Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6004,2,Mod(1,6004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6004, 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("6004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6004 = 2^{2} \cdot 19 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6004.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: | \(47.9421813736\) |
Analytic rank: | \(1\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.24 | ||
Character | \(\chi\) | \(=\) | 6004.1 |
$q$-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 | ||||||||
\(3\) | 2.46349 | 1.42229 | 0.711147 | − | 0.703043i | \(-0.248176\pi\) | ||||
0.711147 | + | 0.703043i | \(0.248176\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.98290 | −1.33400 | −0.666998 | − | 0.745060i | \(-0.732421\pi\) | ||||
−0.666998 | + | 0.745060i | \(0.732421\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.48454 | 0.561104 | 0.280552 | − | 0.959839i | \(-0.409483\pi\) | ||||
0.280552 | + | 0.959839i | \(0.409483\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.06877 | 1.02292 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.74396 | 1.12885 | 0.564423 | − | 0.825486i | \(-0.309099\pi\) | ||||
0.564423 | + | 0.825486i | \(0.309099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.67303 | −1.57342 | −0.786708 | − | 0.617326i | \(-0.788216\pi\) | ||||
−0.786708 | + | 0.617326i | \(0.788216\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.34834 | −1.89733 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.776015 | 0.188211 | 0.0941056 | − | 0.995562i | \(-0.470001\pi\) | ||||
0.0941056 | + | 0.995562i | \(0.470001\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.65715 | 0.798055 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.98298 | −1.03902 | −0.519511 | − | 0.854464i | \(-0.673886\pi\) | ||||
−0.519511 | + | 0.854464i | \(0.673886\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.89772 | 0.779543 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.169406 | 0.0326022 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.20223 | −0.223249 | −0.111625 | − | 0.993750i | \(-0.535605\pi\) | ||||
−0.111625 | + | 0.993750i | \(0.535605\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.15818 | −1.10604 | −0.553021 | − | 0.833168i | \(-0.686525\pi\) | ||||
−0.553021 | + | 0.833168i | \(0.686525\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.22319 | 1.60555 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.42824 | −0.748509 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.57336 | −0.751856 | −0.375928 | − | 0.926649i | \(-0.622676\pi\) | ||||
−0.375928 | + | 0.926649i | \(0.622676\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −13.9754 | −2.23786 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.38928 | −0.997838 | −0.498919 | − | 0.866649i | \(-0.666270\pi\) | ||||
−0.498919 | + | 0.866649i | \(0.666270\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.04640 | 1.07457 | 0.537283 | − | 0.843402i | \(-0.319451\pi\) | ||||
0.537283 | + | 0.843402i | \(0.319451\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.15384 | −1.36457 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.91092 | 0.716331 | 0.358165 | − | 0.933658i | \(-0.383402\pi\) | ||||
0.358165 | + | 0.933658i | \(0.383402\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.79614 | −0.685163 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.91170 | 0.267692 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.3950 | −1.70258 | −0.851292 | − | 0.524693i | \(-0.824180\pi\) | ||||
−0.851292 | + | 0.524693i | \(0.824180\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.1679 | −1.50587 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.46349 | 0.326297 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.5803 | 1.63782 | 0.818910 | − | 0.573922i | \(-0.194579\pi\) | ||||
0.818910 | + | 0.573922i | \(0.194579\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.82838 | −1.13036 | −0.565179 | − | 0.824968i | \(-0.691193\pi\) | ||||
−0.565179 | + | 0.824968i | \(0.691193\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.55571 | 0.573965 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16.9221 | 2.09893 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.66800 | 0.325948 | 0.162974 | − | 0.986630i | \(-0.447891\pi\) | ||||
0.162974 | + | 0.986630i | \(0.447891\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.2755 | −1.47780 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.725716 | 0.0861266 | 0.0430633 | − | 0.999072i | \(-0.486288\pi\) | ||||
0.0430633 | + | 0.999072i | \(0.486288\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.70371 | 0.667569 | 0.333785 | − | 0.942649i | \(-0.391674\pi\) | ||||
0.333785 | + | 0.942649i | \(0.391674\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.60197 | 1.10874 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.55806 | 0.633399 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.00000 | −0.112509 | ||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.78897 | −0.976552 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.75282 | −0.741218 | −0.370609 | − | 0.928789i | \(-0.620851\pi\) | ||||
−0.370609 | + | 0.928789i | \(0.620851\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.31478 | −0.251073 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.96169 | −0.317526 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.60908 | −0.276562 | −0.138281 | − | 0.990393i | \(-0.544158\pi\) | ||||
−0.138281 | + | 0.990393i | \(0.544158\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.42184 | −0.882849 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −15.1706 | −1.57312 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.98290 | −0.306039 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.185948 | 0.0188801 | 0.00944007 | − | 0.999955i | \(-0.496995\pi\) | ||||
0.00944007 | + | 0.999955i | \(0.496995\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.4893 | 1.15472 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.2079 | 1.41374 | 0.706871 | − | 0.707342i | \(-0.250106\pi\) | ||||
0.706871 | + | 0.707342i | \(0.250106\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.703536 | 0.0693214 | 0.0346607 | − | 0.999399i | \(-0.488965\pi\) | ||||
0.0346607 | + | 0.999399i | \(0.488965\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.9089 | −1.06460 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.0528 | −1.45521 | −0.727607 | − | 0.685994i | \(-0.759367\pi\) | ||||
−0.727607 | + | 0.685994i | \(0.759367\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.51819 | 0.911678 | 0.455839 | − | 0.890062i | \(-0.349339\pi\) | ||||
0.455839 | + | 0.890062i | \(0.349339\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.2664 | −1.06936 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.72901 | −0.821156 | −0.410578 | − | 0.911826i | \(-0.634673\pi\) | ||||
−0.410578 | + | 0.911826i | \(0.634673\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.8637 | 1.38605 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −17.4092 | −1.60948 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.15203 | 0.105606 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.01722 | 0.274293 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15.7399 | −1.41922 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.28801 | 0.294088 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.5745 | −0.938334 | −0.469167 | − | 0.883109i | \(-0.655446\pi\) | ||||
−0.469167 | + | 0.883109i | \(0.655446\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 17.3587 | 1.52835 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.1678 | −0.975738 | −0.487869 | − | 0.872917i | \(-0.662226\pi\) | ||||
−0.487869 | + | 0.872917i | \(0.662226\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.48454 | 0.128726 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.505322 | −0.0434912 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.83691 | 0.327809 | 0.163905 | − | 0.986476i | \(-0.447591\pi\) | ||||
0.163905 | + | 0.986476i | \(0.447591\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.6172 | −1.32463 | −0.662317 | − | 0.749224i | \(-0.730427\pi\) | ||||
−0.662317 | + | 0.749224i | \(0.730427\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.0980 | 1.01883 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −21.2396 | −1.77614 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.58615 | 0.297813 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.8152 | −0.974503 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.1279 | −1.40317 | −0.701587 | − | 0.712584i | \(-0.747525\pi\) | ||||
−0.701587 | + | 0.712584i | \(0.747525\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.632870 | 0.0515023 | 0.0257511 | − | 0.999668i | \(-0.491802\pi\) | ||||
0.0257511 | + | 0.999668i | \(0.491802\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.38141 | 0.192525 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.3693 | 1.47545 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.24077 | −0.178833 | −0.0894164 | − | 0.995994i | \(-0.528500\pi\) | ||||
−0.0894164 | + | 0.995994i | \(0.528500\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −30.5349 | −2.42158 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.39743 | −0.582999 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.01895 | 0.706419 | 0.353209 | − | 0.935544i | \(-0.385090\pi\) | ||||
0.353209 | + | 0.935544i | \(0.385090\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −27.5119 | −2.14180 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.1361 | −0.939122 | −0.469561 | − | 0.882900i | \(-0.655588\pi\) | ||||
−0.469561 | + | 0.882900i | \(0.655588\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.1833 | 1.47563 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.06877 | 0.234674 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.4693 | 1.70831 | 0.854154 | − | 0.520020i | \(-0.174076\pi\) | ||||
0.854154 | + | 0.520020i | \(0.174076\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.78632 | 0.437404 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 30.9915 | 2.32946 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.20412 | −0.164744 | −0.0823719 | − | 0.996602i | \(-0.526250\pi\) | ||||
−0.0823719 | + | 0.996602i | \(0.526250\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.82843 | −0.284565 | −0.142282 | − | 0.989826i | \(-0.545444\pi\) | ||||
−0.142282 | + | 0.989826i | \(0.545444\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −21.7486 | −1.60770 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 13.6419 | 1.00297 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.90537 | 0.212461 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.251490 | 0.0182932 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.4697 | −0.974634 | −0.487317 | − | 0.873225i | \(-0.662024\pi\) | ||||
−0.487317 | + | 0.873225i | \(0.662024\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.7367 | 1.49266 | 0.746330 | − | 0.665577i | \(-0.231814\pi\) | ||||
0.746330 | + | 0.665577i | \(0.231814\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 41.6874 | 2.98529 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.92353 | −0.279540 | −0.139770 | − | 0.990184i | \(-0.544636\pi\) | ||||
−0.139770 | + | 0.990184i | \(0.544636\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.8646 | 1.05373 | 0.526863 | − | 0.849950i | \(-0.323368\pi\) | ||||
0.526863 | + | 0.849950i | \(0.323368\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.57258 | 0.463594 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.78477 | −0.125266 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.0586 | 1.33111 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.2916 | −1.06284 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.74396 | 0.258975 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.6197 | −1.48836 | −0.744182 | − | 0.667977i | \(-0.767161\pi\) | ||||
−0.744182 | + | 0.667977i | \(0.767161\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.78779 | 0.122497 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −21.0187 | −1.43347 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.14206 | −0.620604 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.0510 | 0.949480 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.40235 | −0.296134 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.85875 | −0.191436 | −0.0957181 | − | 0.995408i | \(-0.530515\pi\) | ||||
−0.0957181 | + | 0.995408i | \(0.530515\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.9612 | 0.797412 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.5941 | −0.703157 | −0.351578 | − | 0.936158i | \(-0.614355\pi\) | ||||
−0.351578 | + | 0.936158i | \(0.614355\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.38561 | 0.421973 | 0.210986 | − | 0.977489i | \(-0.432332\pi\) | ||||
0.210986 | + | 0.977489i | \(0.432332\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.6922 | 0.900881 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.114938 | 0.00752986 | 0.00376493 | − | 0.999993i | \(-0.498802\pi\) | ||||
0.00376493 | + | 0.999993i | \(0.498802\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.6488 | −0.955582 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.46349 | −0.160021 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.40065 | 0.219970 | 0.109985 | − | 0.993933i | \(-0.464920\pi\) | ||||
0.109985 | + | 0.993933i | \(0.464920\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.1156 | 0.909269 | 0.454634 | − | 0.890678i | \(-0.349770\pi\) | ||||
0.454634 | + | 0.890678i | \(0.349770\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.1597 | −1.42155 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.3064 | 0.914004 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.67303 | −0.360966 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −16.6355 | −1.05423 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.58849 | −0.542101 | −0.271050 | − | 0.962565i | \(-0.587371\pi\) | ||||
−0.271050 | + | 0.962565i | \(0.587371\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.6561 | −1.17290 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.70242 | −0.357100 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.7806 | −0.734851 | −0.367425 | − | 0.930053i | \(-0.619761\pi\) | ||||
−0.367425 | + | 0.930053i | \(0.619761\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.78934 | −0.421869 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.68938 | −0.228367 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.90377 | −0.549030 | −0.274515 | − | 0.961583i | \(-0.588517\pi\) | ||||
−0.274515 | + | 0.961583i | \(0.588517\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 36.9731 | 2.27124 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.42744 | −0.393353 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.78700 | 0.291869 | 0.145934 | − | 0.989294i | \(-0.453381\pi\) | ||||
0.145934 | + | 0.989294i | \(0.453381\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.49157 | −0.272843 | −0.136422 | − | 0.990651i | \(-0.543560\pi\) | ||||
−0.136422 | + | 0.990651i | \(0.543560\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −20.7471 | −1.25567 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14.5929 | 0.879984 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.27428 | −0.316901 | −0.158450 | − | 0.987367i | \(-0.550650\pi\) | ||||
−0.158450 | + | 0.987367i | \(0.550650\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −18.8980 | −1.13139 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.47780 | 0.565398 | 0.282699 | − | 0.959209i | \(-0.408770\pi\) | ||||
0.282699 | + | 0.959209i | \(0.408770\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.7428 | 0.876366 | 0.438183 | − | 0.898886i | \(-0.355622\pi\) | ||||
0.438183 | + | 0.898886i | \(0.355622\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.34834 | −0.435278 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.48515 | −0.559891 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3978 | −0.964577 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.458080 | 0.0268531 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −30.5973 | −1.78752 | −0.893758 | − | 0.448550i | \(-0.851941\pi\) | ||||
−0.893758 | + | 0.448550i | \(0.851941\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −37.5259 | −2.18484 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.634249 | 0.0368029 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 28.2686 | 1.63481 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.4607 | 0.602943 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 35.0011 | 2.01076 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 26.3342 | 1.50789 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.4944 | −0.827238 | −0.413619 | − | 0.910450i | \(-0.635736\pi\) | ||||
−0.413619 | + | 0.910450i | \(0.635736\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.73315 | 0.0985955 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.85849 | −0.559024 | −0.279512 | − | 0.960142i | \(-0.590173\pi\) | ||||
−0.279512 | + | 0.960142i | \(0.590173\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.13440 | 0.233690 | 0.116845 | − | 0.993150i | \(-0.462722\pi\) | ||||
0.116845 | + | 0.993150i | \(0.462722\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −13.5892 | −0.765667 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.3790 | −0.863771 | −0.431885 | − | 0.901929i | \(-0.642151\pi\) | ||||
−0.431885 | + | 0.901929i | \(0.642151\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.50111 | −0.252014 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −37.0825 | −2.06974 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.776015 | 0.0431786 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −22.1119 | −1.22654 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 23.4479 | 1.29667 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.29045 | 0.401936 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.77868 | −0.0977653 | −0.0488827 | − | 0.998805i | \(-0.515566\pi\) | ||||
−0.0488827 | + | 0.998805i | \(0.515566\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.0346 | −0.769090 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.95838 | −0.434813 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.32898 | −0.235815 | −0.117907 | − | 0.993025i | \(-0.537619\pi\) | ||||
−0.117907 | + | 0.993025i | \(0.537619\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −21.5038 | −1.16793 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −23.0560 | −1.24855 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.5118 | −0.945551 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 36.6166 | 1.97137 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.06369 | 0.486564 | 0.243282 | − | 0.969956i | \(-0.421776\pi\) | ||||
0.243282 | + | 0.969956i | \(0.421776\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.21345 | −0.439656 | −0.219828 | − | 0.975539i | \(-0.570550\pi\) | ||||
−0.219828 | + | 0.975539i | \(0.570550\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.961045 | −0.0512968 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.5443 | 0.880563 | 0.440282 | − | 0.897860i | \(-0.354879\pi\) | ||||
0.440282 | + | 0.897860i | \(0.354879\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.16474 | −0.114892 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.83800 | 0.150203 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.62100 | 0.0855532 | 0.0427766 | − | 0.999085i | \(-0.486380\pi\) | ||||
0.0427766 | + | 0.999085i | \(0.486380\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.43288 | 0.390125 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −17.0136 | −0.890534 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.4015 | 1.01275 | 0.506375 | − | 0.862313i | \(-0.330985\pi\) | ||||
0.506375 | + | 0.862313i | \(0.330985\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −19.6072 | −1.02071 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.4009 | −0.955326 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 34.3133 | 1.77668 | 0.888338 | − | 0.459190i | \(-0.151860\pi\) | ||||
0.888338 | + | 0.459190i | \(0.151860\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.09996 | 0.418280 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.82031 | 0.351264 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.7077 | −1.73145 | −0.865725 | − | 0.500521i | \(-0.833142\pi\) | ||||
−0.865725 | + | 0.500521i | \(0.833142\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −26.0501 | −1.33459 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −32.0475 | −1.63755 | −0.818776 | − | 0.574113i | \(-0.805347\pi\) | ||||
−0.818776 | + | 0.574113i | \(0.805347\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.5791 | −0.844952 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 21.6238 | 1.09920 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.7408 | 1.30511 | 0.652556 | − | 0.757741i | \(-0.273697\pi\) | ||||
0.652556 | + | 0.757741i | \(0.273697\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.86686 | −0.195556 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −27.5118 | −1.38779 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.98290 | 0.150086 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.27193 | 0.415156 | 0.207578 | − | 0.978218i | \(-0.433442\pi\) | ||||
0.207578 | + | 0.978218i | \(0.433442\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.65715 | 0.183086 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32.1487 | −1.60543 | −0.802715 | − | 0.596363i | \(-0.796612\pi\) | ||||
−0.802715 | + | 0.596363i | \(0.796612\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 34.9355 | 1.74026 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 26.2167 | 1.30272 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.1225 | −0.848729 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.54609 | −0.323683 | −0.161842 | − | 0.986817i | \(-0.551743\pi\) | ||||
−0.161842 | + | 0.986817i | \(0.551743\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.45217 | 0.466241 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18.6760 | 0.918986 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.1430 | 0.988782 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −38.4728 | −1.88402 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.4824 | 0.609807 | 0.304903 | − | 0.952383i | \(-0.401376\pi\) | ||||
0.304903 | + | 0.952383i | \(0.401376\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.45980 | 0.412306 | 0.206153 | − | 0.978520i | \(-0.433906\pi\) | ||||
0.206153 | + | 0.978520i | \(0.433906\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 15.0705 | 0.732751 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.02468 | 0.146719 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.1061 | −0.634248 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −52.3234 | −2.52620 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.66995 | 0.321280 | 0.160640 | − | 0.987013i | \(-0.448644\pi\) | ||||
0.160640 | + | 0.987013i | \(0.448644\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.79831 | −0.470877 | −0.235438 | − | 0.971889i | \(-0.575653\pi\) | ||||
−0.235438 | + | 0.971889i | \(0.575653\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.83443 | 0.423578 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.98298 | −0.238368 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.97553 | 0.0942869 | 0.0471434 | − | 0.998888i | \(-0.484988\pi\) | ||||
0.0471434 | + | 0.998888i | \(0.484988\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.7182 | −0.700868 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.84638 | −0.277770 | −0.138885 | − | 0.990309i | \(-0.544352\pi\) | ||||
−0.138885 | + | 0.990309i | \(0.544352\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.78264 | 0.368933 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −42.1944 | −1.99573 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −31.2095 | −1.47287 | −0.736434 | − | 0.676510i | \(-0.763492\pi\) | ||||
−0.736434 | + | 0.676510i | \(0.763492\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −23.9212 | −1.12641 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.55907 | 0.0732514 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 25.1215 | 1.17772 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.5289 | −0.492522 | −0.246261 | − | 0.969204i | \(-0.579202\pi\) | ||||
−0.246261 | + | 0.969204i | \(0.579202\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.131462 | 0.00613610 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.27172 | 0.292103 | 0.146052 | − | 0.989277i | \(-0.453343\pi\) | ||||
0.146052 | + | 0.989277i | \(0.453343\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.37514 | 0.0639080 | 0.0319540 | − | 0.999489i | \(-0.489827\pi\) | ||||
0.0319540 | + | 0.999489i | \(0.489827\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 45.2524 | 2.09853 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.63683 | 0.168292 | 0.0841462 | − | 0.996453i | \(-0.473184\pi\) | ||||
0.0841462 | + | 0.996453i | \(0.473184\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.96075 | 0.182891 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.52010 | −0.254353 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 26.3814 | 1.21302 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.89772 | 0.178839 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −38.0374 | −1.74161 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 39.3195 | 1.79655 | 0.898277 | − | 0.439429i | \(-0.144819\pi\) | ||||
0.898277 | + | 0.439429i | \(0.144819\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.9448 | 1.18298 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −18.2235 | −0.829197 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.554665 | −0.0251860 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.9332 | 1.49235 | 0.746173 | − | 0.665752i | \(-0.231889\pi\) | ||||
0.746173 | + | 0.665752i | \(0.231889\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 22.2181 | 1.00474 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.6766 | 0.978252 | 0.489126 | − | 0.872213i | \(-0.337316\pi\) | ||||
0.489126 | + | 0.872213i | \(0.337316\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.932951 | −0.0420180 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −34.2716 | −1.54039 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.07735 | 0.0483259 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.2967 | −0.819072 | −0.409536 | − | 0.912294i | \(-0.634309\pi\) | ||||
−0.409536 | + | 0.912294i | \(0.634309\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −29.8972 | −1.33571 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.4652 | 1.35838 | 0.679188 | − | 0.733964i | \(-0.262332\pi\) | ||||
0.679188 | + | 0.733964i | \(0.262332\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −42.3809 | −1.88593 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 47.2577 | 2.09879 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.24658 | −0.0552539 | −0.0276269 | − | 0.999618i | \(-0.508795\pi\) | ||||
−0.0276269 | + | 0.999618i | \(0.508795\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.46740 | 0.374576 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.169406 | 0.00747946 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.09858 | −0.0924744 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.3863 | 0.808627 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 55.3528 | 2.42972 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.93057 | 0.0845796 | 0.0422898 | − | 0.999105i | \(-0.486535\pi\) | ||||
0.0422898 | + | 0.999105i | \(0.486535\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 43.4590 | 1.90033 | 0.950165 | − | 0.311747i | \(-0.100914\pi\) | ||||
0.950165 | + | 0.311747i | \(0.100914\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 14.2545 | 0.622118 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.77884 | −0.208169 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.83006 | 0.0795677 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 38.6061 | 1.67536 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 36.2466 | 1.57001 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 44.9012 | 1.94125 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.42982 | −0.234314 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −17.9565 | −0.773443 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.9603 | 0.987141 | 0.493571 | − | 0.869706i | \(-0.335691\pi\) | ||||
0.493571 | + | 0.869706i | \(0.335691\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.43128 | −0.404735 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −28.3919 | −1.21617 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.2577 | 1.29373 | 0.646864 | − | 0.762606i | \(-0.276080\pi\) | ||||
0.646864 | + | 0.762606i | \(0.276080\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −27.0922 | −1.15627 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.20223 | −0.0512169 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.48454 | −0.0631291 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 33.6066 | 1.42652 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.0051 | 0.974756 | 0.487378 | − | 0.873191i | \(-0.337953\pi\) | ||||
0.487378 | + | 0.873191i | \(0.337953\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −39.9744 | −1.69074 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.15733 | 0.302183 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.7496 | 0.832348 | 0.416174 | − | 0.909285i | \(-0.363371\pi\) | ||||
0.416174 | + | 0.909285i | \(0.363371\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 26.0378 | 1.09542 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13.0476 | −0.547947 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.6645 | −1.24360 | −0.621801 | − | 0.783175i | \(-0.713599\pi\) | ||||
−0.621801 | + | 0.783175i | \(0.713599\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.09131 | −0.380460 | −0.190230 | − | 0.981740i | \(-0.560923\pi\) | ||||
−0.190230 | + | 0.981740i | \(0.560923\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −33.1825 | −1.38622 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −19.4222 | −0.809963 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.04236 | 0.209916 | 0.104958 | − | 0.994477i | \(-0.466529\pi\) | ||||
0.104958 | + | 0.994477i | \(0.466529\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 51.0845 | 2.12300 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.0248 | −0.415900 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −46.4063 | −1.92195 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 51.9300 | 2.14704 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.0026 | −0.577950 | −0.288975 | − | 0.957337i | \(-0.593314\pi\) | ||||
−0.288975 | + | 0.957337i | \(0.593314\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.15818 | −0.253743 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.66556 | −0.397588 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 33.9610 | 1.39461 | 0.697306 | − | 0.716774i | \(-0.254382\pi\) | ||||
0.697306 | + | 0.716774i | \(0.254382\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.43638 | −0.140878 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 36.6188 | 1.49871 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.6212 | 1.49630 | 0.748150 | − | 0.663529i | \(-0.230942\pi\) | ||||
0.748150 | + | 0.663529i | \(0.230942\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.5665 | 0.716553 | 0.358277 | − | 0.933615i | \(-0.383364\pi\) | ||||
0.358277 | + | 0.933615i | \(0.383364\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.18747 | 0.333419 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.00007 | −0.365905 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.70273 | −0.109701 | −0.0548503 | − | 0.998495i | \(-0.517468\pi\) | ||||
−0.0548503 | + | 0.998495i | \(0.517468\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.39674 | −0.178165 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27.8598 | −1.12709 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 48.2519 | 1.94888 | 0.974439 | − | 0.224654i | \(-0.0721252\pi\) | ||||
0.974439 | + | 0.224654i | \(0.0721252\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 46.9506 | 1.89323 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.58414 | 0.224809 | 0.112405 | − | 0.993663i | \(-0.464145\pi\) | ||||
0.112405 | + | 0.993663i | \(0.464145\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.1367 | −1.45245 | −0.726227 | − | 0.687455i | \(-0.758728\pi\) | ||||
−0.726227 | + | 0.687455i | \(0.758728\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.844146 | −0.0338744 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.87329 | −0.155180 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.2964 | −1.17186 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.22319 | 0.368339 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.54899 | −0.141508 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.9727 | 1.19319 | 0.596596 | − | 0.802541i | \(-0.296519\pi\) | ||||
0.596596 | + | 0.802541i | \(0.296519\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −53.2599 | −2.11689 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 31.5427 | 1.25173 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.2086 | 1.07805 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.22705 | 0.0881008 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.49150 | −0.335394 | −0.167697 | − | 0.985839i | \(-0.553633\pi\) | ||||
−0.167697 | + | 0.985839i | \(0.553633\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.3439 | 1.03890 | 0.519451 | − | 0.854500i | \(-0.326136\pi\) | ||||
0.519451 | + | 0.854500i | \(0.326136\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −51.7794 | −2.03881 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.3732 | −0.761638 | −0.380819 | − | 0.924650i | \(-0.624358\pi\) | ||||
−0.380819 | + | 0.924650i | \(0.624358\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 47.1002 | 1.84885 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −22.5214 | −0.882681 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.14545 | −0.0448249 | −0.0224125 | − | 0.999749i | \(-0.507135\pi\) | ||||
−0.0224125 | + | 0.999749i | \(0.507135\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 33.3126 | 1.30163 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 17.5034 | 0.682872 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.3942 | −1.14504 | −0.572519 | − | 0.819892i | \(-0.694034\pi\) | ||||
−0.572519 | + | 0.819892i | \(0.694034\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.0247 | 1.28451 | 0.642256 | − | 0.766490i | \(-0.277999\pi\) | ||||
0.642256 | + | 0.766490i | \(0.277999\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.8451 | −0.421190 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.42824 | −0.171720 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.99070 | 0.231961 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.04250 | −0.272279 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −33.0531 | −1.27600 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.5562 | 0.946572 | 0.473286 | − | 0.880909i | \(-0.343068\pi\) | ||||
0.473286 | + | 0.880909i | \(0.343068\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.660297 | 0.0254148 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.1017 | 1.11847 | 0.559234 | − | 0.829010i | \(-0.311095\pi\) | ||||
0.559234 | + | 0.829010i | \(0.311095\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.276047 | 0.0105937 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.0985 | −1.00010 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.1310 | −1.22946 | −0.614730 | − | 0.788738i | \(-0.710735\pi\) | ||||
−0.614730 | + | 0.788738i | \(0.710735\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.4451 | −0.437296 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.7309 | 0.600170 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 70.3172 | 2.67887 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.21024 | −0.350374 | −0.175187 | − | 0.984535i | \(-0.556053\pi\) | ||||
−0.175187 | + | 0.984535i | \(0.556053\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 17.0564 | 0.647918 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 46.5846 | 1.76705 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.95818 | −0.187804 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.283149 | 0.0107097 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.8819 | −1.46855 | −0.734274 | − | 0.678853i | \(-0.762477\pi\) | ||||
−0.734274 | + | 0.678853i | \(0.762477\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.57336 | −0.172488 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −36.0871 | −1.35912 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 21.0923 | 0.793256 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.6080 | 0.849062 | 0.424531 | − | 0.905413i | \(-0.360439\pi\) | ||||
0.424531 | + | 0.905413i | \(0.360439\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.06877 | −0.115088 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 30.6861 | 1.14920 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 63.3556 | 2.36937 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.37745 | 0.312862 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28.0851 | −1.04740 | −0.523698 | − | 0.851904i | \(-0.675448\pi\) | ||||
−0.523698 | + | 0.851904i | \(0.675448\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.04443 | 0.0388965 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 34.7737 | 1.29325 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.68597 | −0.174032 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.7897 | 1.58698 | 0.793491 | − | 0.608581i | \(-0.208261\pi\) | ||||
0.793491 | + | 0.608581i | \(0.208261\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28.2233 | −1.04531 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.46811 | 0.202245 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.7829 | 0.915377 | 0.457688 | − | 0.889113i | \(-0.348678\pi\) | ||||
0.457688 | + | 0.889113i | \(0.348678\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 35.2437 | 1.29998 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.98888 | 0.367945 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.0333 | 1.32551 | 0.662753 | − | 0.748838i | \(-0.269388\pi\) | ||||
0.662753 | + | 0.748838i | \(0.269388\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.9754 | −0.513400 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28.9124 | −1.06069 | −0.530347 | − | 0.847781i | \(-0.677938\pi\) | ||||
−0.530347 | + | 0.847781i | \(0.677938\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 51.0909 | 1.87183 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −20.7228 | −0.758209 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −22.3466 | −0.816526 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.50606 | −0.164428 | −0.0822142 | − | 0.996615i | \(-0.526199\pi\) | ||||
−0.0822142 | + | 0.996615i | \(0.526199\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −21.1576 | −0.771027 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.88779 | −0.0687038 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.6921 | 1.11552 | 0.557761 | − | 0.830002i | \(-0.311661\pi\) | ||||
0.557761 | + | 0.830002i | \(0.311661\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −45.9589 | −1.66820 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.5641 | −0.600446 | −0.300223 | − | 0.953869i | \(-0.597061\pi\) | ||||
−0.300223 | + | 0.953869i | \(0.597061\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.1301 | 0.511546 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.10351 | −0.256828 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −71.3686 | −2.57697 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.64468 | −0.239613 | −0.119807 | − | 0.992797i | \(-0.538227\pi\) | ||||
−0.119807 | + | 0.992797i | \(0.538227\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −29.0212 | −1.04517 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.3328 | −0.767286 | −0.383643 | − | 0.923481i | \(-0.625331\pi\) | ||||
−0.383643 | + | 0.923481i | \(0.625331\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.0028 | −0.862207 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.7254 | −0.600022 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.38928 | −0.228920 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.71705 | 0.0972236 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.203666 | −0.00727842 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.68400 | 0.238562 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.238950 | 0.00851765 | 0.00425882 | − | 0.999991i | \(-0.498644\pi\) | ||||
0.00425882 | + | 0.999991i | \(0.498644\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21.9343 | −0.780883 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.9586 | −0.460753 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 50.0837 | 1.77852 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 91.0827 | 3.23037 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.6092 | 1.43845 | 0.719226 | − | 0.694777i | \(-0.244497\pi\) | ||||
0.719226 | + | 0.694777i | \(0.244497\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.81094 | 0.134821 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.00667 | −0.282902 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 21.3545 | 0.753583 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22.0658 | 0.777718 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.7927 | 0.415124 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 52.3709 | 1.84126 | 0.920632 | − | 0.390431i | \(-0.127674\pi\) | ||||
0.920632 | + | 0.390431i | \(0.127674\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.0170 | −0.667776 | −0.333888 | − | 0.942613i | \(-0.608361\pi\) | ||||
−0.333888 | + | 0.942613i | \(0.608361\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.0649 | −0.388063 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −26.9027 | −0.942359 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.04640 | 0.246522 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −25.8447 | −0.903086 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.4288 | −1.02707 | −0.513535 | − | 0.858068i | \(-0.671664\pi\) | ||||
−0.513535 | + | 0.858068i | \(0.671664\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.1108 | −0.840449 | −0.420225 | − | 0.907420i | \(-0.638049\pi\) | ||||
−0.420225 | + | 0.907420i | \(0.638049\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 35.9494 | 1.25160 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.38960 | −0.0830944 | −0.0415472 | − | 0.999137i | \(-0.513229\pi\) | ||||
−0.0415472 | + | 0.999137i | \(0.513229\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −44.2534 | −1.53698 | −0.768492 | − | 0.639860i | \(-0.778992\pi\) | ||||
−0.768492 | + | 0.639860i | \(0.778992\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.9931 | −0.450726 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.72187 | −0.128955 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 36.2009 | 1.25278 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.04323 | −0.0360594 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −46.7820 | −1.61509 | −0.807547 | − | 0.589803i | \(-0.799206\pi\) | ||||
−0.807547 | + | 0.589803i | \(0.799206\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.5546 | −0.950160 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 23.3484 | 0.804163 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −57.2218 | −1.96849 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.47918 | 0.153907 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 36.3186 | 1.24645 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 22.7889 | 0.781195 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.2185 | −0.726509 | −0.363255 | − | 0.931690i | \(-0.618334\pi\) | ||||
−0.363255 | + | 0.931690i | \(0.618334\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.15384 | −0.313055 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −54.2612 | −1.85353 | −0.926763 | − | 0.375645i | \(-0.877421\pi\) | ||||
−0.926763 | + | 0.375645i | \(0.877421\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.93585 | 0.100170 | 0.0500850 | − | 0.998745i | \(-0.484051\pi\) | ||||
0.0500850 | + | 0.998745i | \(0.484051\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −23.3665 | −0.796329 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.75145 | −0.331943 | −0.165972 | − | 0.986131i | \(-0.553076\pi\) | ||||
−0.165972 | + | 0.986131i | \(0.553076\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −67.0237 | −2.27887 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −40.3958 | −1.37191 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.74396 | −0.127005 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.1356 | −0.512851 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.570631 | 0.0193129 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.88118 | 0.165014 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.8712 | 0.603467 | 0.301734 | − | 0.953392i | \(-0.402435\pi\) | ||||
0.301734 | + | 0.953392i | \(0.402435\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −75.3761 | −2.54237 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.816355 | 0.0275037 | 0.0137519 | − | 0.999905i | \(-0.495623\pi\) | ||||
0.0137519 | + | 0.999905i | \(0.495623\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.2581 | 0.950960 | 0.475480 | − | 0.879726i | \(-0.342274\pi\) | ||||
0.475480 | + | 0.879726i | \(0.342274\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −92.4446 | −3.10749 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.805723 | 0.0270535 | 0.0135268 | − | 0.999909i | \(-0.495694\pi\) | ||||
0.0135268 | + | 0.999909i | \(0.495694\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15.6983 | −0.526503 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −32.9055 | −1.10238 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.91092 | 0.164338 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.57468 | 0.219767 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 69.6392 | 2.32519 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.40357 | 0.246923 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.61870 | −0.320445 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 25.7697 | 0.857562 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.4198 | 0.379608 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 54.3897 | 1.80598 | 0.902991 | − | 0.429659i | \(-0.141366\pi\) | ||||
0.902991 | + | 0.429659i | \(0.141366\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 43.6008 | 1.44615 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.0649 | 1.55933 | 0.779665 | − | 0.626196i | \(-0.215389\pi\) | ||||
0.779665 | + | 0.626196i | \(0.215389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −25.2823 | −0.836721 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 64.8740 | 2.14467 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.5791 | −0.547490 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.6447 | −0.779967 | −0.389983 | − | 0.920822i | \(-0.627519\pi\) | ||||
−0.389983 | + | 0.920822i | \(0.627519\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −35.7067 | −1.17658 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.11701 | −0.135513 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.8257 | −0.586104 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.15899 | 0.0709104 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −56.1042 | −1.84072 | −0.920360 | − | 0.391072i | \(-0.872104\pi\) | ||||
−0.920360 | + | 0.391072i | \(0.872104\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.79614 | −0.157187 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.2863 | −0.795096 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.66643 | −0.283423 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.9436 | 0.945545 | 0.472772 | − | 0.881185i | \(-0.343253\pi\) | ||||
0.472772 | + | 0.881185i | \(0.343253\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.1850 | 0.332376 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.9849 | −0.781885 | −0.390942 | − | 0.920415i | \(-0.627851\pi\) | ||||
−0.390942 | + | 0.920415i | \(0.627851\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31.8376 | 1.03678 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.750171 | −0.0244031 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.0634084 | 0.00206050 | 0.00103025 | − | 0.999999i | \(-0.499672\pi\) | ||||
0.00103025 | + | 0.999999i | \(0.499672\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −32.3573 | −1.05036 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −37.8860 | −1.22854 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.789685 | 0.0255804 | 0.0127902 | − | 0.999918i | \(-0.495929\pi\) | ||||
0.0127902 | + | 0.999918i | \(0.495929\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 40.1789 | 1.30016 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.0884 | −0.358438 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.69604 | 0.183935 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.92315 | 0.223327 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −46.1937 | −1.48857 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −61.8555 | −1.99120 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.2811 | −0.780828 | −0.390414 | − | 0.920639i | \(-0.627668\pi\) | ||||
−0.390414 | + | 0.920639i | \(0.627668\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.91170 | 0.0614127 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.9003 | 1.24837 | 0.624185 | − | 0.781276i | \(-0.285431\pi\) | ||||
0.624185 | + | 0.781276i | \(0.285431\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23.1844 | −0.743256 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −54.4723 | −1.74451 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −53.6926 | −1.71778 | −0.858889 | − | 0.512162i | \(-0.828845\pi\) | ||||
−0.858889 | + | 0.512162i | \(0.828845\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.76829 | −0.312196 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29.2091 | 0.932575 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.9429 | −0.827448 | −0.413724 | − | 0.910402i | \(-0.635772\pi\) | ||||
−0.413724 | + | 0.910402i | \(0.635772\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.7035 | 0.372905 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 17.9599 | 0.571671 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −35.1120 | −1.11650 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.3334 | 0.804743 | 0.402372 | − | 0.915476i | \(-0.368186\pi\) | ||||
0.402372 | + | 0.915476i | \(0.368186\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.38177 | −0.139051 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −44.3397 | −1.40566 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.0487709 | 0.00154459 | 0.000772294 | − | 1.00000i | \(-0.499754\pi\) | ||||
0.000772294 | 1.00000i | \(0.499754\pi\) | ||||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.774755 | −0.0245122 |
(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 | 6004.2.a.g.1.24 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6004.2.a.g.1.24 | ✓ | 27 | 1.1 | even | 1 | trivial |