Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8047,2,Mod(1,8047)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8047, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8047.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8047 = 13 \cdot 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8047.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2556185065\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8047.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.61803 | 1.14412 | 0.572061 | − | 0.820211i | \(-0.306144\pi\) | ||||
0.572061 | + | 0.820211i | \(0.306144\pi\) | |||||||
\(3\) | −2.61803 | −1.51152 | −0.755761 | − | 0.654847i | \(-0.772733\pi\) | ||||
−0.755761 | + | 0.654847i | \(0.772733\pi\) | |||||||
\(4\) | 0.618034 | 0.309017 | ||||||||
\(5\) | −1.23607 | −0.552786 | −0.276393 | − | 0.961045i | \(-0.589139\pi\) | ||||
−0.276393 | + | 0.961045i | \(0.589139\pi\) | |||||||
\(6\) | −4.23607 | −1.72937 | ||||||||
\(7\) | −0.381966 | −0.144370 | −0.0721848 | − | 0.997391i | \(-0.522997\pi\) | ||||
−0.0721848 | + | 0.997391i | \(0.522997\pi\) | |||||||
\(8\) | −2.23607 | −0.790569 | ||||||||
\(9\) | 3.85410 | 1.28470 | ||||||||
\(10\) | −2.00000 | −0.632456 | ||||||||
\(11\) | 5.00000 | 1.50756 | 0.753778 | − | 0.657129i | \(-0.228229\pi\) | ||||
0.753778 | + | 0.657129i | \(0.228229\pi\) | |||||||
\(12\) | −1.61803 | −0.467086 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −0.618034 | −0.165177 | ||||||||
\(15\) | 3.23607 | 0.835549 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | −0.236068 | −0.0572549 | −0.0286274 | − | 0.999590i | \(-0.509114\pi\) | ||||
−0.0286274 | + | 0.999590i | \(0.509114\pi\) | |||||||
\(18\) | 6.23607 | 1.46986 | ||||||||
\(19\) | −3.76393 | −0.863505 | −0.431753 | − | 0.901992i | \(-0.642105\pi\) | ||||
−0.431753 | + | 0.901992i | \(0.642105\pi\) | |||||||
\(20\) | −0.763932 | −0.170820 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 8.09017 | 1.72483 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 5.85410 | 1.19496 | ||||||||
\(25\) | −3.47214 | −0.694427 | ||||||||
\(26\) | −1.61803 | −0.317323 | ||||||||
\(27\) | −2.23607 | −0.430331 | ||||||||
\(28\) | −0.236068 | −0.0446127 | ||||||||
\(29\) | 2.76393 | 0.513249 | 0.256625 | − | 0.966511i | \(-0.417390\pi\) | ||||
0.256625 | + | 0.966511i | \(0.417390\pi\) | |||||||
\(30\) | 5.23607 | 0.955971 | ||||||||
\(31\) | −1.76393 | −0.316812 | −0.158406 | − | 0.987374i | \(-0.550635\pi\) | ||||
−0.158406 | + | 0.987374i | \(0.550635\pi\) | |||||||
\(32\) | −3.38197 | −0.597853 | ||||||||
\(33\) | −13.0902 | −2.27871 | ||||||||
\(34\) | −0.381966 | −0.0655066 | ||||||||
\(35\) | 0.472136 | 0.0798055 | ||||||||
\(36\) | 2.38197 | 0.396994 | ||||||||
\(37\) | 6.47214 | 1.06401 | 0.532006 | − | 0.846740i | \(-0.321438\pi\) | ||||
0.532006 | + | 0.846740i | \(0.321438\pi\) | |||||||
\(38\) | −6.09017 | −0.987956 | ||||||||
\(39\) | 2.61803 | 0.419221 | ||||||||
\(40\) | 2.76393 | 0.437016 | ||||||||
\(41\) | −0.236068 | −0.0368676 | −0.0184338 | − | 0.999830i | \(-0.505868\pi\) | ||||
−0.0184338 | + | 0.999830i | \(0.505868\pi\) | |||||||
\(42\) | 1.61803 | 0.249668 | ||||||||
\(43\) | −4.76393 | −0.726493 | −0.363246 | − | 0.931693i | \(-0.618332\pi\) | ||||
−0.363246 | + | 0.931693i | \(0.618332\pi\) | |||||||
\(44\) | 3.09017 | 0.465861 | ||||||||
\(45\) | −4.76393 | −0.710165 | ||||||||
\(46\) | −6.47214 | −0.954264 | ||||||||
\(47\) | 11.8541 | 1.72910 | 0.864549 | − | 0.502548i | \(-0.167604\pi\) | ||||
0.864549 | + | 0.502548i | \(0.167604\pi\) | |||||||
\(48\) | 12.7082 | 1.83427 | ||||||||
\(49\) | −6.85410 | −0.979157 | ||||||||
\(50\) | −5.61803 | −0.794510 | ||||||||
\(51\) | 0.618034 | 0.0865421 | ||||||||
\(52\) | −0.618034 | −0.0857059 | ||||||||
\(53\) | −7.70820 | −1.05880 | −0.529402 | − | 0.848371i | \(-0.677584\pi\) | ||||
−0.529402 | + | 0.848371i | \(0.677584\pi\) | |||||||
\(54\) | −3.61803 | −0.492352 | ||||||||
\(55\) | −6.18034 | −0.833357 | ||||||||
\(56\) | 0.854102 | 0.114134 | ||||||||
\(57\) | 9.85410 | 1.30521 | ||||||||
\(58\) | 4.47214 | 0.587220 | ||||||||
\(59\) | −0.0901699 | −0.0117391 | −0.00586956 | − | 0.999983i | \(-0.501868\pi\) | ||||
−0.00586956 | + | 0.999983i | \(0.501868\pi\) | |||||||
\(60\) | 2.00000 | 0.258199 | ||||||||
\(61\) | −5.94427 | −0.761086 | −0.380543 | − | 0.924763i | \(-0.624263\pi\) | ||||
−0.380543 | + | 0.924763i | \(0.624263\pi\) | |||||||
\(62\) | −2.85410 | −0.362471 | ||||||||
\(63\) | −1.47214 | −0.185472 | ||||||||
\(64\) | 4.23607 | 0.529508 | ||||||||
\(65\) | 1.23607 | 0.153315 | ||||||||
\(66\) | −21.1803 | −2.60712 | ||||||||
\(67\) | 6.70820 | 0.819538 | 0.409769 | − | 0.912189i | \(-0.365609\pi\) | ||||
0.409769 | + | 0.912189i | \(0.365609\pi\) | |||||||
\(68\) | −0.145898 | −0.0176927 | ||||||||
\(69\) | 10.4721 | 1.26070 | ||||||||
\(70\) | 0.763932 | 0.0913073 | ||||||||
\(71\) | −13.1803 | −1.56422 | −0.782109 | − | 0.623141i | \(-0.785856\pi\) | ||||
−0.782109 | + | 0.623141i | \(0.785856\pi\) | |||||||
\(72\) | −8.61803 | −1.01565 | ||||||||
\(73\) | −13.4164 | −1.57027 | −0.785136 | − | 0.619324i | \(-0.787407\pi\) | ||||
−0.785136 | + | 0.619324i | \(0.787407\pi\) | |||||||
\(74\) | 10.4721 | 1.21736 | ||||||||
\(75\) | 9.09017 | 1.04964 | ||||||||
\(76\) | −2.32624 | −0.266838 | ||||||||
\(77\) | −1.90983 | −0.217645 | ||||||||
\(78\) | 4.23607 | 0.479640 | ||||||||
\(79\) | −0.527864 | −0.0593893 | −0.0296947 | − | 0.999559i | \(-0.509453\pi\) | ||||
−0.0296947 | + | 0.999559i | \(0.509453\pi\) | |||||||
\(80\) | 6.00000 | 0.670820 | ||||||||
\(81\) | −5.70820 | −0.634245 | ||||||||
\(82\) | −0.381966 | −0.0421811 | ||||||||
\(83\) | −6.23607 | −0.684497 | −0.342249 | − | 0.939609i | \(-0.611189\pi\) | ||||
−0.342249 | + | 0.939609i | \(0.611189\pi\) | |||||||
\(84\) | 0.618034 | 0.0674330 | ||||||||
\(85\) | 0.291796 | 0.0316497 | ||||||||
\(86\) | −7.70820 | −0.831197 | ||||||||
\(87\) | −7.23607 | −0.775788 | ||||||||
\(88\) | −11.1803 | −1.19183 | ||||||||
\(89\) | 6.85410 | 0.726533 | 0.363267 | − | 0.931685i | \(-0.381661\pi\) | ||||
0.363267 | + | 0.931685i | \(0.381661\pi\) | |||||||
\(90\) | −7.70820 | −0.812516 | ||||||||
\(91\) | 0.381966 | 0.0400409 | ||||||||
\(92\) | −2.47214 | −0.257738 | ||||||||
\(93\) | 4.61803 | 0.478868 | ||||||||
\(94\) | 19.1803 | 1.97830 | ||||||||
\(95\) | 4.65248 | 0.477334 | ||||||||
\(96\) | 8.85410 | 0.903668 | ||||||||
\(97\) | 15.0902 | 1.53217 | 0.766087 | − | 0.642737i | \(-0.222201\pi\) | ||||
0.766087 | + | 0.642737i | \(0.222201\pi\) | |||||||
\(98\) | −11.0902 | −1.12028 | ||||||||
\(99\) | 19.2705 | 1.93676 | ||||||||
\(100\) | −2.14590 | −0.214590 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | 10.7984 | 1.06400 | 0.531998 | − | 0.846746i | \(-0.321441\pi\) | ||||
0.531998 | + | 0.846746i | \(0.321441\pi\) | |||||||
\(104\) | 2.23607 | 0.219265 | ||||||||
\(105\) | −1.23607 | −0.120628 | ||||||||
\(106\) | −12.4721 | −1.21140 | ||||||||
\(107\) | −11.0000 | −1.06341 | −0.531705 | − | 0.846930i | \(-0.678449\pi\) | ||||
−0.531705 | + | 0.846930i | \(0.678449\pi\) | |||||||
\(108\) | −1.38197 | −0.132980 | ||||||||
\(109\) | −5.29180 | −0.506862 | −0.253431 | − | 0.967353i | \(-0.581559\pi\) | ||||
−0.253431 | + | 0.967353i | \(0.581559\pi\) | |||||||
\(110\) | −10.0000 | −0.953463 | ||||||||
\(111\) | −16.9443 | −1.60828 | ||||||||
\(112\) | 1.85410 | 0.175196 | ||||||||
\(113\) | −5.09017 | −0.478843 | −0.239421 | − | 0.970916i | \(-0.576958\pi\) | ||||
−0.239421 | + | 0.970916i | \(0.576958\pi\) | |||||||
\(114\) | 15.9443 | 1.49332 | ||||||||
\(115\) | 4.94427 | 0.461056 | ||||||||
\(116\) | 1.70820 | 0.158603 | ||||||||
\(117\) | −3.85410 | −0.356312 | ||||||||
\(118\) | −0.145898 | −0.0134310 | ||||||||
\(119\) | 0.0901699 | 0.00826587 | ||||||||
\(120\) | −7.23607 | −0.660560 | ||||||||
\(121\) | 14.0000 | 1.27273 | ||||||||
\(122\) | −9.61803 | −0.870776 | ||||||||
\(123\) | 0.618034 | 0.0557262 | ||||||||
\(124\) | −1.09017 | −0.0979002 | ||||||||
\(125\) | 10.4721 | 0.936656 | ||||||||
\(126\) | −2.38197 | −0.212202 | ||||||||
\(127\) | −4.79837 | −0.425787 | −0.212893 | − | 0.977075i | \(-0.568289\pi\) | ||||
−0.212893 | + | 0.977075i | \(0.568289\pi\) | |||||||
\(128\) | 13.6180 | 1.20368 | ||||||||
\(129\) | 12.4721 | 1.09811 | ||||||||
\(130\) | 2.00000 | 0.175412 | ||||||||
\(131\) | 10.4164 | 0.910086 | 0.455043 | − | 0.890470i | \(-0.349624\pi\) | ||||
0.455043 | + | 0.890470i | \(0.349624\pi\) | |||||||
\(132\) | −8.09017 | −0.704159 | ||||||||
\(133\) | 1.43769 | 0.124664 | ||||||||
\(134\) | 10.8541 | 0.937652 | ||||||||
\(135\) | 2.76393 | 0.237881 | ||||||||
\(136\) | 0.527864 | 0.0452640 | ||||||||
\(137\) | 0.291796 | 0.0249298 | 0.0124649 | − | 0.999922i | \(-0.496032\pi\) | ||||
0.0124649 | + | 0.999922i | \(0.496032\pi\) | |||||||
\(138\) | 16.9443 | 1.44239 | ||||||||
\(139\) | −1.23607 | −0.104842 | −0.0524210 | − | 0.998625i | \(-0.516694\pi\) | ||||
−0.0524210 | + | 0.998625i | \(0.516694\pi\) | |||||||
\(140\) | 0.291796 | 0.0246613 | ||||||||
\(141\) | −31.0344 | −2.61357 | ||||||||
\(142\) | −21.3262 | −1.78966 | ||||||||
\(143\) | −5.00000 | −0.418121 | ||||||||
\(144\) | −18.7082 | −1.55902 | ||||||||
\(145\) | −3.41641 | −0.283717 | ||||||||
\(146\) | −21.7082 | −1.79658 | ||||||||
\(147\) | 17.9443 | 1.48002 | ||||||||
\(148\) | 4.00000 | 0.328798 | ||||||||
\(149\) | −14.3820 | −1.17822 | −0.589108 | − | 0.808054i | \(-0.700521\pi\) | ||||
−0.589108 | + | 0.808054i | \(0.700521\pi\) | |||||||
\(150\) | 14.7082 | 1.20092 | ||||||||
\(151\) | 20.9443 | 1.70442 | 0.852210 | − | 0.523199i | \(-0.175262\pi\) | ||||
0.852210 | + | 0.523199i | \(0.175262\pi\) | |||||||
\(152\) | 8.41641 | 0.682661 | ||||||||
\(153\) | −0.909830 | −0.0735554 | ||||||||
\(154\) | −3.09017 | −0.249013 | ||||||||
\(155\) | 2.18034 | 0.175129 | ||||||||
\(156\) | 1.61803 | 0.129546 | ||||||||
\(157\) | 16.9443 | 1.35230 | 0.676150 | − | 0.736764i | \(-0.263647\pi\) | ||||
0.676150 | + | 0.736764i | \(0.263647\pi\) | |||||||
\(158\) | −0.854102 | −0.0679487 | ||||||||
\(159\) | 20.1803 | 1.60041 | ||||||||
\(160\) | 4.18034 | 0.330485 | ||||||||
\(161\) | 1.52786 | 0.120413 | ||||||||
\(162\) | −9.23607 | −0.725654 | ||||||||
\(163\) | −12.7082 | −0.995383 | −0.497692 | − | 0.867354i | \(-0.665819\pi\) | ||||
−0.497692 | + | 0.867354i | \(0.665819\pi\) | |||||||
\(164\) | −0.145898 | −0.0113927 | ||||||||
\(165\) | 16.1803 | 1.25964 | ||||||||
\(166\) | −10.0902 | −0.783149 | ||||||||
\(167\) | 3.05573 | 0.236459 | 0.118230 | − | 0.992986i | \(-0.462278\pi\) | ||||
0.118230 | + | 0.992986i | \(0.462278\pi\) | |||||||
\(168\) | −2.23607 | −0.172516 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0.472136 | 0.0362112 | ||||||||
\(171\) | −14.5066 | −1.10935 | ||||||||
\(172\) | −2.94427 | −0.224499 | ||||||||
\(173\) | 16.7082 | 1.27030 | 0.635151 | − | 0.772388i | \(-0.280938\pi\) | ||||
0.635151 | + | 0.772388i | \(0.280938\pi\) | |||||||
\(174\) | −11.7082 | −0.887597 | ||||||||
\(175\) | 1.32624 | 0.100254 | ||||||||
\(176\) | −24.2705 | −1.82946 | ||||||||
\(177\) | 0.236068 | 0.0177440 | ||||||||
\(178\) | 11.0902 | 0.831243 | ||||||||
\(179\) | 9.29180 | 0.694501 | 0.347251 | − | 0.937772i | \(-0.387115\pi\) | ||||
0.347251 | + | 0.937772i | \(0.387115\pi\) | |||||||
\(180\) | −2.94427 | −0.219453 | ||||||||
\(181\) | 13.7639 | 1.02307 | 0.511533 | − | 0.859264i | \(-0.329078\pi\) | ||||
0.511533 | + | 0.859264i | \(0.329078\pi\) | |||||||
\(182\) | 0.618034 | 0.0458117 | ||||||||
\(183\) | 15.5623 | 1.15040 | ||||||||
\(184\) | 8.94427 | 0.659380 | ||||||||
\(185\) | −8.00000 | −0.588172 | ||||||||
\(186\) | 7.47214 | 0.547884 | ||||||||
\(187\) | −1.18034 | −0.0863150 | ||||||||
\(188\) | 7.32624 | 0.534321 | ||||||||
\(189\) | 0.854102 | 0.0621268 | ||||||||
\(190\) | 7.52786 | 0.546129 | ||||||||
\(191\) | −22.7984 | −1.64963 | −0.824816 | − | 0.565401i | \(-0.808721\pi\) | ||||
−0.824816 | + | 0.565401i | \(0.808721\pi\) | |||||||
\(192\) | −11.0902 | −0.800364 | ||||||||
\(193\) | 6.00000 | 0.431889 | 0.215945 | − | 0.976406i | \(-0.430717\pi\) | ||||
0.215945 | + | 0.976406i | \(0.430717\pi\) | |||||||
\(194\) | 24.4164 | 1.75300 | ||||||||
\(195\) | −3.23607 | −0.231740 | ||||||||
\(196\) | −4.23607 | −0.302576 | ||||||||
\(197\) | −7.56231 | −0.538792 | −0.269396 | − | 0.963029i | \(-0.586824\pi\) | ||||
−0.269396 | + | 0.963029i | \(0.586824\pi\) | |||||||
\(198\) | 31.1803 | 2.21589 | ||||||||
\(199\) | −0.381966 | −0.0270769 | −0.0135384 | − | 0.999908i | \(-0.504310\pi\) | ||||
−0.0135384 | + | 0.999908i | \(0.504310\pi\) | |||||||
\(200\) | 7.76393 | 0.548993 | ||||||||
\(201\) | −17.5623 | −1.23875 | ||||||||
\(202\) | −9.70820 | −0.683067 | ||||||||
\(203\) | −1.05573 | −0.0740976 | ||||||||
\(204\) | 0.381966 | 0.0267430 | ||||||||
\(205\) | 0.291796 | 0.0203799 | ||||||||
\(206\) | 17.4721 | 1.21734 | ||||||||
\(207\) | −15.4164 | −1.07151 | ||||||||
\(208\) | 4.85410 | 0.336571 | ||||||||
\(209\) | −18.8197 | −1.30178 | ||||||||
\(210\) | −2.00000 | −0.138013 | ||||||||
\(211\) | 14.2705 | 0.982422 | 0.491211 | − | 0.871040i | \(-0.336554\pi\) | ||||
0.491211 | + | 0.871040i | \(0.336554\pi\) | |||||||
\(212\) | −4.76393 | −0.327188 | ||||||||
\(213\) | 34.5066 | 2.36435 | ||||||||
\(214\) | −17.7984 | −1.21667 | ||||||||
\(215\) | 5.88854 | 0.401595 | ||||||||
\(216\) | 5.00000 | 0.340207 | ||||||||
\(217\) | 0.673762 | 0.0457380 | ||||||||
\(218\) | −8.56231 | −0.579913 | ||||||||
\(219\) | 35.1246 | 2.37350 | ||||||||
\(220\) | −3.81966 | −0.257521 | ||||||||
\(221\) | 0.236068 | 0.0158797 | ||||||||
\(222\) | −27.4164 | −1.84007 | ||||||||
\(223\) | 7.90983 | 0.529681 | 0.264841 | − | 0.964292i | \(-0.414681\pi\) | ||||
0.264841 | + | 0.964292i | \(0.414681\pi\) | |||||||
\(224\) | 1.29180 | 0.0863118 | ||||||||
\(225\) | −13.3820 | −0.892131 | ||||||||
\(226\) | −8.23607 | −0.547855 | ||||||||
\(227\) | 6.41641 | 0.425872 | 0.212936 | − | 0.977066i | \(-0.431697\pi\) | ||||
0.212936 | + | 0.977066i | \(0.431697\pi\) | |||||||
\(228\) | 6.09017 | 0.403331 | ||||||||
\(229\) | 17.4164 | 1.15091 | 0.575454 | − | 0.817834i | \(-0.304825\pi\) | ||||
0.575454 | + | 0.817834i | \(0.304825\pi\) | |||||||
\(230\) | 8.00000 | 0.527504 | ||||||||
\(231\) | 5.00000 | 0.328976 | ||||||||
\(232\) | −6.18034 | −0.405759 | ||||||||
\(233\) | 15.5623 | 1.01952 | 0.509760 | − | 0.860316i | \(-0.329734\pi\) | ||||
0.509760 | + | 0.860316i | \(0.329734\pi\) | |||||||
\(234\) | −6.23607 | −0.407665 | ||||||||
\(235\) | −14.6525 | −0.955822 | ||||||||
\(236\) | −0.0557281 | −0.00362759 | ||||||||
\(237\) | 1.38197 | 0.0897683 | ||||||||
\(238\) | 0.145898 | 0.00945716 | ||||||||
\(239\) | 2.29180 | 0.148244 | 0.0741220 | − | 0.997249i | \(-0.476385\pi\) | ||||
0.0741220 | + | 0.997249i | \(0.476385\pi\) | |||||||
\(240\) | −15.7082 | −1.01396 | ||||||||
\(241\) | 24.8885 | 1.60321 | 0.801606 | − | 0.597853i | \(-0.203979\pi\) | ||||
0.801606 | + | 0.597853i | \(0.203979\pi\) | |||||||
\(242\) | 22.6525 | 1.45616 | ||||||||
\(243\) | 21.6525 | 1.38901 | ||||||||
\(244\) | −3.67376 | −0.235189 | ||||||||
\(245\) | 8.47214 | 0.541265 | ||||||||
\(246\) | 1.00000 | 0.0637577 | ||||||||
\(247\) | 3.76393 | 0.239493 | ||||||||
\(248\) | 3.94427 | 0.250462 | ||||||||
\(249\) | 16.3262 | 1.03463 | ||||||||
\(250\) | 16.9443 | 1.07165 | ||||||||
\(251\) | 10.5279 | 0.664513 | 0.332256 | − | 0.943189i | \(-0.392190\pi\) | ||||
0.332256 | + | 0.943189i | \(0.392190\pi\) | |||||||
\(252\) | −0.909830 | −0.0573139 | ||||||||
\(253\) | −20.0000 | −1.25739 | ||||||||
\(254\) | −7.76393 | −0.487152 | ||||||||
\(255\) | −0.763932 | −0.0478393 | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | 23.1803 | 1.44595 | 0.722975 | − | 0.690874i | \(-0.242774\pi\) | ||||
0.722975 | + | 0.690874i | \(0.242774\pi\) | |||||||
\(258\) | 20.1803 | 1.25637 | ||||||||
\(259\) | −2.47214 | −0.153611 | ||||||||
\(260\) | 0.763932 | 0.0473771 | ||||||||
\(261\) | 10.6525 | 0.659372 | ||||||||
\(262\) | 16.8541 | 1.04125 | ||||||||
\(263\) | 13.7639 | 0.848720 | 0.424360 | − | 0.905493i | \(-0.360499\pi\) | ||||
0.424360 | + | 0.905493i | \(0.360499\pi\) | |||||||
\(264\) | 29.2705 | 1.80148 | ||||||||
\(265\) | 9.52786 | 0.585292 | ||||||||
\(266\) | 2.32624 | 0.142631 | ||||||||
\(267\) | −17.9443 | −1.09817 | ||||||||
\(268\) | 4.14590 | 0.253251 | ||||||||
\(269\) | 10.7639 | 0.656289 | 0.328144 | − | 0.944628i | \(-0.393577\pi\) | ||||
0.328144 | + | 0.944628i | \(0.393577\pi\) | |||||||
\(270\) | 4.47214 | 0.272166 | ||||||||
\(271\) | −13.0000 | −0.789694 | −0.394847 | − | 0.918747i | \(-0.629202\pi\) | ||||
−0.394847 | + | 0.918747i | \(0.629202\pi\) | |||||||
\(272\) | 1.14590 | 0.0694803 | ||||||||
\(273\) | −1.00000 | −0.0605228 | ||||||||
\(274\) | 0.472136 | 0.0285228 | ||||||||
\(275\) | −17.3607 | −1.04689 | ||||||||
\(276\) | 6.47214 | 0.389577 | ||||||||
\(277\) | 7.03444 | 0.422659 | 0.211329 | − | 0.977415i | \(-0.432221\pi\) | ||||
0.211329 | + | 0.977415i | \(0.432221\pi\) | |||||||
\(278\) | −2.00000 | −0.119952 | ||||||||
\(279\) | −6.79837 | −0.407008 | ||||||||
\(280\) | −1.05573 | −0.0630918 | ||||||||
\(281\) | 13.2918 | 0.792922 | 0.396461 | − | 0.918052i | \(-0.370238\pi\) | ||||
0.396461 | + | 0.918052i | \(0.370238\pi\) | |||||||
\(282\) | −50.2148 | −2.99025 | ||||||||
\(283\) | 20.7082 | 1.23097 | 0.615487 | − | 0.788147i | \(-0.288959\pi\) | ||||
0.615487 | + | 0.788147i | \(0.288959\pi\) | |||||||
\(284\) | −8.14590 | −0.483370 | ||||||||
\(285\) | −12.1803 | −0.721501 | ||||||||
\(286\) | −8.09017 | −0.478382 | ||||||||
\(287\) | 0.0901699 | 0.00532256 | ||||||||
\(288\) | −13.0344 | −0.768062 | ||||||||
\(289\) | −16.9443 | −0.996722 | ||||||||
\(290\) | −5.52786 | −0.324607 | ||||||||
\(291\) | −39.5066 | −2.31592 | ||||||||
\(292\) | −8.29180 | −0.485241 | ||||||||
\(293\) | 19.7426 | 1.15338 | 0.576689 | − | 0.816964i | \(-0.304345\pi\) | ||||
0.576689 | + | 0.816964i | \(0.304345\pi\) | |||||||
\(294\) | 29.0344 | 1.69332 | ||||||||
\(295\) | 0.111456 | 0.00648923 | ||||||||
\(296\) | −14.4721 | −0.841176 | ||||||||
\(297\) | −11.1803 | −0.648749 | ||||||||
\(298\) | −23.2705 | −1.34802 | ||||||||
\(299\) | 4.00000 | 0.231326 | ||||||||
\(300\) | 5.61803 | 0.324357 | ||||||||
\(301\) | 1.81966 | 0.104883 | ||||||||
\(302\) | 33.8885 | 1.95007 | ||||||||
\(303\) | 15.7082 | 0.902413 | ||||||||
\(304\) | 18.2705 | 1.04789 | ||||||||
\(305\) | 7.34752 | 0.420718 | ||||||||
\(306\) | −1.47214 | −0.0841564 | ||||||||
\(307\) | 10.8541 | 0.619476 | 0.309738 | − | 0.950822i | \(-0.399759\pi\) | ||||
0.309738 | + | 0.950822i | \(0.399759\pi\) | |||||||
\(308\) | −1.18034 | −0.0672561 | ||||||||
\(309\) | −28.2705 | −1.60825 | ||||||||
\(310\) | 3.52786 | 0.200369 | ||||||||
\(311\) | −24.7082 | −1.40107 | −0.700537 | − | 0.713616i | \(-0.747056\pi\) | ||||
−0.700537 | + | 0.713616i | \(0.747056\pi\) | |||||||
\(312\) | −5.85410 | −0.331423 | ||||||||
\(313\) | 18.0000 | 1.01742 | 0.508710 | − | 0.860938i | \(-0.330123\pi\) | ||||
0.508710 | + | 0.860938i | \(0.330123\pi\) | |||||||
\(314\) | 27.4164 | 1.54720 | ||||||||
\(315\) | 1.81966 | 0.102526 | ||||||||
\(316\) | −0.326238 | −0.0183523 | ||||||||
\(317\) | −20.8885 | −1.17322 | −0.586609 | − | 0.809870i | \(-0.699537\pi\) | ||||
−0.586609 | + | 0.809870i | \(0.699537\pi\) | |||||||
\(318\) | 32.6525 | 1.83106 | ||||||||
\(319\) | 13.8197 | 0.773752 | ||||||||
\(320\) | −5.23607 | −0.292705 | ||||||||
\(321\) | 28.7984 | 1.60737 | ||||||||
\(322\) | 2.47214 | 0.137767 | ||||||||
\(323\) | 0.888544 | 0.0494399 | ||||||||
\(324\) | −3.52786 | −0.195992 | ||||||||
\(325\) | 3.47214 | 0.192599 | ||||||||
\(326\) | −20.5623 | −1.13884 | ||||||||
\(327\) | 13.8541 | 0.766134 | ||||||||
\(328\) | 0.527864 | 0.0291464 | ||||||||
\(329\) | −4.52786 | −0.249629 | ||||||||
\(330\) | 26.1803 | 1.44118 | ||||||||
\(331\) | 22.0344 | 1.21112 | 0.605561 | − | 0.795799i | \(-0.292949\pi\) | ||||
0.605561 | + | 0.795799i | \(0.292949\pi\) | |||||||
\(332\) | −3.85410 | −0.211521 | ||||||||
\(333\) | 24.9443 | 1.36694 | ||||||||
\(334\) | 4.94427 | 0.270539 | ||||||||
\(335\) | −8.29180 | −0.453029 | ||||||||
\(336\) | −4.85410 | −0.264813 | ||||||||
\(337\) | 24.3262 | 1.32513 | 0.662567 | − | 0.749002i | \(-0.269467\pi\) | ||||
0.662567 | + | 0.749002i | \(0.269467\pi\) | |||||||
\(338\) | 1.61803 | 0.0880094 | ||||||||
\(339\) | 13.3262 | 0.723782 | ||||||||
\(340\) | 0.180340 | 0.00978030 | ||||||||
\(341\) | −8.81966 | −0.477611 | ||||||||
\(342\) | −23.4721 | −1.26923 | ||||||||
\(343\) | 5.29180 | 0.285730 | ||||||||
\(344\) | 10.6525 | 0.574343 | ||||||||
\(345\) | −12.9443 | −0.696896 | ||||||||
\(346\) | 27.0344 | 1.45338 | ||||||||
\(347\) | −0.763932 | −0.0410100 | −0.0205050 | − | 0.999790i | \(-0.506527\pi\) | ||||
−0.0205050 | + | 0.999790i | \(0.506527\pi\) | |||||||
\(348\) | −4.47214 | −0.239732 | ||||||||
\(349\) | −11.4721 | −0.614089 | −0.307045 | − | 0.951695i | \(-0.599340\pi\) | ||||
−0.307045 | + | 0.951695i | \(0.599340\pi\) | |||||||
\(350\) | 2.14590 | 0.114703 | ||||||||
\(351\) | 2.23607 | 0.119352 | ||||||||
\(352\) | −16.9098 | −0.901297 | ||||||||
\(353\) | −19.6525 | −1.04600 | −0.522998 | − | 0.852334i | \(-0.675186\pi\) | ||||
−0.522998 | + | 0.852334i | \(0.675186\pi\) | |||||||
\(354\) | 0.381966 | 0.0203013 | ||||||||
\(355\) | 16.2918 | 0.864679 | ||||||||
\(356\) | 4.23607 | 0.224511 | ||||||||
\(357\) | −0.236068 | −0.0124940 | ||||||||
\(358\) | 15.0344 | 0.794595 | ||||||||
\(359\) | 3.47214 | 0.183252 | 0.0916262 | − | 0.995793i | \(-0.470794\pi\) | ||||
0.0916262 | + | 0.995793i | \(0.470794\pi\) | |||||||
\(360\) | 10.6525 | 0.561435 | ||||||||
\(361\) | −4.83282 | −0.254359 | ||||||||
\(362\) | 22.2705 | 1.17051 | ||||||||
\(363\) | −36.6525 | −1.92376 | ||||||||
\(364\) | 0.236068 | 0.0123733 | ||||||||
\(365\) | 16.5836 | 0.868025 | ||||||||
\(366\) | 25.1803 | 1.31620 | ||||||||
\(367\) | 21.5623 | 1.12554 | 0.562772 | − | 0.826612i | \(-0.309735\pi\) | ||||
0.562772 | + | 0.826612i | \(0.309735\pi\) | |||||||
\(368\) | 19.4164 | 1.01215 | ||||||||
\(369\) | −0.909830 | −0.0473639 | ||||||||
\(370\) | −12.9443 | −0.672941 | ||||||||
\(371\) | 2.94427 | 0.152859 | ||||||||
\(372\) | 2.85410 | 0.147978 | ||||||||
\(373\) | −1.85410 | −0.0960018 | −0.0480009 | − | 0.998847i | \(-0.515285\pi\) | ||||
−0.0480009 | + | 0.998847i | \(0.515285\pi\) | |||||||
\(374\) | −1.90983 | −0.0987550 | ||||||||
\(375\) | −27.4164 | −1.41578 | ||||||||
\(376\) | −26.5066 | −1.36697 | ||||||||
\(377\) | −2.76393 | −0.142350 | ||||||||
\(378\) | 1.38197 | 0.0710807 | ||||||||
\(379\) | −27.1246 | −1.39330 | −0.696649 | − | 0.717412i | \(-0.745326\pi\) | ||||
−0.696649 | + | 0.717412i | \(0.745326\pi\) | |||||||
\(380\) | 2.87539 | 0.147504 | ||||||||
\(381\) | 12.5623 | 0.643586 | ||||||||
\(382\) | −36.8885 | −1.88738 | ||||||||
\(383\) | −25.7082 | −1.31363 | −0.656814 | − | 0.754053i | \(-0.728096\pi\) | ||||
−0.656814 | + | 0.754053i | \(0.728096\pi\) | |||||||
\(384\) | −35.6525 | −1.81938 | ||||||||
\(385\) | 2.36068 | 0.120311 | ||||||||
\(386\) | 9.70820 | 0.494135 | ||||||||
\(387\) | −18.3607 | −0.933326 | ||||||||
\(388\) | 9.32624 | 0.473468 | ||||||||
\(389\) | 25.4164 | 1.28866 | 0.644332 | − | 0.764746i | \(-0.277136\pi\) | ||||
0.644332 | + | 0.764746i | \(0.277136\pi\) | |||||||
\(390\) | −5.23607 | −0.265139 | ||||||||
\(391\) | 0.944272 | 0.0477539 | ||||||||
\(392\) | 15.3262 | 0.774092 | ||||||||
\(393\) | −27.2705 | −1.37562 | ||||||||
\(394\) | −12.2361 | −0.616444 | ||||||||
\(395\) | 0.652476 | 0.0328296 | ||||||||
\(396\) | 11.9098 | 0.598491 | ||||||||
\(397\) | −25.9443 | −1.30211 | −0.651053 | − | 0.759032i | \(-0.725672\pi\) | ||||
−0.651053 | + | 0.759032i | \(0.725672\pi\) | |||||||
\(398\) | −0.618034 | −0.0309792 | ||||||||
\(399\) | −3.76393 | −0.188432 | ||||||||
\(400\) | 16.8541 | 0.842705 | ||||||||
\(401\) | 15.4721 | 0.772642 | 0.386321 | − | 0.922364i | \(-0.373746\pi\) | ||||
0.386321 | + | 0.922364i | \(0.373746\pi\) | |||||||
\(402\) | −28.4164 | −1.41728 | ||||||||
\(403\) | 1.76393 | 0.0878677 | ||||||||
\(404\) | −3.70820 | −0.184490 | ||||||||
\(405\) | 7.05573 | 0.350602 | ||||||||
\(406\) | −1.70820 | −0.0847767 | ||||||||
\(407\) | 32.3607 | 1.60406 | ||||||||
\(408\) | −1.38197 | −0.0684175 | ||||||||
\(409\) | 4.27051 | 0.211163 | 0.105582 | − | 0.994411i | \(-0.466330\pi\) | ||||
0.105582 | + | 0.994411i | \(0.466330\pi\) | |||||||
\(410\) | 0.472136 | 0.0233171 | ||||||||
\(411\) | −0.763932 | −0.0376820 | ||||||||
\(412\) | 6.67376 | 0.328793 | ||||||||
\(413\) | 0.0344419 | 0.00169477 | ||||||||
\(414\) | −24.9443 | −1.22594 | ||||||||
\(415\) | 7.70820 | 0.378381 | ||||||||
\(416\) | 3.38197 | 0.165815 | ||||||||
\(417\) | 3.23607 | 0.158471 | ||||||||
\(418\) | −30.4508 | −1.48940 | ||||||||
\(419\) | 15.6525 | 0.764673 | 0.382337 | − | 0.924023i | \(-0.375119\pi\) | ||||
0.382337 | + | 0.924023i | \(0.375119\pi\) | |||||||
\(420\) | −0.763932 | −0.0372761 | ||||||||
\(421\) | 26.4721 | 1.29017 | 0.645086 | − | 0.764110i | \(-0.276821\pi\) | ||||
0.645086 | + | 0.764110i | \(0.276821\pi\) | |||||||
\(422\) | 23.0902 | 1.12401 | ||||||||
\(423\) | 45.6869 | 2.22137 | ||||||||
\(424\) | 17.2361 | 0.837057 | ||||||||
\(425\) | 0.819660 | 0.0397594 | ||||||||
\(426\) | 55.8328 | 2.70511 | ||||||||
\(427\) | 2.27051 | 0.109878 | ||||||||
\(428\) | −6.79837 | −0.328612 | ||||||||
\(429\) | 13.0902 | 0.631999 | ||||||||
\(430\) | 9.52786 | 0.459474 | ||||||||
\(431\) | 26.4164 | 1.27243 | 0.636217 | − | 0.771510i | \(-0.280498\pi\) | ||||
0.636217 | + | 0.771510i | \(0.280498\pi\) | |||||||
\(432\) | 10.8541 | 0.522218 | ||||||||
\(433\) | 5.43769 | 0.261319 | 0.130659 | − | 0.991427i | \(-0.458291\pi\) | ||||
0.130659 | + | 0.991427i | \(0.458291\pi\) | |||||||
\(434\) | 1.09017 | 0.0523298 | ||||||||
\(435\) | 8.94427 | 0.428845 | ||||||||
\(436\) | −3.27051 | −0.156629 | ||||||||
\(437\) | 15.0557 | 0.720213 | ||||||||
\(438\) | 56.8328 | 2.71558 | ||||||||
\(439\) | 23.0557 | 1.10039 | 0.550195 | − | 0.835036i | \(-0.314553\pi\) | ||||
0.550195 | + | 0.835036i | \(0.314553\pi\) | |||||||
\(440\) | 13.8197 | 0.658826 | ||||||||
\(441\) | −26.4164 | −1.25792 | ||||||||
\(442\) | 0.381966 | 0.0181683 | ||||||||
\(443\) | −15.1459 | −0.719603 | −0.359802 | − | 0.933029i | \(-0.617156\pi\) | ||||
−0.359802 | + | 0.933029i | \(0.617156\pi\) | |||||||
\(444\) | −10.4721 | −0.496986 | ||||||||
\(445\) | −8.47214 | −0.401618 | ||||||||
\(446\) | 12.7984 | 0.606021 | ||||||||
\(447\) | 37.6525 | 1.78090 | ||||||||
\(448\) | −1.61803 | −0.0764449 | ||||||||
\(449\) | −6.12461 | −0.289038 | −0.144519 | − | 0.989502i | \(-0.546164\pi\) | ||||
−0.144519 | + | 0.989502i | \(0.546164\pi\) | |||||||
\(450\) | −21.6525 | −1.02071 | ||||||||
\(451\) | −1.18034 | −0.0555800 | ||||||||
\(452\) | −3.14590 | −0.147971 | ||||||||
\(453\) | −54.8328 | −2.57627 | ||||||||
\(454\) | 10.3820 | 0.487250 | ||||||||
\(455\) | −0.472136 | −0.0221341 | ||||||||
\(456\) | −22.0344 | −1.03186 | ||||||||
\(457\) | 3.76393 | 0.176069 | 0.0880347 | − | 0.996117i | \(-0.471941\pi\) | ||||
0.0880347 | + | 0.996117i | \(0.471941\pi\) | |||||||
\(458\) | 28.1803 | 1.31678 | ||||||||
\(459\) | 0.527864 | 0.0246386 | ||||||||
\(460\) | 3.05573 | 0.142474 | ||||||||
\(461\) | −0.0901699 | −0.00419963 | −0.00209982 | − | 0.999998i | \(-0.500668\pi\) | ||||
−0.00209982 | + | 0.999998i | \(0.500668\pi\) | |||||||
\(462\) | 8.09017 | 0.376389 | ||||||||
\(463\) | −34.1246 | −1.58591 | −0.792953 | − | 0.609283i | \(-0.791457\pi\) | ||||
−0.792953 | + | 0.609283i | \(0.791457\pi\) | |||||||
\(464\) | −13.4164 | −0.622841 | ||||||||
\(465\) | −5.70820 | −0.264712 | ||||||||
\(466\) | 25.1803 | 1.16646 | ||||||||
\(467\) | 21.7082 | 1.00454 | 0.502268 | − | 0.864712i | \(-0.332499\pi\) | ||||
0.502268 | + | 0.864712i | \(0.332499\pi\) | |||||||
\(468\) | −2.38197 | −0.110106 | ||||||||
\(469\) | −2.56231 | −0.118316 | ||||||||
\(470\) | −23.7082 | −1.09358 | ||||||||
\(471\) | −44.3607 | −2.04403 | ||||||||
\(472\) | 0.201626 | 0.00928059 | ||||||||
\(473\) | −23.8197 | −1.09523 | ||||||||
\(474\) | 2.23607 | 0.102706 | ||||||||
\(475\) | 13.0689 | 0.599642 | ||||||||
\(476\) | 0.0557281 | 0.00255429 | ||||||||
\(477\) | −29.7082 | −1.36025 | ||||||||
\(478\) | 3.70820 | 0.169609 | ||||||||
\(479\) | −25.3607 | −1.15876 | −0.579380 | − | 0.815058i | \(-0.696705\pi\) | ||||
−0.579380 | + | 0.815058i | \(0.696705\pi\) | |||||||
\(480\) | −10.9443 | −0.499535 | ||||||||
\(481\) | −6.47214 | −0.295104 | ||||||||
\(482\) | 40.2705 | 1.83427 | ||||||||
\(483\) | −4.00000 | −0.182006 | ||||||||
\(484\) | 8.65248 | 0.393294 | ||||||||
\(485\) | −18.6525 | −0.846965 | ||||||||
\(486\) | 35.0344 | 1.58919 | ||||||||
\(487\) | −16.6869 | −0.756156 | −0.378078 | − | 0.925774i | \(-0.623415\pi\) | ||||
−0.378078 | + | 0.925774i | \(0.623415\pi\) | |||||||
\(488\) | 13.2918 | 0.601691 | ||||||||
\(489\) | 33.2705 | 1.50454 | ||||||||
\(490\) | 13.7082 | 0.619274 | ||||||||
\(491\) | 7.23607 | 0.326559 | 0.163280 | − | 0.986580i | \(-0.447793\pi\) | ||||
0.163280 | + | 0.986580i | \(0.447793\pi\) | |||||||
\(492\) | 0.381966 | 0.0172204 | ||||||||
\(493\) | −0.652476 | −0.0293860 | ||||||||
\(494\) | 6.09017 | 0.274010 | ||||||||
\(495\) | −23.8197 | −1.07061 | ||||||||
\(496\) | 8.56231 | 0.384459 | ||||||||
\(497\) | 5.03444 | 0.225826 | ||||||||
\(498\) | 26.4164 | 1.18375 | ||||||||
\(499\) | −26.9787 | −1.20773 | −0.603867 | − | 0.797085i | \(-0.706374\pi\) | ||||
−0.603867 | + | 0.797085i | \(0.706374\pi\) | |||||||
\(500\) | 6.47214 | 0.289443 | ||||||||
\(501\) | −8.00000 | −0.357414 | ||||||||
\(502\) | 17.0344 | 0.760284 | ||||||||
\(503\) | −34.5410 | −1.54011 | −0.770054 | − | 0.637979i | \(-0.779771\pi\) | ||||
−0.770054 | + | 0.637979i | \(0.779771\pi\) | |||||||
\(504\) | 3.29180 | 0.146628 | ||||||||
\(505\) | 7.41641 | 0.330026 | ||||||||
\(506\) | −32.3607 | −1.43861 | ||||||||
\(507\) | −2.61803 | −0.116271 | ||||||||
\(508\) | −2.96556 | −0.131575 | ||||||||
\(509\) | 1.85410 | 0.0821816 | 0.0410908 | − | 0.999155i | \(-0.486917\pi\) | ||||
0.0410908 | + | 0.999155i | \(0.486917\pi\) | |||||||
\(510\) | −1.23607 | −0.0547340 | ||||||||
\(511\) | 5.12461 | 0.226699 | ||||||||
\(512\) | −5.29180 | −0.233867 | ||||||||
\(513\) | 8.41641 | 0.371593 | ||||||||
\(514\) | 37.5066 | 1.65434 | ||||||||
\(515\) | −13.3475 | −0.588162 | ||||||||
\(516\) | 7.70820 | 0.339335 | ||||||||
\(517\) | 59.2705 | 2.60671 | ||||||||
\(518\) | −4.00000 | −0.175750 | ||||||||
\(519\) | −43.7426 | −1.92009 | ||||||||
\(520\) | −2.76393 | −0.121206 | ||||||||
\(521\) | −38.2148 | −1.67422 | −0.837110 | − | 0.547035i | \(-0.815757\pi\) | ||||
−0.837110 | + | 0.547035i | \(0.815757\pi\) | |||||||
\(522\) | 17.2361 | 0.754402 | ||||||||
\(523\) | 42.6525 | 1.86506 | 0.932531 | − | 0.361089i | \(-0.117595\pi\) | ||||
0.932531 | + | 0.361089i | \(0.117595\pi\) | |||||||
\(524\) | 6.43769 | 0.281232 | ||||||||
\(525\) | −3.47214 | −0.151536 | ||||||||
\(526\) | 22.2705 | 0.971040 | ||||||||
\(527\) | 0.416408 | 0.0181390 | ||||||||
\(528\) | 63.5410 | 2.76527 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 15.4164 | 0.669646 | ||||||||
\(531\) | −0.347524 | −0.0150813 | ||||||||
\(532\) | 0.888544 | 0.0385233 | ||||||||
\(533\) | 0.236068 | 0.0102252 | ||||||||
\(534\) | −29.0344 | −1.25644 | ||||||||
\(535\) | 13.5967 | 0.587839 | ||||||||
\(536\) | −15.0000 | −0.647901 | ||||||||
\(537\) | −24.3262 | −1.04975 | ||||||||
\(538\) | 17.4164 | 0.750875 | ||||||||
\(539\) | −34.2705 | −1.47614 | ||||||||
\(540\) | 1.70820 | 0.0735094 | ||||||||
\(541\) | −5.94427 | −0.255564 | −0.127782 | − | 0.991802i | \(-0.540786\pi\) | ||||
−0.127782 | + | 0.991802i | \(0.540786\pi\) | |||||||
\(542\) | −21.0344 | −0.903507 | ||||||||
\(543\) | −36.0344 | −1.54639 | ||||||||
\(544\) | 0.798374 | 0.0342300 | ||||||||
\(545\) | 6.54102 | 0.280186 | ||||||||
\(546\) | −1.61803 | −0.0692455 | ||||||||
\(547\) | 36.1803 | 1.54696 | 0.773480 | − | 0.633821i | \(-0.218514\pi\) | ||||
0.773480 | + | 0.633821i | \(0.218514\pi\) | |||||||
\(548\) | 0.180340 | 0.00770374 | ||||||||
\(549\) | −22.9098 | −0.977768 | ||||||||
\(550\) | −28.0902 | −1.19777 | ||||||||
\(551\) | −10.4033 | −0.443193 | ||||||||
\(552\) | −23.4164 | −0.996669 | ||||||||
\(553\) | 0.201626 | 0.00857401 | ||||||||
\(554\) | 11.3820 | 0.483573 | ||||||||
\(555\) | 20.9443 | 0.889035 | ||||||||
\(556\) | −0.763932 | −0.0323979 | ||||||||
\(557\) | −11.6180 | −0.492272 | −0.246136 | − | 0.969235i | \(-0.579161\pi\) | ||||
−0.246136 | + | 0.969235i | \(0.579161\pi\) | |||||||
\(558\) | −11.0000 | −0.465667 | ||||||||
\(559\) | 4.76393 | 0.201493 | ||||||||
\(560\) | −2.29180 | −0.0968461 | ||||||||
\(561\) | 3.09017 | 0.130467 | ||||||||
\(562\) | 21.5066 | 0.907200 | ||||||||
\(563\) | −2.09017 | −0.0880902 | −0.0440451 | − | 0.999030i | \(-0.514025\pi\) | ||||
−0.0440451 | + | 0.999030i | \(0.514025\pi\) | |||||||
\(564\) | −19.1803 | −0.807638 | ||||||||
\(565\) | 6.29180 | 0.264698 | ||||||||
\(566\) | 33.5066 | 1.40839 | ||||||||
\(567\) | 2.18034 | 0.0915657 | ||||||||
\(568\) | 29.4721 | 1.23662 | ||||||||
\(569\) | 29.0902 | 1.21952 | 0.609762 | − | 0.792585i | \(-0.291265\pi\) | ||||
0.609762 | + | 0.792585i | \(0.291265\pi\) | |||||||
\(570\) | −19.7082 | −0.825486 | ||||||||
\(571\) | −38.7771 | −1.62277 | −0.811385 | − | 0.584512i | \(-0.801286\pi\) | ||||
−0.811385 | + | 0.584512i | \(0.801286\pi\) | |||||||
\(572\) | −3.09017 | −0.129206 | ||||||||
\(573\) | 59.6869 | 2.49346 | ||||||||
\(574\) | 0.145898 | 0.00608967 | ||||||||
\(575\) | 13.8885 | 0.579192 | ||||||||
\(576\) | 16.3262 | 0.680260 | ||||||||
\(577\) | 17.1246 | 0.712907 | 0.356453 | − | 0.934313i | \(-0.383986\pi\) | ||||
0.356453 | + | 0.934313i | \(0.383986\pi\) | |||||||
\(578\) | −27.4164 | −1.14037 | ||||||||
\(579\) | −15.7082 | −0.652811 | ||||||||
\(580\) | −2.11146 | −0.0876734 | ||||||||
\(581\) | 2.38197 | 0.0988206 | ||||||||
\(582\) | −63.9230 | −2.64969 | ||||||||
\(583\) | −38.5410 | −1.59621 | ||||||||
\(584\) | 30.0000 | 1.24141 | ||||||||
\(585\) | 4.76393 | 0.196964 | ||||||||
\(586\) | 31.9443 | 1.31961 | ||||||||
\(587\) | −12.2016 | −0.503615 | −0.251808 | − | 0.967777i | \(-0.581025\pi\) | ||||
−0.251808 | + | 0.967777i | \(0.581025\pi\) | |||||||
\(588\) | 11.0902 | 0.457351 | ||||||||
\(589\) | 6.63932 | 0.273568 | ||||||||
\(590\) | 0.180340 | 0.00742448 | ||||||||
\(591\) | 19.7984 | 0.814396 | ||||||||
\(592\) | −31.4164 | −1.29121 | ||||||||
\(593\) | −8.03444 | −0.329935 | −0.164967 | − | 0.986299i | \(-0.552752\pi\) | ||||
−0.164967 | + | 0.986299i | \(0.552752\pi\) | |||||||
\(594\) | −18.0902 | −0.742249 | ||||||||
\(595\) | −0.111456 | −0.00456926 | ||||||||
\(596\) | −8.88854 | −0.364089 | ||||||||
\(597\) | 1.00000 | 0.0409273 | ||||||||
\(598\) | 6.47214 | 0.264665 | ||||||||
\(599\) | 38.1246 | 1.55773 | 0.778865 | − | 0.627192i | \(-0.215796\pi\) | ||||
0.778865 | + | 0.627192i | \(0.215796\pi\) | |||||||
\(600\) | −20.3262 | −0.829815 | ||||||||
\(601\) | 4.72949 | 0.192920 | 0.0964600 | − | 0.995337i | \(-0.469248\pi\) | ||||
0.0964600 | + | 0.995337i | \(0.469248\pi\) | |||||||
\(602\) | 2.94427 | 0.120000 | ||||||||
\(603\) | 25.8541 | 1.05286 | ||||||||
\(604\) | 12.9443 | 0.526695 | ||||||||
\(605\) | −17.3050 | −0.703546 | ||||||||
\(606\) | 25.4164 | 1.03247 | ||||||||
\(607\) | −25.3607 | −1.02936 | −0.514679 | − | 0.857383i | \(-0.672089\pi\) | ||||
−0.514679 | + | 0.857383i | \(0.672089\pi\) | |||||||
\(608\) | 12.7295 | 0.516249 | ||||||||
\(609\) | 2.76393 | 0.112000 | ||||||||
\(610\) | 11.8885 | 0.481353 | ||||||||
\(611\) | −11.8541 | −0.479566 | ||||||||
\(612\) | −0.562306 | −0.0227299 | ||||||||
\(613\) | −17.0344 | −0.688015 | −0.344007 | − | 0.938967i | \(-0.611785\pi\) | ||||
−0.344007 | + | 0.938967i | \(0.611785\pi\) | |||||||
\(614\) | 17.5623 | 0.708757 | ||||||||
\(615\) | −0.763932 | −0.0308047 | ||||||||
\(616\) | 4.27051 | 0.172064 | ||||||||
\(617\) | 7.34752 | 0.295800 | 0.147900 | − | 0.989002i | \(-0.452749\pi\) | ||||
0.147900 | + | 0.989002i | \(0.452749\pi\) | |||||||
\(618\) | −45.7426 | −1.84004 | ||||||||
\(619\) | 1.00000 | 0.0401934 | ||||||||
\(620\) | 1.34752 | 0.0541179 | ||||||||
\(621\) | 8.94427 | 0.358921 | ||||||||
\(622\) | −39.9787 | −1.60300 | ||||||||
\(623\) | −2.61803 | −0.104889 | ||||||||
\(624\) | −12.7082 | −0.508735 | ||||||||
\(625\) | 4.41641 | 0.176656 | ||||||||
\(626\) | 29.1246 | 1.16405 | ||||||||
\(627\) | 49.2705 | 1.96767 | ||||||||
\(628\) | 10.4721 | 0.417884 | ||||||||
\(629\) | −1.52786 | −0.0609199 | ||||||||
\(630\) | 2.94427 | 0.117303 | ||||||||
\(631\) | 21.2148 | 0.844547 | 0.422274 | − | 0.906468i | \(-0.361232\pi\) | ||||
0.422274 | + | 0.906468i | \(0.361232\pi\) | |||||||
\(632\) | 1.18034 | 0.0469514 | ||||||||
\(633\) | −37.3607 | −1.48495 | ||||||||
\(634\) | −33.7984 | −1.34230 | ||||||||
\(635\) | 5.93112 | 0.235369 | ||||||||
\(636\) | 12.4721 | 0.494552 | ||||||||
\(637\) | 6.85410 | 0.271569 | ||||||||
\(638\) | 22.3607 | 0.885268 | ||||||||
\(639\) | −50.7984 | −2.00955 | ||||||||
\(640\) | −16.8328 | −0.665375 | ||||||||
\(641\) | 24.0000 | 0.947943 | 0.473972 | − | 0.880540i | \(-0.342820\pi\) | ||||
0.473972 | + | 0.880540i | \(0.342820\pi\) | |||||||
\(642\) | 46.5967 | 1.83903 | ||||||||
\(643\) | −14.4164 | −0.568528 | −0.284264 | − | 0.958746i | \(-0.591749\pi\) | ||||
−0.284264 | + | 0.958746i | \(0.591749\pi\) | |||||||
\(644\) | 0.944272 | 0.0372095 | ||||||||
\(645\) | −15.4164 | −0.607020 | ||||||||
\(646\) | 1.43769 | 0.0565653 | ||||||||
\(647\) | −45.1246 | −1.77403 | −0.887016 | − | 0.461739i | \(-0.847226\pi\) | ||||
−0.887016 | + | 0.461739i | \(0.847226\pi\) | |||||||
\(648\) | 12.7639 | 0.501415 | ||||||||
\(649\) | −0.450850 | −0.0176974 | ||||||||
\(650\) | 5.61803 | 0.220357 | ||||||||
\(651\) | −1.76393 | −0.0691339 | ||||||||
\(652\) | −7.85410 | −0.307590 | ||||||||
\(653\) | 1.00000 | 0.0391330 | 0.0195665 | − | 0.999809i | \(-0.493771\pi\) | ||||
0.0195665 | + | 0.999809i | \(0.493771\pi\) | |||||||
\(654\) | 22.4164 | 0.876551 | ||||||||
\(655\) | −12.8754 | −0.503083 | ||||||||
\(656\) | 1.14590 | 0.0447398 | ||||||||
\(657\) | −51.7082 | −2.01733 | ||||||||
\(658\) | −7.32624 | −0.285606 | ||||||||
\(659\) | −22.0000 | −0.856998 | −0.428499 | − | 0.903542i | \(-0.640958\pi\) | ||||
−0.428499 | + | 0.903542i | \(0.640958\pi\) | |||||||
\(660\) | 10.0000 | 0.389249 | ||||||||
\(661\) | −7.29180 | −0.283618 | −0.141809 | − | 0.989894i | \(-0.545292\pi\) | ||||
−0.141809 | + | 0.989894i | \(0.545292\pi\) | |||||||
\(662\) | 35.6525 | 1.38567 | ||||||||
\(663\) | −0.618034 | −0.0240025 | ||||||||
\(664\) | 13.9443 | 0.541143 | ||||||||
\(665\) | −1.77709 | −0.0689125 | ||||||||
\(666\) | 40.3607 | 1.56394 | ||||||||
\(667\) | −11.0557 | −0.428080 | ||||||||
\(668\) | 1.88854 | 0.0730700 | ||||||||
\(669\) | −20.7082 | −0.800625 | ||||||||
\(670\) | −13.4164 | −0.518321 | ||||||||
\(671\) | −29.7214 | −1.14738 | ||||||||
\(672\) | −3.38197 | −0.130462 | ||||||||
\(673\) | −6.43769 | −0.248155 | −0.124077 | − | 0.992273i | \(-0.539597\pi\) | ||||
−0.124077 | + | 0.992273i | \(0.539597\pi\) | |||||||
\(674\) | 39.3607 | 1.51612 | ||||||||
\(675\) | 7.76393 | 0.298834 | ||||||||
\(676\) | 0.618034 | 0.0237705 | ||||||||
\(677\) | −24.7082 | −0.949613 | −0.474807 | − | 0.880090i | \(-0.657482\pi\) | ||||
−0.474807 | + | 0.880090i | \(0.657482\pi\) | |||||||
\(678\) | 21.5623 | 0.828095 | ||||||||
\(679\) | −5.76393 | −0.221199 | ||||||||
\(680\) | −0.652476 | −0.0250213 | ||||||||
\(681\) | −16.7984 | −0.643715 | ||||||||
\(682\) | −14.2705 | −0.546446 | ||||||||
\(683\) | −9.43769 | −0.361123 | −0.180562 | − | 0.983564i | \(-0.557792\pi\) | ||||
−0.180562 | + | 0.983564i | \(0.557792\pi\) | |||||||
\(684\) | −8.96556 | −0.342807 | ||||||||
\(685\) | −0.360680 | −0.0137809 | ||||||||
\(686\) | 8.56231 | 0.326910 | ||||||||
\(687\) | −45.5967 | −1.73962 | ||||||||
\(688\) | 23.1246 | 0.881618 | ||||||||
\(689\) | 7.70820 | 0.293659 | ||||||||
\(690\) | −20.9443 | −0.797335 | ||||||||
\(691\) | −17.8328 | −0.678392 | −0.339196 | − | 0.940716i | \(-0.610155\pi\) | ||||
−0.339196 | + | 0.940716i | \(0.610155\pi\) | |||||||
\(692\) | 10.3262 | 0.392545 | ||||||||
\(693\) | −7.36068 | −0.279609 | ||||||||
\(694\) | −1.23607 | −0.0469205 | ||||||||
\(695\) | 1.52786 | 0.0579552 | ||||||||
\(696\) | 16.1803 | 0.613314 | ||||||||
\(697\) | 0.0557281 | 0.00211085 | ||||||||
\(698\) | −18.5623 | −0.702594 | ||||||||
\(699\) | −40.7426 | −1.54103 | ||||||||
\(700\) | 0.819660 | 0.0309802 | ||||||||
\(701\) | 25.7639 | 0.973090 | 0.486545 | − | 0.873655i | \(-0.338257\pi\) | ||||
0.486545 | + | 0.873655i | \(0.338257\pi\) | |||||||
\(702\) | 3.61803 | 0.136554 | ||||||||
\(703\) | −24.3607 | −0.918780 | ||||||||
\(704\) | 21.1803 | 0.798264 | ||||||||
\(705\) | 38.3607 | 1.44475 | ||||||||
\(706\) | −31.7984 | −1.19675 | ||||||||
\(707\) | 2.29180 | 0.0861919 | ||||||||
\(708\) | 0.145898 | 0.00548318 | ||||||||
\(709\) | −6.87539 | −0.258211 | −0.129105 | − | 0.991631i | \(-0.541211\pi\) | ||||
−0.129105 | + | 0.991631i | \(0.541211\pi\) | |||||||
\(710\) | 26.3607 | 0.989299 | ||||||||
\(711\) | −2.03444 | −0.0762975 | ||||||||
\(712\) | −15.3262 | −0.574375 | ||||||||
\(713\) | 7.05573 | 0.264239 | ||||||||
\(714\) | −0.381966 | −0.0142947 | ||||||||
\(715\) | 6.18034 | 0.231132 | ||||||||
\(716\) | 5.74265 | 0.214613 | ||||||||
\(717\) | −6.00000 | −0.224074 | ||||||||
\(718\) | 5.61803 | 0.209663 | ||||||||
\(719\) | 45.7082 | 1.70463 | 0.852314 | − | 0.523030i | \(-0.175198\pi\) | ||||
0.852314 | + | 0.523030i | \(0.175198\pi\) | |||||||
\(720\) | 23.1246 | 0.861803 | ||||||||
\(721\) | −4.12461 | −0.153609 | ||||||||
\(722\) | −7.81966 | −0.291018 | ||||||||
\(723\) | −65.1591 | −2.42329 | ||||||||
\(724\) | 8.50658 | 0.316144 | ||||||||
\(725\) | −9.59675 | −0.356414 | ||||||||
\(726\) | −59.3050 | −2.20101 | ||||||||
\(727\) | 21.8197 | 0.809246 | 0.404623 | − | 0.914483i | \(-0.367403\pi\) | ||||
0.404623 | + | 0.914483i | \(0.367403\pi\) | |||||||
\(728\) | −0.854102 | −0.0316551 | ||||||||
\(729\) | −39.5623 | −1.46527 | ||||||||
\(730\) | 26.8328 | 0.993127 | ||||||||
\(731\) | 1.12461 | 0.0415953 | ||||||||
\(732\) | 9.61803 | 0.355493 | ||||||||
\(733\) | 47.4164 | 1.75136 | 0.875682 | − | 0.482887i | \(-0.160412\pi\) | ||||
0.875682 | + | 0.482887i | \(0.160412\pi\) | |||||||
\(734\) | 34.8885 | 1.28776 | ||||||||
\(735\) | −22.1803 | −0.818134 | ||||||||
\(736\) | 13.5279 | 0.498644 | ||||||||
\(737\) | 33.5410 | 1.23550 | ||||||||
\(738\) | −1.47214 | −0.0541901 | ||||||||
\(739\) | −4.18034 | −0.153776 | −0.0768881 | − | 0.997040i | \(-0.524498\pi\) | ||||
−0.0768881 | + | 0.997040i | \(0.524498\pi\) | |||||||
\(740\) | −4.94427 | −0.181755 | ||||||||
\(741\) | −9.85410 | −0.361999 | ||||||||
\(742\) | 4.76393 | 0.174889 | ||||||||
\(743\) | −4.14590 | −0.152098 | −0.0760491 | − | 0.997104i | \(-0.524231\pi\) | ||||
−0.0760491 | + | 0.997104i | \(0.524231\pi\) | |||||||
\(744\) | −10.3262 | −0.378578 | ||||||||
\(745\) | 17.7771 | 0.651302 | ||||||||
\(746\) | −3.00000 | −0.109838 | ||||||||
\(747\) | −24.0344 | −0.879374 | ||||||||
\(748\) | −0.729490 | −0.0266728 | ||||||||
\(749\) | 4.20163 | 0.153524 | ||||||||
\(750\) | −44.3607 | −1.61982 | ||||||||
\(751\) | −7.21478 | −0.263271 | −0.131636 | − | 0.991298i | \(-0.542023\pi\) | ||||
−0.131636 | + | 0.991298i | \(0.542023\pi\) | |||||||
\(752\) | −57.5410 | −2.09831 | ||||||||
\(753\) | −27.5623 | −1.00443 | ||||||||
\(754\) | −4.47214 | −0.162866 | ||||||||
\(755\) | −25.8885 | −0.942181 | ||||||||
\(756\) | 0.527864 | 0.0191982 | ||||||||
\(757\) | −23.6180 | −0.858412 | −0.429206 | − | 0.903207i | \(-0.641207\pi\) | ||||
−0.429206 | + | 0.903207i | \(0.641207\pi\) | |||||||
\(758\) | −43.8885 | −1.59410 | ||||||||
\(759\) | 52.3607 | 1.90057 | ||||||||
\(760\) | −10.4033 | −0.377366 | ||||||||
\(761\) | −24.0902 | −0.873268 | −0.436634 | − | 0.899639i | \(-0.643830\pi\) | ||||
−0.436634 | + | 0.899639i | \(0.643830\pi\) | |||||||
\(762\) | 20.3262 | 0.736342 | ||||||||
\(763\) | 2.02129 | 0.0731755 | ||||||||
\(764\) | −14.0902 | −0.509764 | ||||||||
\(765\) | 1.12461 | 0.0406604 | ||||||||
\(766\) | −41.5967 | −1.50295 | ||||||||
\(767\) | 0.0901699 | 0.00325585 | ||||||||
\(768\) | −35.5066 | −1.28123 | ||||||||
\(769\) | −50.9787 | −1.83834 | −0.919170 | − | 0.393862i | \(-0.871139\pi\) | ||||
−0.919170 | + | 0.393862i | \(0.871139\pi\) | |||||||
\(770\) | 3.81966 | 0.137651 | ||||||||
\(771\) | −60.6869 | −2.18559 | ||||||||
\(772\) | 3.70820 | 0.133461 | ||||||||
\(773\) | 12.7426 | 0.458321 | 0.229161 | − | 0.973389i | \(-0.426402\pi\) | ||||
0.229161 | + | 0.973389i | \(0.426402\pi\) | |||||||
\(774\) | −29.7082 | −1.06784 | ||||||||
\(775\) | 6.12461 | 0.220003 | ||||||||
\(776\) | −33.7426 | −1.21129 | ||||||||
\(777\) | 6.47214 | 0.232187 | ||||||||
\(778\) | 41.1246 | 1.47439 | ||||||||
\(779\) | 0.888544 | 0.0318354 | ||||||||
\(780\) | −2.00000 | −0.0716115 | ||||||||
\(781\) | −65.9017 | −2.35815 | ||||||||
\(782\) | 1.52786 | 0.0546363 | ||||||||
\(783\) | −6.18034 | −0.220867 | ||||||||
\(784\) | 33.2705 | 1.18823 | ||||||||
\(785\) | −20.9443 | −0.747533 | ||||||||
\(786\) | −44.1246 | −1.57387 | ||||||||
\(787\) | 43.0000 | 1.53278 | 0.766392 | − | 0.642373i | \(-0.222050\pi\) | ||||
0.766392 | + | 0.642373i | \(0.222050\pi\) | |||||||
\(788\) | −4.67376 | −0.166496 | ||||||||
\(789\) | −36.0344 | −1.28286 | ||||||||
\(790\) | 1.05573 | 0.0375611 | ||||||||
\(791\) | 1.94427 | 0.0691304 | ||||||||
\(792\) | −43.0902 | −1.53114 | ||||||||
\(793\) | 5.94427 | 0.211087 | ||||||||
\(794\) | −41.9787 | −1.48977 | ||||||||
\(795\) | −24.9443 | −0.884682 | ||||||||
\(796\) | −0.236068 | −0.00836721 | ||||||||
\(797\) | 8.83282 | 0.312874 | 0.156437 | − | 0.987688i | \(-0.449999\pi\) | ||||
0.156437 | + | 0.987688i | \(0.449999\pi\) | |||||||
\(798\) | −6.09017 | −0.215590 | ||||||||
\(799\) | −2.79837 | −0.0989994 | ||||||||
\(800\) | 11.7426 | 0.415165 | ||||||||
\(801\) | 26.4164 | 0.933378 | ||||||||
\(802\) | 25.0344 | 0.883997 | ||||||||
\(803\) | −67.0820 | −2.36727 | ||||||||
\(804\) | −10.8541 | −0.382795 | ||||||||
\(805\) | −1.88854 | −0.0665624 | ||||||||
\(806\) | 2.85410 | 0.100531 | ||||||||
\(807\) | −28.1803 | −0.991995 | ||||||||
\(808\) | 13.4164 | 0.471988 | ||||||||
\(809\) | −3.74265 | −0.131584 | −0.0657922 | − | 0.997833i | \(-0.520957\pi\) | ||||
−0.0657922 | + | 0.997833i | \(0.520957\pi\) | |||||||
\(810\) | 11.4164 | 0.401132 | ||||||||
\(811\) | −20.0557 | −0.704252 | −0.352126 | − | 0.935953i | \(-0.614541\pi\) | ||||
−0.352126 | + | 0.935953i | \(0.614541\pi\) | |||||||
\(812\) | −0.652476 | −0.0228974 | ||||||||
\(813\) | 34.0344 | 1.19364 | ||||||||
\(814\) | 52.3607 | 1.83524 | ||||||||
\(815\) | 15.7082 | 0.550234 | ||||||||
\(816\) | −3.00000 | −0.105021 | ||||||||
\(817\) | 17.9311 | 0.627330 | ||||||||
\(818\) | 6.90983 | 0.241597 | ||||||||
\(819\) | 1.47214 | 0.0514406 | ||||||||
\(820\) | 0.180340 | 0.00629774 | ||||||||
\(821\) | 12.2361 | 0.427042 | 0.213521 | − | 0.976939i | \(-0.431507\pi\) | ||||
0.213521 | + | 0.976939i | \(0.431507\pi\) | |||||||
\(822\) | −1.23607 | −0.0431128 | ||||||||
\(823\) | 26.2361 | 0.914532 | 0.457266 | − | 0.889330i | \(-0.348829\pi\) | ||||
0.457266 | + | 0.889330i | \(0.348829\pi\) | |||||||
\(824\) | −24.1459 | −0.841162 | ||||||||
\(825\) | 45.4508 | 1.58240 | ||||||||
\(826\) | 0.0557281 | 0.00193903 | ||||||||
\(827\) | −53.9574 | −1.87628 | −0.938142 | − | 0.346251i | \(-0.887454\pi\) | ||||
−0.938142 | + | 0.346251i | \(0.887454\pi\) | |||||||
\(828\) | −9.52786 | −0.331116 | ||||||||
\(829\) | −5.20163 | −0.180660 | −0.0903300 | − | 0.995912i | \(-0.528792\pi\) | ||||
−0.0903300 | + | 0.995912i | \(0.528792\pi\) | |||||||
\(830\) | 12.4721 | 0.432914 | ||||||||
\(831\) | −18.4164 | −0.638858 | ||||||||
\(832\) | −4.23607 | −0.146859 | ||||||||
\(833\) | 1.61803 | 0.0560616 | ||||||||
\(834\) | 5.23607 | 0.181310 | ||||||||
\(835\) | −3.77709 | −0.130712 | ||||||||
\(836\) | −11.6312 | −0.402273 | ||||||||
\(837\) | 3.94427 | 0.136334 | ||||||||
\(838\) | 25.3262 | 0.874880 | ||||||||
\(839\) | −17.0344 | −0.588094 | −0.294047 | − | 0.955791i | \(-0.595002\pi\) | ||||
−0.294047 | + | 0.955791i | \(0.595002\pi\) | |||||||
\(840\) | 2.76393 | 0.0953647 | ||||||||
\(841\) | −21.3607 | −0.736575 | ||||||||
\(842\) | 42.8328 | 1.47612 | ||||||||
\(843\) | −34.7984 | −1.19852 | ||||||||
\(844\) | 8.81966 | 0.303585 | ||||||||
\(845\) | −1.23607 | −0.0425220 | ||||||||
\(846\) | 73.9230 | 2.54152 | ||||||||
\(847\) | −5.34752 | −0.183743 | ||||||||
\(848\) | 37.4164 | 1.28488 | ||||||||
\(849\) | −54.2148 | −1.86065 | ||||||||
\(850\) | 1.32624 | 0.0454896 | ||||||||
\(851\) | −25.8885 | −0.887448 | ||||||||
\(852\) | 21.3262 | 0.730625 | ||||||||
\(853\) | 25.4721 | 0.872149 | 0.436075 | − | 0.899910i | \(-0.356368\pi\) | ||||
0.436075 | + | 0.899910i | \(0.356368\pi\) | |||||||
\(854\) | 3.67376 | 0.125714 | ||||||||
\(855\) | 17.9311 | 0.613231 | ||||||||
\(856\) | 24.5967 | 0.840700 | ||||||||
\(857\) | −27.9230 | −0.953831 | −0.476916 | − | 0.878949i | \(-0.658245\pi\) | ||||
−0.476916 | + | 0.878949i | \(0.658245\pi\) | |||||||
\(858\) | 21.1803 | 0.723085 | ||||||||
\(859\) | −50.4508 | −1.72136 | −0.860680 | − | 0.509146i | \(-0.829961\pi\) | ||||
−0.860680 | + | 0.509146i | \(0.829961\pi\) | |||||||
\(860\) | 3.63932 | 0.124100 | ||||||||
\(861\) | −0.236068 | −0.00804518 | ||||||||
\(862\) | 42.7426 | 1.45582 | ||||||||
\(863\) | 46.2148 | 1.57317 | 0.786585 | − | 0.617482i | \(-0.211847\pi\) | ||||
0.786585 | + | 0.617482i | \(0.211847\pi\) | |||||||
\(864\) | 7.56231 | 0.257275 | ||||||||
\(865\) | −20.6525 | −0.702205 | ||||||||
\(866\) | 8.79837 | 0.298981 | ||||||||
\(867\) | 44.3607 | 1.50657 | ||||||||
\(868\) | 0.416408 | 0.0141338 | ||||||||
\(869\) | −2.63932 | −0.0895328 | ||||||||
\(870\) | 14.4721 | 0.490651 | ||||||||
\(871\) | −6.70820 | −0.227299 | ||||||||
\(872\) | 11.8328 | 0.400710 | ||||||||
\(873\) | 58.1591 | 1.96839 | ||||||||
\(874\) | 24.3607 | 0.824012 | ||||||||
\(875\) | −4.00000 | −0.135225 | ||||||||
\(876\) | 21.7082 | 0.733452 | ||||||||
\(877\) | 35.8328 | 1.20999 | 0.604994 | − | 0.796230i | \(-0.293175\pi\) | ||||
0.604994 | + | 0.796230i | \(0.293175\pi\) | |||||||
\(878\) | 37.3050 | 1.25898 | ||||||||
\(879\) | −51.6869 | −1.74336 | ||||||||
\(880\) | 30.0000 | 1.01130 | ||||||||
\(881\) | 21.2148 | 0.714744 | 0.357372 | − | 0.933962i | \(-0.383673\pi\) | ||||
0.357372 | + | 0.933962i | \(0.383673\pi\) | |||||||
\(882\) | −42.7426 | −1.43922 | ||||||||
\(883\) | −44.2148 | −1.48795 | −0.743973 | − | 0.668210i | \(-0.767061\pi\) | ||||
−0.743973 | + | 0.668210i | \(0.767061\pi\) | |||||||
\(884\) | 0.145898 | 0.00490708 | ||||||||
\(885\) | −0.291796 | −0.00980862 | ||||||||
\(886\) | −24.5066 | −0.823315 | ||||||||
\(887\) | 19.3262 | 0.648912 | 0.324456 | − | 0.945901i | \(-0.394819\pi\) | ||||
0.324456 | + | 0.945901i | \(0.394819\pi\) | |||||||
\(888\) | 37.8885 | 1.27146 | ||||||||
\(889\) | 1.83282 | 0.0614707 | ||||||||
\(890\) | −13.7082 | −0.459500 | ||||||||
\(891\) | −28.5410 | −0.956160 | ||||||||
\(892\) | 4.88854 | 0.163681 | ||||||||
\(893\) | −44.6180 | −1.49309 | ||||||||
\(894\) | 60.9230 | 2.03757 | ||||||||
\(895\) | −11.4853 | −0.383911 | ||||||||
\(896\) | −5.20163 | −0.173774 | ||||||||
\(897\) | −10.4721 | −0.349654 | ||||||||
\(898\) | −9.90983 | −0.330695 | ||||||||
\(899\) | −4.87539 | −0.162603 | ||||||||
\(900\) | −8.27051 | −0.275684 | ||||||||
\(901\) | 1.81966 | 0.0606217 | ||||||||
\(902\) | −1.90983 | −0.0635904 | ||||||||
\(903\) | −4.76393 | −0.158534 | ||||||||
\(904\) | 11.3820 | 0.378559 | ||||||||
\(905\) | −17.0132 | −0.565536 | ||||||||
\(906\) | −88.7214 | −2.94757 | ||||||||
\(907\) | 23.9230 | 0.794350 | 0.397175 | − | 0.917743i | \(-0.369991\pi\) | ||||
0.397175 | + | 0.917743i | \(0.369991\pi\) | |||||||
\(908\) | 3.96556 | 0.131602 | ||||||||
\(909\) | −23.1246 | −0.766995 | ||||||||
\(910\) | −0.763932 | −0.0253241 | ||||||||
\(911\) | 28.4377 | 0.942183 | 0.471091 | − | 0.882084i | \(-0.343860\pi\) | ||||
0.471091 | + | 0.882084i | \(0.343860\pi\) | |||||||
\(912\) | −47.8328 | −1.58390 | ||||||||
\(913\) | −31.1803 | −1.03192 | ||||||||
\(914\) | 6.09017 | 0.201445 | ||||||||
\(915\) | −19.2361 | −0.635925 | ||||||||
\(916\) | 10.7639 | 0.355650 | ||||||||
\(917\) | −3.97871 | −0.131389 | ||||||||
\(918\) | 0.854102 | 0.0281896 | ||||||||
\(919\) | −4.41641 | −0.145684 | −0.0728419 | − | 0.997343i | \(-0.523207\pi\) | ||||
−0.0728419 | + | 0.997343i | \(0.523207\pi\) | |||||||
\(920\) | −11.0557 | −0.364497 | ||||||||
\(921\) | −28.4164 | −0.936352 | ||||||||
\(922\) | −0.145898 | −0.00480490 | ||||||||
\(923\) | 13.1803 | 0.433836 | ||||||||
\(924\) | 3.09017 | 0.101659 | ||||||||
\(925\) | −22.4721 | −0.738879 | ||||||||
\(926\) | −55.2148 | −1.81447 | ||||||||
\(927\) | 41.6180 | 1.36692 | ||||||||
\(928\) | −9.34752 | −0.306848 | ||||||||
\(929\) | −15.3607 | −0.503968 | −0.251984 | − | 0.967731i | \(-0.581083\pi\) | ||||
−0.251984 | + | 0.967731i | \(0.581083\pi\) | |||||||
\(930\) | −9.23607 | −0.302863 | ||||||||
\(931\) | 25.7984 | 0.845508 | ||||||||
\(932\) | 9.61803 | 0.315049 | ||||||||
\(933\) | 64.6869 | 2.11775 | ||||||||
\(934\) | 35.1246 | 1.14931 | ||||||||
\(935\) | 1.45898 | 0.0477138 | ||||||||
\(936\) | 8.61803 | 0.281689 | ||||||||
\(937\) | 44.6525 | 1.45873 | 0.729366 | − | 0.684123i | \(-0.239815\pi\) | ||||
0.729366 | + | 0.684123i | \(0.239815\pi\) | |||||||
\(938\) | −4.14590 | −0.135368 | ||||||||
\(939\) | −47.1246 | −1.53785 | ||||||||
\(940\) | −9.05573 | −0.295365 | ||||||||
\(941\) | 2.72949 | 0.0889788 | 0.0444894 | − | 0.999010i | \(-0.485834\pi\) | ||||
0.0444894 | + | 0.999010i | \(0.485834\pi\) | |||||||
\(942\) | −71.7771 | −2.33862 | ||||||||
\(943\) | 0.944272 | 0.0307497 | ||||||||
\(944\) | 0.437694 | 0.0142457 | ||||||||
\(945\) | −1.05573 | −0.0343428 | ||||||||
\(946\) | −38.5410 | −1.25308 | ||||||||
\(947\) | 41.5410 | 1.34990 | 0.674951 | − | 0.737863i | \(-0.264165\pi\) | ||||
0.674951 | + | 0.737863i | \(0.264165\pi\) | |||||||
\(948\) | 0.854102 | 0.0277399 | ||||||||
\(949\) | 13.4164 | 0.435515 | ||||||||
\(950\) | 21.1459 | 0.686064 | ||||||||
\(951\) | 54.6869 | 1.77334 | ||||||||
\(952\) | −0.201626 | −0.00653474 | ||||||||
\(953\) | 44.7771 | 1.45047 | 0.725236 | − | 0.688500i | \(-0.241731\pi\) | ||||
0.725236 | + | 0.688500i | \(0.241731\pi\) | |||||||
\(954\) | −48.0689 | −1.55629 | ||||||||
\(955\) | 28.1803 | 0.911894 | ||||||||
\(956\) | 1.41641 | 0.0458099 | ||||||||
\(957\) | −36.1803 | −1.16954 | ||||||||
\(958\) | −41.0344 | −1.32576 | ||||||||
\(959\) | −0.111456 | −0.00359911 | ||||||||
\(960\) | 13.7082 | 0.442430 | ||||||||
\(961\) | −27.8885 | −0.899630 | ||||||||
\(962\) | −10.4721 | −0.337635 | ||||||||
\(963\) | −42.3951 | −1.36616 | ||||||||
\(964\) | 15.3820 | 0.495420 | ||||||||
\(965\) | −7.41641 | −0.238743 | ||||||||
\(966\) | −6.47214 | −0.208238 | ||||||||
\(967\) | 57.3951 | 1.84570 | 0.922851 | − | 0.385156i | \(-0.125852\pi\) | ||||
0.922851 | + | 0.385156i | \(0.125852\pi\) | |||||||
\(968\) | −31.3050 | −1.00618 | ||||||||
\(969\) | −2.32624 | −0.0747295 | ||||||||
\(970\) | −30.1803 | −0.969032 | ||||||||
\(971\) | 22.1246 | 0.710013 | 0.355006 | − | 0.934864i | \(-0.384479\pi\) | ||||
0.355006 | + | 0.934864i | \(0.384479\pi\) | |||||||
\(972\) | 13.3820 | 0.429227 | ||||||||
\(973\) | 0.472136 | 0.0151360 | ||||||||
\(974\) | −27.0000 | −0.865136 | ||||||||
\(975\) | −9.09017 | −0.291118 | ||||||||
\(976\) | 28.8541 | 0.923597 | ||||||||
\(977\) | 48.3262 | 1.54609 | 0.773047 | − | 0.634349i | \(-0.218732\pi\) | ||||
0.773047 | + | 0.634349i | \(0.218732\pi\) | |||||||
\(978\) | 53.8328 | 1.72138 | ||||||||
\(979\) | 34.2705 | 1.09529 | ||||||||
\(980\) | 5.23607 | 0.167260 | ||||||||
\(981\) | −20.3951 | −0.651166 | ||||||||
\(982\) | 11.7082 | 0.373624 | ||||||||
\(983\) | 16.7771 | 0.535106 | 0.267553 | − | 0.963543i | \(-0.413785\pi\) | ||||
0.267553 | + | 0.963543i | \(0.413785\pi\) | |||||||
\(984\) | −1.38197 | −0.0440555 | ||||||||
\(985\) | 9.34752 | 0.297837 | ||||||||
\(986\) | −1.05573 | −0.0336212 | ||||||||
\(987\) | 11.8541 | 0.377320 | ||||||||
\(988\) | 2.32624 | 0.0740075 | ||||||||
\(989\) | 19.0557 | 0.605937 | ||||||||
\(990\) | −38.5410 | −1.22491 | ||||||||
\(991\) | −13.3050 | −0.422646 | −0.211323 | − | 0.977416i | \(-0.567777\pi\) | ||||
−0.211323 | + | 0.977416i | \(0.567777\pi\) | |||||||
\(992\) | 5.96556 | 0.189407 | ||||||||
\(993\) | −57.6869 | −1.83064 | ||||||||
\(994\) | 8.14590 | 0.258372 | ||||||||
\(995\) | 0.472136 | 0.0149677 | ||||||||
\(996\) | 10.0902 | 0.319719 | ||||||||
\(997\) | 32.4508 | 1.02773 | 0.513864 | − | 0.857871i | \(-0.328213\pi\) | ||||
0.513864 | + | 0.857871i | \(0.328213\pi\) | |||||||
\(998\) | −43.6525 | −1.38179 | ||||||||
\(999\) | −14.4721 | −0.457878 |
(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 | 8047.2.a.a.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8047.2.a.a.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial |