Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2738,2,Mod(1,2738)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2738, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2738.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2738 = 2 \cdot 37^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2738.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: | \(21.8630400734\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 74) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2738.1 |
$q$-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 | ||||||||
\(3\) | 0.618034 | 0.356822 | 0.178411 | − | 0.983956i | \(-0.442904\pi\) | ||||
0.178411 | + | 0.983956i | \(0.442904\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.85410 | 1.27639 | 0.638197 | − | 0.769873i | \(-0.279681\pi\) | ||||
0.638197 | + | 0.769873i | \(0.279681\pi\) | |||||||
\(6\) | −0.618034 | −0.252311 | ||||||||
\(7\) | 1.23607 | 0.467190 | 0.233595 | − | 0.972334i | \(-0.424951\pi\) | ||||
0.233595 | + | 0.972334i | \(0.424951\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.61803 | −0.872678 | ||||||||
\(10\) | −2.85410 | −0.902546 | ||||||||
\(11\) | −3.61803 | −1.09088 | −0.545439 | − | 0.838150i | \(-0.683637\pi\) | ||||
−0.545439 | + | 0.838150i | \(0.683637\pi\) | |||||||
\(12\) | 0.618034 | 0.178411 | ||||||||
\(13\) | −3.85410 | −1.06894 | −0.534468 | − | 0.845189i | \(-0.679488\pi\) | ||||
−0.534468 | + | 0.845189i | \(0.679488\pi\) | |||||||
\(14\) | −1.23607 | −0.330353 | ||||||||
\(15\) | 1.76393 | 0.455445 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.47214 | −1.08465 | −0.542326 | − | 0.840168i | \(-0.682456\pi\) | ||||
−0.542326 | + | 0.840168i | \(0.682456\pi\) | |||||||
\(18\) | 2.61803 | 0.617077 | ||||||||
\(19\) | 4.47214 | 1.02598 | 0.512989 | − | 0.858395i | \(-0.328538\pi\) | ||||
0.512989 | + | 0.858395i | \(0.328538\pi\) | |||||||
\(20\) | 2.85410 | 0.638197 | ||||||||
\(21\) | 0.763932 | 0.166704 | ||||||||
\(22\) | 3.61803 | 0.771367 | ||||||||
\(23\) | 3.85410 | 0.803636 | 0.401818 | − | 0.915720i | \(-0.368378\pi\) | ||||
0.401818 | + | 0.915720i | \(0.368378\pi\) | |||||||
\(24\) | −0.618034 | −0.126156 | ||||||||
\(25\) | 3.14590 | 0.629180 | ||||||||
\(26\) | 3.85410 | 0.755852 | ||||||||
\(27\) | −3.47214 | −0.668213 | ||||||||
\(28\) | 1.23607 | 0.233595 | ||||||||
\(29\) | −6.32624 | −1.17475 | −0.587376 | − | 0.809314i | \(-0.699839\pi\) | ||||
−0.587376 | + | 0.809314i | \(0.699839\pi\) | |||||||
\(30\) | −1.76393 | −0.322048 | ||||||||
\(31\) | −9.61803 | −1.72745 | −0.863725 | − | 0.503964i | \(-0.831875\pi\) | ||||
−0.863725 | + | 0.503964i | \(0.831875\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.23607 | −0.389249 | ||||||||
\(34\) | 4.47214 | 0.766965 | ||||||||
\(35\) | 3.52786 | 0.596318 | ||||||||
\(36\) | −2.61803 | −0.436339 | ||||||||
\(37\) | 0 | 0 | ||||||||
\(38\) | −4.47214 | −0.725476 | ||||||||
\(39\) | −2.38197 | −0.381420 | ||||||||
\(40\) | −2.85410 | −0.451273 | ||||||||
\(41\) | 7.38197 | 1.15287 | 0.576435 | − | 0.817143i | \(-0.304444\pi\) | ||||
0.576435 | + | 0.817143i | \(0.304444\pi\) | |||||||
\(42\) | −0.763932 | −0.117877 | ||||||||
\(43\) | 0.763932 | 0.116499 | 0.0582493 | − | 0.998302i | \(-0.481448\pi\) | ||||
0.0582493 | + | 0.998302i | \(0.481448\pi\) | |||||||
\(44\) | −3.61803 | −0.545439 | ||||||||
\(45\) | −7.47214 | −1.11388 | ||||||||
\(46\) | −3.85410 | −0.568256 | ||||||||
\(47\) | 3.23607 | 0.472029 | 0.236015 | − | 0.971750i | \(-0.424159\pi\) | ||||
0.236015 | + | 0.971750i | \(0.424159\pi\) | |||||||
\(48\) | 0.618034 | 0.0892055 | ||||||||
\(49\) | −5.47214 | −0.781734 | ||||||||
\(50\) | −3.14590 | −0.444897 | ||||||||
\(51\) | −2.76393 | −0.387028 | ||||||||
\(52\) | −3.85410 | −0.534468 | ||||||||
\(53\) | −8.47214 | −1.16374 | −0.581869 | − | 0.813283i | \(-0.697678\pi\) | ||||
−0.581869 | + | 0.813283i | \(0.697678\pi\) | |||||||
\(54\) | 3.47214 | 0.472498 | ||||||||
\(55\) | −10.3262 | −1.39239 | ||||||||
\(56\) | −1.23607 | −0.165177 | ||||||||
\(57\) | 2.76393 | 0.366092 | ||||||||
\(58\) | 6.32624 | 0.830676 | ||||||||
\(59\) | 9.23607 | 1.20243 | 0.601217 | − | 0.799086i | \(-0.294683\pi\) | ||||
0.601217 | + | 0.799086i | \(0.294683\pi\) | |||||||
\(60\) | 1.76393 | 0.227723 | ||||||||
\(61\) | −8.38197 | −1.07320 | −0.536600 | − | 0.843836i | \(-0.680292\pi\) | ||||
−0.536600 | + | 0.843836i | \(0.680292\pi\) | |||||||
\(62\) | 9.61803 | 1.22149 | ||||||||
\(63\) | −3.23607 | −0.407706 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −11.0000 | −1.36438 | ||||||||
\(66\) | 2.23607 | 0.275241 | ||||||||
\(67\) | −10.0902 | −1.23271 | −0.616355 | − | 0.787468i | \(-0.711391\pi\) | ||||
−0.616355 | + | 0.787468i | \(0.711391\pi\) | |||||||
\(68\) | −4.47214 | −0.542326 | ||||||||
\(69\) | 2.38197 | 0.286755 | ||||||||
\(70\) | −3.52786 | −0.421660 | ||||||||
\(71\) | −14.9443 | −1.77356 | −0.886779 | − | 0.462193i | \(-0.847063\pi\) | ||||
−0.886779 | + | 0.462193i | \(0.847063\pi\) | |||||||
\(72\) | 2.61803 | 0.308538 | ||||||||
\(73\) | −4.09017 | −0.478718 | −0.239359 | − | 0.970931i | \(-0.576937\pi\) | ||||
−0.239359 | + | 0.970931i | \(0.576937\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.94427 | 0.224505 | ||||||||
\(76\) | 4.47214 | 0.512989 | ||||||||
\(77\) | −4.47214 | −0.509647 | ||||||||
\(78\) | 2.38197 | 0.269705 | ||||||||
\(79\) | −11.5623 | −1.30086 | −0.650431 | − | 0.759566i | \(-0.725411\pi\) | ||||
−0.650431 | + | 0.759566i | \(0.725411\pi\) | |||||||
\(80\) | 2.85410 | 0.319098 | ||||||||
\(81\) | 5.70820 | 0.634245 | ||||||||
\(82\) | −7.38197 | −0.815202 | ||||||||
\(83\) | −5.52786 | −0.606762 | −0.303381 | − | 0.952869i | \(-0.598115\pi\) | ||||
−0.303381 | + | 0.952869i | \(0.598115\pi\) | |||||||
\(84\) | 0.763932 | 0.0833518 | ||||||||
\(85\) | −12.7639 | −1.38444 | ||||||||
\(86\) | −0.763932 | −0.0823769 | ||||||||
\(87\) | −3.90983 | −0.419178 | ||||||||
\(88\) | 3.61803 | 0.385684 | ||||||||
\(89\) | 10.4721 | 1.11004 | 0.555022 | − | 0.831836i | \(-0.312710\pi\) | ||||
0.555022 | + | 0.831836i | \(0.312710\pi\) | |||||||
\(90\) | 7.47214 | 0.787632 | ||||||||
\(91\) | −4.76393 | −0.499396 | ||||||||
\(92\) | 3.85410 | 0.401818 | ||||||||
\(93\) | −5.94427 | −0.616392 | ||||||||
\(94\) | −3.23607 | −0.333775 | ||||||||
\(95\) | 12.7639 | 1.30955 | ||||||||
\(96\) | −0.618034 | −0.0630778 | ||||||||
\(97\) | −8.47214 | −0.860215 | −0.430108 | − | 0.902778i | \(-0.641524\pi\) | ||||
−0.430108 | + | 0.902778i | \(0.641524\pi\) | |||||||
\(98\) | 5.47214 | 0.552769 | ||||||||
\(99\) | 9.47214 | 0.951985 | ||||||||
\(100\) | 3.14590 | 0.314590 | ||||||||
\(101\) | 12.4721 | 1.24102 | 0.620512 | − | 0.784197i | \(-0.286925\pi\) | ||||
0.620512 | + | 0.784197i | \(0.286925\pi\) | |||||||
\(102\) | 2.76393 | 0.273670 | ||||||||
\(103\) | 16.2705 | 1.60318 | 0.801590 | − | 0.597873i | \(-0.203987\pi\) | ||||
0.801590 | + | 0.597873i | \(0.203987\pi\) | |||||||
\(104\) | 3.85410 | 0.377926 | ||||||||
\(105\) | 2.18034 | 0.212779 | ||||||||
\(106\) | 8.47214 | 0.822887 | ||||||||
\(107\) | 8.32624 | 0.804928 | 0.402464 | − | 0.915436i | \(-0.368154\pi\) | ||||
0.402464 | + | 0.915436i | \(0.368154\pi\) | |||||||
\(108\) | −3.47214 | −0.334106 | ||||||||
\(109\) | 14.9443 | 1.43140 | 0.715701 | − | 0.698407i | \(-0.246107\pi\) | ||||
0.715701 | + | 0.698407i | \(0.246107\pi\) | |||||||
\(110\) | 10.3262 | 0.984568 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.23607 | 0.116797 | ||||||||
\(113\) | −10.9443 | −1.02955 | −0.514775 | − | 0.857325i | \(-0.672125\pi\) | ||||
−0.514775 | + | 0.857325i | \(0.672125\pi\) | |||||||
\(114\) | −2.76393 | −0.258866 | ||||||||
\(115\) | 11.0000 | 1.02576 | ||||||||
\(116\) | −6.32624 | −0.587376 | ||||||||
\(117\) | 10.0902 | 0.932837 | ||||||||
\(118\) | −9.23607 | −0.850249 | ||||||||
\(119\) | −5.52786 | −0.506738 | ||||||||
\(120\) | −1.76393 | −0.161024 | ||||||||
\(121\) | 2.09017 | 0.190015 | ||||||||
\(122\) | 8.38197 | 0.758868 | ||||||||
\(123\) | 4.56231 | 0.411369 | ||||||||
\(124\) | −9.61803 | −0.863725 | ||||||||
\(125\) | −5.29180 | −0.473313 | ||||||||
\(126\) | 3.23607 | 0.288292 | ||||||||
\(127\) | 0.472136 | 0.0418953 | 0.0209476 | − | 0.999781i | \(-0.493332\pi\) | ||||
0.0209476 | + | 0.999781i | \(0.493332\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.472136 | 0.0415693 | ||||||||
\(130\) | 11.0000 | 0.964764 | ||||||||
\(131\) | −8.65248 | −0.755970 | −0.377985 | − | 0.925812i | \(-0.623383\pi\) | ||||
−0.377985 | + | 0.925812i | \(0.623383\pi\) | |||||||
\(132\) | −2.23607 | −0.194625 | ||||||||
\(133\) | 5.52786 | 0.479327 | ||||||||
\(134\) | 10.0902 | 0.871658 | ||||||||
\(135\) | −9.90983 | −0.852902 | ||||||||
\(136\) | 4.47214 | 0.383482 | ||||||||
\(137\) | 19.3262 | 1.65115 | 0.825576 | − | 0.564291i | \(-0.190850\pi\) | ||||
0.825576 | + | 0.564291i | \(0.190850\pi\) | |||||||
\(138\) | −2.38197 | −0.202766 | ||||||||
\(139\) | −1.85410 | −0.157263 | −0.0786314 | − | 0.996904i | \(-0.525055\pi\) | ||||
−0.0786314 | + | 0.996904i | \(0.525055\pi\) | |||||||
\(140\) | 3.52786 | 0.298159 | ||||||||
\(141\) | 2.00000 | 0.168430 | ||||||||
\(142\) | 14.9443 | 1.25410 | ||||||||
\(143\) | 13.9443 | 1.16608 | ||||||||
\(144\) | −2.61803 | −0.218169 | ||||||||
\(145\) | −18.0557 | −1.49945 | ||||||||
\(146\) | 4.09017 | 0.338505 | ||||||||
\(147\) | −3.38197 | −0.278940 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.18034 | −0.506313 | −0.253157 | − | 0.967425i | \(-0.581469\pi\) | ||||
−0.253157 | + | 0.967425i | \(0.581469\pi\) | |||||||
\(150\) | −1.94427 | −0.158749 | ||||||||
\(151\) | 17.7082 | 1.44107 | 0.720537 | − | 0.693417i | \(-0.243896\pi\) | ||||
0.720537 | + | 0.693417i | \(0.243896\pi\) | |||||||
\(152\) | −4.47214 | −0.362738 | ||||||||
\(153\) | 11.7082 | 0.946552 | ||||||||
\(154\) | 4.47214 | 0.360375 | ||||||||
\(155\) | −27.4508 | −2.20491 | ||||||||
\(156\) | −2.38197 | −0.190710 | ||||||||
\(157\) | −7.52786 | −0.600789 | −0.300394 | − | 0.953815i | \(-0.597118\pi\) | ||||
−0.300394 | + | 0.953815i | \(0.597118\pi\) | |||||||
\(158\) | 11.5623 | 0.919848 | ||||||||
\(159\) | −5.23607 | −0.415247 | ||||||||
\(160\) | −2.85410 | −0.225637 | ||||||||
\(161\) | 4.76393 | 0.375450 | ||||||||
\(162\) | −5.70820 | −0.448479 | ||||||||
\(163\) | 12.4721 | 0.976893 | 0.488447 | − | 0.872594i | \(-0.337564\pi\) | ||||
0.488447 | + | 0.872594i | \(0.337564\pi\) | |||||||
\(164\) | 7.38197 | 0.576435 | ||||||||
\(165\) | −6.38197 | −0.496835 | ||||||||
\(166\) | 5.52786 | 0.429045 | ||||||||
\(167\) | −7.14590 | −0.552966 | −0.276483 | − | 0.961019i | \(-0.589169\pi\) | ||||
−0.276483 | + | 0.961019i | \(0.589169\pi\) | |||||||
\(168\) | −0.763932 | −0.0589386 | ||||||||
\(169\) | 1.85410 | 0.142623 | ||||||||
\(170\) | 12.7639 | 0.978949 | ||||||||
\(171\) | −11.7082 | −0.895349 | ||||||||
\(172\) | 0.763932 | 0.0582493 | ||||||||
\(173\) | 8.47214 | 0.644125 | 0.322062 | − | 0.946718i | \(-0.395624\pi\) | ||||
0.322062 | + | 0.946718i | \(0.395624\pi\) | |||||||
\(174\) | 3.90983 | 0.296403 | ||||||||
\(175\) | 3.88854 | 0.293946 | ||||||||
\(176\) | −3.61803 | −0.272720 | ||||||||
\(177\) | 5.70820 | 0.429055 | ||||||||
\(178\) | −10.4721 | −0.784920 | ||||||||
\(179\) | −18.6525 | −1.39415 | −0.697076 | − | 0.716997i | \(-0.745516\pi\) | ||||
−0.697076 | + | 0.716997i | \(0.745516\pi\) | |||||||
\(180\) | −7.47214 | −0.556940 | ||||||||
\(181\) | 5.52786 | 0.410883 | 0.205441 | − | 0.978669i | \(-0.434137\pi\) | ||||
0.205441 | + | 0.978669i | \(0.434137\pi\) | |||||||
\(182\) | 4.76393 | 0.353126 | ||||||||
\(183\) | −5.18034 | −0.382942 | ||||||||
\(184\) | −3.85410 | −0.284128 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.94427 | 0.435855 | ||||||||
\(187\) | 16.1803 | 1.18322 | ||||||||
\(188\) | 3.23607 | 0.236015 | ||||||||
\(189\) | −4.29180 | −0.312182 | ||||||||
\(190\) | −12.7639 | −0.925993 | ||||||||
\(191\) | −4.09017 | −0.295954 | −0.147977 | − | 0.988991i | \(-0.547276\pi\) | ||||
−0.147977 | + | 0.988991i | \(0.547276\pi\) | |||||||
\(192\) | 0.618034 | 0.0446028 | ||||||||
\(193\) | −4.00000 | −0.287926 | −0.143963 | − | 0.989583i | \(-0.545985\pi\) | ||||
−0.143963 | + | 0.989583i | \(0.545985\pi\) | |||||||
\(194\) | 8.47214 | 0.608264 | ||||||||
\(195\) | −6.79837 | −0.486842 | ||||||||
\(196\) | −5.47214 | −0.390867 | ||||||||
\(197\) | −16.4721 | −1.17359 | −0.586796 | − | 0.809735i | \(-0.699611\pi\) | ||||
−0.586796 | + | 0.809735i | \(0.699611\pi\) | |||||||
\(198\) | −9.47214 | −0.673155 | ||||||||
\(199\) | −20.9443 | −1.48470 | −0.742350 | − | 0.670012i | \(-0.766289\pi\) | ||||
−0.742350 | + | 0.670012i | \(0.766289\pi\) | |||||||
\(200\) | −3.14590 | −0.222449 | ||||||||
\(201\) | −6.23607 | −0.439858 | ||||||||
\(202\) | −12.4721 | −0.877536 | ||||||||
\(203\) | −7.81966 | −0.548833 | ||||||||
\(204\) | −2.76393 | −0.193514 | ||||||||
\(205\) | 21.0689 | 1.47151 | ||||||||
\(206\) | −16.2705 | −1.13362 | ||||||||
\(207\) | −10.0902 | −0.701315 | ||||||||
\(208\) | −3.85410 | −0.267234 | ||||||||
\(209\) | −16.1803 | −1.11922 | ||||||||
\(210\) | −2.18034 | −0.150458 | ||||||||
\(211\) | −22.2705 | −1.53317 | −0.766583 | − | 0.642146i | \(-0.778044\pi\) | ||||
−0.766583 | + | 0.642146i | \(0.778044\pi\) | |||||||
\(212\) | −8.47214 | −0.581869 | ||||||||
\(213\) | −9.23607 | −0.632845 | ||||||||
\(214\) | −8.32624 | −0.569170 | ||||||||
\(215\) | 2.18034 | 0.148698 | ||||||||
\(216\) | 3.47214 | 0.236249 | ||||||||
\(217\) | −11.8885 | −0.807047 | ||||||||
\(218\) | −14.9443 | −1.01215 | ||||||||
\(219\) | −2.52786 | −0.170817 | ||||||||
\(220\) | −10.3262 | −0.696195 | ||||||||
\(221\) | 17.2361 | 1.15942 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.18034 | −0.547796 | −0.273898 | − | 0.961759i | \(-0.588313\pi\) | ||||
−0.273898 | + | 0.961759i | \(0.588313\pi\) | |||||||
\(224\) | −1.23607 | −0.0825883 | ||||||||
\(225\) | −8.23607 | −0.549071 | ||||||||
\(226\) | 10.9443 | 0.728002 | ||||||||
\(227\) | 17.7082 | 1.17533 | 0.587667 | − | 0.809103i | \(-0.300046\pi\) | ||||
0.587667 | + | 0.809103i | \(0.300046\pi\) | |||||||
\(228\) | 2.76393 | 0.183046 | ||||||||
\(229\) | 17.1246 | 1.13163 | 0.565813 | − | 0.824534i | \(-0.308562\pi\) | ||||
0.565813 | + | 0.824534i | \(0.308562\pi\) | |||||||
\(230\) | −11.0000 | −0.725319 | ||||||||
\(231\) | −2.76393 | −0.181853 | ||||||||
\(232\) | 6.32624 | 0.415338 | ||||||||
\(233\) | 13.5623 | 0.888496 | 0.444248 | − | 0.895904i | \(-0.353471\pi\) | ||||
0.444248 | + | 0.895904i | \(0.353471\pi\) | |||||||
\(234\) | −10.0902 | −0.659615 | ||||||||
\(235\) | 9.23607 | 0.602495 | ||||||||
\(236\) | 9.23607 | 0.601217 | ||||||||
\(237\) | −7.14590 | −0.464176 | ||||||||
\(238\) | 5.52786 | 0.358318 | ||||||||
\(239\) | −3.14590 | −0.203491 | −0.101746 | − | 0.994810i | \(-0.532443\pi\) | ||||
−0.101746 | + | 0.994810i | \(0.532443\pi\) | |||||||
\(240\) | 1.76393 | 0.113861 | ||||||||
\(241\) | 10.4721 | 0.674570 | 0.337285 | − | 0.941403i | \(-0.390491\pi\) | ||||
0.337285 | + | 0.941403i | \(0.390491\pi\) | |||||||
\(242\) | −2.09017 | −0.134361 | ||||||||
\(243\) | 13.9443 | 0.894525 | ||||||||
\(244\) | −8.38197 | −0.536600 | ||||||||
\(245\) | −15.6180 | −0.997800 | ||||||||
\(246\) | −4.56231 | −0.290882 | ||||||||
\(247\) | −17.2361 | −1.09670 | ||||||||
\(248\) | 9.61803 | 0.610746 | ||||||||
\(249\) | −3.41641 | −0.216506 | ||||||||
\(250\) | 5.29180 | 0.334683 | ||||||||
\(251\) | 3.05573 | 0.192876 | 0.0964379 | − | 0.995339i | \(-0.469255\pi\) | ||||
0.0964379 | + | 0.995339i | \(0.469255\pi\) | |||||||
\(252\) | −3.23607 | −0.203853 | ||||||||
\(253\) | −13.9443 | −0.876669 | ||||||||
\(254\) | −0.472136 | −0.0296244 | ||||||||
\(255\) | −7.88854 | −0.494000 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.9443 | 1.18171 | 0.590856 | − | 0.806777i | \(-0.298790\pi\) | ||||
0.590856 | + | 0.806777i | \(0.298790\pi\) | |||||||
\(258\) | −0.472136 | −0.0293939 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −11.0000 | −0.682191 | ||||||||
\(261\) | 16.5623 | 1.02518 | ||||||||
\(262\) | 8.65248 | 0.534552 | ||||||||
\(263\) | −8.76393 | −0.540407 | −0.270204 | − | 0.962803i | \(-0.587091\pi\) | ||||
−0.270204 | + | 0.962803i | \(0.587091\pi\) | |||||||
\(264\) | 2.23607 | 0.137620 | ||||||||
\(265\) | −24.1803 | −1.48539 | ||||||||
\(266\) | −5.52786 | −0.338935 | ||||||||
\(267\) | 6.47214 | 0.396088 | ||||||||
\(268\) | −10.0902 | −0.616355 | ||||||||
\(269\) | 4.00000 | 0.243884 | 0.121942 | − | 0.992537i | \(-0.461088\pi\) | ||||
0.121942 | + | 0.992537i | \(0.461088\pi\) | |||||||
\(270\) | 9.90983 | 0.603093 | ||||||||
\(271\) | −4.94427 | −0.300343 | −0.150172 | − | 0.988660i | \(-0.547983\pi\) | ||||
−0.150172 | + | 0.988660i | \(0.547983\pi\) | |||||||
\(272\) | −4.47214 | −0.271163 | ||||||||
\(273\) | −2.94427 | −0.178195 | ||||||||
\(274\) | −19.3262 | −1.16754 | ||||||||
\(275\) | −11.3820 | −0.686358 | ||||||||
\(276\) | 2.38197 | 0.143378 | ||||||||
\(277\) | 7.79837 | 0.468559 | 0.234279 | − | 0.972169i | \(-0.424727\pi\) | ||||
0.234279 | + | 0.972169i | \(0.424727\pi\) | |||||||
\(278\) | 1.85410 | 0.111202 | ||||||||
\(279\) | 25.1803 | 1.50751 | ||||||||
\(280\) | −3.52786 | −0.210830 | ||||||||
\(281\) | 5.88854 | 0.351281 | 0.175641 | − | 0.984454i | \(-0.443800\pi\) | ||||
0.175641 | + | 0.984454i | \(0.443800\pi\) | |||||||
\(282\) | −2.00000 | −0.119098 | ||||||||
\(283\) | −11.2361 | −0.667915 | −0.333957 | − | 0.942588i | \(-0.608384\pi\) | ||||
−0.333957 | + | 0.942588i | \(0.608384\pi\) | |||||||
\(284\) | −14.9443 | −0.886779 | ||||||||
\(285\) | 7.88854 | 0.467277 | ||||||||
\(286\) | −13.9443 | −0.824542 | ||||||||
\(287\) | 9.12461 | 0.538609 | ||||||||
\(288\) | 2.61803 | 0.154269 | ||||||||
\(289\) | 3.00000 | 0.176471 | ||||||||
\(290\) | 18.0557 | 1.06027 | ||||||||
\(291\) | −5.23607 | −0.306944 | ||||||||
\(292\) | −4.09017 | −0.239359 | ||||||||
\(293\) | 18.6525 | 1.08969 | 0.544845 | − | 0.838537i | \(-0.316589\pi\) | ||||
0.544845 | + | 0.838537i | \(0.316589\pi\) | |||||||
\(294\) | 3.38197 | 0.197240 | ||||||||
\(295\) | 26.3607 | 1.53478 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.5623 | 0.728939 | ||||||||
\(298\) | 6.18034 | 0.358017 | ||||||||
\(299\) | −14.8541 | −0.859035 | ||||||||
\(300\) | 1.94427 | 0.112253 | ||||||||
\(301\) | 0.944272 | 0.0544269 | ||||||||
\(302\) | −17.7082 | −1.01899 | ||||||||
\(303\) | 7.70820 | 0.442825 | ||||||||
\(304\) | 4.47214 | 0.256495 | ||||||||
\(305\) | −23.9230 | −1.36983 | ||||||||
\(306\) | −11.7082 | −0.669313 | ||||||||
\(307\) | −6.14590 | −0.350765 | −0.175382 | − | 0.984500i | \(-0.556116\pi\) | ||||
−0.175382 | + | 0.984500i | \(0.556116\pi\) | |||||||
\(308\) | −4.47214 | −0.254824 | ||||||||
\(309\) | 10.0557 | 0.572050 | ||||||||
\(310\) | 27.4508 | 1.55910 | ||||||||
\(311\) | −2.03444 | −0.115363 | −0.0576813 | − | 0.998335i | \(-0.518371\pi\) | ||||
−0.0576813 | + | 0.998335i | \(0.518371\pi\) | |||||||
\(312\) | 2.38197 | 0.134852 | ||||||||
\(313\) | −5.81966 | −0.328947 | −0.164473 | − | 0.986382i | \(-0.552592\pi\) | ||||
−0.164473 | + | 0.986382i | \(0.552592\pi\) | |||||||
\(314\) | 7.52786 | 0.424822 | ||||||||
\(315\) | −9.23607 | −0.520393 | ||||||||
\(316\) | −11.5623 | −0.650431 | ||||||||
\(317\) | 3.05573 | 0.171627 | 0.0858134 | − | 0.996311i | \(-0.472651\pi\) | ||||
0.0858134 | + | 0.996311i | \(0.472651\pi\) | |||||||
\(318\) | 5.23607 | 0.293624 | ||||||||
\(319\) | 22.8885 | 1.28151 | ||||||||
\(320\) | 2.85410 | 0.159549 | ||||||||
\(321\) | 5.14590 | 0.287216 | ||||||||
\(322\) | −4.76393 | −0.265484 | ||||||||
\(323\) | −20.0000 | −1.11283 | ||||||||
\(324\) | 5.70820 | 0.317122 | ||||||||
\(325\) | −12.1246 | −0.672552 | ||||||||
\(326\) | −12.4721 | −0.690768 | ||||||||
\(327\) | 9.23607 | 0.510756 | ||||||||
\(328\) | −7.38197 | −0.407601 | ||||||||
\(329\) | 4.00000 | 0.220527 | ||||||||
\(330\) | 6.38197 | 0.351316 | ||||||||
\(331\) | −28.0000 | −1.53902 | −0.769510 | − | 0.638635i | \(-0.779499\pi\) | ||||
−0.769510 | + | 0.638635i | \(0.779499\pi\) | |||||||
\(332\) | −5.52786 | −0.303381 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.14590 | 0.391006 | ||||||||
\(335\) | −28.7984 | −1.57342 | ||||||||
\(336\) | 0.763932 | 0.0416759 | ||||||||
\(337\) | −17.0344 | −0.927925 | −0.463963 | − | 0.885855i | \(-0.653573\pi\) | ||||
−0.463963 | + | 0.885855i | \(0.653573\pi\) | |||||||
\(338\) | −1.85410 | −0.100850 | ||||||||
\(339\) | −6.76393 | −0.367366 | ||||||||
\(340\) | −12.7639 | −0.692221 | ||||||||
\(341\) | 34.7984 | 1.88444 | ||||||||
\(342\) | 11.7082 | 0.633107 | ||||||||
\(343\) | −15.4164 | −0.832408 | ||||||||
\(344\) | −0.763932 | −0.0411885 | ||||||||
\(345\) | 6.79837 | 0.366012 | ||||||||
\(346\) | −8.47214 | −0.455465 | ||||||||
\(347\) | −12.7639 | −0.685204 | −0.342602 | − | 0.939481i | \(-0.611308\pi\) | ||||
−0.342602 | + | 0.939481i | \(0.611308\pi\) | |||||||
\(348\) | −3.90983 | −0.209589 | ||||||||
\(349\) | 12.1803 | 0.651999 | 0.325999 | − | 0.945370i | \(-0.394299\pi\) | ||||
0.325999 | + | 0.945370i | \(0.394299\pi\) | |||||||
\(350\) | −3.88854 | −0.207851 | ||||||||
\(351\) | 13.3820 | 0.714277 | ||||||||
\(352\) | 3.61803 | 0.192842 | ||||||||
\(353\) | −29.7082 | −1.58121 | −0.790604 | − | 0.612328i | \(-0.790233\pi\) | ||||
−0.790604 | + | 0.612328i | \(0.790233\pi\) | |||||||
\(354\) | −5.70820 | −0.303388 | ||||||||
\(355\) | −42.6525 | −2.26376 | ||||||||
\(356\) | 10.4721 | 0.555022 | ||||||||
\(357\) | −3.41641 | −0.180815 | ||||||||
\(358\) | 18.6525 | 0.985814 | ||||||||
\(359\) | 4.47214 | 0.236030 | 0.118015 | − | 0.993012i | \(-0.462347\pi\) | ||||
0.118015 | + | 0.993012i | \(0.462347\pi\) | |||||||
\(360\) | 7.47214 | 0.393816 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −5.52786 | −0.290538 | ||||||||
\(363\) | 1.29180 | 0.0678017 | ||||||||
\(364\) | −4.76393 | −0.249698 | ||||||||
\(365\) | −11.6738 | −0.611033 | ||||||||
\(366\) | 5.18034 | 0.270781 | ||||||||
\(367\) | −27.1246 | −1.41589 | −0.707947 | − | 0.706266i | \(-0.750378\pi\) | ||||
−0.707947 | + | 0.706266i | \(0.750378\pi\) | |||||||
\(368\) | 3.85410 | 0.200909 | ||||||||
\(369\) | −19.3262 | −1.00608 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.4721 | −0.543686 | ||||||||
\(372\) | −5.94427 | −0.308196 | ||||||||
\(373\) | 14.2918 | 0.740001 | 0.370001 | − | 0.929032i | \(-0.379357\pi\) | ||||
0.370001 | + | 0.929032i | \(0.379357\pi\) | |||||||
\(374\) | −16.1803 | −0.836665 | ||||||||
\(375\) | −3.27051 | −0.168888 | ||||||||
\(376\) | −3.23607 | −0.166887 | ||||||||
\(377\) | 24.3820 | 1.25574 | ||||||||
\(378\) | 4.29180 | 0.220746 | ||||||||
\(379\) | 16.9098 | 0.868600 | 0.434300 | − | 0.900768i | \(-0.356996\pi\) | ||||
0.434300 | + | 0.900768i | \(0.356996\pi\) | |||||||
\(380\) | 12.7639 | 0.654776 | ||||||||
\(381\) | 0.291796 | 0.0149492 | ||||||||
\(382\) | 4.09017 | 0.209271 | ||||||||
\(383\) | 17.8885 | 0.914062 | 0.457031 | − | 0.889451i | \(-0.348913\pi\) | ||||
0.457031 | + | 0.889451i | \(0.348913\pi\) | |||||||
\(384\) | −0.618034 | −0.0315389 | ||||||||
\(385\) | −12.7639 | −0.650510 | ||||||||
\(386\) | 4.00000 | 0.203595 | ||||||||
\(387\) | −2.00000 | −0.101666 | ||||||||
\(388\) | −8.47214 | −0.430108 | ||||||||
\(389\) | 0.145898 | 0.00739732 | 0.00369866 | − | 0.999993i | \(-0.498823\pi\) | ||||
0.00369866 | + | 0.999993i | \(0.498823\pi\) | |||||||
\(390\) | 6.79837 | 0.344249 | ||||||||
\(391\) | −17.2361 | −0.871665 | ||||||||
\(392\) | 5.47214 | 0.276385 | ||||||||
\(393\) | −5.34752 | −0.269747 | ||||||||
\(394\) | 16.4721 | 0.829854 | ||||||||
\(395\) | −33.0000 | −1.66041 | ||||||||
\(396\) | 9.47214 | 0.475993 | ||||||||
\(397\) | −10.6525 | −0.534632 | −0.267316 | − | 0.963609i | \(-0.586137\pi\) | ||||
−0.267316 | + | 0.963609i | \(0.586137\pi\) | |||||||
\(398\) | 20.9443 | 1.04984 | ||||||||
\(399\) | 3.41641 | 0.171034 | ||||||||
\(400\) | 3.14590 | 0.157295 | ||||||||
\(401\) | 9.23607 | 0.461227 | 0.230614 | − | 0.973045i | \(-0.425927\pi\) | ||||
0.230614 | + | 0.973045i | \(0.425927\pi\) | |||||||
\(402\) | 6.23607 | 0.311027 | ||||||||
\(403\) | 37.0689 | 1.84653 | ||||||||
\(404\) | 12.4721 | 0.620512 | ||||||||
\(405\) | 16.2918 | 0.809546 | ||||||||
\(406\) | 7.81966 | 0.388083 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 2.76393 | 0.136835 | ||||||||
\(409\) | 3.81966 | 0.188870 | 0.0944350 | − | 0.995531i | \(-0.469896\pi\) | ||||
0.0944350 | + | 0.995531i | \(0.469896\pi\) | |||||||
\(410\) | −21.0689 | −1.04052 | ||||||||
\(411\) | 11.9443 | 0.589167 | ||||||||
\(412\) | 16.2705 | 0.801590 | ||||||||
\(413\) | 11.4164 | 0.561765 | ||||||||
\(414\) | 10.0902 | 0.495905 | ||||||||
\(415\) | −15.7771 | −0.774467 | ||||||||
\(416\) | 3.85410 | 0.188963 | ||||||||
\(417\) | −1.14590 | −0.0561149 | ||||||||
\(418\) | 16.1803 | 0.791406 | ||||||||
\(419\) | 9.56231 | 0.467149 | 0.233575 | − | 0.972339i | \(-0.424958\pi\) | ||||
0.233575 | + | 0.972339i | \(0.424958\pi\) | |||||||
\(420\) | 2.18034 | 0.106390 | ||||||||
\(421\) | 1.96556 | 0.0957954 | 0.0478977 | − | 0.998852i | \(-0.484748\pi\) | ||||
0.0478977 | + | 0.998852i | \(0.484748\pi\) | |||||||
\(422\) | 22.2705 | 1.08411 | ||||||||
\(423\) | −8.47214 | −0.411929 | ||||||||
\(424\) | 8.47214 | 0.411443 | ||||||||
\(425\) | −14.0689 | −0.682441 | ||||||||
\(426\) | 9.23607 | 0.447489 | ||||||||
\(427\) | −10.3607 | −0.501388 | ||||||||
\(428\) | 8.32624 | 0.402464 | ||||||||
\(429\) | 8.61803 | 0.416083 | ||||||||
\(430\) | −2.18034 | −0.105145 | ||||||||
\(431\) | 32.3607 | 1.55876 | 0.779380 | − | 0.626552i | \(-0.215534\pi\) | ||||
0.779380 | + | 0.626552i | \(0.215534\pi\) | |||||||
\(432\) | −3.47214 | −0.167053 | ||||||||
\(433\) | −36.3262 | −1.74573 | −0.872864 | − | 0.487964i | \(-0.837740\pi\) | ||||
−0.872864 | + | 0.487964i | \(0.837740\pi\) | |||||||
\(434\) | 11.8885 | 0.570668 | ||||||||
\(435\) | −11.1591 | −0.535036 | ||||||||
\(436\) | 14.9443 | 0.715701 | ||||||||
\(437\) | 17.2361 | 0.824513 | ||||||||
\(438\) | 2.52786 | 0.120786 | ||||||||
\(439\) | 16.7984 | 0.801743 | 0.400871 | − | 0.916134i | \(-0.368707\pi\) | ||||
0.400871 | + | 0.916134i | \(0.368707\pi\) | |||||||
\(440\) | 10.3262 | 0.492284 | ||||||||
\(441\) | 14.3262 | 0.682202 | ||||||||
\(442\) | −17.2361 | −0.819836 | ||||||||
\(443\) | −18.2705 | −0.868058 | −0.434029 | − | 0.900899i | \(-0.642908\pi\) | ||||
−0.434029 | + | 0.900899i | \(0.642908\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 29.8885 | 1.41685 | ||||||||
\(446\) | 8.18034 | 0.387350 | ||||||||
\(447\) | −3.81966 | −0.180664 | ||||||||
\(448\) | 1.23607 | 0.0583987 | ||||||||
\(449\) | 19.5279 | 0.921577 | 0.460788 | − | 0.887510i | \(-0.347567\pi\) | ||||
0.460788 | + | 0.887510i | \(0.347567\pi\) | |||||||
\(450\) | 8.23607 | 0.388252 | ||||||||
\(451\) | −26.7082 | −1.25764 | ||||||||
\(452\) | −10.9443 | −0.514775 | ||||||||
\(453\) | 10.9443 | 0.514207 | ||||||||
\(454\) | −17.7082 | −0.831087 | ||||||||
\(455\) | −13.5967 | −0.637425 | ||||||||
\(456\) | −2.76393 | −0.129433 | ||||||||
\(457\) | 29.2361 | 1.36761 | 0.683803 | − | 0.729667i | \(-0.260325\pi\) | ||||
0.683803 | + | 0.729667i | \(0.260325\pi\) | |||||||
\(458\) | −17.1246 | −0.800181 | ||||||||
\(459\) | 15.5279 | 0.724779 | ||||||||
\(460\) | 11.0000 | 0.512878 | ||||||||
\(461\) | 21.0557 | 0.980663 | 0.490332 | − | 0.871536i | \(-0.336876\pi\) | ||||
0.490332 | + | 0.871536i | \(0.336876\pi\) | |||||||
\(462\) | 2.76393 | 0.128590 | ||||||||
\(463\) | −15.5623 | −0.723242 | −0.361621 | − | 0.932325i | \(-0.617777\pi\) | ||||
−0.361621 | + | 0.932325i | \(0.617777\pi\) | |||||||
\(464\) | −6.32624 | −0.293688 | ||||||||
\(465\) | −16.9656 | −0.786759 | ||||||||
\(466\) | −13.5623 | −0.628262 | ||||||||
\(467\) | −20.3607 | −0.942180 | −0.471090 | − | 0.882085i | \(-0.656139\pi\) | ||||
−0.471090 | + | 0.882085i | \(0.656139\pi\) | |||||||
\(468\) | 10.0902 | 0.466418 | ||||||||
\(469\) | −12.4721 | −0.575910 | ||||||||
\(470\) | −9.23607 | −0.426028 | ||||||||
\(471\) | −4.65248 | −0.214375 | ||||||||
\(472\) | −9.23607 | −0.425124 | ||||||||
\(473\) | −2.76393 | −0.127086 | ||||||||
\(474\) | 7.14590 | 0.328222 | ||||||||
\(475\) | 14.0689 | 0.645525 | ||||||||
\(476\) | −5.52786 | −0.253369 | ||||||||
\(477\) | 22.1803 | 1.01557 | ||||||||
\(478\) | 3.14590 | 0.143890 | ||||||||
\(479\) | −16.4377 | −0.751057 | −0.375529 | − | 0.926811i | \(-0.622539\pi\) | ||||
−0.375529 | + | 0.926811i | \(0.622539\pi\) | |||||||
\(480\) | −1.76393 | −0.0805121 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −10.4721 | −0.476993 | ||||||||
\(483\) | 2.94427 | 0.133969 | ||||||||
\(484\) | 2.09017 | 0.0950077 | ||||||||
\(485\) | −24.1803 | −1.09797 | ||||||||
\(486\) | −13.9443 | −0.632525 | ||||||||
\(487\) | 25.3050 | 1.14668 | 0.573338 | − | 0.819319i | \(-0.305648\pi\) | ||||
0.573338 | + | 0.819319i | \(0.305648\pi\) | |||||||
\(488\) | 8.38197 | 0.379434 | ||||||||
\(489\) | 7.70820 | 0.348577 | ||||||||
\(490\) | 15.6180 | 0.705551 | ||||||||
\(491\) | 27.4508 | 1.23884 | 0.619420 | − | 0.785060i | \(-0.287368\pi\) | ||||
0.619420 | + | 0.785060i | \(0.287368\pi\) | |||||||
\(492\) | 4.56231 | 0.205685 | ||||||||
\(493\) | 28.2918 | 1.27420 | ||||||||
\(494\) | 17.2361 | 0.775487 | ||||||||
\(495\) | 27.0344 | 1.21511 | ||||||||
\(496\) | −9.61803 | −0.431862 | ||||||||
\(497\) | −18.4721 | −0.828589 | ||||||||
\(498\) | 3.41641 | 0.153093 | ||||||||
\(499\) | −23.7082 | −1.06132 | −0.530662 | − | 0.847583i | \(-0.678057\pi\) | ||||
−0.530662 | + | 0.847583i | \(0.678057\pi\) | |||||||
\(500\) | −5.29180 | −0.236656 | ||||||||
\(501\) | −4.41641 | −0.197311 | ||||||||
\(502\) | −3.05573 | −0.136384 | ||||||||
\(503\) | −7.90983 | −0.352682 | −0.176341 | − | 0.984329i | \(-0.556426\pi\) | ||||
−0.176341 | + | 0.984329i | \(0.556426\pi\) | |||||||
\(504\) | 3.23607 | 0.144146 | ||||||||
\(505\) | 35.5967 | 1.58403 | ||||||||
\(506\) | 13.9443 | 0.619898 | ||||||||
\(507\) | 1.14590 | 0.0508911 | ||||||||
\(508\) | 0.472136 | 0.0209476 | ||||||||
\(509\) | −4.29180 | −0.190231 | −0.0951153 | − | 0.995466i | \(-0.530322\pi\) | ||||
−0.0951153 | + | 0.995466i | \(0.530322\pi\) | |||||||
\(510\) | 7.88854 | 0.349311 | ||||||||
\(511\) | −5.05573 | −0.223652 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −15.5279 | −0.685572 | ||||||||
\(514\) | −18.9443 | −0.835596 | ||||||||
\(515\) | 46.4377 | 2.04629 | ||||||||
\(516\) | 0.472136 | 0.0207846 | ||||||||
\(517\) | −11.7082 | −0.514926 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.23607 | 0.229838 | ||||||||
\(520\) | 11.0000 | 0.482382 | ||||||||
\(521\) | 25.4164 | 1.11351 | 0.556757 | − | 0.830676i | \(-0.312046\pi\) | ||||
0.556757 | + | 0.830676i | \(0.312046\pi\) | |||||||
\(522\) | −16.5623 | −0.724912 | ||||||||
\(523\) | −34.1803 | −1.49460 | −0.747301 | − | 0.664486i | \(-0.768651\pi\) | ||||
−0.747301 | + | 0.664486i | \(0.768651\pi\) | |||||||
\(524\) | −8.65248 | −0.377985 | ||||||||
\(525\) | 2.40325 | 0.104887 | ||||||||
\(526\) | 8.76393 | 0.382126 | ||||||||
\(527\) | 43.0132 | 1.87368 | ||||||||
\(528\) | −2.23607 | −0.0973124 | ||||||||
\(529\) | −8.14590 | −0.354169 | ||||||||
\(530\) | 24.1803 | 1.05033 | ||||||||
\(531\) | −24.1803 | −1.04934 | ||||||||
\(532\) | 5.52786 | 0.239663 | ||||||||
\(533\) | −28.4508 | −1.23234 | ||||||||
\(534\) | −6.47214 | −0.280077 | ||||||||
\(535\) | 23.7639 | 1.02740 | ||||||||
\(536\) | 10.0902 | 0.435829 | ||||||||
\(537\) | −11.5279 | −0.497464 | ||||||||
\(538\) | −4.00000 | −0.172452 | ||||||||
\(539\) | 19.7984 | 0.852776 | ||||||||
\(540\) | −9.90983 | −0.426451 | ||||||||
\(541\) | −5.32624 | −0.228993 | −0.114496 | − | 0.993424i | \(-0.536525\pi\) | ||||
−0.114496 | + | 0.993424i | \(0.536525\pi\) | |||||||
\(542\) | 4.94427 | 0.212375 | ||||||||
\(543\) | 3.41641 | 0.146612 | ||||||||
\(544\) | 4.47214 | 0.191741 | ||||||||
\(545\) | 42.6525 | 1.82703 | ||||||||
\(546\) | 2.94427 | 0.126003 | ||||||||
\(547\) | −42.0689 | −1.79874 | −0.899368 | − | 0.437193i | \(-0.855973\pi\) | ||||
−0.899368 | + | 0.437193i | \(0.855973\pi\) | |||||||
\(548\) | 19.3262 | 0.825576 | ||||||||
\(549\) | 21.9443 | 0.936559 | ||||||||
\(550\) | 11.3820 | 0.485329 | ||||||||
\(551\) | −28.2918 | −1.20527 | ||||||||
\(552\) | −2.38197 | −0.101383 | ||||||||
\(553\) | −14.2918 | −0.607749 | ||||||||
\(554\) | −7.79837 | −0.331321 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.85410 | −0.0786314 | ||||||||
\(557\) | 0.562306 | 0.0238257 | 0.0119128 | − | 0.999929i | \(-0.496208\pi\) | ||||
0.0119128 | + | 0.999929i | \(0.496208\pi\) | |||||||
\(558\) | −25.1803 | −1.06597 | ||||||||
\(559\) | −2.94427 | −0.124529 | ||||||||
\(560\) | 3.52786 | 0.149079 | ||||||||
\(561\) | 10.0000 | 0.422200 | ||||||||
\(562\) | −5.88854 | −0.248393 | ||||||||
\(563\) | 27.8885 | 1.17536 | 0.587681 | − | 0.809093i | \(-0.300041\pi\) | ||||
0.587681 | + | 0.809093i | \(0.300041\pi\) | |||||||
\(564\) | 2.00000 | 0.0842152 | ||||||||
\(565\) | −31.2361 | −1.31411 | ||||||||
\(566\) | 11.2361 | 0.472287 | ||||||||
\(567\) | 7.05573 | 0.296313 | ||||||||
\(568\) | 14.9443 | 0.627048 | ||||||||
\(569\) | 21.8885 | 0.917615 | 0.458808 | − | 0.888536i | \(-0.348277\pi\) | ||||
0.458808 | + | 0.888536i | \(0.348277\pi\) | |||||||
\(570\) | −7.88854 | −0.330415 | ||||||||
\(571\) | 9.56231 | 0.400170 | 0.200085 | − | 0.979779i | \(-0.435878\pi\) | ||||
0.200085 | + | 0.979779i | \(0.435878\pi\) | |||||||
\(572\) | 13.9443 | 0.583039 | ||||||||
\(573\) | −2.52786 | −0.105603 | ||||||||
\(574\) | −9.12461 | −0.380854 | ||||||||
\(575\) | 12.1246 | 0.505631 | ||||||||
\(576\) | −2.61803 | −0.109085 | ||||||||
\(577\) | 20.6525 | 0.859774 | 0.429887 | − | 0.902883i | \(-0.358553\pi\) | ||||
0.429887 | + | 0.902883i | \(0.358553\pi\) | |||||||
\(578\) | −3.00000 | −0.124784 | ||||||||
\(579\) | −2.47214 | −0.102738 | ||||||||
\(580\) | −18.0557 | −0.749723 | ||||||||
\(581\) | −6.83282 | −0.283473 | ||||||||
\(582\) | 5.23607 | 0.217042 | ||||||||
\(583\) | 30.6525 | 1.26950 | ||||||||
\(584\) | 4.09017 | 0.169252 | ||||||||
\(585\) | 28.7984 | 1.19067 | ||||||||
\(586\) | −18.6525 | −0.770527 | ||||||||
\(587\) | 30.9443 | 1.27721 | 0.638603 | − | 0.769536i | \(-0.279512\pi\) | ||||
0.638603 | + | 0.769536i | \(0.279512\pi\) | |||||||
\(588\) | −3.38197 | −0.139470 | ||||||||
\(589\) | −43.0132 | −1.77233 | ||||||||
\(590\) | −26.3607 | −1.08525 | ||||||||
\(591\) | −10.1803 | −0.418763 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.56231 | −0.105221 | −0.0526106 | − | 0.998615i | \(-0.516754\pi\) | ||||
−0.0526106 | + | 0.998615i | \(0.516754\pi\) | |||||||
\(594\) | −12.5623 | −0.515438 | ||||||||
\(595\) | −15.7771 | −0.646798 | ||||||||
\(596\) | −6.18034 | −0.253157 | ||||||||
\(597\) | −12.9443 | −0.529774 | ||||||||
\(598\) | 14.8541 | 0.607429 | ||||||||
\(599\) | 38.3607 | 1.56737 | 0.783687 | − | 0.621155i | \(-0.213336\pi\) | ||||
0.783687 | + | 0.621155i | \(0.213336\pi\) | |||||||
\(600\) | −1.94427 | −0.0793746 | ||||||||
\(601\) | 35.6869 | 1.45570 | 0.727850 | − | 0.685737i | \(-0.240520\pi\) | ||||
0.727850 | + | 0.685737i | \(0.240520\pi\) | |||||||
\(602\) | −0.944272 | −0.0384856 | ||||||||
\(603\) | 26.4164 | 1.07576 | ||||||||
\(604\) | 17.7082 | 0.720537 | ||||||||
\(605\) | 5.96556 | 0.242534 | ||||||||
\(606\) | −7.70820 | −0.313124 | ||||||||
\(607\) | −5.96556 | −0.242135 | −0.121067 | − | 0.992644i | \(-0.538632\pi\) | ||||
−0.121067 | + | 0.992644i | \(0.538632\pi\) | |||||||
\(608\) | −4.47214 | −0.181369 | ||||||||
\(609\) | −4.83282 | −0.195836 | ||||||||
\(610\) | 23.9230 | 0.968613 | ||||||||
\(611\) | −12.4721 | −0.504569 | ||||||||
\(612\) | 11.7082 | 0.473276 | ||||||||
\(613\) | −36.1803 | −1.46131 | −0.730655 | − | 0.682747i | \(-0.760785\pi\) | ||||
−0.730655 | + | 0.682747i | \(0.760785\pi\) | |||||||
\(614\) | 6.14590 | 0.248028 | ||||||||
\(615\) | 13.0213 | 0.525069 | ||||||||
\(616\) | 4.47214 | 0.180187 | ||||||||
\(617\) | −11.0902 | −0.446473 | −0.223237 | − | 0.974764i | \(-0.571662\pi\) | ||||
−0.223237 | + | 0.974764i | \(0.571662\pi\) | |||||||
\(618\) | −10.0557 | −0.404501 | ||||||||
\(619\) | 18.2705 | 0.734354 | 0.367177 | − | 0.930151i | \(-0.380324\pi\) | ||||
0.367177 | + | 0.930151i | \(0.380324\pi\) | |||||||
\(620\) | −27.4508 | −1.10245 | ||||||||
\(621\) | −13.3820 | −0.537000 | ||||||||
\(622\) | 2.03444 | 0.0815737 | ||||||||
\(623\) | 12.9443 | 0.518601 | ||||||||
\(624\) | −2.38197 | −0.0953550 | ||||||||
\(625\) | −30.8328 | −1.23331 | ||||||||
\(626\) | 5.81966 | 0.232600 | ||||||||
\(627\) | −10.0000 | −0.399362 | ||||||||
\(628\) | −7.52786 | −0.300394 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 9.23607 | 0.367974 | ||||||||
\(631\) | −26.3951 | −1.05077 | −0.525387 | − | 0.850864i | \(-0.676079\pi\) | ||||
−0.525387 | + | 0.850864i | \(0.676079\pi\) | |||||||
\(632\) | 11.5623 | 0.459924 | ||||||||
\(633\) | −13.7639 | −0.547067 | ||||||||
\(634\) | −3.05573 | −0.121358 | ||||||||
\(635\) | 1.34752 | 0.0534749 | ||||||||
\(636\) | −5.23607 | −0.207624 | ||||||||
\(637\) | 21.0902 | 0.835623 | ||||||||
\(638\) | −22.8885 | −0.906166 | ||||||||
\(639\) | 39.1246 | 1.54775 | ||||||||
\(640\) | −2.85410 | −0.112818 | ||||||||
\(641\) | −22.5066 | −0.888956 | −0.444478 | − | 0.895790i | \(-0.646611\pi\) | ||||
−0.444478 | + | 0.895790i | \(0.646611\pi\) | |||||||
\(642\) | −5.14590 | −0.203092 | ||||||||
\(643\) | 33.2361 | 1.31070 | 0.655351 | − | 0.755324i | \(-0.272521\pi\) | ||||
0.655351 | + | 0.755324i | \(0.272521\pi\) | |||||||
\(644\) | 4.76393 | 0.187725 | ||||||||
\(645\) | 1.34752 | 0.0530587 | ||||||||
\(646\) | 20.0000 | 0.786889 | ||||||||
\(647\) | −18.9098 | −0.743422 | −0.371711 | − | 0.928348i | \(-0.621229\pi\) | ||||
−0.371711 | + | 0.928348i | \(0.621229\pi\) | |||||||
\(648\) | −5.70820 | −0.224239 | ||||||||
\(649\) | −33.4164 | −1.31171 | ||||||||
\(650\) | 12.1246 | 0.475566 | ||||||||
\(651\) | −7.34752 | −0.287972 | ||||||||
\(652\) | 12.4721 | 0.488447 | ||||||||
\(653\) | 4.72949 | 0.185079 | 0.0925396 | − | 0.995709i | \(-0.470502\pi\) | ||||
0.0925396 | + | 0.995709i | \(0.470502\pi\) | |||||||
\(654\) | −9.23607 | −0.361159 | ||||||||
\(655\) | −24.6950 | −0.964915 | ||||||||
\(656\) | 7.38197 | 0.288217 | ||||||||
\(657\) | 10.7082 | 0.417767 | ||||||||
\(658\) | −4.00000 | −0.155936 | ||||||||
\(659\) | −15.4508 | −0.601880 | −0.300940 | − | 0.953643i | \(-0.597300\pi\) | ||||
−0.300940 | + | 0.953643i | \(0.597300\pi\) | |||||||
\(660\) | −6.38197 | −0.248418 | ||||||||
\(661\) | −1.67376 | −0.0651018 | −0.0325509 | − | 0.999470i | \(-0.510363\pi\) | ||||
−0.0325509 | + | 0.999470i | \(0.510363\pi\) | |||||||
\(662\) | 28.0000 | 1.08825 | ||||||||
\(663\) | 10.6525 | 0.413708 | ||||||||
\(664\) | 5.52786 | 0.214523 | ||||||||
\(665\) | 15.7771 | 0.611809 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.3820 | −0.944073 | ||||||||
\(668\) | −7.14590 | −0.276483 | ||||||||
\(669\) | −5.05573 | −0.195466 | ||||||||
\(670\) | 28.7984 | 1.11258 | ||||||||
\(671\) | 30.3262 | 1.17073 | ||||||||
\(672\) | −0.763932 | −0.0294693 | ||||||||
\(673\) | 17.8541 | 0.688225 | 0.344113 | − | 0.938928i | \(-0.388180\pi\) | ||||
0.344113 | + | 0.938928i | \(0.388180\pi\) | |||||||
\(674\) | 17.0344 | 0.656142 | ||||||||
\(675\) | −10.9230 | −0.420426 | ||||||||
\(676\) | 1.85410 | 0.0713116 | ||||||||
\(677\) | 3.34752 | 0.128656 | 0.0643279 | − | 0.997929i | \(-0.479510\pi\) | ||||
0.0643279 | + | 0.997929i | \(0.479510\pi\) | |||||||
\(678\) | 6.76393 | 0.259767 | ||||||||
\(679\) | −10.4721 | −0.401884 | ||||||||
\(680\) | 12.7639 | 0.489474 | ||||||||
\(681\) | 10.9443 | 0.419385 | ||||||||
\(682\) | −34.7984 | −1.33250 | ||||||||
\(683\) | 35.4164 | 1.35517 | 0.677586 | − | 0.735444i | \(-0.263026\pi\) | ||||
0.677586 | + | 0.735444i | \(0.263026\pi\) | |||||||
\(684\) | −11.7082 | −0.447674 | ||||||||
\(685\) | 55.1591 | 2.10752 | ||||||||
\(686\) | 15.4164 | 0.588601 | ||||||||
\(687\) | 10.5836 | 0.403789 | ||||||||
\(688\) | 0.763932 | 0.0291246 | ||||||||
\(689\) | 32.6525 | 1.24396 | ||||||||
\(690\) | −6.79837 | −0.258810 | ||||||||
\(691\) | −35.7771 | −1.36102 | −0.680512 | − | 0.732737i | \(-0.738243\pi\) | ||||
−0.680512 | + | 0.732737i | \(0.738243\pi\) | |||||||
\(692\) | 8.47214 | 0.322062 | ||||||||
\(693\) | 11.7082 | 0.444758 | ||||||||
\(694\) | 12.7639 | 0.484512 | ||||||||
\(695\) | −5.29180 | −0.200729 | ||||||||
\(696\) | 3.90983 | 0.148202 | ||||||||
\(697\) | −33.0132 | −1.25046 | ||||||||
\(698\) | −12.1803 | −0.461033 | ||||||||
\(699\) | 8.38197 | 0.317035 | ||||||||
\(700\) | 3.88854 | 0.146973 | ||||||||
\(701\) | −3.97871 | −0.150274 | −0.0751370 | − | 0.997173i | \(-0.523939\pi\) | ||||
−0.0751370 | + | 0.997173i | \(0.523939\pi\) | |||||||
\(702\) | −13.3820 | −0.505070 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −3.61803 | −0.136360 | ||||||||
\(705\) | 5.70820 | 0.214983 | ||||||||
\(706\) | 29.7082 | 1.11808 | ||||||||
\(707\) | 15.4164 | 0.579794 | ||||||||
\(708\) | 5.70820 | 0.214527 | ||||||||
\(709\) | −43.2148 | −1.62297 | −0.811483 | − | 0.584377i | \(-0.801339\pi\) | ||||
−0.811483 | + | 0.584377i | \(0.801339\pi\) | |||||||
\(710\) | 42.6525 | 1.60072 | ||||||||
\(711\) | 30.2705 | 1.13523 | ||||||||
\(712\) | −10.4721 | −0.392460 | ||||||||
\(713\) | −37.0689 | −1.38824 | ||||||||
\(714\) | 3.41641 | 0.127856 | ||||||||
\(715\) | 39.7984 | 1.48837 | ||||||||
\(716\) | −18.6525 | −0.697076 | ||||||||
\(717\) | −1.94427 | −0.0726102 | ||||||||
\(718\) | −4.47214 | −0.166899 | ||||||||
\(719\) | 0.583592 | 0.0217643 | 0.0108822 | − | 0.999941i | \(-0.496536\pi\) | ||||
0.0108822 | + | 0.999941i | \(0.496536\pi\) | |||||||
\(720\) | −7.47214 | −0.278470 | ||||||||
\(721\) | 20.1115 | 0.748990 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 6.47214 | 0.240701 | ||||||||
\(724\) | 5.52786 | 0.205441 | ||||||||
\(725\) | −19.9017 | −0.739131 | ||||||||
\(726\) | −1.29180 | −0.0479430 | ||||||||
\(727\) | 23.1459 | 0.858434 | 0.429217 | − | 0.903201i | \(-0.358790\pi\) | ||||
0.429217 | + | 0.903201i | \(0.358790\pi\) | |||||||
\(728\) | 4.76393 | 0.176563 | ||||||||
\(729\) | −8.50658 | −0.315058 | ||||||||
\(730\) | 11.6738 | 0.432065 | ||||||||
\(731\) | −3.41641 | −0.126360 | ||||||||
\(732\) | −5.18034 | −0.191471 | ||||||||
\(733\) | 36.4721 | 1.34713 | 0.673565 | − | 0.739128i | \(-0.264762\pi\) | ||||
0.673565 | + | 0.739128i | \(0.264762\pi\) | |||||||
\(734\) | 27.1246 | 1.00119 | ||||||||
\(735\) | −9.65248 | −0.356037 | ||||||||
\(736\) | −3.85410 | −0.142064 | ||||||||
\(737\) | 36.5066 | 1.34474 | ||||||||
\(738\) | 19.3262 | 0.711409 | ||||||||
\(739\) | −22.0902 | −0.812600 | −0.406300 | − | 0.913740i | \(-0.633181\pi\) | ||||
−0.406300 | + | 0.913740i | \(0.633181\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.6525 | −0.391328 | ||||||||
\(742\) | 10.4721 | 0.384444 | ||||||||
\(743\) | 10.0689 | 0.369392 | 0.184696 | − | 0.982796i | \(-0.440870\pi\) | ||||
0.184696 | + | 0.982796i | \(0.440870\pi\) | |||||||
\(744\) | 5.94427 | 0.217928 | ||||||||
\(745\) | −17.6393 | −0.646255 | ||||||||
\(746\) | −14.2918 | −0.523260 | ||||||||
\(747\) | 14.4721 | 0.529508 | ||||||||
\(748\) | 16.1803 | 0.591612 | ||||||||
\(749\) | 10.2918 | 0.376054 | ||||||||
\(750\) | 3.27051 | 0.119422 | ||||||||
\(751\) | −18.9443 | −0.691286 | −0.345643 | − | 0.938366i | \(-0.612339\pi\) | ||||
−0.345643 | + | 0.938366i | \(0.612339\pi\) | |||||||
\(752\) | 3.23607 | 0.118007 | ||||||||
\(753\) | 1.88854 | 0.0688224 | ||||||||
\(754\) | −24.3820 | −0.887939 | ||||||||
\(755\) | 50.5410 | 1.83938 | ||||||||
\(756\) | −4.29180 | −0.156091 | ||||||||
\(757\) | 10.8541 | 0.394499 | 0.197250 | − | 0.980353i | \(-0.436799\pi\) | ||||
0.197250 | + | 0.980353i | \(0.436799\pi\) | |||||||
\(758\) | −16.9098 | −0.614193 | ||||||||
\(759\) | −8.61803 | −0.312815 | ||||||||
\(760\) | −12.7639 | −0.462996 | ||||||||
\(761\) | −25.8541 | −0.937210 | −0.468605 | − | 0.883408i | \(-0.655243\pi\) | ||||
−0.468605 | + | 0.883408i | \(0.655243\pi\) | |||||||
\(762\) | −0.291796 | −0.0105707 | ||||||||
\(763\) | 18.4721 | 0.668736 | ||||||||
\(764\) | −4.09017 | −0.147977 | ||||||||
\(765\) | 33.4164 | 1.20817 | ||||||||
\(766\) | −17.8885 | −0.646339 | ||||||||
\(767\) | −35.5967 | −1.28532 | ||||||||
\(768\) | 0.618034 | 0.0223014 | ||||||||
\(769\) | 11.8885 | 0.428712 | 0.214356 | − | 0.976756i | \(-0.431235\pi\) | ||||
0.214356 | + | 0.976756i | \(0.431235\pi\) | |||||||
\(770\) | 12.7639 | 0.459980 | ||||||||
\(771\) | 11.7082 | 0.421661 | ||||||||
\(772\) | −4.00000 | −0.143963 | ||||||||
\(773\) | −24.0000 | −0.863220 | −0.431610 | − | 0.902060i | \(-0.642054\pi\) | ||||
−0.431610 | + | 0.902060i | \(0.642054\pi\) | |||||||
\(774\) | 2.00000 | 0.0718885 | ||||||||
\(775\) | −30.2574 | −1.08688 | ||||||||
\(776\) | 8.47214 | 0.304132 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.145898 | −0.00523070 | ||||||||
\(779\) | 33.0132 | 1.18282 | ||||||||
\(780\) | −6.79837 | −0.243421 | ||||||||
\(781\) | 54.0689 | 1.93474 | ||||||||
\(782\) | 17.2361 | 0.616361 | ||||||||
\(783\) | 21.9656 | 0.784985 | ||||||||
\(784\) | −5.47214 | −0.195433 | ||||||||
\(785\) | −21.4853 | −0.766843 | ||||||||
\(786\) | 5.34752 | 0.190740 | ||||||||
\(787\) | −34.4721 | −1.22880 | −0.614399 | − | 0.788995i | \(-0.710602\pi\) | ||||
−0.614399 | + | 0.788995i | \(0.710602\pi\) | |||||||
\(788\) | −16.4721 | −0.586796 | ||||||||
\(789\) | −5.41641 | −0.192829 | ||||||||
\(790\) | 33.0000 | 1.17409 | ||||||||
\(791\) | −13.5279 | −0.480995 | ||||||||
\(792\) | −9.47214 | −0.336578 | ||||||||
\(793\) | 32.3050 | 1.14718 | ||||||||
\(794\) | 10.6525 | 0.378042 | ||||||||
\(795\) | −14.9443 | −0.530019 | ||||||||
\(796\) | −20.9443 | −0.742350 | ||||||||
\(797\) | −12.7295 | −0.450902 | −0.225451 | − | 0.974255i | \(-0.572386\pi\) | ||||
−0.225451 | + | 0.974255i | \(0.572386\pi\) | |||||||
\(798\) | −3.41641 | −0.120940 | ||||||||
\(799\) | −14.4721 | −0.511987 | ||||||||
\(800\) | −3.14590 | −0.111224 | ||||||||
\(801\) | −27.4164 | −0.968711 | ||||||||
\(802\) | −9.23607 | −0.326137 | ||||||||
\(803\) | 14.7984 | 0.522223 | ||||||||
\(804\) | −6.23607 | −0.219929 | ||||||||
\(805\) | 13.5967 | 0.479222 | ||||||||
\(806\) | −37.0689 | −1.30570 | ||||||||
\(807\) | 2.47214 | 0.0870233 | ||||||||
\(808\) | −12.4721 | −0.438768 | ||||||||
\(809\) | −27.1246 | −0.953651 | −0.476825 | − | 0.878998i | \(-0.658213\pi\) | ||||
−0.476825 | + | 0.878998i | \(0.658213\pi\) | |||||||
\(810\) | −16.2918 | −0.572435 | ||||||||
\(811\) | 53.1033 | 1.86471 | 0.932355 | − | 0.361544i | \(-0.117750\pi\) | ||||
0.932355 | + | 0.361544i | \(0.117750\pi\) | |||||||
\(812\) | −7.81966 | −0.274416 | ||||||||
\(813\) | −3.05573 | −0.107169 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 35.5967 | 1.24690 | ||||||||
\(816\) | −2.76393 | −0.0967570 | ||||||||
\(817\) | 3.41641 | 0.119525 | ||||||||
\(818\) | −3.81966 | −0.133551 | ||||||||
\(819\) | 12.4721 | 0.435812 | ||||||||
\(820\) | 21.0689 | 0.735757 | ||||||||
\(821\) | 21.4164 | 0.747438 | 0.373719 | − | 0.927542i | \(-0.378082\pi\) | ||||
0.373719 | + | 0.927542i | \(0.378082\pi\) | |||||||
\(822\) | −11.9443 | −0.416604 | ||||||||
\(823\) | −33.8885 | −1.18128 | −0.590640 | − | 0.806935i | \(-0.701125\pi\) | ||||
−0.590640 | + | 0.806935i | \(0.701125\pi\) | |||||||
\(824\) | −16.2705 | −0.566810 | ||||||||
\(825\) | −7.03444 | −0.244908 | ||||||||
\(826\) | −11.4164 | −0.397228 | ||||||||
\(827\) | −56.0689 | −1.94971 | −0.974853 | − | 0.222849i | \(-0.928464\pi\) | ||||
−0.974853 | + | 0.222849i | \(0.928464\pi\) | |||||||
\(828\) | −10.0902 | −0.350658 | ||||||||
\(829\) | −31.2016 | −1.08368 | −0.541839 | − | 0.840483i | \(-0.682272\pi\) | ||||
−0.541839 | + | 0.840483i | \(0.682272\pi\) | |||||||
\(830\) | 15.7771 | 0.547631 | ||||||||
\(831\) | 4.81966 | 0.167192 | ||||||||
\(832\) | −3.85410 | −0.133617 | ||||||||
\(833\) | 24.4721 | 0.847909 | ||||||||
\(834\) | 1.14590 | 0.0396792 | ||||||||
\(835\) | −20.3951 | −0.705802 | ||||||||
\(836\) | −16.1803 | −0.559609 | ||||||||
\(837\) | 33.3951 | 1.15430 | ||||||||
\(838\) | −9.56231 | −0.330324 | ||||||||
\(839\) | −5.34752 | −0.184617 | −0.0923085 | − | 0.995730i | \(-0.529425\pi\) | ||||
−0.0923085 | + | 0.995730i | \(0.529425\pi\) | |||||||
\(840\) | −2.18034 | −0.0752289 | ||||||||
\(841\) | 11.0213 | 0.380044 | ||||||||
\(842\) | −1.96556 | −0.0677376 | ||||||||
\(843\) | 3.63932 | 0.125345 | ||||||||
\(844\) | −22.2705 | −0.766583 | ||||||||
\(845\) | 5.29180 | 0.182043 | ||||||||
\(846\) | 8.47214 | 0.291278 | ||||||||
\(847\) | 2.58359 | 0.0887733 | ||||||||
\(848\) | −8.47214 | −0.290934 | ||||||||
\(849\) | −6.94427 | −0.238327 | ||||||||
\(850\) | 14.0689 | 0.482559 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −9.23607 | −0.316422 | ||||||||
\(853\) | 12.7426 | 0.436300 | 0.218150 | − | 0.975915i | \(-0.429998\pi\) | ||||
0.218150 | + | 0.975915i | \(0.429998\pi\) | |||||||
\(854\) | 10.3607 | 0.354535 | ||||||||
\(855\) | −33.4164 | −1.14282 | ||||||||
\(856\) | −8.32624 | −0.284585 | ||||||||
\(857\) | 26.9443 | 0.920399 | 0.460199 | − | 0.887816i | \(-0.347778\pi\) | ||||
0.460199 | + | 0.887816i | \(0.347778\pi\) | |||||||
\(858\) | −8.61803 | −0.294215 | ||||||||
\(859\) | −26.5836 | −0.907020 | −0.453510 | − | 0.891251i | \(-0.649828\pi\) | ||||
−0.453510 | + | 0.891251i | \(0.649828\pi\) | |||||||
\(860\) | 2.18034 | 0.0743490 | ||||||||
\(861\) | 5.63932 | 0.192188 | ||||||||
\(862\) | −32.3607 | −1.10221 | ||||||||
\(863\) | −7.41641 | −0.252457 | −0.126229 | − | 0.992001i | \(-0.540287\pi\) | ||||
−0.126229 | + | 0.992001i | \(0.540287\pi\) | |||||||
\(864\) | 3.47214 | 0.118124 | ||||||||
\(865\) | 24.1803 | 0.822156 | ||||||||
\(866\) | 36.3262 | 1.23442 | ||||||||
\(867\) | 1.85410 | 0.0629686 | ||||||||
\(868\) | −11.8885 | −0.403523 | ||||||||
\(869\) | 41.8328 | 1.41908 | ||||||||
\(870\) | 11.1591 | 0.378327 | ||||||||
\(871\) | 38.8885 | 1.31769 | ||||||||
\(872\) | −14.9443 | −0.506077 | ||||||||
\(873\) | 22.1803 | 0.750691 | ||||||||
\(874\) | −17.2361 | −0.583019 | ||||||||
\(875\) | −6.54102 | −0.221127 | ||||||||
\(876\) | −2.52786 | −0.0854086 | ||||||||
\(877\) | 36.8328 | 1.24376 | 0.621878 | − | 0.783114i | \(-0.286370\pi\) | ||||
0.621878 | + | 0.783114i | \(0.286370\pi\) | |||||||
\(878\) | −16.7984 | −0.566918 | ||||||||
\(879\) | 11.5279 | 0.388825 | ||||||||
\(880\) | −10.3262 | −0.348097 | ||||||||
\(881\) | −22.7426 | −0.766219 | −0.383110 | − | 0.923703i | \(-0.625147\pi\) | ||||
−0.383110 | + | 0.923703i | \(0.625147\pi\) | |||||||
\(882\) | −14.3262 | −0.482390 | ||||||||
\(883\) | −29.3050 | −0.986190 | −0.493095 | − | 0.869975i | \(-0.664135\pi\) | ||||
−0.493095 | + | 0.869975i | \(0.664135\pi\) | |||||||
\(884\) | 17.2361 | 0.579712 | ||||||||
\(885\) | 16.2918 | 0.547643 | ||||||||
\(886\) | 18.2705 | 0.613810 | ||||||||
\(887\) | −7.88854 | −0.264871 | −0.132436 | − | 0.991192i | \(-0.542280\pi\) | ||||
−0.132436 | + | 0.991192i | \(0.542280\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.583592 | 0.0195731 | ||||||||
\(890\) | −29.8885 | −1.00187 | ||||||||
\(891\) | −20.6525 | −0.691884 | ||||||||
\(892\) | −8.18034 | −0.273898 | ||||||||
\(893\) | 14.4721 | 0.484292 | ||||||||
\(894\) | 3.81966 | 0.127749 | ||||||||
\(895\) | −53.2361 | −1.77949 | ||||||||
\(896\) | −1.23607 | −0.0412941 | ||||||||
\(897\) | −9.18034 | −0.306523 | ||||||||
\(898\) | −19.5279 | −0.651653 | ||||||||
\(899\) | 60.8460 | 2.02933 | ||||||||
\(900\) | −8.23607 | −0.274536 | ||||||||
\(901\) | 37.8885 | 1.26225 | ||||||||
\(902\) | 26.7082 | 0.889286 | ||||||||
\(903\) | 0.583592 | 0.0194207 | ||||||||
\(904\) | 10.9443 | 0.364001 | ||||||||
\(905\) | 15.7771 | 0.524448 | ||||||||
\(906\) | −10.9443 | −0.363599 | ||||||||
\(907\) | 20.1115 | 0.667790 | 0.333895 | − | 0.942610i | \(-0.391637\pi\) | ||||
0.333895 | + | 0.942610i | \(0.391637\pi\) | |||||||
\(908\) | 17.7082 | 0.587667 | ||||||||
\(909\) | −32.6525 | −1.08301 | ||||||||
\(910\) | 13.5967 | 0.450728 | ||||||||
\(911\) | 21.8885 | 0.725200 | 0.362600 | − | 0.931945i | \(-0.381889\pi\) | ||||
0.362600 | + | 0.931945i | \(0.381889\pi\) | |||||||
\(912\) | 2.76393 | 0.0915229 | ||||||||
\(913\) | 20.0000 | 0.661903 | ||||||||
\(914\) | −29.2361 | −0.967043 | ||||||||
\(915\) | −14.7852 | −0.488784 | ||||||||
\(916\) | 17.1246 | 0.565813 | ||||||||
\(917\) | −10.6950 | −0.353182 | ||||||||
\(918\) | −15.5279 | −0.512496 | ||||||||
\(919\) | −29.8885 | −0.985932 | −0.492966 | − | 0.870049i | \(-0.664087\pi\) | ||||
−0.492966 | + | 0.870049i | \(0.664087\pi\) | |||||||
\(920\) | −11.0000 | −0.362659 | ||||||||
\(921\) | −3.79837 | −0.125161 | ||||||||
\(922\) | −21.0557 | −0.693433 | ||||||||
\(923\) | 57.5967 | 1.89582 | ||||||||
\(924\) | −2.76393 | −0.0909267 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 15.5623 | 0.511409 | ||||||||
\(927\) | −42.5967 | −1.39906 | ||||||||
\(928\) | 6.32624 | 0.207669 | ||||||||
\(929\) | 28.4508 | 0.933442 | 0.466721 | − | 0.884405i | \(-0.345435\pi\) | ||||
0.466721 | + | 0.884405i | \(0.345435\pi\) | |||||||
\(930\) | 16.9656 | 0.556323 | ||||||||
\(931\) | −24.4721 | −0.802042 | ||||||||
\(932\) | 13.5623 | 0.444248 | ||||||||
\(933\) | −1.25735 | −0.0411639 | ||||||||
\(934\) | 20.3607 | 0.666222 | ||||||||
\(935\) | 46.1803 | 1.51026 | ||||||||
\(936\) | −10.0902 | −0.329808 | ||||||||
\(937\) | 57.0476 | 1.86366 | 0.931832 | − | 0.362890i | \(-0.118210\pi\) | ||||
0.931832 | + | 0.362890i | \(0.118210\pi\) | |||||||
\(938\) | 12.4721 | 0.407230 | ||||||||
\(939\) | −3.59675 | −0.117375 | ||||||||
\(940\) | 9.23607 | 0.301247 | ||||||||
\(941\) | −3.81966 | −0.124517 | −0.0622587 | − | 0.998060i | \(-0.519830\pi\) | ||||
−0.0622587 | + | 0.998060i | \(0.519830\pi\) | |||||||
\(942\) | 4.65248 | 0.151586 | ||||||||
\(943\) | 28.4508 | 0.926487 | ||||||||
\(944\) | 9.23607 | 0.300608 | ||||||||
\(945\) | −12.2492 | −0.398467 | ||||||||
\(946\) | 2.76393 | 0.0898632 | ||||||||
\(947\) | 34.8328 | 1.13191 | 0.565957 | − | 0.824435i | \(-0.308507\pi\) | ||||
0.565957 | + | 0.824435i | \(0.308507\pi\) | |||||||
\(948\) | −7.14590 | −0.232088 | ||||||||
\(949\) | 15.7639 | 0.511719 | ||||||||
\(950\) | −14.0689 | −0.456455 | ||||||||
\(951\) | 1.88854 | 0.0612402 | ||||||||
\(952\) | 5.52786 | 0.179159 | ||||||||
\(953\) | −44.4508 | −1.43990 | −0.719952 | − | 0.694024i | \(-0.755836\pi\) | ||||
−0.719952 | + | 0.694024i | \(0.755836\pi\) | |||||||
\(954\) | −22.1803 | −0.718115 | ||||||||
\(955\) | −11.6738 | −0.377754 | ||||||||
\(956\) | −3.14590 | −0.101746 | ||||||||
\(957\) | 14.1459 | 0.457272 | ||||||||
\(958\) | 16.4377 | 0.531078 | ||||||||
\(959\) | 23.8885 | 0.771401 | ||||||||
\(960\) | 1.76393 | 0.0569307 | ||||||||
\(961\) | 61.5066 | 1.98408 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −21.7984 | −0.702443 | ||||||||
\(964\) | 10.4721 | 0.337285 | ||||||||
\(965\) | −11.4164 | −0.367507 | ||||||||
\(966\) | −2.94427 | −0.0947304 | ||||||||
\(967\) | −11.7295 | −0.377195 | −0.188597 | − | 0.982054i | \(-0.560394\pi\) | ||||
−0.188597 | + | 0.982054i | \(0.560394\pi\) | |||||||
\(968\) | −2.09017 | −0.0671806 | ||||||||
\(969\) | −12.3607 | −0.397082 | ||||||||
\(970\) | 24.1803 | 0.776384 | ||||||||
\(971\) | 26.6738 | 0.856002 | 0.428001 | − | 0.903778i | \(-0.359218\pi\) | ||||
0.428001 | + | 0.903778i | \(0.359218\pi\) | |||||||
\(972\) | 13.9443 | 0.447263 | ||||||||
\(973\) | −2.29180 | −0.0734716 | ||||||||
\(974\) | −25.3050 | −0.810823 | ||||||||
\(975\) | −7.49342 | −0.239982 | ||||||||
\(976\) | −8.38197 | −0.268300 | ||||||||
\(977\) | −52.4721 | −1.67873 | −0.839366 | − | 0.543566i | \(-0.817074\pi\) | ||||
−0.839366 | + | 0.543566i | \(0.817074\pi\) | |||||||
\(978\) | −7.70820 | −0.246481 | ||||||||
\(979\) | −37.8885 | −1.21092 | ||||||||
\(980\) | −15.6180 | −0.498900 | ||||||||
\(981\) | −39.1246 | −1.24915 | ||||||||
\(982\) | −27.4508 | −0.875992 | ||||||||
\(983\) | 39.7771 | 1.26869 | 0.634346 | − | 0.773049i | \(-0.281269\pi\) | ||||
0.634346 | + | 0.773049i | \(0.281269\pi\) | |||||||
\(984\) | −4.56231 | −0.145441 | ||||||||
\(985\) | −47.0132 | −1.49796 | ||||||||
\(986\) | −28.2918 | −0.900994 | ||||||||
\(987\) | 2.47214 | 0.0786890 | ||||||||
\(988\) | −17.2361 | −0.548352 | ||||||||
\(989\) | 2.94427 | 0.0936224 | ||||||||
\(990\) | −27.0344 | −0.859211 | ||||||||
\(991\) | 54.1033 | 1.71865 | 0.859324 | − | 0.511431i | \(-0.170884\pi\) | ||||
0.859324 | + | 0.511431i | \(0.170884\pi\) | |||||||
\(992\) | 9.61803 | 0.305373 | ||||||||
\(993\) | −17.3050 | −0.549156 | ||||||||
\(994\) | 18.4721 | 0.585901 | ||||||||
\(995\) | −59.7771 | −1.89506 | ||||||||
\(996\) | −3.41641 | −0.108253 | ||||||||
\(997\) | −53.7771 | −1.70314 | −0.851569 | − | 0.524243i | \(-0.824348\pi\) | ||||
−0.851569 | + | 0.524243i | \(0.824348\pi\) | |||||||
\(998\) | 23.7082 | 0.750470 | ||||||||
\(999\) | 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 | 2738.2.a.g.1.2 | 2 | ||
37.36 | even | 2 | 74.2.a.b.1.2 | ✓ | 2 | ||
111.110 | odd | 2 | 666.2.a.i.1.2 | 2 | |||
148.147 | odd | 2 | 592.2.a.g.1.1 | 2 | |||
185.73 | odd | 4 | 1850.2.b.j.149.2 | 4 | |||
185.147 | odd | 4 | 1850.2.b.j.149.3 | 4 | |||
185.184 | even | 2 | 1850.2.a.t.1.1 | 2 | |||
259.258 | odd | 2 | 3626.2.a.s.1.1 | 2 | |||
296.147 | odd | 2 | 2368.2.a.u.1.2 | 2 | |||
296.221 | even | 2 | 2368.2.a.y.1.1 | 2 | |||
407.406 | odd | 2 | 8954.2.a.j.1.2 | 2 | |||
444.443 | even | 2 | 5328.2.a.bc.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.2.a.b.1.2 | ✓ | 2 | 37.36 | even | 2 | ||
592.2.a.g.1.1 | 2 | 148.147 | odd | 2 | |||
666.2.a.i.1.2 | 2 | 111.110 | odd | 2 | |||
1850.2.a.t.1.1 | 2 | 185.184 | even | 2 | |||
1850.2.b.j.149.2 | 4 | 185.73 | odd | 4 | |||
1850.2.b.j.149.3 | 4 | 185.147 | odd | 4 | |||
2368.2.a.u.1.2 | 2 | 296.147 | odd | 2 | |||
2368.2.a.y.1.1 | 2 | 296.221 | even | 2 | |||
2738.2.a.g.1.2 | 2 | 1.1 | even | 1 | trivial | ||
3626.2.a.s.1.1 | 2 | 259.258 | odd | 2 | |||
5328.2.a.bc.1.2 | 2 | 444.443 | even | 2 | |||
8954.2.a.j.1.2 | 2 | 407.406 | odd | 2 |