.577568\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.07962 | −0.363888 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.836593 | 0.0375263 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.6798 | 1.14958 | 0.574792 | − | 0.818300i | \(-0.305083\pi\) | ||||
0.574792 | + | 0.818300i | \(0.305083\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.01295 | −0.134609 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.2572 | −0.769461 | −0.384731 | − | 0.923029i | \(-0.625706\pi\) | ||||
−0.384731 | + | 0.923029i | \(0.625706\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.6674 | 1.14218 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 54.1666 | 2.40562 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −34.9229 | −1.54793 | −0.773966 | − | 0.633227i | \(-0.781730\pi\) | ||||
−0.773966 | + | 0.633227i | \(0.781730\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.37843 | −0.0609780 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −46.1900 | −2.03934 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.2999 | 0.630128 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −53.3178 | −2.34039 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.96986 | −0.349166 | −0.174583 | − | 0.984642i | \(-0.555858\pi\) | ||||
−0.174583 | + | 0.984642i | \(0.555858\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.8353 | −0.998518 | −0.499259 | − | 0.866453i | \(-0.666394\pi\) | ||||
−0.499259 | + | 0.866453i | \(0.666394\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.96333 | −0.0856869 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.1704 | 0.573713 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 26.0293 | 1.13171 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −19.4151 | −0.842542 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.22841 | −0.356412 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.15109 | 0.352402 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.68944 | −0.374977 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 39.9578 | 1.71792 | 0.858959 | − | 0.512044i | \(-0.171112\pi\) | ||||
0.858959 | + | 0.512044i | \(0.171112\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.40604 | 0.274910 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 36.8106 | 1.57679 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.6384 | 0.711409 | 0.355704 | − | 0.934599i | \(-0.384241\pi\) | ||||
0.355704 | + | 0.934599i | \(0.384241\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −47.7850 | −2.03942 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.78598 | −0.416897 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.45083 | 0.0616954 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.44870 | −0.401075 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.7600 | −0.837258 | −0.418629 | − | 0.908157i | \(-0.637489\pi\) | ||||
−0.418629 | + | 0.908157i | \(0.637489\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.8018 | −0.922116 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −24.2663 | −1.02270 | −0.511352 | − | 0.859371i | \(-0.670855\pi\) | ||||
−0.511352 | + | 0.859371i | \(0.670855\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.6890 | −0.660041 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.10450 | 0.172373 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.4513 | 1.19274 | 0.596371 | − | 0.802709i | \(-0.296609\pi\) | ||||
0.596371 | + | 0.802709i | \(0.296609\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.9485 | 1.12776 | 0.563879 | − | 0.825858i | \(-0.309308\pi\) | ||||
0.563879 | + | 0.825858i | \(0.309308\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 52.1644 | 2.17920 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.7802 | −0.532970 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.8780 | 0.452857 | 0.226428 | − | 0.974028i | \(-0.427295\pi\) | ||||
0.226428 | + | 0.974028i | \(0.427295\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −61.3280 | −2.54871 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.288931 | −0.0119869 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 62.1065 | 2.56779 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.0501 | −1.11648 | −0.558238 | − | 0.829681i | \(-0.688522\pi\) | ||||
−0.558238 | + | 0.829681i | \(0.688522\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.9519 | 0.657288 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 38.2642 | 1.57398 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.72088 | −0.275993 | −0.137997 | − | 0.990433i | \(-0.544066\pi\) | ||||
−0.137997 | + | 0.990433i | \(0.544066\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.39854 | 0.0983306 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.1446 | 0.415191 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.0336 | −1.14542 | −0.572711 | − | 0.819757i | \(-0.694108\pi\) | ||||
−0.572711 | + | 0.819757i | \(0.694108\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.1250 | 0.698544 | 0.349272 | − | 0.937021i | \(-0.386429\pi\) | ||||
0.349272 | + | 0.937021i | \(0.386429\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.37301 | 0.300252 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.5051 | 1.52229 | 0.761143 | − | 0.648584i | \(-0.224638\pi\) | ||||
0.761143 | + | 0.648584i | \(0.224638\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.27946 | 0.0923685 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.71586 | −0.271695 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.6202 | 1.07518 | 0.537590 | − | 0.843207i | \(-0.319335\pi\) | ||||
0.537590 | + | 0.843207i | \(0.319335\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.05179 | −0.324680 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.8616 | 0.558047 | 0.279024 | − | 0.960284i | \(-0.409989\pi\) | ||||
0.279024 | + | 0.960284i | \(0.409989\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.21318 | 0.330116 | 0.165058 | − | 0.986284i | \(-0.447219\pi\) | ||||
0.165058 | + | 0.986284i | \(0.447219\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 70.0355 | 2.81043 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.681325 | −0.0272967 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5427 | −0.501708 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.63616 | −0.264601 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.4638 | −1.57103 | −0.785515 | − | 0.618843i | \(-0.787602\pi\) | ||||
−0.785515 | + | 0.618843i | \(0.787602\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 73.4101 | 2.91779 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −31.7031 | −1.25810 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 38.1432 | 1.51129 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.8876 | 0.588946 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −36.1424 | −1.42754 | −0.713770 | − | 0.700380i | \(-0.753014\pi\) | ||||
−0.713770 | + | 0.700380i | \(0.753014\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.9855 | −0.945895 | −0.472947 | − | 0.881091i | \(-0.656810\pi\) | ||||
−0.472947 | + | 0.881091i | \(0.656810\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −21.3338 | −0.840018 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.5698 | 1.63428 | 0.817139 | − | 0.576440i | \(-0.195559\pi\) | ||||
0.817139 | + | 0.576440i | \(0.195559\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.71571 | −0.145630 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −30.0501 | −1.17595 | −0.587976 | − | 0.808878i | \(-0.700075\pi\) | ||||
−0.587976 | + | 0.808878i | \(0.700075\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 32.7112 | 1.27813 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −24.5299 | −0.957001 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.2450 | −0.983405 | −0.491702 | − | 0.870763i | \(-0.663625\pi\) | ||||
−0.491702 | + | 0.870763i | \(0.663625\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.51852 | −0.370227 | −0.185114 | − | 0.982717i | \(-0.559265\pi\) | ||||
−0.185114 | + | 0.982717i | \(0.559265\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 64.4476 | 2.50294 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.90510 | 0.112655 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.8380 | 0.574529 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.61240 | −0.0623391 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.2923 | −0.435287 | −0.217643 | − | 0.976028i | \(-0.569837\pi\) | ||||
−0.217643 | + | 0.976028i | \(0.569837\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −18.2557 | −0.702664 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −35.4830 | −1.36372 | −0.681862 | − | 0.731481i | \(-0.738830\pi\) | ||||
−0.681862 | + | 0.731481i | \(0.738830\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.34613 | −0.128413 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 38.6332 | 1.48043 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.8947 | 0.952569 | 0.476284 | − | 0.879291i | \(-0.341983\pi\) | ||||
0.476284 | + | 0.879291i | \(0.341983\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.0144 | 0.917543 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.5931 | 0.709373 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 43.9743 | 1.67529 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.634549 | −0.0241394 | −0.0120697 | − | 0.999927i | \(-0.503842\pi\) | ||||
−0.0120697 | + | 0.999927i | \(0.503842\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 25.4271 | 0.964504 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.65506 | −0.214201 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.58903 | 0.287043 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.4622 | 0.659539 | 0.329770 | − | 0.944061i | \(-0.393029\pi\) | ||||
0.329770 | + | 0.944061i | \(0.393029\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.03767 | −0.303146 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.57171 | −0.247505 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.08589 | −0.191275 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32.6051 | −1.22451 | −0.612256 | − | 0.790660i | \(-0.709738\pi\) | ||||
−0.612256 | + | 0.790660i | \(0.709738\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 25.8183 | 0.968261 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24.1871 | −0.905814 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 68.1508 | 2.54514 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34.9849 | 1.30472 | 0.652359 | − | 0.757910i | \(-0.273780\pi\) | ||||
0.652359 | + | 0.757910i | \(0.273780\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.83347 | −0.105524 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 73.4348 | 2.73107 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.86773 | −0.143644 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.2644 | 0.603214 | 0.301607 | − | 0.953432i | \(-0.402477\pi\) | ||||
0.301607 | + | 0.953432i | \(0.402477\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.3806 | −0.680762 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14.9835 | −0.554184 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.0811 | 1.66511 | 0.832553 | − | 0.553945i | \(-0.186878\pi\) | ||||
0.832553 | + | 0.553945i | \(0.186878\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 37.3245 | 1.37674 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.6482 | 0.538843 | 0.269421 | − | 0.963022i | \(-0.413168\pi\) | ||||
0.269421 | + | 0.963022i | \(0.413168\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 78.0585 | 2.86755 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.23352 | 0.155313 | 0.0776564 | − | 0.996980i | \(-0.475256\pi\) | ||||
0.0776564 | + | 0.996980i | \(0.475256\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.1795 | 0.666045 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.14168 | −0.188124 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.61511 | −0.0590148 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.8387 | 0.833397 | 0.416698 | − | 0.909045i | \(-0.363187\pi\) | ||||
0.416698 | + | 0.909045i | \(0.363187\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −21.1174 | −0.769562 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.81994 | −0.284597 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.9973 | 1.12661 | 0.563307 | − | 0.826248i | \(-0.309529\pi\) | ||||
0.563307 | + | 0.826248i | \(0.309529\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.9137 | 1.04812 | 0.524061 | − | 0.851681i | \(-0.324416\pi\) | ||||
0.524061 | + | 0.851681i | \(0.324416\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.29389 | −0.264056 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 42.6834 | 1.54322 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.1437 | 0.619023 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.37741 | −0.193914 | −0.0969571 | − | 0.995289i | \(-0.530911\pi\) | ||||
−0.0969571 | + | 0.995289i | \(0.530911\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −44.6440 | −1.60782 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −44.5996 | −1.60414 | −0.802068 | − | 0.597233i | \(-0.796267\pi\) | ||||
−0.802068 | + | 0.597233i | \(0.796267\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.30471 | 0.226472 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.87222 | 0.0671657 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.84937 | −0.245404 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 21.1952 | 0.757455 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 39.5222 | 1.41061 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.6282 | 1.48389 | 0.741943 | − | 0.670463i | \(-0.233905\pi\) | ||||
0.741943 | + | 0.670463i | \(0.233905\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −70.0355 | −2.49333 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.10871 | 0.110533 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 42.1947 | 1.49838 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 43.0304 | 1.52613 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.04266 | 0.178620 | 0.0893100 | − | 0.996004i | \(-0.471534\pi\) | ||||
0.0893100 | + | 0.996004i | \(0.471534\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.61555 | −0.163286 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.1246 | −0.428400 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.40485 | −0.155251 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.9030 | 0.595013 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.0083 | −0.984718 | −0.492359 | − | 0.870392i | \(-0.663865\pi\) | ||||
−0.492359 | + | 0.870392i | \(0.663865\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.3989 | 1.17279 | 0.586397 | − | 0.810024i | \(-0.300546\pi\) | ||||
0.586397 | + | 0.810024i | \(0.300546\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −41.2396 | −1.44634 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −35.1552 | −1.23143 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.1479 | −0.634914 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.3062 | −0.430013 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.3529 | 1.05932 | 0.529661 | − | 0.848209i | \(-0.322319\pi\) | ||||
0.529661 | + | 0.848209i | \(0.322319\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.75910 | −0.235607 | −0.117804 | − | 0.993037i | \(-0.537585\pi\) | ||||
−0.117804 | + | 0.993037i | \(0.537585\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.8311 | 1.14165 | 0.570825 | − | 0.821072i | \(-0.306623\pi\) | ||||
0.570825 | + | 0.821072i | \(0.306623\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.4529 | −0.536701 | −0.268350 | − | 0.963321i | \(-0.586478\pi\) | ||||
−0.268350 | + | 0.963321i | \(0.586478\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.01860 | −0.312852 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26.2143 | 0.908273 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.76202 | 0.0609771 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −34.5499 | −1.19422 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.9580 | −0.965219 | −0.482609 | − | 0.875836i | \(-0.660311\pi\) | ||||
−0.482609 | + | 0.875836i | \(0.660311\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.5095 | −0.845155 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 27.3082 | 0.940544 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −31.6774 | −1.08974 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −54.9658 | −1.88642 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.1871 | 0.417769 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.0787 | 0.482045 | 0.241023 | − | 0.970520i | \(-0.422517\pi\) | ||||
0.241023 | + | 0.970520i | \(0.422517\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 51.6978 | 1.76803 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.4776 | −0.904457 | −0.452228 | − | 0.891902i | \(-0.649371\pi\) | ||||
−0.452228 | + | 0.891902i | \(0.649371\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −47.5614 | −1.62277 | −0.811387 | − | 0.584510i | \(-0.801287\pi\) | ||||
−0.811387 | + | 0.584510i | \(0.801287\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.59543 | 0.0543722 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −43.4169 | −1.47793 | −0.738964 | − | 0.673745i | \(-0.764684\pi\) | ||||
−0.738964 | + | 0.673745i | \(0.764684\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 31.1810 | 1.06019 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.50290 | −0.254812 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.51045 | −0.220598 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −59.5463 | −2.01534 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.29357 | 0.145149 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.1347 | 0.443527 | 0.221764 | − | 0.975100i | \(-0.428819\pi\) | ||||
0.221764 | + | 0.975100i | \(0.428819\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 84.2128 | 2.84043 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.3388 | −1.22429 | −0.612143 | − | 0.790747i | \(-0.709692\pi\) | ||||
−0.612143 | + | 0.790747i | \(0.709692\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.6371 | 1.13198 | 0.565989 | − | 0.824413i | \(-0.308495\pi\) | ||||
0.565989 | + | 0.824413i | \(0.308495\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16.7757 | 0.563910 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −35.0138 | −1.17565 | −0.587824 | − | 0.808989i | \(-0.700015\pi\) | ||||
−0.587824 | + | 0.808989i | \(0.700015\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.28185 | 0.210686 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.59032 | −0.187073 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.08171 | 0.169863 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −118.356 | −3.95180 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.31987 | −0.244131 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30.2218 | 1.00683 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.22721 | 0.140673 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.74635 | −0.124533 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 51.8416 | 1.72137 | 0.860686 | − | 0.509137i | \(-0.170035\pi\) | ||||
0.860686 | + | 0.509137i | \(0.170035\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −90.5063 | −3.00190 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.6304 | 0.981700 | 0.490850 | − | 0.871244i | \(-0.336686\pi\) | ||||
0.490850 | + | 0.871244i | \(0.336686\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 41.2891 | 1.36497 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.48160 | −0.214041 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30.1065 | −0.993123 | −0.496562 | − | 0.868001i | \(-0.665404\pi\) | ||||
−0.496562 | + | 0.868001i | \(0.665404\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.01747 | −0.0664779 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.1460 | −0.432704 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.17674 | −0.104451 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −50.4231 | −1.65611 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −51.0725 | −1.67564 | −0.837818 | − | 0.545950i | \(-0.816169\pi\) | ||||
−0.837818 | + | 0.545950i | \(0.816169\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 31.7506 | 1.04058 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 39.8217 | 1.30370 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.35131 | 0.272825 | 0.136413 | − | 0.990652i | \(-0.456443\pi\) | ||||
0.136413 | + | 0.990652i | \(0.456443\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 60.3652 | 1.96994 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 53.3937 | 1.74058 | 0.870292 | − | 0.492536i | \(-0.163930\pi\) | ||||
0.870292 | + | 0.492536i | \(0.163930\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.3853 | 0.338193 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.29208 | −0.204681 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.2532 | −0.625646 | −0.312823 | − | 0.949811i | \(-0.601275\pi\) | ||||
−0.312823 | + | 0.949811i | \(0.601275\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.6601 | 0.703118 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 60.1406 | 1.95019 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.6494 | 1.18719 | 0.593595 | − | 0.804764i | \(-0.297708\pi\) | ||||
0.593595 | + | 0.804764i | \(0.297708\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −30.5065 | −0.987167 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.75836 | −0.153656 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.0680 | −0.615098 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −28.7417 | −0.926190 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 35.8655 | 1.15455 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45.6501 | −1.46801 | −0.734004 | − | 0.679146i | \(-0.762351\pi\) | ||||
−0.734004 | + | 0.679146i | \(0.762351\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 53.6465 | 1.72337 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 46.1836 | 1.48210 | 0.741051 | − | 0.671449i | \(-0.234328\pi\) | ||||
0.741051 | + | 0.671449i | \(0.234328\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.03828 | −0.161520 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 30.8512 | 0.988028 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 53.3452 | 1.70666 | 0.853332 | − | 0.521368i | \(-0.174578\pi\) | ||||
0.853332 | + | 0.521368i | \(0.174578\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −129.799 | −4.14416 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.0857 | −0.385475 | −0.192738 | − | 0.981250i | \(-0.561737\pi\) | ||||
−0.192738 | + | 0.981250i | \(0.561737\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.3775 | −0.713006 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.30216 | 0.0414482 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.5167 | 0.874981 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.0620 | 1.14555 | 0.572774 | − | 0.819714i | \(-0.305867\pi\) | ||||
0.572774 | + | 0.819714i | \(0.305867\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 64.2442 | 2.03873 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.93271 | −0.188080 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.32212 | −0.295234 | −0.147617 | − | 0.989045i | \(-0.547160\pi\) | ||||
−0.147617 | + | 0.989045i | \(0.547160\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 17.4086 | 0.550783 |
(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 | 7744.2.a.ds.1.4 | 4 | ||
4.3 | odd | 2 | 7744.2.a.dh.1.1 | 4 | |||
8.3 | odd | 2 | 968.2.a.m.1.4 | 4 | |||
8.5 | even | 2 | 1936.2.a.bc.1.1 | 4 | |||
11.2 | odd | 10 | 704.2.m.i.257.2 | 8 | |||
11.6 | odd | 10 | 704.2.m.i.641.2 | 8 | |||
11.10 | odd | 2 | 7744.2.a.dr.1.4 | 4 | |||
24.11 | even | 2 | 8712.2.a.cd.1.2 | 4 | |||
44.35 | even | 10 | 704.2.m.l.257.1 | 8 | |||
44.39 | even | 10 | 704.2.m.l.641.1 | 8 | |||
44.43 | even | 2 | 7744.2.a.di.1.1 | 4 | |||
88.3 | odd | 10 | 968.2.i.t.9.1 | 8 | |||
88.13 | odd | 10 | 176.2.m.d.81.1 | 8 | |||
88.19 | even | 10 | 968.2.i.s.9.1 | 8 | |||
88.21 | odd | 2 | 1936.2.a.bb.1.1 | 4 | |||
88.27 | odd | 10 | 968.2.i.p.729.2 | 8 | |||
88.35 | even | 10 | 88.2.i.b.81.2 | yes | 8 | ||
88.43 | even | 2 | 968.2.a.n.1.4 | 4 | |||
88.51 | even | 10 | 968.2.i.s.753.1 | 8 | |||
88.59 | odd | 10 | 968.2.i.t.753.1 | 8 | |||
88.61 | odd | 10 | 176.2.m.d.113.1 | 8 | |||
88.75 | odd | 10 | 968.2.i.p.81.2 | 8 | |||
88.83 | even | 10 | 88.2.i.b.25.2 | ✓ | 8 | ||
264.35 | odd | 10 | 792.2.r.g.433.2 | 8 | |||
264.83 | odd | 10 | 792.2.r.g.289.2 | 8 | |||
264.131 | odd | 2 | 8712.2.a.ce.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
88.2.i.b.25.2 | ✓ | 8 | 88.83 | even | 10 | ||
88.2.i.b.81.2 | yes | 8 | 88.35 | even | 10 | ||
176.2.m.d.81.1 | 8 | 88.13 | odd | 10 | |||
176.2.m.d.113.1 | 8 | 88.61 | odd | 10 | |||
704.2.m.i.257.2 | 8 | 11.2 | odd | 10 | |||
704.2.m.i.641.2 | 8 | 11.6 | odd | 10 | |||
704.2.m.l.257.1 | 8 | 44.35 | even | 10 | |||
704.2.m.l.641.1 | 8 | 44.39 | even | 10 | |||
792.2.r.g.289.2 | 8 | 264.83 | odd | 10 | |||
792.2.r.g.433.2 | 8 | 264.35 | odd | 10 | |||
968.2.a.m.1.4 | 4 | 8.3 | odd | 2 | |||
968.2.a.n.1.4 | 4 | 88.43 | even | 2 | |||
968.2.i.p.81.2 | 8 | 88.75 | odd | 10 | |||
968.2.i.p.729.2 | 8 | 88.27 | odd | 10 | |||
968.2.i.s.9.1 | 8 | 88.19 | even | 10 | |||
968.2.i.s.753.1 | 8 | 88.51 | even | 10 | |||
968.2.i.t.9.1 | 8 | 88.3 | odd | 10 | |||
968.2.i.t.753.1 | 8 | 88.59 | odd | 10 | |||
1936.2.a.bb.1.1 | 4 | 88.21 | odd | 2 | |||
1936.2.a.bc.1.1 | 4 | 8.5 | even | 2 | |||
7744.2.a.dh.1.1 | 4 | 4.3 | odd | 2 | |||
7744.2.a.di.1.1 | 4 | 44.43 | even | 2 | |||
7744.2.a.dr.1.4 | 4 | 11.10 | odd | 2 | |||
7744.2.a.ds.1.4 | 4 | 1.1 | even | 1 | trivial | ||
8712.2.a.cd.1.2 | 4 | 24.11 | even | 2 | |||
8712.2.a.ce.1.2 | 4 | 264.131 | odd | 2 |