Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, 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("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(0\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-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 | ||||||||
\(3\) | −1.42091 | −0.820362 | −0.410181 | − | 0.912004i | \(-0.634534\pi\) | ||||
−0.410181 | + | 0.912004i | \(0.634534\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.43075 | −1.53428 | −0.767139 | − | 0.641481i | \(-0.778320\pi\) | ||||
−0.767139 | + | 0.641481i | \(0.778320\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.534513 | 0.202027 | 0.101013 | − | 0.994885i | \(-0.467791\pi\) | ||||
0.101013 | + | 0.994885i | \(0.467791\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.981020 | −0.327007 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.02073 | 0.609273 | 0.304637 | − | 0.952469i | \(-0.401465\pi\) | ||||
0.304637 | + | 0.952469i | \(0.401465\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.33304 | −0.369720 | −0.184860 | − | 0.982765i | \(-0.559183\pi\) | ||||
−0.184860 | + | 0.982765i | \(0.559183\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.87478 | 1.25866 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.74602 | −0.666007 | −0.333004 | − | 0.942926i | \(-0.608062\pi\) | ||||
−0.333004 | + | 0.942926i | \(0.608062\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.29614 | −0.526771 | −0.263385 | − | 0.964691i | \(-0.584839\pi\) | ||||
−0.263385 | + | 0.964691i | \(0.584839\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.759494 | −0.165735 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.13304 | −1.48734 | −0.743671 | − | 0.668546i | \(-0.766917\pi\) | ||||
−0.743671 | + | 0.668546i | \(0.766917\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.77004 | 1.35401 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.65666 | 1.08863 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.32409 | −1.36005 | −0.680025 | − | 0.733189i | \(-0.738031\pi\) | ||||
−0.680025 | + | 0.733189i | \(0.738031\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.25667 | 0.225705 | 0.112852 | − | 0.993612i | \(-0.464001\pi\) | ||||
0.112852 | + | 0.993612i | \(0.464001\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.87127 | −0.499824 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.83378 | −0.309965 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.73951 | −0.450373 | −0.225186 | − | 0.974316i | \(-0.572299\pi\) | ||||
−0.225186 | + | 0.974316i | \(0.572299\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.89413 | 0.303304 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.4882 | −1.63798 | −0.818990 | − | 0.573808i | \(-0.805465\pi\) | ||||
−0.818990 | + | 0.573808i | \(0.805465\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.16757 | 0.940545 | 0.470273 | − | 0.882521i | \(-0.344156\pi\) | ||||
0.470273 | + | 0.882521i | \(0.344156\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.36563 | 0.501719 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.32098 | 0.776145 | 0.388072 | − | 0.921629i | \(-0.373141\pi\) | ||||
0.388072 | + | 0.921629i | \(0.373141\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.71430 | −0.959185 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.90184 | 0.546367 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.73392 | 0.375533 | 0.187766 | − | 0.982214i | \(-0.439875\pi\) | ||||
0.187766 | + | 0.982214i | \(0.439875\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.93262 | −0.934794 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.26260 | 0.432143 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.37055 | 0.308620 | 0.154310 | − | 0.988022i | \(-0.450685\pi\) | ||||
0.154310 | + | 0.988022i | \(0.450685\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.88421 | −0.369285 | −0.184642 | − | 0.982806i | \(-0.559113\pi\) | ||||
−0.184642 | + | 0.982806i | \(0.559113\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.524368 | −0.0660641 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.57334 | 0.567252 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.96331 | −0.972873 | −0.486437 | − | 0.873716i | \(-0.661704\pi\) | ||||
−0.486437 | + | 0.873716i | \(0.661704\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.1354 | 1.22016 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.75154 | −1.15729 | −0.578647 | − | 0.815578i | \(-0.696419\pi\) | ||||
−0.578647 | + | 0.815578i | \(0.696419\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.03091 | 0.237701 | 0.118850 | − | 0.992912i | \(-0.462079\pi\) | ||||
0.118850 | + | 0.992912i | \(0.462079\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9.61961 | −1.11078 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.08011 | 0.123090 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.43818 | 0.274317 | 0.137158 | − | 0.990549i | \(-0.456203\pi\) | ||||
0.137158 | + | 0.990549i | \(0.456203\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.09454 | −0.566060 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16.3530 | −1.79497 | −0.897485 | − | 0.441044i | \(-0.854608\pi\) | ||||
−0.897485 | + | 0.441044i | \(0.854608\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.42090 | 1.02184 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.4069 | 1.11573 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.73118 | −0.183505 | −0.0917524 | − | 0.995782i | \(-0.529247\pi\) | ||||
−0.0917524 | + | 0.995782i | \(0.529247\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.712528 | −0.0746933 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.78561 | −0.185159 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.87748 | 0.808213 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.8188 | −1.09848 | −0.549242 | − | 0.835664i | \(-0.685083\pi\) | ||||
−0.549242 | + | 0.835664i | \(0.685083\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.98238 | −0.199236 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.6266 | 1.85342 | 0.926709 | − | 0.375779i | \(-0.122625\pi\) | ||||
0.926709 | + | 0.375779i | \(0.122625\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.2212 | −1.10566 | −0.552830 | − | 0.833294i | \(-0.686452\pi\) | ||||
−0.552830 | + | 0.833294i | \(0.686452\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.60563 | 0.254284 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.3155 | −1.67395 | −0.836976 | − | 0.547240i | \(-0.815679\pi\) | ||||
−0.836976 | + | 0.547240i | \(0.815679\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.23092 | −0.596814 | −0.298407 | − | 0.954439i | \(-0.596455\pi\) | ||||
−0.298407 | + | 0.954439i | \(0.596455\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.89259 | 0.369469 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.26670 | −0.495450 | −0.247725 | − | 0.968830i | \(-0.579683\pi\) | ||||
−0.247725 | + | 0.968830i | \(0.579683\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 24.4717 | 2.28200 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.30774 | 0.120901 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.46778 | −0.134551 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.91665 | −0.628786 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 14.9028 | 1.34374 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.07258 | −0.543148 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.62744 | 0.321884 | 0.160942 | − | 0.986964i | \(-0.448547\pi\) | ||||
0.160942 | + | 0.986964i | \(0.448547\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.76355 | −0.771587 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.36615 | −0.468842 | −0.234421 | − | 0.972135i | \(-0.575319\pi\) | ||||
−0.234421 | + | 0.972135i | \(0.575319\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.22732 | −0.106422 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −19.4066 | −1.67025 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.5089 | −1.06871 | −0.534355 | − | 0.845260i | \(-0.679445\pi\) | ||||
−0.534355 | + | 0.845260i | \(0.679445\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.9616 | 1.01457 | 0.507284 | − | 0.861779i | \(-0.330650\pi\) | ||||
0.507284 | + | 0.861779i | \(0.330650\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.56062 | −0.636719 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.69372 | −0.225260 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 25.1271 | 2.08669 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.54040 | 0.786879 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.81477 | 0.558288 | 0.279144 | − | 0.960249i | \(-0.409949\pi\) | ||||
0.279144 | + | 0.960249i | \(0.409949\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.3242 | 0.921554 | 0.460777 | − | 0.887516i | \(-0.347571\pi\) | ||||
0.460777 | + | 0.887516i | \(0.347571\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.69390 | 0.217789 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.31132 | −0.346294 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.15016 | 0.331219 | 0.165609 | − | 0.986191i | \(-0.447041\pi\) | ||||
0.165609 | + | 0.986191i | \(0.447041\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.88465 | −0.308073 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.81270 | −0.300483 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.0540 | 0.944139 | 0.472070 | − | 0.881561i | \(-0.343507\pi\) | ||||
0.472070 | + | 0.881561i | \(0.343507\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.85062 | 0.766870 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.9165 | 1.77334 | 0.886668 | − | 0.462407i | \(-0.153014\pi\) | ||||
0.886668 | + | 0.462407i | \(0.153014\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.2230 | −0.863307 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.25256 | 0.172257 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.2546 | −0.855670 | −0.427835 | − | 0.903857i | \(-0.640724\pi\) | ||||
−0.427835 | + | 0.903857i | \(0.640724\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.61868 | 0.273546 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.36834 | −0.253180 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.42395 | −0.480148 | −0.240074 | − | 0.970755i | \(-0.577172\pi\) | ||||
−0.240074 | + | 0.970755i | \(0.577172\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.2203 | 1.35430 | 0.677150 | − | 0.735845i | \(-0.263215\pi\) | ||||
0.677150 | + | 0.735845i | \(0.263215\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.09819 | 0.302947 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.39858 | 0.690997 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.54896 | −0.405780 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.02356 | 0.219932 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.1949 | −1.75068 | −0.875341 | − | 0.483506i | \(-0.839363\pi\) | ||||
−0.875341 | + | 0.483506i | \(0.839363\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.721920 | 0.0519649 | 0.0259825 | − | 0.999662i | \(-0.491729\pi\) | ||||
0.0259825 | + | 0.999662i | \(0.491729\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.49829 | −0.465352 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.5422 | 1.32108 | 0.660538 | − | 0.750793i | \(-0.270328\pi\) | ||||
0.660538 | + | 0.750793i | \(0.270328\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.5856 | 1.17572 | 0.587862 | − | 0.808961i | \(-0.299970\pi\) | ||||
0.587862 | + | 0.808961i | \(0.299970\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.3151 | 0.798108 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.91482 | −0.274767 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 35.9823 | 2.51312 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.99765 | 0.486370 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.63988 | −0.320947 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.2846 | 1.32761 | 0.663805 | − | 0.747906i | \(-0.268941\pi\) | ||||
0.663805 | + | 0.747906i | \(0.268941\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.8560 | 0.949400 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −21.1594 | −1.44306 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.671706 | 0.0455984 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.88574 | −0.195000 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.66056 | 0.246236 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.72788 | −0.450532 | −0.225266 | − | 0.974297i | \(-0.572325\pi\) | ||||
−0.225266 | + | 0.974297i | \(0.572325\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.64155 | −0.442770 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.8744 | −0.987245 | −0.493623 | − | 0.869676i | \(-0.664328\pi\) | ||||
−0.493623 | + | 0.869676i | \(0.664328\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.46475 | −0.361121 | −0.180560 | − | 0.983564i | \(-0.557791\pi\) | ||||
−0.180560 | + | 0.983564i | \(0.557791\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.53473 | −0.100978 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.81016 | 0.249612 | 0.124806 | − | 0.992181i | \(-0.460169\pi\) | ||||
0.124806 | + | 0.992181i | \(0.460169\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.2549 | −1.19082 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.46443 | −0.225039 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 30.7876 | 1.99148 | 0.995742 | − | 0.0921882i | \(-0.0293861\pi\) | ||||
0.995742 | + | 0.0921882i | \(0.0293861\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.9658 | 1.15728 | 0.578638 | − | 0.815585i | \(-0.303584\pi\) | ||||
0.578638 | + | 0.815585i | \(0.303584\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.73111 | −0.624251 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 23.0351 | 1.47166 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.06085 | 0.194757 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 23.2361 | 1.47253 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.04855 | −0.192423 | −0.0962113 | − | 0.995361i | \(-0.530672\pi\) | ||||
−0.0962113 | + | 0.995361i | \(0.530672\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.4140 | −0.906197 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −13.3862 | −0.838279 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.3990 | 1.08532 | 0.542660 | − | 0.839953i | \(-0.317417\pi\) | ||||
0.542660 | + | 0.839953i | \(0.317417\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.46430 | −0.0909874 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.18508 | 0.444745 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.3874 | −1.44213 | −0.721064 | − | 0.692868i | \(-0.756347\pi\) | ||||
−0.721064 | + | 0.692868i | \(0.756347\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.37940 | −0.576172 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.45985 | 0.150540 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.1181 | 1.16565 | 0.582825 | − | 0.812598i | \(-0.301947\pi\) | ||||
0.582825 | + | 0.812598i | \(0.301947\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.62607 | −0.463251 | −0.231625 | − | 0.972805i | \(-0.574404\pi\) | ||||
−0.231625 | + | 0.972805i | \(0.574404\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.01244 | 0.0612755 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.6804 | 0.824961 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.6187 | 1.77961 | 0.889807 | − | 0.456336i | \(-0.150839\pi\) | ||||
0.889807 | + | 0.456336i | \(0.150839\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.23282 | −0.0738069 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.0003 | 1.13346 | 0.566731 | − | 0.823903i | \(-0.308208\pi\) | ||||
0.566731 | + | 0.823903i | \(0.308208\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.3732 | 1.09217 | 0.546087 | − | 0.837729i | \(-0.316117\pi\) | ||||
0.546087 | + | 0.837729i | \(0.316117\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −11.1932 | −0.663027 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.60607 | −0.330916 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.45938 | −0.556434 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.3725 | 0.901154 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 29.4043 | 1.71782 | 0.858909 | − | 0.512129i | \(-0.171143\pi\) | ||||
0.858909 | + | 0.512129i | \(0.171143\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.13278 | −0.473509 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.4306 | 0.663270 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.50865 | 0.549899 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.29664 | 0.190015 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −26.4667 | −1.52047 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.89499 | 0.566585 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.7169 | 1.46774 | 0.733871 | − | 0.679289i | \(-0.237712\pi\) | ||||
0.733871 | + | 0.679289i | \(0.237712\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.9443 | 0.907041 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −30.0912 | −1.70631 | −0.853156 | − | 0.521655i | \(-0.825315\pi\) | ||||
−0.853156 | + | 0.521655i | \(0.825315\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.10566 | 0.401636 | 0.200818 | − | 0.979629i | \(-0.435640\pi\) | ||||
0.200818 | + | 0.979629i | \(0.435640\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.79897 | 0.101361 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.94735 | 0.502533 | 0.251267 | − | 0.967918i | \(-0.419153\pi\) | ||||
0.251267 | + | 0.967918i | \(0.419153\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.8000 | −0.828642 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 24.6037 | 1.37325 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.30524 | 0.350833 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.02476 | −0.500603 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.85357 | 0.489604 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.84413 | 0.156802 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.50527 | −0.247632 | −0.123816 | − | 0.992305i | \(-0.539513\pi\) | ||||
−0.123816 | + | 0.992305i | \(0.539513\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.68751 | 0.147275 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 27.3201 | 1.49266 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.6487 | 1.66954 | 0.834772 | − | 0.550596i | \(-0.185600\pi\) | ||||
0.834772 | + | 0.550596i | \(0.185600\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.48350 | 0.406448 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.53939 | 0.137516 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.33047 | −0.395808 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −34.7720 | −1.87206 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.6588 | 0.786923 | 0.393462 | − | 0.919341i | \(-0.371277\pi\) | ||||
0.393462 | + | 0.919341i | \(0.371277\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.0146 | −1.44606 | −0.723030 | − | 0.690817i | \(-0.757251\pi\) | ||||
−0.723030 | + | 0.690817i | \(0.757251\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.54057 | −0.402486 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.73538 | 0.464938 | 0.232469 | − | 0.972604i | \(-0.425320\pi\) | ||||
0.232469 | + | 0.972604i | \(0.425320\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 33.4551 | 1.77561 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.08558 | 0.110381 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.12674 | 0.0594669 | 0.0297334 | − | 0.999558i | \(-0.490534\pi\) | ||||
0.0297334 | + | 0.999558i | \(0.490534\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.7277 | −0.722513 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.82792 | 0.515832 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.96756 | −0.364699 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.7255 | −1.60386 | −0.801928 | − | 0.597421i | \(-0.796192\pi\) | ||||
−0.801928 | + | 0.597421i | \(0.796192\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.2891 | 0.535630 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.46132 | 0.0758677 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.67812 | 0.242224 | 0.121112 | − | 0.992639i | \(-0.461354\pi\) | ||||
0.121112 | + | 0.992639i | \(0.461354\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.62858 | 0.445578 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.76332 | 0.502837 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.98838 | −0.513069 | −0.256534 | − | 0.966535i | \(-0.582581\pi\) | ||||
−0.256534 | + | 0.966535i | \(0.582581\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.15426 | −0.264061 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.5330 | −0.589310 | −0.294655 | − | 0.955604i | \(-0.595205\pi\) | ||||
−0.294655 | + | 0.955604i | \(0.595205\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.70558 | −0.188854 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.05050 | −0.307564 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.2244 | 0.822609 | 0.411304 | − | 0.911498i | \(-0.365073\pi\) | ||||
0.411304 | + | 0.911498i | \(0.365073\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.5875 | 0.990581 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.62480 | 0.384620 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.36479 | −0.420878 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.9202 | 1.45147 | 0.725733 | − | 0.687977i | \(-0.241501\pi\) | ||||
0.725733 | + | 0.687977i | \(0.241501\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.74390 | 0.0873044 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.49304 | −0.424122 | −0.212061 | − | 0.977256i | \(-0.568018\pi\) | ||||
−0.212061 | + | 0.977256i | \(0.568018\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.67519 | −0.0834474 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 17.4781 | 0.868494 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.53581 | −0.274400 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.0666 | 1.19002 | 0.595008 | − | 0.803720i | \(-0.297149\pi\) | ||||
0.595008 | + | 0.803720i | \(0.297149\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.7740 | 0.876729 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.26709 | 0.0623495 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 56.1029 | 2.75398 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.9963 | −0.832313 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.4107 | 0.704009 | 0.352004 | − | 0.935998i | \(-0.385500\pi\) | ||||
0.352004 | + | 0.935998i | \(0.385500\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.3454 | −1.23526 | −0.617630 | − | 0.786468i | \(-0.711907\pi\) | ||||
−0.617630 | + | 0.786468i | \(0.711907\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.21998 | −0.253804 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −18.5907 | −0.901780 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.54165 | −0.0746055 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.82753 | 0.184795 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.8824 | −1.19854 | −0.599272 | − | 0.800546i | \(-0.704543\pi\) | ||||
−0.599272 | + | 0.800546i | \(0.704543\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.5652 | −1.42081 | −0.710406 | − | 0.703792i | \(-0.751489\pi\) | ||||
−0.710406 | + | 0.703792i | \(0.751489\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −35.7033 | −1.71184 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.3785 | 0.783488 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.8822 | 0.614836 | 0.307418 | − | 0.951575i | \(-0.400535\pi\) | ||||
0.307418 | + | 0.951575i | \(0.400535\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.58686 | 0.313660 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.52766 | 0.357650 | 0.178825 | − | 0.983881i | \(-0.442770\pi\) | ||||
0.178825 | + | 0.983881i | \(0.442770\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.93925 | 0.281547 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.68316 | −0.457998 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.3085 | −1.19438 | −0.597190 | − | 0.802100i | \(-0.703716\pi\) | ||||
−0.597190 | + | 0.802100i | \(0.703716\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.1938 | −0.997977 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.0907 | −0.756007 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.44451 | 0.114600 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.3782 | 0.719363 | 0.359682 | − | 0.933075i | \(-0.382885\pi\) | ||||
0.359682 | + | 0.933075i | \(0.382885\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −15.5333 | −0.725033 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.4478 | −0.812624 | −0.406312 | − | 0.913734i | \(-0.633185\pi\) | ||||
−0.406312 | + | 0.913734i | \(0.633185\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.6244 | −0.726130 | −0.363065 | − | 0.931764i | \(-0.618270\pi\) | ||||
−0.363065 | + | 0.931764i | \(0.618270\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.12599 | 0.284086 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.57103 | −0.442895 | −0.221447 | − | 0.975172i | \(-0.571078\pi\) | ||||
−0.221447 | + | 0.975172i | \(0.571078\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.25649 | −0.196547 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.89699 | −0.271719 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.4630 | 0.573049 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15.5450 | −0.713252 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.68203 | −0.122802 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 28.0103 | 1.27982 | 0.639912 | − | 0.768448i | \(-0.278971\pi\) | ||||
0.639912 | + | 0.768448i | \(0.278971\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.65189 | 0.166512 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.41750 | 0.246505 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 37.1166 | 1.68538 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.40682 | −0.109063 | −0.0545317 | − | 0.998512i | \(-0.517367\pi\) | ||||
−0.0545317 | + | 0.998512i | \(0.517367\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.1276 | −0.774536 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.7804 | −0.892677 | −0.446339 | − | 0.894864i | \(-0.647272\pi\) | ||||
−0.446339 | + | 0.894864i | \(0.647272\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.1121 | 0.905803 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.80104 | 0.305684 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.21232 | −0.233805 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.4300 | 0.466911 | 0.233455 | − | 0.972368i | \(-0.424997\pi\) | ||||
0.233455 | + | 0.972368i | \(0.424997\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −32.5623 | −1.45478 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.51291 | −0.201221 | −0.100610 | − | 0.994926i | \(-0.532080\pi\) | ||||
−0.100610 | + | 0.994926i | \(0.532080\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −63.9033 | −2.84366 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.9469 | 0.708224 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.16980 | −0.229147 | −0.114574 | − | 0.993415i | \(-0.536550\pi\) | ||||
−0.114574 | + | 0.993415i | \(0.536550\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.08555 | 0.0480219 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.9885 | −0.573456 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 38.4972 | 1.69639 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.7523 | 0.472884 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.9917 | 0.701959 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.32701 | 0.0581373 | 0.0290687 | − | 0.999577i | \(-0.490746\pi\) | ||||
0.0290687 | + | 0.999577i | \(0.490746\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −37.7140 | −1.64912 | −0.824560 | − | 0.565774i | \(-0.808577\pi\) | ||||
−0.824560 | + | 0.565774i | \(0.808577\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.14181 | −0.224407 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.45084 | −0.150321 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.8803 | 1.21219 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.32556 | −0.100921 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.9812 | 0.605593 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 59.4051 | 2.56831 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.12784 | 0.393895 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.5678 | −0.584406 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.5239 | 0.753410 | 0.376705 | − | 0.926333i | \(-0.377057\pi\) | ||||
0.376705 | + | 0.926333i | \(0.377057\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −25.8893 | −1.11102 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 21.3767 | 0.915679 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −43.4808 | −1.85911 | −0.929553 | − | 0.368689i | \(-0.879807\pi\) | ||||
−0.929553 | + | 0.368689i | \(0.879807\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.82946 | 0.120759 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.8171 | 0.716434 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.30324 | 0.0554194 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.3545 | −0.566868 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.8982 | −0.716000 | −0.358000 | − | 0.933722i | \(-0.616541\pi\) | ||||
−0.358000 | + | 0.933722i | \(0.616541\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.22163 | −0.347738 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.88457 | 0.332887 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.5645 | 0.445241 | 0.222621 | − | 0.974905i | \(-0.428539\pi\) | ||||
0.222621 | + | 0.974905i | \(0.428539\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.0687 | 0.760158 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.72310 | −0.114359 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −38.9609 | −1.63333 | −0.816663 | − | 0.577115i | \(-0.804179\pi\) | ||||
−0.816663 | + | 0.577115i | \(0.804179\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.89631 | 0.121207 | 0.0606034 | − | 0.998162i | \(-0.480698\pi\) | ||||
0.0606034 | + | 0.998162i | \(0.480698\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 34.3788 | 1.43619 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −48.2910 | −2.01387 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.7421 | 0.447198 | 0.223599 | − | 0.974681i | \(-0.428219\pi\) | ||||
0.223599 | + | 0.974681i | \(0.428219\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.02578 | −0.0426300 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.74087 | −0.362632 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.52452 | 0.228802 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.48653 | −0.185495 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.34105 | 0.385546 | 0.192773 | − | 0.981243i | \(-0.438252\pi\) | ||||
0.192773 | + | 0.981243i | \(0.438252\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.88549 | −0.118895 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −26.3467 | −1.08376 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.7326 | 0.481802 | 0.240901 | − | 0.970550i | \(-0.422557\pi\) | ||||
0.240901 | + | 0.970550i | \(0.422557\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.03559 | 0.206439 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −23.5667 | −0.964520 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.93707 | 0.242582 | 0.121291 | − | 0.992617i | \(-0.461297\pi\) | ||||
0.121291 | + | 0.992617i | \(0.461297\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.3099 | 1.19558 | 0.597788 | − | 0.801654i | \(-0.296046\pi\) | ||||
0.597788 | + | 0.801654i | \(0.296046\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.81216 | 0.318136 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 23.7293 | 0.964733 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 36.4339 | 1.47881 | 0.739403 | − | 0.673263i | \(-0.235108\pi\) | ||||
0.739403 | + | 0.673263i | \(0.235108\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.56260 | 0.225408 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.09309 | −0.286956 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.1098 | −0.691059 | −0.345529 | − | 0.938408i | \(-0.612301\pi\) | ||||
−0.345529 | + | 0.938408i | \(0.612301\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −51.1276 | −2.06166 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.4037 | −0.942197 | −0.471098 | − | 0.882081i | \(-0.656142\pi\) | ||||
−0.471098 | + | 0.882081i | \(0.656142\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −46.2329 | −1.85826 | −0.929129 | − | 0.369755i | \(-0.879442\pi\) | ||||
−0.929129 | + | 0.369755i | \(0.879442\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −40.3492 | −1.61916 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.925339 | −0.0370729 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.0167 | −0.520669 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.59285 | 0.263293 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.52275 | 0.299952 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.1563 | −1.24031 | −0.620157 | − | 0.784478i | \(-0.712931\pi\) | ||||
−0.620157 | + | 0.784478i | \(0.712931\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −27.4017 | −1.08912 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.4449 | −0.493859 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.95044 | 0.354629 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.56645 | 0.378443 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.7425 | 0.898276 | 0.449138 | − | 0.893463i | \(-0.351731\pi\) | ||||
0.449138 | + | 0.893463i | \(0.351731\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.9350 | 0.825596 | 0.412798 | − | 0.910823i | \(-0.364551\pi\) | ||||
0.412798 | + | 0.910823i | \(0.364551\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 30.0655 | 1.18383 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.4638 | 1.07971 | 0.539856 | − | 0.841757i | \(-0.318479\pi\) | ||||
0.539856 | + | 0.841757i | \(0.318479\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.79025 | 0.188034 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.954433 | −0.0374072 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.7438 | 0.850900 | 0.425450 | − | 0.904982i | \(-0.360116\pi\) | ||||
0.425450 | + | 0.904982i | \(0.360116\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.4099 | 0.719334 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.99237 | −0.0777296 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.5840 | −0.723931 | −0.361966 | − | 0.932191i | \(-0.617894\pi\) | ||||
−0.361966 | + | 0.932191i | \(0.617894\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.0551 | 1.05232 | 0.526161 | − | 0.850385i | \(-0.323631\pi\) | ||||
0.526161 | + | 0.850385i | \(0.323631\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.20132 | −0.202003 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.21062 | 0.163281 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 52.2430 | 2.02286 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.55971 | 0.369600 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.82820 | −0.224995 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.4382 | −1.55878 | −0.779389 | − | 0.626541i | \(-0.784470\pi\) | ||||
−0.779389 | + | 0.626541i | \(0.784470\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 38.2959 | 1.47401 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 39.4535 | 1.51632 | 0.758161 | − | 0.652068i | \(-0.226098\pi\) | ||||
0.758161 | + | 0.652068i | \(0.226098\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.78279 | −0.221923 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.1351 | 0.809898 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.44550 | 0.131838 | 0.0659192 | − | 0.997825i | \(-0.479002\pi\) | ||||
0.0659192 | + | 0.997825i | \(0.479002\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 42.9150 | 1.63970 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.76491 | 0.296250 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.64443 | −0.138842 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.3908 | −0.737659 | −0.368830 | − | 0.929497i | \(-0.620241\pi\) | ||||
−0.368830 | + | 0.929497i | \(0.620241\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.05961 | −0.0402511 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −41.0372 | −1.55663 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 28.8008 | 1.09091 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.41388 | −0.204772 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.6975 | −0.706194 | −0.353097 | − | 0.935587i | \(-0.614871\pi\) | ||||
−0.353097 | + | 0.935587i | \(0.614871\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.29030 | 0.237243 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 25.9386 | 0.976904 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.95617 | 0.374440 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.27090 | 0.0477298 | 0.0238649 | − | 0.999715i | \(-0.492403\pi\) | ||||
0.0238649 | + | 0.999715i | \(0.492403\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.39190 | −0.0897034 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.96388 | −0.335700 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.24148 | 0.345612 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −43.7463 | −1.63374 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.16395 | 0.341758 | 0.170879 | − | 0.985292i | \(-0.445339\pi\) | ||||
0.170879 | + | 0.985292i | \(0.445339\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.99788 | −0.223373 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −25.5277 | −0.949385 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −49.5844 | −1.84152 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.0913 | 0.448440 | 0.224220 | − | 0.974539i | \(-0.428017\pi\) | ||||
0.224220 | + | 0.974539i | \(0.428017\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.1106 | 1.07817 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.9363 | −0.626410 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.0391 | 0.444673 | 0.222337 | − | 0.974970i | \(-0.428632\pi\) | ||||
0.222337 | + | 0.974970i | \(0.428632\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −32.7307 | −1.20729 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.0917 | −0.592745 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.4300 | 1.19296 | 0.596478 | − | 0.802630i | \(-0.296566\pi\) | ||||
0.596478 | + | 0.802630i | \(0.296566\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.34919 | −0.159772 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.2839 | 0.780830 | 0.390415 | − | 0.920639i | \(-0.372332\pi\) | ||||
0.390415 | + | 0.920639i | \(0.372332\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.3798 | −0.856568 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 16.0426 | 0.586967 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.25535 | −0.338183 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.33170 | 0.157856 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −38.8506 | −1.41392 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.7941 | −1.15558 | −0.577788 | − | 0.816187i | \(-0.696084\pi\) | ||||
−0.577788 | + | 0.816187i | \(0.696084\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.4809 | 0.743410 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −44.1947 | −1.60206 | −0.801029 | − | 0.598625i | \(-0.795714\pi\) | ||||
−0.801029 | + | 0.598625i | \(0.795714\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.33051 | −0.120573 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.24209 | −0.334148 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.16005 | −0.114103 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.10314 | 0.184024 | 0.0920120 | − | 0.995758i | \(-0.470670\pi\) | ||||
0.0920120 | + | 0.995758i | \(0.470670\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.7224 | −0.890354 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.8193 | −0.712850 | −0.356425 | − | 0.934324i | \(-0.616005\pi\) | ||||
−0.356425 | + | 0.934324i | \(0.616005\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.50771 | 0.305606 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.08064 | 0.0746426 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.0823 | 0.862840 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.7052 | −0.705108 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −41.4299 | −1.48058 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.2382 | −0.508181 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.7823 | 0.954686 | 0.477343 | − | 0.878717i | \(-0.341600\pi\) | ||||
0.477343 | + | 0.878717i | \(0.341600\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 33.2313 | 1.18307 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.81512 | −0.100094 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.84477 | 0.136532 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13.3273 | 0.472669 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31.3741 | 1.11133 | 0.555664 | − | 0.831407i | \(-0.312464\pi\) | ||||
0.555664 | + | 0.831407i | \(0.312464\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.6115 | −0.516918 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.69832 | 0.0600073 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.10393 | 0.144825 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.0804 | 0.461024 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −27.1650 | −0.956255 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36.2157 | −1.27328 | −0.636638 | − | 0.771163i | \(-0.719675\pi\) | ||||
−0.636638 | + | 0.771163i | \(0.719675\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.2165 | −0.534324 | −0.267162 | − | 0.963652i | \(-0.586086\pi\) | ||||
−0.267162 | + | 0.963652i | \(0.586086\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.8360 | 0.380033 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −41.3541 | −1.44857 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.1616 | −0.495452 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.699004 | 0.0244252 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.00689 | 0.0700409 | 0.0350204 | − | 0.999387i | \(-0.488850\pi\) | ||||
0.0350204 | + | 0.999387i | \(0.488850\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.3096 | 0.777664 | 0.388832 | − | 0.921309i | \(-0.372879\pi\) | ||||
0.388832 | + | 0.921309i | \(0.372879\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −19.4386 | −0.676767 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −41.4512 | −1.44140 | −0.720700 | − | 0.693247i | \(-0.756180\pi\) | ||||
−0.720700 | + | 0.693247i | \(0.756180\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.4228 | −1.23028 | −0.615142 | − | 0.788417i | \(-0.710901\pi\) | ||||
−0.615142 | + | 0.788417i | \(0.710901\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −42.0854 | −1.45993 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.4376 | 0.638824 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −78.6209 | −2.72079 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.10856 | 0.245708 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −45.1507 | −1.55878 | −0.779388 | − | 0.626542i | \(-0.784470\pi\) | ||||
−0.779388 | + | 0.626542i | \(0.784470\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.6423 | 0.849735 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −26.9977 | −0.929850 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 38.5033 | 1.32455 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.69704 | −0.127032 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −26.1066 | −0.895977 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.5410 | 0.669858 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39.6427 | 1.35734 | 0.678670 | − | 0.734443i | \(-0.262557\pi\) | ||||
0.678670 | + | 0.734443i | \(0.262557\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.72796 | −0.264291 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 53.2397 | 1.81863 | 0.909317 | − | 0.416105i | \(-0.136605\pi\) | ||||
0.909317 | + | 0.416105i | \(0.136605\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.1333 | −1.09637 | −0.548186 | − | 0.836356i | \(-0.684682\pi\) | ||||
−0.548186 | + | 0.836356i | \(0.684682\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.96571 | 0.271471 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.3278 | −0.930248 | −0.465124 | − | 0.885246i | \(-0.653990\pi\) | ||||
−0.465124 | + | 0.885246i | \(0.653990\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 38.6117 | 1.31284 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.4409 | 0.456477 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.92691 | 0.167134 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.6154 | 0.359690 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.6135 | 0.359211 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.24587 | −0.109730 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.6237 | 0.730180 | 0.365090 | − | 0.930972i | \(-0.381038\pi\) | ||||
0.365090 | + | 0.930972i | \(0.381038\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −41.7808 | −1.40923 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −51.1335 | −1.72273 | −0.861366 | − | 0.507985i | \(-0.830391\pi\) | ||||
−0.861366 | + | 0.507985i | \(0.830391\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.9290 | 0.569708 | 0.284854 | − | 0.958571i | \(-0.408055\pi\) | ||||
0.284854 | + | 0.958571i | \(0.408055\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.5559 | 0.388449 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −43.8163 | −1.47121 | −0.735604 | − | 0.677412i | \(-0.763102\pi\) | ||||
−0.735604 | + | 0.677412i | \(0.763102\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.93892 | 0.0650291 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.2947 | −0.344885 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.2177 | −0.408850 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.0389 | 0.736681 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −13.5109 | −0.451116 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.20397 | −0.306969 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.50739 | −0.250108 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.68423 | −0.155881 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −62.5091 | −2.07787 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 52.2717 | 1.73565 | 0.867827 | − | 0.496867i | \(-0.165516\pi\) | ||||
0.867827 | + | 0.496867i | \(0.165516\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.2731 | −0.606080 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.4449 | −0.611106 | −0.305553 | − | 0.952175i | \(-0.598841\pi\) | ||||
−0.305553 | + | 0.952175i | \(0.598841\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −33.0449 | −1.09363 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −14.0599 | −0.464805 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.86827 | −0.0947188 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.355688 | −0.0117331 | −0.00586653 | − | 0.999983i | \(-0.501867\pi\) | ||||
−0.00586653 | + | 0.999983i | \(0.501867\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −36.5414 | −1.20408 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.9992 | 0.427874 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.5466 | −0.609809 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.0082 | 0.361558 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.90560 | −0.292183 | −0.146092 | − | 0.989271i | \(-0.546669\pi\) | ||||
−0.146092 | + | 0.989271i | \(0.546669\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.4170 | 0.505271 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 42.7568 | 1.39979 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.0371 | 0.622580 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.8456 | 0.452316 | 0.226158 | − | 0.974091i | \(-0.427384\pi\) | ||||
0.226158 | + | 0.974091i | \(0.427384\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.0965 | −0.329486 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 43.9045 | 1.43125 | 0.715623 | − | 0.698486i | \(-0.246143\pi\) | ||||
0.715623 | + | 0.698486i | \(0.246143\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 74.8127 | 2.43624 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −10.3731 | −0.337436 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.4787 | 0.535485 | 0.267742 | − | 0.963491i | \(-0.413722\pi\) | ||||
0.267742 | + | 0.963491i | \(0.413722\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.70730 | −0.0878825 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.7134 | −0.412259 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.5958 | 0.829129 | 0.414564 | − | 0.910020i | \(-0.363934\pi\) | ||||
0.414564 | + | 0.910020i | \(0.363934\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 83.0067 | 2.68603 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 21.0295 | 0.679786 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.68618 | −0.215908 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.4208 | −0.949057 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.9868 | 0.547393 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.47673 | −0.0797286 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.7793 | 0.443111 | 0.221556 | − | 0.975148i | \(-0.428887\pi\) | ||||
0.221556 | + | 0.975148i | \(0.428887\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.95917 | −0.287810 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.7294 | 1.14661 | 0.573306 | − | 0.819341i | \(-0.305661\pi\) | ||||
0.573306 | + | 0.819341i | \(0.305661\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.39362 | 0.204970 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12.8234 | 0.410676 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −40.7899 | −1.30498 | −0.652492 | − | 0.757795i | \(-0.726276\pi\) | ||||
−0.652492 | + | 0.757795i | \(0.726276\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.49825 | −0.111805 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.11266 | 0.195162 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.7071 | −0.883719 | −0.441860 | − | 0.897084i | \(-0.645681\pi\) | ||||
−0.441860 | + | 0.897084i | \(0.645681\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −63.6136 | −2.02690 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.04125 | −0.128634 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −43.9935 | −1.39891 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.84738 | −0.185748 | −0.0928740 | − | 0.995678i | \(-0.529605\pi\) | ||||
−0.0928740 | + | 0.995678i | \(0.529605\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.40157 | 0.203148 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −56.9012 | −1.80389 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.2585 | 0.388231 | 0.194115 | − | 0.980979i | \(-0.437816\pi\) | ||||
0.194115 | + | 0.980979i | \(0.437816\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −15.4965 | −0.490287 |
(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 | 6008.2.a.e.1.13 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.e.1.13 | ✓ | 50 | 1.1 | even | 1 | trivial |