Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(1,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, 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("605.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.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: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.725.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 3x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 55) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.737640\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.737640 | 0.521590 | 0.260795 | − | 0.965394i | \(-0.416015\pi\) | ||||
0.260795 | + | 0.965394i | \(0.416015\pi\) | |||||||
\(3\) | −2.81156 | −1.62326 | −0.811628 | − | 0.584175i | \(-0.801418\pi\) | ||||
−0.811628 | + | 0.584175i | \(0.801418\pi\) | |||||||
\(4\) | −1.45589 | −0.727943 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −2.07392 | −0.846675 | ||||||||
\(7\) | −1.03138 | −0.389825 | −0.194912 | − | 0.980821i | \(-0.562442\pi\) | ||||
−0.194912 | + | 0.980821i | \(0.562442\pi\) | |||||||
\(8\) | −2.54920 | −0.901279 | ||||||||
\(9\) | 4.90488 | 1.63496 | ||||||||
\(10\) | −0.737640 | −0.233262 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 4.09331 | 1.18164 | ||||||||
\(13\) | −3.44899 | −0.956577 | −0.478289 | − | 0.878203i | \(-0.658743\pi\) | ||||
−0.478289 | + | 0.878203i | \(0.658743\pi\) | |||||||
\(14\) | −0.760787 | −0.203329 | ||||||||
\(15\) | 2.81156 | 0.725942 | ||||||||
\(16\) | 1.03138 | 0.257845 | ||||||||
\(17\) | −2.39822 | −0.581653 | −0.290826 | − | 0.956776i | \(-0.593930\pi\) | ||||
−0.290826 | + | 0.956776i | \(0.593930\pi\) | |||||||
\(18\) | 3.61803 | 0.852779 | ||||||||
\(19\) | 7.66881 | 1.75935 | 0.879673 | − | 0.475580i | \(-0.157762\pi\) | ||||
0.879673 | + | 0.475580i | \(0.157762\pi\) | |||||||
\(20\) | 1.45589 | 0.325546 | ||||||||
\(21\) | 2.89979 | 0.632786 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.45589 | 0.512088 | 0.256044 | − | 0.966665i | \(-0.417581\pi\) | ||||
0.256044 | + | 0.966665i | \(0.417581\pi\) | |||||||
\(24\) | 7.16724 | 1.46301 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.54411 | −0.498942 | ||||||||
\(27\) | −5.35567 | −1.03070 | ||||||||
\(28\) | 1.50157 | 0.283770 | ||||||||
\(29\) | 5.95431 | 1.10569 | 0.552844 | − | 0.833285i | \(-0.313542\pi\) | ||||
0.552844 | + | 0.833285i | \(0.313542\pi\) | |||||||
\(30\) | 2.07392 | 0.378644 | ||||||||
\(31\) | −3.68820 | −0.662421 | −0.331210 | − | 0.943557i | \(-0.607457\pi\) | ||||
−0.331210 | + | 0.943557i | \(0.607457\pi\) | |||||||
\(32\) | 5.85919 | 1.03577 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.76902 | −0.303384 | ||||||||
\(35\) | 1.03138 | 0.174335 | ||||||||
\(36\) | −7.14094 | −1.19016 | ||||||||
\(37\) | 5.95858 | 0.979584 | 0.489792 | − | 0.871839i | \(-0.337073\pi\) | ||||
0.489792 | + | 0.871839i | \(0.337073\pi\) | |||||||
\(38\) | 5.65682 | 0.917658 | ||||||||
\(39\) | 9.69704 | 1.55277 | ||||||||
\(40\) | 2.54920 | 0.403064 | ||||||||
\(41\) | −3.93626 | −0.614740 | −0.307370 | − | 0.951590i | \(-0.599449\pi\) | ||||
−0.307370 | + | 0.951590i | \(0.599449\pi\) | |||||||
\(42\) | 2.13900 | 0.330055 | ||||||||
\(43\) | 7.64941 | 1.16652 | 0.583262 | − | 0.812284i | \(-0.301776\pi\) | ||||
0.583262 | + | 0.812284i | \(0.301776\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.90488 | −0.731176 | ||||||||
\(46\) | 1.81156 | 0.267100 | ||||||||
\(47\) | 5.84294 | 0.852281 | 0.426140 | − | 0.904657i | \(-0.359873\pi\) | ||||
0.426140 | + | 0.904657i | \(0.359873\pi\) | |||||||
\(48\) | −2.89979 | −0.418548 | ||||||||
\(49\) | −5.93626 | −0.848037 | ||||||||
\(50\) | 0.737640 | 0.104318 | ||||||||
\(51\) | 6.74273 | 0.944171 | ||||||||
\(52\) | 5.02134 | 0.696334 | ||||||||
\(53\) | −11.8480 | −1.62745 | −0.813726 | − | 0.581249i | \(-0.802564\pi\) | ||||
−0.813726 | + | 0.581249i | \(0.802564\pi\) | |||||||
\(54\) | −3.95056 | −0.537603 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.62920 | 0.351341 | ||||||||
\(57\) | −21.5613 | −2.85587 | ||||||||
\(58\) | 4.39214 | 0.576717 | ||||||||
\(59\) | 2.94630 | 0.383575 | 0.191788 | − | 0.981436i | \(-0.438572\pi\) | ||||
0.191788 | + | 0.981436i | \(0.438572\pi\) | |||||||
\(60\) | −4.09331 | −0.528445 | ||||||||
\(61\) | −2.48037 | −0.317579 | −0.158789 | − | 0.987312i | \(-0.550759\pi\) | ||||
−0.158789 | + | 0.987312i | \(0.550759\pi\) | |||||||
\(62\) | −2.72057 | −0.345512 | ||||||||
\(63\) | −5.05879 | −0.637348 | ||||||||
\(64\) | 2.25922 | 0.282402 | ||||||||
\(65\) | 3.44899 | 0.427794 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.14702 | −0.750978 | −0.375489 | − | 0.926827i | \(-0.622525\pi\) | ||||
−0.375489 | + | 0.926827i | \(0.622525\pi\) | |||||||
\(68\) | 3.49153 | 0.423410 | ||||||||
\(69\) | −6.90488 | −0.831249 | ||||||||
\(70\) | 0.760787 | 0.0909315 | ||||||||
\(71\) | 2.02315 | 0.240103 | 0.120052 | − | 0.992768i | \(-0.461694\pi\) | ||||
0.120052 | + | 0.992768i | \(0.461694\pi\) | |||||||
\(72\) | −12.5035 | −1.47355 | ||||||||
\(73\) | 0.825867 | 0.0966604 | 0.0483302 | − | 0.998831i | \(-0.484610\pi\) | ||||
0.0483302 | + | 0.998831i | \(0.484610\pi\) | |||||||
\(74\) | 4.39529 | 0.510942 | ||||||||
\(75\) | −2.81156 | −0.324651 | ||||||||
\(76\) | −11.1649 | −1.28070 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 7.15293 | 0.809910 | ||||||||
\(79\) | 12.0782 | 1.35890 | 0.679451 | − | 0.733721i | \(-0.262218\pi\) | ||||
0.679451 | + | 0.733721i | \(0.262218\pi\) | |||||||
\(80\) | −1.03138 | −0.115312 | ||||||||
\(81\) | 0.343178 | 0.0381309 | ||||||||
\(82\) | −2.90354 | −0.320642 | ||||||||
\(83\) | −1.61002 | −0.176722 | −0.0883612 | − | 0.996088i | \(-0.528163\pi\) | ||||
−0.0883612 | + | 0.996088i | \(0.528163\pi\) | |||||||
\(84\) | −4.22176 | −0.460632 | ||||||||
\(85\) | 2.39822 | 0.260123 | ||||||||
\(86\) | 5.64252 | 0.608448 | ||||||||
\(87\) | −16.7409 | −1.79481 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.16116 | 0.865081 | 0.432541 | − | 0.901614i | \(-0.357617\pi\) | ||||
0.432541 | + | 0.901614i | \(0.357617\pi\) | |||||||
\(90\) | −3.61803 | −0.381374 | ||||||||
\(91\) | 3.55722 | 0.372898 | ||||||||
\(92\) | −3.57549 | −0.372771 | ||||||||
\(93\) | 10.3696 | 1.07528 | ||||||||
\(94\) | 4.30999 | 0.444541 | ||||||||
\(95\) | −7.66881 | −0.786803 | ||||||||
\(96\) | −16.4735 | −1.68132 | ||||||||
\(97\) | 2.44278 | 0.248027 | 0.124013 | − | 0.992281i | \(-0.460423\pi\) | ||||
0.124013 | + | 0.992281i | \(0.460423\pi\) | |||||||
\(98\) | −4.37882 | −0.442328 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.45589 | −0.145589 | ||||||||
\(101\) | 7.52373 | 0.748640 | 0.374320 | − | 0.927300i | \(-0.377876\pi\) | ||||
0.374320 | + | 0.927300i | \(0.377876\pi\) | |||||||
\(102\) | 4.97371 | 0.492471 | ||||||||
\(103\) | −9.48231 | −0.934320 | −0.467160 | − | 0.884173i | \(-0.654723\pi\) | ||||
−0.467160 | + | 0.884173i | \(0.654723\pi\) | |||||||
\(104\) | 8.79217 | 0.862143 | ||||||||
\(105\) | −2.89979 | −0.282990 | ||||||||
\(106\) | −8.73958 | −0.848863 | ||||||||
\(107\) | 4.64678 | 0.449221 | 0.224611 | − | 0.974449i | \(-0.427889\pi\) | ||||
0.224611 | + | 0.974449i | \(0.427889\pi\) | |||||||
\(108\) | 7.79726 | 0.750291 | ||||||||
\(109\) | 5.32826 | 0.510355 | 0.255178 | − | 0.966894i | \(-0.417866\pi\) | ||||
0.255178 | + | 0.966894i | \(0.417866\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −16.7529 | −1.59012 | ||||||||
\(112\) | −1.06374 | −0.100514 | ||||||||
\(113\) | 0.304901 | 0.0286826 | 0.0143413 | − | 0.999897i | \(-0.495435\pi\) | ||||
0.0143413 | + | 0.999897i | \(0.495435\pi\) | |||||||
\(114\) | −15.9045 | −1.48959 | ||||||||
\(115\) | −2.45589 | −0.229013 | ||||||||
\(116\) | −8.66881 | −0.804879 | ||||||||
\(117\) | −16.9169 | −1.56396 | ||||||||
\(118\) | 2.17331 | 0.200069 | ||||||||
\(119\) | 2.47347 | 0.226743 | ||||||||
\(120\) | −7.16724 | −0.654276 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.82962 | −0.165646 | ||||||||
\(123\) | 11.0670 | 0.997880 | ||||||||
\(124\) | 5.36960 | 0.482205 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −3.73157 | −0.332434 | ||||||||
\(127\) | 11.9100 | 1.05684 | 0.528419 | − | 0.848984i | \(-0.322785\pi\) | ||||
0.528419 | + | 0.848984i | \(0.322785\pi\) | |||||||
\(128\) | −10.0519 | −0.888470 | ||||||||
\(129\) | −21.5068 | −1.89357 | ||||||||
\(130\) | 2.54411 | 0.223133 | ||||||||
\(131\) | 11.1875 | 0.977452 | 0.488726 | − | 0.872437i | \(-0.337462\pi\) | ||||
0.488726 | + | 0.872437i | \(0.337462\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.90945 | −0.685837 | ||||||||
\(134\) | −4.53429 | −0.391703 | ||||||||
\(135\) | 5.35567 | 0.460943 | ||||||||
\(136\) | 6.11353 | 0.524231 | ||||||||
\(137\) | −4.28124 | −0.365771 | −0.182886 | − | 0.983134i | \(-0.558544\pi\) | ||||
−0.182886 | + | 0.983134i | \(0.558544\pi\) | |||||||
\(138\) | −5.09331 | −0.433572 | ||||||||
\(139\) | 5.95320 | 0.504943 | 0.252472 | − | 0.967604i | \(-0.418757\pi\) | ||||
0.252472 | + | 0.967604i | \(0.418757\pi\) | |||||||
\(140\) | −1.50157 | −0.126906 | ||||||||
\(141\) | −16.4278 | −1.38347 | ||||||||
\(142\) | 1.49235 | 0.125236 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 5.05879 | 0.421566 | ||||||||
\(145\) | −5.95431 | −0.494479 | ||||||||
\(146\) | 0.609193 | 0.0504171 | ||||||||
\(147\) | 16.6901 | 1.37658 | ||||||||
\(148\) | −8.67501 | −0.713082 | ||||||||
\(149\) | 3.78444 | 0.310034 | 0.155017 | − | 0.987912i | \(-0.450457\pi\) | ||||
0.155017 | + | 0.987912i | \(0.450457\pi\) | |||||||
\(150\) | −2.07392 | −0.169335 | ||||||||
\(151\) | 24.3566 | 1.98211 | 0.991057 | − | 0.133437i | \(-0.0426013\pi\) | ||||
0.991057 | + | 0.133437i | \(0.0426013\pi\) | |||||||
\(152\) | −19.5493 | −1.58566 | ||||||||
\(153\) | −11.7629 | −0.950978 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.68820 | 0.296243 | ||||||||
\(156\) | −14.1178 | −1.13033 | ||||||||
\(157\) | 7.23210 | 0.577184 | 0.288592 | − | 0.957452i | \(-0.406813\pi\) | ||||
0.288592 | + | 0.957452i | \(0.406813\pi\) | |||||||
\(158\) | 8.90936 | 0.708790 | ||||||||
\(159\) | 33.3115 | 2.64177 | ||||||||
\(160\) | −5.85919 | −0.463210 | ||||||||
\(161\) | −2.53295 | −0.199625 | ||||||||
\(162\) | 0.253142 | 0.0198887 | ||||||||
\(163\) | 18.6892 | 1.46385 | 0.731924 | − | 0.681386i | \(-0.238623\pi\) | ||||
0.731924 | + | 0.681386i | \(0.238623\pi\) | |||||||
\(164\) | 5.73074 | 0.447496 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.18761 | −0.0921767 | ||||||||
\(167\) | −7.85328 | −0.607705 | −0.303852 | − | 0.952719i | \(-0.598273\pi\) | ||||
−0.303852 | + | 0.952719i | \(0.598273\pi\) | |||||||
\(168\) | −7.39214 | −0.570316 | ||||||||
\(169\) | −1.10448 | −0.0849597 | ||||||||
\(170\) | 1.76902 | 0.135678 | ||||||||
\(171\) | 37.6145 | 2.87646 | ||||||||
\(172\) | −11.1367 | −0.849164 | ||||||||
\(173\) | −11.2047 | −0.851877 | −0.425938 | − | 0.904752i | \(-0.640056\pi\) | ||||
−0.425938 | + | 0.904752i | \(0.640056\pi\) | |||||||
\(174\) | −12.3488 | −0.936158 | ||||||||
\(175\) | −1.03138 | −0.0779650 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.28370 | −0.622641 | ||||||||
\(178\) | 6.02000 | 0.451218 | ||||||||
\(179\) | 1.46463 | 0.109472 | 0.0547358 | − | 0.998501i | \(-0.482568\pi\) | ||||
0.0547358 | + | 0.998501i | \(0.482568\pi\) | |||||||
\(180\) | 7.14094 | 0.532255 | ||||||||
\(181\) | 9.28900 | 0.690446 | 0.345223 | − | 0.938521i | \(-0.387803\pi\) | ||||
0.345223 | + | 0.938521i | \(0.387803\pi\) | |||||||
\(182\) | 2.62395 | 0.194500 | ||||||||
\(183\) | 6.97371 | 0.515511 | ||||||||
\(184\) | −6.26055 | −0.461534 | ||||||||
\(185\) | −5.95858 | −0.438083 | ||||||||
\(186\) | 7.64904 | 0.560855 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −8.50666 | −0.620412 | ||||||||
\(189\) | 5.52373 | 0.401793 | ||||||||
\(190\) | −5.65682 | −0.410389 | ||||||||
\(191\) | −4.47296 | −0.323652 | −0.161826 | − | 0.986819i | \(-0.551738\pi\) | ||||
−0.161826 | + | 0.986819i | \(0.551738\pi\) | |||||||
\(192\) | −6.35192 | −0.458410 | ||||||||
\(193\) | 22.6660 | 1.63154 | 0.815768 | − | 0.578380i | \(-0.196315\pi\) | ||||
0.815768 | + | 0.578380i | \(0.196315\pi\) | |||||||
\(194\) | 1.80189 | 0.129368 | ||||||||
\(195\) | −9.69704 | −0.694420 | ||||||||
\(196\) | 8.64252 | 0.617323 | ||||||||
\(197\) | 11.2080 | 0.798535 | 0.399267 | − | 0.916835i | \(-0.369265\pi\) | ||||
0.399267 | + | 0.916835i | \(0.369265\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.81979 | −0.554330 | −0.277165 | − | 0.960822i | \(-0.589395\pi\) | ||||
−0.277165 | + | 0.960822i | \(0.589395\pi\) | |||||||
\(200\) | −2.54920 | −0.180256 | ||||||||
\(201\) | 17.2827 | 1.21903 | ||||||||
\(202\) | 5.54981 | 0.390483 | ||||||||
\(203\) | −6.14116 | −0.431025 | ||||||||
\(204\) | −9.81665 | −0.687303 | ||||||||
\(205\) | 3.93626 | 0.274920 | ||||||||
\(206\) | −6.99454 | −0.487332 | ||||||||
\(207\) | 12.0458 | 0.837242 | ||||||||
\(208\) | −3.55722 | −0.246649 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −2.13900 | −0.147605 | ||||||||
\(211\) | 22.7670 | 1.56734 | 0.783672 | − | 0.621175i | \(-0.213344\pi\) | ||||
0.783672 | + | 0.621175i | \(0.213344\pi\) | |||||||
\(212\) | 17.2494 | 1.18469 | ||||||||
\(213\) | −5.68820 | −0.389749 | ||||||||
\(214\) | 3.42765 | 0.234309 | ||||||||
\(215\) | −7.64941 | −0.521686 | ||||||||
\(216\) | 13.6527 | 0.928948 | ||||||||
\(217\) | 3.80394 | 0.258228 | ||||||||
\(218\) | 3.93034 | 0.266196 | ||||||||
\(219\) | −2.32197 | −0.156905 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.27142 | 0.556396 | ||||||||
\(222\) | −12.3576 | −0.829389 | ||||||||
\(223\) | −16.0427 | −1.07430 | −0.537148 | − | 0.843488i | \(-0.680499\pi\) | ||||
−0.537148 | + | 0.843488i | \(0.680499\pi\) | |||||||
\(224\) | −6.04305 | −0.403768 | ||||||||
\(225\) | 4.90488 | 0.326992 | ||||||||
\(226\) | 0.224907 | 0.0149606 | ||||||||
\(227\) | 24.1562 | 1.60330 | 0.801652 | − | 0.597791i | \(-0.203955\pi\) | ||||
0.801652 | + | 0.597791i | \(0.203955\pi\) | |||||||
\(228\) | 31.3908 | 2.07891 | ||||||||
\(229\) | −15.0143 | −0.992172 | −0.496086 | − | 0.868274i | \(-0.665230\pi\) | ||||
−0.496086 | + | 0.868274i | \(0.665230\pi\) | |||||||
\(230\) | −1.81156 | −0.119451 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −15.1787 | −0.996534 | ||||||||
\(233\) | −11.4259 | −0.748538 | −0.374269 | − | 0.927320i | \(-0.622106\pi\) | ||||
−0.374269 | + | 0.927320i | \(0.622106\pi\) | |||||||
\(234\) | −12.4786 | −0.815749 | ||||||||
\(235\) | −5.84294 | −0.381151 | ||||||||
\(236\) | −4.28948 | −0.279221 | ||||||||
\(237\) | −33.9586 | −2.20584 | ||||||||
\(238\) | 1.82453 | 0.118267 | ||||||||
\(239\) | −27.4067 | −1.77279 | −0.886397 | − | 0.462927i | \(-0.846799\pi\) | ||||
−0.886397 | + | 0.462927i | \(0.846799\pi\) | |||||||
\(240\) | 2.89979 | 0.187180 | ||||||||
\(241\) | −10.9387 | −0.704624 | −0.352312 | − | 0.935883i | \(-0.614604\pi\) | ||||
−0.352312 | + | 0.935883i | \(0.614604\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.1022 | 0.968804 | ||||||||
\(244\) | 3.61114 | 0.231179 | ||||||||
\(245\) | 5.93626 | 0.379253 | ||||||||
\(246\) | 8.16348 | 0.520485 | ||||||||
\(247\) | −26.4496 | −1.68295 | ||||||||
\(248\) | 9.40197 | 0.597026 | ||||||||
\(249\) | 4.52666 | 0.286866 | ||||||||
\(250\) | −0.737640 | −0.0466525 | ||||||||
\(251\) | 17.2311 | 1.08762 | 0.543809 | − | 0.839209i | \(-0.316982\pi\) | ||||
0.543809 | + | 0.839209i | \(0.316982\pi\) | |||||||
\(252\) | 7.36503 | 0.463953 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 8.78527 | 0.551237 | ||||||||
\(255\) | −6.74273 | −0.422246 | ||||||||
\(256\) | −11.9331 | −0.745819 | ||||||||
\(257\) | 18.4954 | 1.15371 | 0.576856 | − | 0.816846i | \(-0.304279\pi\) | ||||
0.576856 | + | 0.816846i | \(0.304279\pi\) | |||||||
\(258\) | −15.8643 | −0.987667 | ||||||||
\(259\) | −6.14556 | −0.381866 | ||||||||
\(260\) | −5.02134 | −0.311410 | ||||||||
\(261\) | 29.2052 | 1.80775 | ||||||||
\(262\) | 8.25232 | 0.509830 | ||||||||
\(263\) | −3.69135 | −0.227618 | −0.113809 | − | 0.993503i | \(-0.536305\pi\) | ||||
−0.113809 | + | 0.993503i | \(0.536305\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.8480 | 0.727819 | ||||||||
\(266\) | −5.83433 | −0.357726 | ||||||||
\(267\) | −22.9456 | −1.40425 | ||||||||
\(268\) | 8.94936 | 0.546669 | ||||||||
\(269\) | −9.94510 | −0.606363 | −0.303182 | − | 0.952933i | \(-0.598049\pi\) | ||||
−0.303182 | + | 0.952933i | \(0.598049\pi\) | |||||||
\(270\) | 3.95056 | 0.240423 | ||||||||
\(271\) | −1.25365 | −0.0761539 | −0.0380770 | − | 0.999275i | \(-0.512123\pi\) | ||||
−0.0380770 | + | 0.999275i | \(0.512123\pi\) | |||||||
\(272\) | −2.47347 | −0.149976 | ||||||||
\(273\) | −10.0013 | −0.605308 | ||||||||
\(274\) | −3.15802 | −0.190783 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 10.0527 | 0.605102 | ||||||||
\(277\) | 8.09331 | 0.486280 | 0.243140 | − | 0.969991i | \(-0.421823\pi\) | ||||
0.243140 | + | 0.969991i | \(0.421823\pi\) | |||||||
\(278\) | 4.39132 | 0.263374 | ||||||||
\(279\) | −18.0902 | −1.08303 | ||||||||
\(280\) | −2.62920 | −0.157124 | ||||||||
\(281\) | −25.3702 | −1.51346 | −0.756731 | − | 0.653726i | \(-0.773205\pi\) | ||||
−0.756731 | + | 0.653726i | \(0.773205\pi\) | |||||||
\(282\) | −12.1178 | −0.721604 | ||||||||
\(283\) | 20.4424 | 1.21517 | 0.607587 | − | 0.794253i | \(-0.292137\pi\) | ||||
0.607587 | + | 0.794253i | \(0.292137\pi\) | |||||||
\(284\) | −2.94547 | −0.174782 | ||||||||
\(285\) | 21.5613 | 1.27718 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.05977 | 0.239641 | ||||||||
\(288\) | 28.7386 | 1.69344 | ||||||||
\(289\) | −11.2486 | −0.661680 | ||||||||
\(290\) | −4.39214 | −0.257915 | ||||||||
\(291\) | −6.86803 | −0.402611 | ||||||||
\(292\) | −1.20237 | −0.0703633 | ||||||||
\(293\) | −2.54907 | −0.148918 | −0.0744591 | − | 0.997224i | \(-0.523723\pi\) | ||||
−0.0744591 | + | 0.997224i | \(0.523723\pi\) | |||||||
\(294\) | 12.3113 | 0.718011 | ||||||||
\(295\) | −2.94630 | −0.171540 | ||||||||
\(296\) | −15.1896 | −0.882878 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.79156 | 0.161711 | ||||||||
\(299\) | −8.47033 | −0.489852 | ||||||||
\(300\) | 4.09331 | 0.236328 | ||||||||
\(301\) | −7.88945 | −0.454740 | ||||||||
\(302\) | 17.9664 | 1.03385 | ||||||||
\(303\) | −21.1534 | −1.21523 | ||||||||
\(304\) | 7.90945 | 0.453638 | ||||||||
\(305\) | 2.48037 | 0.142026 | ||||||||
\(306\) | −8.67682 | −0.496021 | ||||||||
\(307\) | −8.99273 | −0.513242 | −0.256621 | − | 0.966512i | \(-0.582609\pi\) | ||||
−0.256621 | + | 0.966512i | \(0.582609\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 26.6601 | 1.51664 | ||||||||
\(310\) | 2.72057 | 0.154518 | ||||||||
\(311\) | −20.1232 | −1.14108 | −0.570540 | − | 0.821270i | \(-0.693266\pi\) | ||||
−0.570540 | + | 0.821270i | \(0.693266\pi\) | |||||||
\(312\) | −24.7197 | −1.39948 | ||||||||
\(313\) | 7.10483 | 0.401589 | 0.200794 | − | 0.979633i | \(-0.435648\pi\) | ||||
0.200794 | + | 0.979633i | \(0.435648\pi\) | |||||||
\(314\) | 5.33469 | 0.301054 | ||||||||
\(315\) | 5.05879 | 0.285031 | ||||||||
\(316\) | −17.5845 | −0.989204 | ||||||||
\(317\) | 2.29323 | 0.128801 | 0.0644003 | − | 0.997924i | \(-0.479487\pi\) | ||||
0.0644003 | + | 0.997924i | \(0.479487\pi\) | |||||||
\(318\) | 24.5719 | 1.37792 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −2.25922 | −0.126294 | ||||||||
\(321\) | −13.0647 | −0.729201 | ||||||||
\(322\) | −1.86841 | −0.104122 | ||||||||
\(323\) | −18.3915 | −1.02333 | ||||||||
\(324\) | −0.499629 | −0.0277572 | ||||||||
\(325\) | −3.44899 | −0.191315 | ||||||||
\(326\) | 13.7859 | 0.763529 | ||||||||
\(327\) | −14.9807 | −0.828437 | ||||||||
\(328\) | 10.0343 | 0.554052 | ||||||||
\(329\) | −6.02629 | −0.332240 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.3951 | 0.846192 | 0.423096 | − | 0.906085i | \(-0.360943\pi\) | ||||
0.423096 | + | 0.906085i | \(0.360943\pi\) | |||||||
\(332\) | 2.34400 | 0.128644 | ||||||||
\(333\) | 29.2261 | 1.60158 | ||||||||
\(334\) | −5.79289 | −0.316973 | ||||||||
\(335\) | 6.14702 | 0.335847 | ||||||||
\(336\) | 2.99078 | 0.163161 | ||||||||
\(337\) | 19.4968 | 1.06206 | 0.531030 | − | 0.847353i | \(-0.321805\pi\) | ||||
0.531030 | + | 0.847353i | \(0.321805\pi\) | |||||||
\(338\) | −0.814706 | −0.0443141 | ||||||||
\(339\) | −0.857247 | −0.0465592 | ||||||||
\(340\) | −3.49153 | −0.189355 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 27.7460 | 1.50033 | ||||||||
\(343\) | 13.3422 | 0.720411 | ||||||||
\(344\) | −19.4999 | −1.05136 | ||||||||
\(345\) | 6.90488 | 0.371746 | ||||||||
\(346\) | −8.26503 | −0.444331 | ||||||||
\(347\) | 2.16905 | 0.116440 | 0.0582202 | − | 0.998304i | \(-0.481457\pi\) | ||||
0.0582202 | + | 0.998304i | \(0.481457\pi\) | |||||||
\(348\) | 24.3729 | 1.30652 | ||||||||
\(349\) | 25.0520 | 1.34100 | 0.670502 | − | 0.741908i | \(-0.266079\pi\) | ||||
0.670502 | + | 0.741908i | \(0.266079\pi\) | |||||||
\(350\) | −0.760787 | −0.0406658 | ||||||||
\(351\) | 18.4717 | 0.985944 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.2532 | −1.23764 | −0.618821 | − | 0.785532i | \(-0.712389\pi\) | ||||
−0.618821 | + | 0.785532i | \(0.712389\pi\) | |||||||
\(354\) | −6.11039 | −0.324764 | ||||||||
\(355\) | −2.02315 | −0.107377 | ||||||||
\(356\) | −11.8817 | −0.629730 | ||||||||
\(357\) | −6.95431 | −0.368061 | ||||||||
\(358\) | 1.08037 | 0.0570993 | ||||||||
\(359\) | −10.1224 | −0.534239 | −0.267119 | − | 0.963663i | \(-0.586072\pi\) | ||||
−0.267119 | + | 0.963663i | \(0.586072\pi\) | |||||||
\(360\) | 12.5035 | 0.658993 | ||||||||
\(361\) | 39.8106 | 2.09530 | ||||||||
\(362\) | 6.85194 | 0.360130 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.17891 | −0.271448 | ||||||||
\(365\) | −0.825867 | −0.0432278 | ||||||||
\(366\) | 5.14409 | 0.268886 | ||||||||
\(367\) | 3.70925 | 0.193621 | 0.0968105 | − | 0.995303i | \(-0.469136\pi\) | ||||
0.0968105 | + | 0.995303i | \(0.469136\pi\) | |||||||
\(368\) | 2.53295 | 0.132039 | ||||||||
\(369\) | −19.3068 | −1.00507 | ||||||||
\(370\) | −4.39529 | −0.228500 | ||||||||
\(371\) | 12.2198 | 0.634421 | ||||||||
\(372\) | −15.0970 | −0.782741 | ||||||||
\(373\) | 9.34017 | 0.483616 | 0.241808 | − | 0.970324i | \(-0.422260\pi\) | ||||
0.241808 | + | 0.970324i | \(0.422260\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.81156 | 0.145188 | ||||||||
\(376\) | −14.8948 | −0.768142 | ||||||||
\(377\) | −20.5364 | −1.05768 | ||||||||
\(378\) | 4.07453 | 0.209571 | ||||||||
\(379\) | −9.81169 | −0.503993 | −0.251996 | − | 0.967728i | \(-0.581087\pi\) | ||||
−0.251996 | + | 0.967728i | \(0.581087\pi\) | |||||||
\(380\) | 11.1649 | 0.572748 | ||||||||
\(381\) | −33.4856 | −1.71552 | ||||||||
\(382\) | −3.29944 | −0.168814 | ||||||||
\(383\) | −18.0468 | −0.922149 | −0.461074 | − | 0.887362i | \(-0.652536\pi\) | ||||
−0.461074 | + | 0.887362i | \(0.652536\pi\) | |||||||
\(384\) | 28.2615 | 1.44221 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 16.7194 | 0.850993 | ||||||||
\(387\) | 37.5194 | 1.90722 | ||||||||
\(388\) | −3.55641 | −0.180550 | ||||||||
\(389\) | 31.1915 | 1.58147 | 0.790737 | − | 0.612156i | \(-0.209698\pi\) | ||||
0.790737 | + | 0.612156i | \(0.209698\pi\) | |||||||
\(390\) | −7.15293 | −0.362203 | ||||||||
\(391\) | −5.88974 | −0.297857 | ||||||||
\(392\) | 15.1327 | 0.764317 | ||||||||
\(393\) | −31.4542 | −1.58666 | ||||||||
\(394\) | 8.26745 | 0.416508 | ||||||||
\(395\) | −12.0782 | −0.607719 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.6212 | −0.533062 | −0.266531 | − | 0.963826i | \(-0.585877\pi\) | ||||
−0.266531 | + | 0.963826i | \(0.585877\pi\) | |||||||
\(398\) | −5.76820 | −0.289133 | ||||||||
\(399\) | 22.2379 | 1.11329 | ||||||||
\(400\) | 1.03138 | 0.0515690 | ||||||||
\(401\) | −27.5679 | −1.37668 | −0.688338 | − | 0.725390i | \(-0.741659\pi\) | ||||
−0.688338 | + | 0.725390i | \(0.741659\pi\) | |||||||
\(402\) | 12.7484 | 0.635834 | ||||||||
\(403\) | 12.7206 | 0.633657 | ||||||||
\(404\) | −10.9537 | −0.544967 | ||||||||
\(405\) | −0.343178 | −0.0170527 | ||||||||
\(406\) | −4.52997 | −0.224818 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −17.1886 | −0.850961 | ||||||||
\(409\) | −14.3682 | −0.710460 | −0.355230 | − | 0.934779i | \(-0.615598\pi\) | ||||
−0.355230 | + | 0.934779i | \(0.615598\pi\) | |||||||
\(410\) | 2.90354 | 0.143396 | ||||||||
\(411\) | 12.0370 | 0.593740 | ||||||||
\(412\) | 13.8052 | 0.680132 | ||||||||
\(413\) | −3.03875 | −0.149527 | ||||||||
\(414\) | 8.88548 | 0.436698 | ||||||||
\(415\) | 1.61002 | 0.0790327 | ||||||||
\(416\) | −20.2083 | −0.990793 | ||||||||
\(417\) | −16.7378 | −0.819652 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −31.4707 | −1.53744 | −0.768722 | − | 0.639584i | \(-0.779107\pi\) | ||||
−0.768722 | + | 0.639584i | \(0.779107\pi\) | |||||||
\(420\) | 4.22176 | 0.206001 | ||||||||
\(421\) | 26.5712 | 1.29500 | 0.647500 | − | 0.762065i | \(-0.275815\pi\) | ||||
0.647500 | + | 0.762065i | \(0.275815\pi\) | |||||||
\(422\) | 16.7939 | 0.817512 | ||||||||
\(423\) | 28.6589 | 1.39344 | ||||||||
\(424\) | 30.2030 | 1.46679 | ||||||||
\(425\) | −2.39822 | −0.116331 | ||||||||
\(426\) | −4.19585 | −0.203289 | ||||||||
\(427\) | 2.55820 | 0.123800 | ||||||||
\(428\) | −6.76518 | −0.327008 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.64252 | −0.272106 | ||||||||
\(431\) | 3.86870 | 0.186349 | 0.0931744 | − | 0.995650i | \(-0.470299\pi\) | ||||
0.0931744 | + | 0.995650i | \(0.470299\pi\) | |||||||
\(432\) | −5.52373 | −0.265761 | ||||||||
\(433\) | 40.1388 | 1.92895 | 0.964474 | − | 0.264179i | \(-0.0851010\pi\) | ||||
0.964474 | + | 0.264179i | \(0.0851010\pi\) | |||||||
\(434\) | 2.80594 | 0.134689 | ||||||||
\(435\) | 16.7409 | 0.802666 | ||||||||
\(436\) | −7.75735 | −0.371510 | ||||||||
\(437\) | 18.8337 | 0.900939 | ||||||||
\(438\) | −1.71278 | −0.0818399 | ||||||||
\(439\) | −1.02336 | −0.0488425 | −0.0244212 | − | 0.999702i | \(-0.507774\pi\) | ||||
−0.0244212 | + | 0.999702i | \(0.507774\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −29.1166 | −1.38650 | ||||||||
\(442\) | 6.10133 | 0.290211 | ||||||||
\(443\) | −16.0728 | −0.763644 | −0.381822 | − | 0.924236i | \(-0.624703\pi\) | ||||
−0.381822 | + | 0.924236i | \(0.624703\pi\) | |||||||
\(444\) | 24.3903 | 1.15751 | ||||||||
\(445\) | −8.16116 | −0.386876 | ||||||||
\(446\) | −11.8337 | −0.560343 | ||||||||
\(447\) | −10.6402 | −0.503264 | ||||||||
\(448\) | −2.33011 | −0.110087 | ||||||||
\(449\) | 35.8421 | 1.69149 | 0.845746 | − | 0.533585i | \(-0.179156\pi\) | ||||
0.845746 | + | 0.533585i | \(0.179156\pi\) | |||||||
\(450\) | 3.61803 | 0.170556 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.443901 | −0.0208793 | ||||||||
\(453\) | −68.4802 | −3.21748 | ||||||||
\(454\) | 17.8186 | 0.836268 | ||||||||
\(455\) | −3.55722 | −0.166765 | ||||||||
\(456\) | 54.9641 | 2.57393 | ||||||||
\(457\) | 25.1525 | 1.17658 | 0.588291 | − | 0.808649i | \(-0.299801\pi\) | ||||
0.588291 | + | 0.808649i | \(0.299801\pi\) | |||||||
\(458\) | −11.0751 | −0.517507 | ||||||||
\(459\) | 12.8441 | 0.599509 | ||||||||
\(460\) | 3.57549 | 0.166708 | ||||||||
\(461\) | −6.65631 | −0.310015 | −0.155008 | − | 0.987913i | \(-0.549540\pi\) | ||||
−0.155008 | + | 0.987913i | \(0.549540\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.7730 | 1.80194 | 0.900968 | − | 0.433886i | \(-0.142858\pi\) | ||||
0.900968 | + | 0.433886i | \(0.142858\pi\) | |||||||
\(464\) | 6.14116 | 0.285096 | ||||||||
\(465\) | −10.3696 | −0.480879 | ||||||||
\(466\) | −8.42823 | −0.390430 | ||||||||
\(467\) | 22.5494 | 1.04346 | 0.521731 | − | 0.853110i | \(-0.325286\pi\) | ||||
0.521731 | + | 0.853110i | \(0.325286\pi\) | |||||||
\(468\) | 24.6290 | 1.13848 | ||||||||
\(469\) | 6.33991 | 0.292750 | ||||||||
\(470\) | −4.30999 | −0.198805 | ||||||||
\(471\) | −20.3335 | −0.936918 | ||||||||
\(472\) | −7.51071 | −0.345708 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −25.0492 | −1.15055 | ||||||||
\(475\) | 7.66881 | 0.351869 | ||||||||
\(476\) | −3.60109 | −0.165056 | ||||||||
\(477\) | −58.1131 | −2.66082 | ||||||||
\(478\) | −20.2163 | −0.924672 | ||||||||
\(479\) | 1.63186 | 0.0745618 | 0.0372809 | − | 0.999305i | \(-0.488130\pi\) | ||||
0.0372809 | + | 0.999305i | \(0.488130\pi\) | |||||||
\(480\) | 16.4735 | 0.751908 | ||||||||
\(481\) | −20.5511 | −0.937048 | ||||||||
\(482\) | −8.06883 | −0.367525 | ||||||||
\(483\) | 7.12155 | 0.324042 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.44278 | −0.110921 | ||||||||
\(486\) | 11.1400 | 0.505319 | ||||||||
\(487\) | 1.05030 | 0.0475936 | 0.0237968 | − | 0.999717i | \(-0.492425\pi\) | ||||
0.0237968 | + | 0.999717i | \(0.492425\pi\) | |||||||
\(488\) | 6.32296 | 0.286227 | ||||||||
\(489\) | −52.5457 | −2.37620 | ||||||||
\(490\) | 4.37882 | 0.197815 | ||||||||
\(491\) | 13.9141 | 0.627934 | 0.313967 | − | 0.949434i | \(-0.398342\pi\) | ||||
0.313967 | + | 0.949434i | \(0.398342\pi\) | |||||||
\(492\) | −16.1123 | −0.726400 | ||||||||
\(493\) | −14.2797 | −0.643127 | ||||||||
\(494\) | −19.5103 | −0.877811 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.80394 | −0.170802 | ||||||||
\(497\) | −2.08663 | −0.0935983 | ||||||||
\(498\) | 3.33905 | 0.149626 | ||||||||
\(499\) | 17.3673 | 0.777466 | 0.388733 | − | 0.921350i | \(-0.372913\pi\) | ||||
0.388733 | + | 0.921350i | \(0.372913\pi\) | |||||||
\(500\) | 1.45589 | 0.0651092 | ||||||||
\(501\) | 22.0800 | 0.986460 | ||||||||
\(502\) | 12.7104 | 0.567291 | ||||||||
\(503\) | −35.8536 | −1.59863 | −0.799316 | − | 0.600910i | \(-0.794805\pi\) | ||||
−0.799316 | + | 0.600910i | \(0.794805\pi\) | |||||||
\(504\) | 12.8959 | 0.574428 | ||||||||
\(505\) | −7.52373 | −0.334802 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.10530 | 0.137911 | ||||||||
\(508\) | −17.3396 | −0.769319 | ||||||||
\(509\) | 2.13878 | 0.0947999 | 0.0474000 | − | 0.998876i | \(-0.484906\pi\) | ||||
0.0474000 | + | 0.998876i | \(0.484906\pi\) | |||||||
\(510\) | −4.97371 | −0.220240 | ||||||||
\(511\) | −0.851782 | −0.0376806 | ||||||||
\(512\) | 11.3014 | 0.499458 | ||||||||
\(513\) | −41.0716 | −1.81336 | ||||||||
\(514\) | 13.6430 | 0.601765 | ||||||||
\(515\) | 9.48231 | 0.417841 | ||||||||
\(516\) | 31.3115 | 1.37841 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −4.53321 | −0.199178 | ||||||||
\(519\) | 31.5027 | 1.38281 | ||||||||
\(520\) | −8.79217 | −0.385562 | ||||||||
\(521\) | −12.7352 | −0.557940 | −0.278970 | − | 0.960300i | \(-0.589993\pi\) | ||||
−0.278970 | + | 0.960300i | \(0.589993\pi\) | |||||||
\(522\) | 21.5429 | 0.942908 | ||||||||
\(523\) | −23.9088 | −1.04546 | −0.522729 | − | 0.852499i | \(-0.675086\pi\) | ||||
−0.522729 | + | 0.852499i | \(0.675086\pi\) | |||||||
\(524\) | −16.2877 | −0.711530 | ||||||||
\(525\) | 2.89979 | 0.126557 | ||||||||
\(526\) | −2.72289 | −0.118723 | ||||||||
\(527\) | 8.84510 | 0.385299 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.9686 | −0.737766 | ||||||||
\(530\) | 8.73958 | 0.379623 | ||||||||
\(531\) | 14.4512 | 0.627130 | ||||||||
\(532\) | 11.5153 | 0.499250 | ||||||||
\(533\) | 13.5761 | 0.588046 | ||||||||
\(534\) | −16.9256 | −0.732443 | ||||||||
\(535\) | −4.64678 | −0.200898 | ||||||||
\(536\) | 15.6700 | 0.676840 | ||||||||
\(537\) | −4.11790 | −0.177700 | ||||||||
\(538\) | −7.33590 | −0.316273 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −7.79726 | −0.335540 | ||||||||
\(541\) | −1.31921 | −0.0567171 | −0.0283586 | − | 0.999598i | \(-0.509028\pi\) | ||||
−0.0283586 | + | 0.999598i | \(0.509028\pi\) | |||||||
\(542\) | −0.924744 | −0.0397212 | ||||||||
\(543\) | −26.1166 | −1.12077 | ||||||||
\(544\) | −14.0516 | −0.602457 | ||||||||
\(545\) | −5.32826 | −0.228238 | ||||||||
\(546\) | −7.37739 | −0.315723 | ||||||||
\(547\) | −9.32128 | −0.398549 | −0.199275 | − | 0.979944i | \(-0.563859\pi\) | ||||
−0.199275 | + | 0.979944i | \(0.563859\pi\) | |||||||
\(548\) | 6.23301 | 0.266261 | ||||||||
\(549\) | −12.1659 | −0.519228 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 45.6625 | 1.94529 | ||||||||
\(552\) | 17.6019 | 0.749187 | ||||||||
\(553\) | −12.4572 | −0.529734 | ||||||||
\(554\) | 5.96996 | 0.253639 | ||||||||
\(555\) | 16.7529 | 0.711121 | ||||||||
\(556\) | −8.66718 | −0.367570 | ||||||||
\(557\) | −39.3172 | −1.66592 | −0.832961 | − | 0.553331i | \(-0.813356\pi\) | ||||
−0.832961 | + | 0.553331i | \(0.813356\pi\) | |||||||
\(558\) | −13.3440 | −0.564898 | ||||||||
\(559\) | −26.3827 | −1.11587 | ||||||||
\(560\) | 1.06374 | 0.0449514 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −18.7141 | −0.789407 | ||||||||
\(563\) | −19.9810 | −0.842097 | −0.421048 | − | 0.907038i | \(-0.638338\pi\) | ||||
−0.421048 | + | 0.907038i | \(0.638338\pi\) | |||||||
\(564\) | 23.9170 | 1.00709 | ||||||||
\(565\) | −0.304901 | −0.0128273 | ||||||||
\(566\) | 15.0791 | 0.633824 | ||||||||
\(567\) | −0.353947 | −0.0148644 | ||||||||
\(568\) | −5.15741 | −0.216400 | ||||||||
\(569\) | 34.5647 | 1.44903 | 0.724515 | − | 0.689260i | \(-0.242064\pi\) | ||||
0.724515 | + | 0.689260i | \(0.242064\pi\) | |||||||
\(570\) | 15.9045 | 0.666166 | ||||||||
\(571\) | −3.15090 | −0.131861 | −0.0659306 | − | 0.997824i | \(-0.521002\pi\) | ||||
−0.0659306 | + | 0.997824i | \(0.521002\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.5760 | 0.525370 | ||||||||
\(574\) | 2.99465 | 0.124994 | ||||||||
\(575\) | 2.45589 | 0.102418 | ||||||||
\(576\) | 11.0812 | 0.461715 | ||||||||
\(577\) | 27.3226 | 1.13745 | 0.568727 | − | 0.822526i | \(-0.307436\pi\) | ||||
0.568727 | + | 0.822526i | \(0.307436\pi\) | |||||||
\(578\) | −8.29739 | −0.345126 | ||||||||
\(579\) | −63.7269 | −2.64840 | ||||||||
\(580\) | 8.66881 | 0.359953 | ||||||||
\(581\) | 1.66054 | 0.0688908 | ||||||||
\(582\) | −5.06614 | −0.209998 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −2.10530 | −0.0871180 | ||||||||
\(585\) | 16.9169 | 0.699426 | ||||||||
\(586\) | −1.88030 | −0.0776743 | ||||||||
\(587\) | −46.1679 | −1.90555 | −0.952776 | − | 0.303675i | \(-0.901786\pi\) | ||||
−0.952776 | + | 0.303675i | \(0.901786\pi\) | |||||||
\(588\) | −24.2990 | −1.00207 | ||||||||
\(589\) | −28.2841 | −1.16543 | ||||||||
\(590\) | −2.17331 | −0.0894737 | ||||||||
\(591\) | −31.5119 | −1.29623 | ||||||||
\(592\) | 6.14556 | 0.252581 | ||||||||
\(593\) | −39.4265 | −1.61905 | −0.809525 | − | 0.587085i | \(-0.800275\pi\) | ||||
−0.809525 | + | 0.587085i | \(0.800275\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.47347 | −0.101402 | ||||||||
\(596\) | −5.50972 | −0.225687 | ||||||||
\(597\) | 21.9858 | 0.899820 | ||||||||
\(598\) | −6.24805 | −0.255502 | ||||||||
\(599\) | 1.04875 | 0.0428507 | 0.0214253 | − | 0.999770i | \(-0.493180\pi\) | ||||
0.0214253 | + | 0.999770i | \(0.493180\pi\) | |||||||
\(600\) | 7.16724 | 0.292601 | ||||||||
\(601\) | −27.2498 | −1.11154 | −0.555771 | − | 0.831336i | \(-0.687577\pi\) | ||||
−0.555771 | + | 0.831336i | \(0.687577\pi\) | |||||||
\(602\) | −5.81958 | −0.237188 | ||||||||
\(603\) | −30.1504 | −1.22782 | ||||||||
\(604\) | −35.4605 | −1.44287 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −15.6036 | −0.633854 | ||||||||
\(607\) | −21.9217 | −0.889774 | −0.444887 | − | 0.895587i | \(-0.646756\pi\) | ||||
−0.444887 | + | 0.895587i | \(0.646756\pi\) | |||||||
\(608\) | 44.9330 | 1.82227 | ||||||||
\(609\) | 17.2662 | 0.699664 | ||||||||
\(610\) | 1.82962 | 0.0740791 | ||||||||
\(611\) | −20.1522 | −0.815272 | ||||||||
\(612\) | 17.1255 | 0.692258 | ||||||||
\(613\) | −10.5921 | −0.427809 | −0.213905 | − | 0.976855i | \(-0.568618\pi\) | ||||
−0.213905 | + | 0.976855i | \(0.568618\pi\) | |||||||
\(614\) | −6.63340 | −0.267702 | ||||||||
\(615\) | −11.0670 | −0.446265 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.60402 | 0.185351 | 0.0926755 | − | 0.995696i | \(-0.470458\pi\) | ||||
0.0926755 | + | 0.995696i | \(0.470458\pi\) | |||||||
\(618\) | 19.6656 | 0.791065 | ||||||||
\(619\) | 37.0037 | 1.48731 | 0.743653 | − | 0.668566i | \(-0.233092\pi\) | ||||
0.743653 | + | 0.668566i | \(0.233092\pi\) | |||||||
\(620\) | −5.36960 | −0.215648 | ||||||||
\(621\) | −13.1529 | −0.527809 | ||||||||
\(622\) | −14.8437 | −0.595177 | ||||||||
\(623\) | −8.41726 | −0.337230 | ||||||||
\(624\) | 10.0013 | 0.400374 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 5.24081 | 0.209465 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.5291 | −0.420157 | ||||||||
\(629\) | −14.2900 | −0.569778 | ||||||||
\(630\) | 3.73157 | 0.148669 | ||||||||
\(631\) | −24.8406 | −0.988889 | −0.494444 | − | 0.869209i | \(-0.664628\pi\) | ||||
−0.494444 | + | 0.869209i | \(0.664628\pi\) | |||||||
\(632\) | −30.7897 | −1.22475 | ||||||||
\(633\) | −64.0108 | −2.54420 | ||||||||
\(634\) | 1.69158 | 0.0671812 | ||||||||
\(635\) | −11.9100 | −0.472632 | ||||||||
\(636\) | −48.4977 | −1.92306 | ||||||||
\(637\) | 20.4741 | 0.811213 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.92328 | 0.392559 | ||||||||
\(640\) | 10.0519 | 0.397336 | ||||||||
\(641\) | −44.4293 | −1.75485 | −0.877425 | − | 0.479714i | \(-0.840740\pi\) | ||||
−0.877425 | + | 0.479714i | \(0.840740\pi\) | |||||||
\(642\) | −9.63705 | −0.380344 | ||||||||
\(643\) | 25.8610 | 1.01986 | 0.509929 | − | 0.860217i | \(-0.329672\pi\) | ||||
0.509929 | + | 0.860217i | \(0.329672\pi\) | |||||||
\(644\) | 3.68769 | 0.145315 | ||||||||
\(645\) | 21.5068 | 0.846829 | ||||||||
\(646\) | −13.5663 | −0.533758 | ||||||||
\(647\) | 19.4865 | 0.766093 | 0.383047 | − | 0.923729i | \(-0.374875\pi\) | ||||
0.383047 | + | 0.923729i | \(0.374875\pi\) | |||||||
\(648\) | −0.874831 | −0.0343666 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −2.54411 | −0.0997883 | ||||||||
\(651\) | −10.6950 | −0.419170 | ||||||||
\(652\) | −27.2093 | −1.06560 | ||||||||
\(653\) | −16.7298 | −0.654687 | −0.327344 | − | 0.944905i | \(-0.606153\pi\) | ||||
−0.327344 | + | 0.944905i | \(0.606153\pi\) | |||||||
\(654\) | −11.0504 | −0.432105 | ||||||||
\(655\) | −11.1875 | −0.437130 | ||||||||
\(656\) | −4.05977 | −0.158508 | ||||||||
\(657\) | 4.05077 | 0.158036 | ||||||||
\(658\) | −4.44524 | −0.173293 | ||||||||
\(659\) | 1.66127 | 0.0647137 | 0.0323569 | − | 0.999476i | \(-0.489699\pi\) | ||||
0.0323569 | + | 0.999476i | \(0.489699\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −44.0130 | −1.71191 | −0.855953 | − | 0.517053i | \(-0.827029\pi\) | ||||
−0.855953 | + | 0.517053i | \(0.827029\pi\) | |||||||
\(662\) | 11.3561 | 0.441365 | ||||||||
\(663\) | −23.2556 | −0.903172 | ||||||||
\(664\) | 4.10426 | 0.159276 | ||||||||
\(665\) | 7.90945 | 0.306715 | ||||||||
\(666\) | 21.5583 | 0.835369 | ||||||||
\(667\) | 14.6231 | 0.566210 | ||||||||
\(668\) | 11.4335 | 0.442375 | ||||||||
\(669\) | 45.1050 | 1.74386 | ||||||||
\(670\) | 4.53429 | 0.175175 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 16.9904 | 0.655419 | ||||||||
\(673\) | 38.5949 | 1.48772 | 0.743862 | − | 0.668333i | \(-0.232992\pi\) | ||||
0.743862 | + | 0.668333i | \(0.232992\pi\) | |||||||
\(674\) | 14.3817 | 0.553960 | ||||||||
\(675\) | −5.35567 | −0.206140 | ||||||||
\(676\) | 1.60799 | 0.0618458 | ||||||||
\(677\) | 38.5988 | 1.48347 | 0.741737 | − | 0.670691i | \(-0.234002\pi\) | ||||
0.741737 | + | 0.670691i | \(0.234002\pi\) | |||||||
\(678\) | −0.632340 | −0.0242849 | ||||||||
\(679\) | −2.51944 | −0.0966871 | ||||||||
\(680\) | −6.11353 | −0.234443 | ||||||||
\(681\) | −67.9167 | −2.60257 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.748158 | −0.0286275 | −0.0143137 | − | 0.999898i | \(-0.504556\pi\) | ||||
−0.0143137 | + | 0.999898i | \(0.504556\pi\) | |||||||
\(684\) | −54.7625 | −2.09390 | ||||||||
\(685\) | 4.28124 | 0.163578 | ||||||||
\(686\) | 9.84174 | 0.375759 | ||||||||
\(687\) | 42.2136 | 1.61055 | ||||||||
\(688\) | 7.88945 | 0.300783 | ||||||||
\(689\) | 40.8637 | 1.55678 | ||||||||
\(690\) | 5.09331 | 0.193899 | ||||||||
\(691\) | 5.22184 | 0.198648 | 0.0993242 | − | 0.995055i | \(-0.468332\pi\) | ||||
0.0993242 | + | 0.995055i | \(0.468332\pi\) | |||||||
\(692\) | 16.3128 | 0.620118 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.59998 | 0.0607342 | ||||||||
\(695\) | −5.95320 | −0.225818 | ||||||||
\(696\) | 42.6760 | 1.61763 | ||||||||
\(697\) | 9.43999 | 0.357565 | ||||||||
\(698\) | 18.4794 | 0.699455 | ||||||||
\(699\) | 32.1247 | 1.21507 | ||||||||
\(700\) | 1.50157 | 0.0567541 | ||||||||
\(701\) | 14.1580 | 0.534740 | 0.267370 | − | 0.963594i | \(-0.413845\pi\) | ||||
0.267370 | + | 0.963594i | \(0.413845\pi\) | |||||||
\(702\) | 13.6254 | 0.514259 | ||||||||
\(703\) | 45.6952 | 1.72343 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.4278 | 0.618706 | ||||||||
\(706\) | −17.1525 | −0.645542 | ||||||||
\(707\) | −7.75983 | −0.291838 | ||||||||
\(708\) | 12.0601 | 0.453247 | ||||||||
\(709\) | −17.2144 | −0.646499 | −0.323249 | − | 0.946314i | \(-0.604775\pi\) | ||||
−0.323249 | + | 0.946314i | \(0.604775\pi\) | |||||||
\(710\) | −1.49235 | −0.0560071 | ||||||||
\(711\) | 59.2420 | 2.22175 | ||||||||
\(712\) | −20.8044 | −0.779680 | ||||||||
\(713\) | −9.05781 | −0.339217 | ||||||||
\(714\) | −5.12978 | −0.191977 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.13233 | −0.0796891 | ||||||||
\(717\) | 77.0557 | 2.87770 | ||||||||
\(718\) | −7.46667 | −0.278654 | ||||||||
\(719\) | −26.5559 | −0.990369 | −0.495185 | − | 0.868788i | \(-0.664900\pi\) | ||||
−0.495185 | + | 0.868788i | \(0.664900\pi\) | |||||||
\(720\) | −5.05879 | −0.188530 | ||||||||
\(721\) | 9.77987 | 0.364221 | ||||||||
\(722\) | 29.3659 | 1.09289 | ||||||||
\(723\) | 30.7548 | 1.14379 | ||||||||
\(724\) | −13.5237 | −0.502606 | ||||||||
\(725\) | 5.95431 | 0.221138 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 44.1917 | 1.63898 | 0.819490 | − | 0.573094i | \(-0.194257\pi\) | ||||
0.819490 | + | 0.573094i | \(0.194257\pi\) | |||||||
\(728\) | −9.06806 | −0.336085 | ||||||||
\(729\) | −43.4902 | −1.61075 | ||||||||
\(730\) | −0.609193 | −0.0225472 | ||||||||
\(731\) | −18.3449 | −0.678512 | ||||||||
\(732\) | −10.1529 | −0.375263 | ||||||||
\(733\) | −24.9604 | −0.921935 | −0.460968 | − | 0.887417i | \(-0.652498\pi\) | ||||
−0.460968 | + | 0.887417i | \(0.652498\pi\) | |||||||
\(734\) | 2.73609 | 0.100991 | ||||||||
\(735\) | −16.6901 | −0.615625 | ||||||||
\(736\) | 14.3895 | 0.530404 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −14.2415 | −0.524237 | ||||||||
\(739\) | −21.2342 | −0.781114 | −0.390557 | − | 0.920579i | \(-0.627718\pi\) | ||||
−0.390557 | + | 0.920579i | \(0.627718\pi\) | |||||||
\(740\) | 8.67501 | 0.318900 | ||||||||
\(741\) | 74.3648 | 2.73186 | ||||||||
\(742\) | 9.01383 | 0.330908 | ||||||||
\(743\) | 30.6527 | 1.12454 | 0.562270 | − | 0.826954i | \(-0.309928\pi\) | ||||
0.562270 | + | 0.826954i | \(0.309928\pi\) | |||||||
\(744\) | −26.4342 | −0.969125 | ||||||||
\(745\) | −3.78444 | −0.138651 | ||||||||
\(746\) | 6.88968 | 0.252249 | ||||||||
\(747\) | −7.89694 | −0.288934 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.79259 | −0.175118 | ||||||||
\(750\) | 2.07392 | 0.0757289 | ||||||||
\(751\) | −30.3073 | −1.10593 | −0.552965 | − | 0.833204i | \(-0.686504\pi\) | ||||
−0.552965 | + | 0.833204i | \(0.686504\pi\) | |||||||
\(752\) | 6.02629 | 0.219756 | ||||||||
\(753\) | −48.4463 | −1.76548 | ||||||||
\(754\) | −15.1485 | −0.551674 | ||||||||
\(755\) | −24.3566 | −0.886429 | ||||||||
\(756\) | −8.04193 | −0.292482 | ||||||||
\(757\) | −34.8694 | −1.26735 | −0.633674 | − | 0.773600i | \(-0.718454\pi\) | ||||
−0.633674 | + | 0.773600i | \(0.718454\pi\) | |||||||
\(758\) | −7.23750 | −0.262878 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 19.5493 | 0.709129 | ||||||||
\(761\) | 2.68972 | 0.0975022 | 0.0487511 | − | 0.998811i | \(-0.484476\pi\) | ||||
0.0487511 | + | 0.998811i | \(0.484476\pi\) | |||||||
\(762\) | −24.7003 | −0.894798 | ||||||||
\(763\) | −5.49546 | −0.198949 | ||||||||
\(764\) | 6.51212 | 0.235600 | ||||||||
\(765\) | 11.7629 | 0.425290 | ||||||||
\(766\) | −13.3121 | −0.480984 | ||||||||
\(767\) | −10.1617 | −0.366920 | ||||||||
\(768\) | 33.5507 | 1.21066 | ||||||||
\(769\) | 32.5735 | 1.17463 | 0.587315 | − | 0.809359i | \(-0.300185\pi\) | ||||
0.587315 | + | 0.809359i | \(0.300185\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −52.0010 | −1.87277 | ||||||||
\(772\) | −32.9991 | −1.18767 | ||||||||
\(773\) | 41.6637 | 1.49854 | 0.749270 | − | 0.662265i | \(-0.230405\pi\) | ||||
0.749270 | + | 0.662265i | \(0.230405\pi\) | |||||||
\(774\) | 27.6758 | 0.994788 | ||||||||
\(775\) | −3.68820 | −0.132484 | ||||||||
\(776\) | −6.22714 | −0.223541 | ||||||||
\(777\) | 17.2786 | 0.619867 | ||||||||
\(778\) | 23.0081 | 0.824882 | ||||||||
\(779\) | −30.1864 | −1.08154 | ||||||||
\(780\) | 14.1178 | 0.505498 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −4.34451 | −0.155359 | ||||||||
\(783\) | −31.8894 | −1.13963 | ||||||||
\(784\) | −6.12253 | −0.218662 | ||||||||
\(785\) | −7.23210 | −0.258125 | ||||||||
\(786\) | −23.2019 | −0.827584 | ||||||||
\(787\) | 35.9207 | 1.28044 | 0.640218 | − | 0.768193i | \(-0.278844\pi\) | ||||
0.640218 | + | 0.768193i | \(0.278844\pi\) | |||||||
\(788\) | −16.3175 | −0.581288 | ||||||||
\(789\) | 10.3784 | 0.369482 | ||||||||
\(790\) | −8.90936 | −0.316981 | ||||||||
\(791\) | −0.314468 | −0.0111812 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.55476 | 0.303789 | ||||||||
\(794\) | −7.83461 | −0.278040 | ||||||||
\(795\) | −33.3115 | −1.18144 | ||||||||
\(796\) | 11.3847 | 0.403521 | ||||||||
\(797\) | −31.7197 | −1.12357 | −0.561785 | − | 0.827283i | \(-0.689885\pi\) | ||||
−0.561785 | + | 0.827283i | \(0.689885\pi\) | |||||||
\(798\) | 16.4036 | 0.580680 | ||||||||
\(799\) | −14.0126 | −0.495731 | ||||||||
\(800\) | 5.85919 | 0.207154 | ||||||||
\(801\) | 40.0295 | 1.41437 | ||||||||
\(802\) | −20.3352 | −0.718061 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −25.1617 | −0.887384 | ||||||||
\(805\) | 2.53295 | 0.0892748 | ||||||||
\(806\) | 9.38320 | 0.330509 | ||||||||
\(807\) | 27.9612 | 0.984283 | ||||||||
\(808\) | −19.1795 | −0.674733 | ||||||||
\(809\) | 8.51572 | 0.299397 | 0.149698 | − | 0.988732i | \(-0.452170\pi\) | ||||
0.149698 | + | 0.988732i | \(0.452170\pi\) | |||||||
\(810\) | −0.253142 | −0.00889451 | ||||||||
\(811\) | −9.03030 | −0.317097 | −0.158548 | − | 0.987351i | \(-0.550681\pi\) | ||||
−0.158548 | + | 0.987351i | \(0.550681\pi\) | |||||||
\(812\) | 8.94083 | 0.313762 | ||||||||
\(813\) | 3.52472 | 0.123617 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.6892 | −0.654653 | ||||||||
\(816\) | 6.95431 | 0.243450 | ||||||||
\(817\) | 58.6619 | 2.05232 | ||||||||
\(818\) | −10.5985 | −0.370569 | ||||||||
\(819\) | 17.4477 | 0.609672 | ||||||||
\(820\) | −5.73074 | −0.200126 | ||||||||
\(821\) | 54.3225 | 1.89587 | 0.947935 | − | 0.318465i | \(-0.103167\pi\) | ||||
0.947935 | + | 0.318465i | \(0.103167\pi\) | |||||||
\(822\) | 8.87896 | 0.309689 | ||||||||
\(823\) | 17.8594 | 0.622541 | 0.311271 | − | 0.950321i | \(-0.399245\pi\) | ||||
0.311271 | + | 0.950321i | \(0.399245\pi\) | |||||||
\(824\) | 24.1723 | 0.842083 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.24151 | −0.0779920 | ||||||||
\(827\) | 51.9494 | 1.80646 | 0.903229 | − | 0.429159i | \(-0.141190\pi\) | ||||
0.903229 | + | 0.429159i | \(0.141190\pi\) | |||||||
\(828\) | −17.5373 | −0.609465 | ||||||||
\(829\) | −19.7460 | −0.685807 | −0.342904 | − | 0.939371i | \(-0.611410\pi\) | ||||
−0.342904 | + | 0.939371i | \(0.611410\pi\) | |||||||
\(830\) | 1.18761 | 0.0412227 | ||||||||
\(831\) | −22.7548 | −0.789357 | ||||||||
\(832\) | −7.79201 | −0.270139 | ||||||||
\(833\) | 14.2364 | 0.493263 | ||||||||
\(834\) | −12.3465 | −0.427523 | ||||||||
\(835\) | 7.85328 | 0.271774 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 19.7528 | 0.682757 | ||||||||
\(838\) | −23.2140 | −0.801916 | ||||||||
\(839\) | −4.11650 | −0.142117 | −0.0710586 | − | 0.997472i | \(-0.522638\pi\) | ||||
−0.0710586 | + | 0.997472i | \(0.522638\pi\) | |||||||
\(840\) | 7.39214 | 0.255053 | ||||||||
\(841\) | 6.45386 | 0.222547 | ||||||||
\(842\) | 19.6000 | 0.675460 | ||||||||
\(843\) | 71.3300 | 2.45674 | ||||||||
\(844\) | −33.1462 | −1.14094 | ||||||||
\(845\) | 1.10448 | 0.0379951 | ||||||||
\(846\) | 21.1400 | 0.726807 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −12.2198 | −0.419630 | ||||||||
\(849\) | −57.4751 | −1.97254 | ||||||||
\(850\) | −1.76902 | −0.0606769 | ||||||||
\(851\) | 14.6336 | 0.501633 | ||||||||
\(852\) | 8.28138 | 0.283715 | ||||||||
\(853\) | −5.50285 | −0.188414 | −0.0942070 | − | 0.995553i | \(-0.530032\pi\) | ||||
−0.0942070 | + | 0.995553i | \(0.530032\pi\) | |||||||
\(854\) | 1.88703 | 0.0645729 | ||||||||
\(855\) | −37.6145 | −1.28639 | ||||||||
\(856\) | −11.8456 | −0.404873 | ||||||||
\(857\) | 26.9281 | 0.919847 | 0.459924 | − | 0.887959i | \(-0.347877\pi\) | ||||
0.459924 | + | 0.887959i | \(0.347877\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.1519 | 0.653456 | 0.326728 | − | 0.945118i | \(-0.394054\pi\) | ||||
0.326728 | + | 0.945118i | \(0.394054\pi\) | |||||||
\(860\) | 11.1367 | 0.379758 | ||||||||
\(861\) | −11.4143 | −0.388998 | ||||||||
\(862\) | 2.85371 | 0.0971977 | ||||||||
\(863\) | 4.96151 | 0.168892 | 0.0844458 | − | 0.996428i | \(-0.473088\pi\) | ||||
0.0844458 | + | 0.996428i | \(0.473088\pi\) | |||||||
\(864\) | −31.3799 | −1.06757 | ||||||||
\(865\) | 11.2047 | 0.380971 | ||||||||
\(866\) | 29.6080 | 1.00612 | ||||||||
\(867\) | 31.6260 | 1.07408 | ||||||||
\(868\) | −5.53810 | −0.187975 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 12.3488 | 0.418663 | ||||||||
\(871\) | 21.2010 | 0.718368 | ||||||||
\(872\) | −13.5828 | −0.459972 | ||||||||
\(873\) | 11.9815 | 0.405514 | ||||||||
\(874\) | 13.8925 | 0.469921 | ||||||||
\(875\) | 1.03138 | 0.0348670 | ||||||||
\(876\) | 3.38053 | 0.114218 | ||||||||
\(877\) | 27.2053 | 0.918659 | 0.459329 | − | 0.888266i | \(-0.348090\pi\) | ||||
0.459329 | + | 0.888266i | \(0.348090\pi\) | |||||||
\(878\) | −0.754874 | −0.0254758 | ||||||||
\(879\) | 7.16686 | 0.241732 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.3570 | 0.348935 | 0.174467 | − | 0.984663i | \(-0.444180\pi\) | ||||
0.174467 | + | 0.984663i | \(0.444180\pi\) | |||||||
\(882\) | −21.4776 | −0.723188 | ||||||||
\(883\) | 7.39489 | 0.248858 | 0.124429 | − | 0.992229i | \(-0.460290\pi\) | ||||
0.124429 | + | 0.992229i | \(0.460290\pi\) | |||||||
\(884\) | −12.0422 | −0.405025 | ||||||||
\(885\) | 8.28370 | 0.278453 | ||||||||
\(886\) | −11.8560 | −0.398309 | ||||||||
\(887\) | 18.0590 | 0.606363 | 0.303181 | − | 0.952933i | \(-0.401951\pi\) | ||||
0.303181 | + | 0.952933i | \(0.401951\pi\) | |||||||
\(888\) | 42.7065 | 1.43314 | ||||||||
\(889\) | −12.2837 | −0.411982 | ||||||||
\(890\) | −6.02000 | −0.201791 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 23.3563 | 0.782027 | ||||||||
\(893\) | 44.8084 | 1.49946 | ||||||||
\(894\) | −7.84864 | −0.262498 | ||||||||
\(895\) | −1.46463 | −0.0489572 | ||||||||
\(896\) | 10.3673 | 0.346348 | ||||||||
\(897\) | 23.8148 | 0.795154 | ||||||||
\(898\) | 26.4386 | 0.882267 | ||||||||
\(899\) | −21.9607 | −0.732431 | ||||||||
\(900\) | −7.14094 | −0.238031 | ||||||||
\(901\) | 28.4141 | 0.946612 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 22.1817 | 0.738160 | ||||||||
\(904\) | −0.777253 | −0.0258511 | ||||||||
\(905\) | −9.28900 | −0.308777 | ||||||||
\(906\) | −50.5137 | −1.67821 | ||||||||
\(907\) | 26.2971 | 0.873179 | 0.436590 | − | 0.899661i | \(-0.356186\pi\) | ||||
0.436590 | + | 0.899661i | \(0.356186\pi\) | |||||||
\(908\) | −35.1687 | −1.16711 | ||||||||
\(909\) | 36.9030 | 1.22399 | ||||||||
\(910\) | −2.62395 | −0.0869830 | ||||||||
\(911\) | 28.6489 | 0.949179 | 0.474589 | − | 0.880207i | \(-0.342597\pi\) | ||||
0.474589 | + | 0.880207i | \(0.342597\pi\) | |||||||
\(912\) | −22.2379 | −0.736371 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 18.5535 | 0.613694 | ||||||||
\(915\) | −6.97371 | −0.230544 | ||||||||
\(916\) | 21.8591 | 0.722245 | ||||||||
\(917\) | −11.5385 | −0.381035 | ||||||||
\(918\) | 9.47430 | 0.312698 | ||||||||
\(919\) | −38.8568 | −1.28177 | −0.640884 | − | 0.767638i | \(-0.721432\pi\) | ||||
−0.640884 | + | 0.767638i | \(0.721432\pi\) | |||||||
\(920\) | 6.26055 | 0.206404 | ||||||||
\(921\) | 25.2836 | 0.833123 | ||||||||
\(922\) | −4.90996 | −0.161701 | ||||||||
\(923\) | −6.97781 | −0.229677 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.95858 | 0.195917 | ||||||||
\(926\) | 28.6006 | 0.939873 | ||||||||
\(927\) | −46.5096 | −1.52757 | ||||||||
\(928\) | 34.8875 | 1.14524 | ||||||||
\(929\) | 7.42132 | 0.243486 | 0.121743 | − | 0.992562i | \(-0.461152\pi\) | ||||
0.121743 | + | 0.992562i | \(0.461152\pi\) | |||||||
\(930\) | −7.64904 | −0.250822 | ||||||||
\(931\) | −45.5240 | −1.49199 | ||||||||
\(932\) | 16.6349 | 0.544893 | ||||||||
\(933\) | 56.5775 | 1.85227 | ||||||||
\(934\) | 16.6334 | 0.544260 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 43.1245 | 1.40957 | ||||||||
\(937\) | 14.9360 | 0.487937 | 0.243968 | − | 0.969783i | \(-0.421551\pi\) | ||||
0.243968 | + | 0.969783i | \(0.421551\pi\) | |||||||
\(938\) | 4.67657 | 0.152696 | ||||||||
\(939\) | −19.9757 | −0.651881 | ||||||||
\(940\) | 8.50666 | 0.277457 | ||||||||
\(941\) | 52.3409 | 1.70626 | 0.853132 | − | 0.521695i | \(-0.174700\pi\) | ||||
0.853132 | + | 0.521695i | \(0.174700\pi\) | |||||||
\(942\) | −14.9988 | −0.488687 | ||||||||
\(943\) | −9.66700 | −0.314801 | ||||||||
\(944\) | 3.03875 | 0.0989030 | ||||||||
\(945\) | −5.52373 | −0.179687 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.69553 | −0.120088 | −0.0600442 | − | 0.998196i | \(-0.519124\pi\) | ||||
−0.0600442 | + | 0.998196i | \(0.519124\pi\) | |||||||
\(948\) | 49.4398 | 1.60573 | ||||||||
\(949\) | −2.84841 | −0.0924631 | ||||||||
\(950\) | 5.65682 | 0.183532 | ||||||||
\(951\) | −6.44756 | −0.209076 | ||||||||
\(952\) | −6.30538 | −0.204358 | ||||||||
\(953\) | −43.1526 | −1.39785 | −0.698925 | − | 0.715195i | \(-0.746338\pi\) | ||||
−0.698925 | + | 0.715195i | \(0.746338\pi\) | |||||||
\(954\) | −42.8666 | −1.38786 | ||||||||
\(955\) | 4.47296 | 0.144742 | ||||||||
\(956\) | 39.9011 | 1.29049 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.20373 | 0.0388907 | ||||||||
\(959\) | 4.41559 | 0.142587 | ||||||||
\(960\) | 6.35192 | 0.205007 | ||||||||
\(961\) | −17.3972 | −0.561199 | ||||||||
\(962\) | −15.1593 | −0.488755 | ||||||||
\(963\) | 22.7919 | 0.734458 | ||||||||
\(964\) | 15.9255 | 0.512927 | ||||||||
\(965\) | −22.6660 | −0.729645 | ||||||||
\(966\) | 5.25314 | 0.169017 | ||||||||
\(967\) | 29.2144 | 0.939471 | 0.469736 | − | 0.882807i | \(-0.344349\pi\) | ||||
0.469736 | + | 0.882807i | \(0.344349\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 51.7087 | 1.66112 | ||||||||
\(970\) | −1.80189 | −0.0578554 | ||||||||
\(971\) | −26.4046 | −0.847365 | −0.423683 | − | 0.905811i | \(-0.639263\pi\) | ||||
−0.423683 | + | 0.905811i | \(0.639263\pi\) | |||||||
\(972\) | −21.9870 | −0.705234 | ||||||||
\(973\) | −6.14001 | −0.196840 | ||||||||
\(974\) | 0.774743 | 0.0248244 | ||||||||
\(975\) | 9.69704 | 0.310554 | ||||||||
\(976\) | −2.55820 | −0.0818861 | ||||||||
\(977\) | −15.8434 | −0.506875 | −0.253437 | − | 0.967352i | \(-0.581561\pi\) | ||||
−0.253437 | + | 0.967352i | \(0.581561\pi\) | |||||||
\(978\) | −38.7598 | −1.23940 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −8.64252 | −0.276075 | ||||||||
\(981\) | 26.1345 | 0.834410 | ||||||||
\(982\) | 10.2636 | 0.327525 | ||||||||
\(983\) | 35.1039 | 1.11964 | 0.559821 | − | 0.828614i | \(-0.310870\pi\) | ||||
0.559821 | + | 0.828614i | \(0.310870\pi\) | |||||||
\(984\) | −28.2121 | −0.899368 | ||||||||
\(985\) | −11.2080 | −0.357116 | ||||||||
\(986\) | −10.5333 | −0.335449 | ||||||||
\(987\) | 16.9433 | 0.539311 | ||||||||
\(988\) | 38.5077 | 1.22509 | ||||||||
\(989\) | 18.7861 | 0.597363 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.9700 | 0.602600 | 0.301300 | − | 0.953529i | \(-0.402579\pi\) | ||||
0.301300 | + | 0.953529i | \(0.402579\pi\) | |||||||
\(992\) | −21.6099 | −0.686114 | ||||||||
\(993\) | −43.2843 | −1.37359 | ||||||||
\(994\) | −1.53918 | −0.0488200 | ||||||||
\(995\) | 7.81979 | 0.247904 | ||||||||
\(996\) | −6.59031 | −0.208822 | ||||||||
\(997\) | −30.1347 | −0.954375 | −0.477188 | − | 0.878801i | \(-0.658344\pi\) | ||||
−0.477188 | + | 0.878801i | \(0.658344\pi\) | |||||||
\(998\) | 12.8108 | 0.405519 | ||||||||
\(999\) | −31.9122 | −1.00966 |
(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 | 605.2.a.k.1.3 | 4 | ||
3.2 | odd | 2 | 5445.2.a.bi.1.2 | 4 | |||
4.3 | odd | 2 | 9680.2.a.cm.1.4 | 4 | |||
5.4 | even | 2 | 3025.2.a.w.1.2 | 4 | |||
11.2 | odd | 10 | 55.2.g.b.26.2 | ✓ | 8 | ||
11.3 | even | 5 | 605.2.g.e.251.2 | 8 | |||
11.4 | even | 5 | 605.2.g.e.511.2 | 8 | |||
11.5 | even | 5 | 605.2.g.k.366.1 | 8 | |||
11.6 | odd | 10 | 55.2.g.b.36.2 | yes | 8 | ||
11.7 | odd | 10 | 605.2.g.m.511.1 | 8 | |||
11.8 | odd | 10 | 605.2.g.m.251.1 | 8 | |||
11.9 | even | 5 | 605.2.g.k.81.1 | 8 | |||
11.10 | odd | 2 | 605.2.a.j.1.2 | 4 | |||
33.2 | even | 10 | 495.2.n.e.136.1 | 8 | |||
33.17 | even | 10 | 495.2.n.e.91.1 | 8 | |||
33.32 | even | 2 | 5445.2.a.bp.1.3 | 4 | |||
44.35 | even | 10 | 880.2.bo.h.81.2 | 8 | |||
44.39 | even | 10 | 880.2.bo.h.641.2 | 8 | |||
44.43 | even | 2 | 9680.2.a.cn.1.4 | 4 | |||
55.2 | even | 20 | 275.2.z.a.224.2 | 16 | |||
55.13 | even | 20 | 275.2.z.a.224.3 | 16 | |||
55.17 | even | 20 | 275.2.z.a.124.3 | 16 | |||
55.24 | odd | 10 | 275.2.h.a.26.1 | 8 | |||
55.28 | even | 20 | 275.2.z.a.124.2 | 16 | |||
55.39 | odd | 10 | 275.2.h.a.201.1 | 8 | |||
55.54 | odd | 2 | 3025.2.a.bd.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.2.g.b.26.2 | ✓ | 8 | 11.2 | odd | 10 | ||
55.2.g.b.36.2 | yes | 8 | 11.6 | odd | 10 | ||
275.2.h.a.26.1 | 8 | 55.24 | odd | 10 | |||
275.2.h.a.201.1 | 8 | 55.39 | odd | 10 | |||
275.2.z.a.124.2 | 16 | 55.28 | even | 20 | |||
275.2.z.a.124.3 | 16 | 55.17 | even | 20 | |||
275.2.z.a.224.2 | 16 | 55.2 | even | 20 | |||
275.2.z.a.224.3 | 16 | 55.13 | even | 20 | |||
495.2.n.e.91.1 | 8 | 33.17 | even | 10 | |||
495.2.n.e.136.1 | 8 | 33.2 | even | 10 | |||
605.2.a.j.1.2 | 4 | 11.10 | odd | 2 | |||
605.2.a.k.1.3 | 4 | 1.1 | even | 1 | trivial | ||
605.2.g.e.251.2 | 8 | 11.3 | even | 5 | |||
605.2.g.e.511.2 | 8 | 11.4 | even | 5 | |||
605.2.g.k.81.1 | 8 | 11.9 | even | 5 | |||
605.2.g.k.366.1 | 8 | 11.5 | even | 5 | |||
605.2.g.m.251.1 | 8 | 11.8 | odd | 10 | |||
605.2.g.m.511.1 | 8 | 11.7 | odd | 10 | |||
880.2.bo.h.81.2 | 8 | 44.35 | even | 10 | |||
880.2.bo.h.641.2 | 8 | 44.39 | even | 10 | |||
3025.2.a.w.1.2 | 4 | 5.4 | even | 2 | |||
3025.2.a.bd.1.3 | 4 | 55.54 | odd | 2 | |||
5445.2.a.bi.1.2 | 4 | 3.2 | odd | 2 | |||
5445.2.a.bp.1.3 | 4 | 33.32 | even | 2 | |||
9680.2.a.cm.1.4 | 4 | 4.3 | odd | 2 | |||
9680.2.a.cn.1.4 | 4 | 44.43 | even | 2 |