Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(1,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.54764.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 9x^{2} + 3x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.36007\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1110.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0.487359 | 0.184204 | 0.0921022 | − | 0.995750i | \(-0.470641\pi\) | ||||
0.0921022 | + | 0.995750i | \(0.470641\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −5.20750 | −1.57012 | −0.785061 | − | 0.619419i | \(-0.787368\pi\) | ||||
−0.785061 | + | 0.619419i | \(0.787368\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 4.12492 | 1.14405 | 0.572023 | − | 0.820237i | \(-0.306159\pi\) | ||||
0.572023 | + | 0.820237i | \(0.306159\pi\) | |||||||
\(14\) | 0.487359 | 0.130252 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.67781 | 0.892000 | 0.446000 | − | 0.895033i | \(-0.352848\pi\) | ||||
0.446000 | + | 0.895033i | \(0.352848\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 0.430057 | 0.0986618 | 0.0493309 | − | 0.998782i | \(-0.484291\pi\) | ||||
0.0493309 | + | 0.998782i | \(0.484291\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0.487359 | 0.106350 | ||||||||
\(22\) | −5.20750 | −1.11024 | ||||||||
\(23\) | 7.31537 | 1.52536 | 0.762680 | − | 0.646776i | \(-0.223883\pi\) | ||||
0.762680 | + | 0.646776i | \(0.223883\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.12492 | 0.808963 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.487359 | 0.0921022 | ||||||||
\(29\) | −6.77745 | −1.25854 | −0.629270 | − | 0.777187i | \(-0.716646\pi\) | ||||
−0.629270 | + | 0.777187i | \(0.716646\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 7.80273 | 1.40141 | 0.700706 | − | 0.713450i | \(-0.252869\pi\) | ||||
0.700706 | + | 0.713450i | \(0.252869\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −5.20750 | −0.906510 | ||||||||
\(34\) | 3.67781 | 0.630739 | ||||||||
\(35\) | 0.487359 | 0.0823787 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | 0.430057 | 0.0697645 | ||||||||
\(39\) | 4.12492 | 0.660516 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −9.80273 | −1.53093 | −0.765465 | − | 0.643478i | \(-0.777491\pi\) | ||||
−0.765465 | + | 0.643478i | \(0.777491\pi\) | |||||||
\(42\) | 0.487359 | 0.0752011 | ||||||||
\(43\) | 4.77745 | 0.728554 | 0.364277 | − | 0.931291i | \(-0.381316\pi\) | ||||
0.364277 | + | 0.931291i | \(0.381316\pi\) | |||||||
\(44\) | −5.20750 | −0.785061 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 7.31537 | 1.07859 | ||||||||
\(47\) | 3.52969 | 0.514859 | 0.257429 | − | 0.966297i | \(-0.417125\pi\) | ||||
0.257429 | + | 0.966297i | \(0.417125\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −6.76248 | −0.966069 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 3.67781 | 0.514996 | ||||||||
\(52\) | 4.12492 | 0.572023 | ||||||||
\(53\) | −7.67781 | −1.05463 | −0.527314 | − | 0.849670i | \(-0.676801\pi\) | ||||
−0.527314 | + | 0.849670i | \(0.676801\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −5.20750 | −0.702180 | ||||||||
\(56\) | 0.487359 | 0.0651261 | ||||||||
\(57\) | 0.430057 | 0.0569624 | ||||||||
\(58\) | −6.77745 | −0.889922 | ||||||||
\(59\) | −0.974718 | −0.126897 | −0.0634487 | − | 0.997985i | \(-0.520210\pi\) | ||||
−0.0634487 | + | 0.997985i | \(0.520210\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | −14.5229 | −1.85946 | −0.929732 | − | 0.368237i | \(-0.879961\pi\) | ||||
−0.929732 | + | 0.368237i | \(0.879961\pi\) | |||||||
\(62\) | 7.80273 | 0.990948 | ||||||||
\(63\) | 0.487359 | 0.0614014 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.12492 | 0.511633 | ||||||||
\(66\) | −5.20750 | −0.640999 | ||||||||
\(67\) | −1.19045 | −0.145437 | −0.0727183 | − | 0.997353i | \(-0.523167\pi\) | ||||
−0.0727183 | + | 0.997353i | \(0.523167\pi\) | |||||||
\(68\) | 3.67781 | 0.446000 | ||||||||
\(69\) | 7.31537 | 0.880667 | ||||||||
\(70\) | 0.487359 | 0.0582505 | ||||||||
\(71\) | 8.58018 | 1.01828 | 0.509140 | − | 0.860684i | \(-0.329964\pi\) | ||||
0.509140 | + | 0.860684i | \(0.329964\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −7.15020 | −0.836868 | −0.418434 | − | 0.908247i | \(-0.637421\pi\) | ||||
−0.418434 | + | 0.908247i | \(0.637421\pi\) | |||||||
\(74\) | −1.00000 | −0.116248 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0.430057 | 0.0493309 | ||||||||
\(77\) | −2.53792 | −0.289223 | ||||||||
\(78\) | 4.12492 | 0.467055 | ||||||||
\(79\) | 4.00000 | 0.450035 | 0.225018 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −9.80273 | −1.08253 | ||||||||
\(83\) | −16.5399 | −1.81549 | −0.907747 | − | 0.419519i | \(-0.862199\pi\) | ||||
−0.907747 | + | 0.419519i | \(0.862199\pi\) | |||||||
\(84\) | 0.487359 | 0.0531752 | ||||||||
\(85\) | 3.67781 | 0.398914 | ||||||||
\(86\) | 4.77745 | 0.515165 | ||||||||
\(87\) | −6.77745 | −0.726619 | ||||||||
\(88\) | −5.20750 | −0.555122 | ||||||||
\(89\) | 16.7051 | 1.77074 | 0.885368 | − | 0.464890i | \(-0.153906\pi\) | ||||
0.885368 | + | 0.464890i | \(0.153906\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 2.01032 | 0.210738 | ||||||||
\(92\) | 7.31537 | 0.762680 | ||||||||
\(93\) | 7.80273 | 0.809105 | ||||||||
\(94\) | 3.52969 | 0.364060 | ||||||||
\(95\) | 0.430057 | 0.0441229 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −7.16726 | −0.727725 | −0.363862 | − | 0.931453i | \(-0.618542\pi\) | ||||
−0.363862 | + | 0.931453i | \(0.618542\pi\) | |||||||
\(98\) | −6.76248 | −0.683114 | ||||||||
\(99\) | −5.20750 | −0.523374 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −13.7454 | −1.36772 | −0.683861 | − | 0.729613i | \(-0.739700\pi\) | ||||
−0.683861 | + | 0.729613i | \(0.739700\pi\) | |||||||
\(102\) | 3.67781 | 0.364157 | ||||||||
\(103\) | −3.52969 | −0.347791 | −0.173896 | − | 0.984764i | \(-0.555636\pi\) | ||||
−0.173896 | + | 0.984764i | \(0.555636\pi\) | |||||||
\(104\) | 4.12492 | 0.404482 | ||||||||
\(105\) | 0.487359 | 0.0475614 | ||||||||
\(106\) | −7.67781 | −0.745735 | ||||||||
\(107\) | 7.09964 | 0.686348 | 0.343174 | − | 0.939272i | \(-0.388498\pi\) | ||||
0.343174 | + | 0.939272i | \(0.388498\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 16.4321 | 1.57391 | 0.786953 | − | 0.617013i | \(-0.211657\pi\) | ||||
0.786953 | + | 0.617013i | \(0.211657\pi\) | |||||||
\(110\) | −5.20750 | −0.496516 | ||||||||
\(111\) | −1.00000 | −0.0949158 | ||||||||
\(112\) | 0.487359 | 0.0460511 | ||||||||
\(113\) | −1.22255 | −0.115008 | −0.0575040 | − | 0.998345i | \(-0.518314\pi\) | ||||
−0.0575040 | + | 0.998345i | \(0.518314\pi\) | |||||||
\(114\) | 0.430057 | 0.0402785 | ||||||||
\(115\) | 7.31537 | 0.682162 | ||||||||
\(116\) | −6.77745 | −0.629270 | ||||||||
\(117\) | 4.12492 | 0.381349 | ||||||||
\(118\) | −0.974718 | −0.0897300 | ||||||||
\(119\) | 1.79241 | 0.164310 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 16.1181 | 1.46528 | ||||||||
\(122\) | −14.5229 | −1.31484 | ||||||||
\(123\) | −9.80273 | −0.883882 | ||||||||
\(124\) | 7.80273 | 0.700706 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0.487359 | 0.0434174 | ||||||||
\(127\) | 15.5652 | 1.38119 | 0.690595 | − | 0.723242i | \(-0.257349\pi\) | ||||
0.690595 | + | 0.723242i | \(0.257349\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 4.77745 | 0.420631 | ||||||||
\(130\) | 4.12492 | 0.361779 | ||||||||
\(131\) | −17.5549 | −1.53378 | −0.766889 | − | 0.641780i | \(-0.778196\pi\) | ||||
−0.766889 | + | 0.641780i | \(0.778196\pi\) | |||||||
\(132\) | −5.20750 | −0.453255 | ||||||||
\(133\) | 0.209592 | 0.0181739 | ||||||||
\(134\) | −1.19045 | −0.102839 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 3.67781 | 0.315370 | ||||||||
\(137\) | −21.2498 | −1.81549 | −0.907745 | − | 0.419523i | \(-0.862197\pi\) | ||||
−0.907745 | + | 0.419523i | \(0.862197\pi\) | |||||||
\(138\) | 7.31537 | 0.622726 | ||||||||
\(139\) | −15.4082 | −1.30691 | −0.653453 | − | 0.756967i | \(-0.726680\pi\) | ||||
−0.653453 | + | 0.756967i | \(0.726680\pi\) | |||||||
\(140\) | 0.487359 | 0.0411893 | ||||||||
\(141\) | 3.52969 | 0.297254 | ||||||||
\(142\) | 8.58018 | 0.720032 | ||||||||
\(143\) | −21.4805 | −1.79629 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −6.77745 | −0.562836 | ||||||||
\(146\) | −7.15020 | −0.591755 | ||||||||
\(147\) | −6.76248 | −0.557760 | ||||||||
\(148\) | −1.00000 | −0.0821995 | ||||||||
\(149\) | −3.47913 | −0.285021 | −0.142511 | − | 0.989793i | \(-0.545518\pi\) | ||||
−0.142511 | + | 0.989793i | \(0.545518\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | −17.7304 | −1.44288 | −0.721439 | − | 0.692478i | \(-0.756519\pi\) | ||||
−0.721439 | + | 0.692478i | \(0.756519\pi\) | |||||||
\(152\) | 0.430057 | 0.0348822 | ||||||||
\(153\) | 3.67781 | 0.297333 | ||||||||
\(154\) | −2.53792 | −0.204512 | ||||||||
\(155\) | 7.80273 | 0.626730 | ||||||||
\(156\) | 4.12492 | 0.330258 | ||||||||
\(157\) | 11.8533 | 0.945996 | 0.472998 | − | 0.881064i | \(-0.343172\pi\) | ||||
0.472998 | + | 0.881064i | \(0.343172\pi\) | |||||||
\(158\) | 4.00000 | 0.318223 | ||||||||
\(159\) | −7.67781 | −0.608890 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 3.56521 | 0.280978 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 5.89354 | 0.461618 | 0.230809 | − | 0.972999i | \(-0.425863\pi\) | ||||
0.230809 | + | 0.972999i | \(0.425863\pi\) | |||||||
\(164\) | −9.80273 | −0.765465 | ||||||||
\(165\) | −5.20750 | −0.405404 | ||||||||
\(166\) | −16.5399 | −1.28375 | ||||||||
\(167\) | 24.8362 | 1.92188 | 0.960940 | − | 0.276758i | \(-0.0892599\pi\) | ||||
0.960940 | + | 0.276758i | \(0.0892599\pi\) | |||||||
\(168\) | 0.487359 | 0.0376006 | ||||||||
\(169\) | 4.01497 | 0.308844 | ||||||||
\(170\) | 3.67781 | 0.282075 | ||||||||
\(171\) | 0.430057 | 0.0328873 | ||||||||
\(172\) | 4.77745 | 0.364277 | ||||||||
\(173\) | −19.9276 | −1.51507 | −0.757536 | − | 0.652794i | \(-0.773597\pi\) | ||||
−0.757536 | + | 0.652794i | \(0.773597\pi\) | |||||||
\(174\) | −6.77745 | −0.513797 | ||||||||
\(175\) | 0.487359 | 0.0368409 | ||||||||
\(176\) | −5.20750 | −0.392530 | ||||||||
\(177\) | −0.974718 | −0.0732643 | ||||||||
\(178\) | 16.7051 | 1.25210 | ||||||||
\(179\) | −4.33034 | −0.323665 | −0.161832 | − | 0.986818i | \(-0.551740\pi\) | ||||
−0.161832 | + | 0.986818i | \(0.551740\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | −0.0505645 | −0.00375843 | −0.00187922 | − | 0.999998i | \(-0.500598\pi\) | ||||
−0.00187922 | + | 0.999998i | \(0.500598\pi\) | |||||||
\(182\) | 2.01032 | 0.149015 | ||||||||
\(183\) | −14.5229 | −1.07356 | ||||||||
\(184\) | 7.31537 | 0.539296 | ||||||||
\(185\) | −1.00000 | −0.0735215 | ||||||||
\(186\) | 7.80273 | 0.572124 | ||||||||
\(187\) | −19.1522 | −1.40055 | ||||||||
\(188\) | 3.52969 | 0.257429 | ||||||||
\(189\) | 0.487359 | 0.0354501 | ||||||||
\(190\) | 0.430057 | 0.0311996 | ||||||||
\(191\) | −4.37276 | −0.316401 | −0.158201 | − | 0.987407i | \(-0.550569\pi\) | ||||
−0.158201 | + | 0.987407i | \(0.550569\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −2.47031 | −0.177816 | −0.0889082 | − | 0.996040i | \(-0.528338\pi\) | ||||
−0.0889082 | + | 0.996040i | \(0.528338\pi\) | |||||||
\(194\) | −7.16726 | −0.514579 | ||||||||
\(195\) | 4.12492 | 0.295392 | ||||||||
\(196\) | −6.76248 | −0.483034 | ||||||||
\(197\) | −13.3154 | −0.948681 | −0.474340 | − | 0.880341i | \(-0.657313\pi\) | ||||
−0.474340 | + | 0.880341i | \(0.657313\pi\) | |||||||
\(198\) | −5.20750 | −0.370081 | ||||||||
\(199\) | 21.4403 | 1.51986 | 0.759931 | − | 0.650004i | \(-0.225233\pi\) | ||||
0.759931 | + | 0.650004i | \(0.225233\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −1.19045 | −0.0839679 | ||||||||
\(202\) | −13.7454 | −0.967125 | ||||||||
\(203\) | −3.30305 | −0.231829 | ||||||||
\(204\) | 3.67781 | 0.257498 | ||||||||
\(205\) | −9.80273 | −0.684652 | ||||||||
\(206\) | −3.52969 | −0.245925 | ||||||||
\(207\) | 7.31537 | 0.508453 | ||||||||
\(208\) | 4.12492 | 0.286012 | ||||||||
\(209\) | −2.23952 | −0.154911 | ||||||||
\(210\) | 0.487359 | 0.0336310 | ||||||||
\(211\) | 13.9679 | 0.961590 | 0.480795 | − | 0.876833i | \(-0.340348\pi\) | ||||
0.480795 | + | 0.876833i | \(0.340348\pi\) | |||||||
\(212\) | −7.67781 | −0.527314 | ||||||||
\(213\) | 8.58018 | 0.587904 | ||||||||
\(214\) | 7.09964 | 0.485321 | ||||||||
\(215\) | 4.77745 | 0.325819 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 3.80273 | 0.258146 | ||||||||
\(218\) | 16.4321 | 1.11292 | ||||||||
\(219\) | −7.15020 | −0.483166 | ||||||||
\(220\) | −5.20750 | −0.351090 | ||||||||
\(221\) | 15.1707 | 1.02049 | ||||||||
\(222\) | −1.00000 | −0.0671156 | ||||||||
\(223\) | −22.4335 | −1.50226 | −0.751128 | − | 0.660156i | \(-0.770490\pi\) | ||||
−0.751128 | + | 0.660156i | \(0.770490\pi\) | |||||||
\(224\) | 0.487359 | 0.0325630 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −1.22255 | −0.0813230 | ||||||||
\(227\) | 23.8368 | 1.58211 | 0.791053 | − | 0.611747i | \(-0.209533\pi\) | ||||
0.791053 | + | 0.611747i | \(0.209533\pi\) | |||||||
\(228\) | 0.430057 | 0.0284812 | ||||||||
\(229\) | 10.2157 | 0.675075 | 0.337537 | − | 0.941312i | \(-0.390406\pi\) | ||||
0.337537 | + | 0.941312i | \(0.390406\pi\) | |||||||
\(230\) | 7.31537 | 0.482361 | ||||||||
\(231\) | −2.53792 | −0.166983 | ||||||||
\(232\) | −6.77745 | −0.444961 | ||||||||
\(233\) | 2.07576 | 0.135988 | 0.0679939 | − | 0.997686i | \(-0.478340\pi\) | ||||
0.0679939 | + | 0.997686i | \(0.478340\pi\) | |||||||
\(234\) | 4.12492 | 0.269654 | ||||||||
\(235\) | 3.52969 | 0.230252 | ||||||||
\(236\) | −0.974718 | −0.0634487 | ||||||||
\(237\) | 4.00000 | 0.259828 | ||||||||
\(238\) | 1.79241 | 0.116185 | ||||||||
\(239\) | −28.2683 | −1.82852 | −0.914262 | − | 0.405123i | \(-0.867229\pi\) | ||||
−0.914262 | + | 0.405123i | \(0.867229\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | 20.4491 | 1.31724 | 0.658622 | − | 0.752474i | \(-0.271140\pi\) | ||||
0.658622 | + | 0.752474i | \(0.271140\pi\) | |||||||
\(242\) | 16.1181 | 1.03611 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −14.5229 | −0.929732 | ||||||||
\(245\) | −6.76248 | −0.432039 | ||||||||
\(246\) | −9.80273 | −0.624999 | ||||||||
\(247\) | 1.77395 | 0.112874 | ||||||||
\(248\) | 7.80273 | 0.495474 | ||||||||
\(249\) | −16.5399 | −1.04818 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −19.3092 | −1.21879 | −0.609394 | − | 0.792868i | \(-0.708587\pi\) | ||||
−0.609394 | + | 0.792868i | \(0.708587\pi\) | |||||||
\(252\) | 0.487359 | 0.0307007 | ||||||||
\(253\) | −38.0948 | −2.39500 | ||||||||
\(254\) | 15.5652 | 0.976648 | ||||||||
\(255\) | 3.67781 | 0.230313 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.735194 | 0.0458601 | 0.0229301 | − | 0.999737i | \(-0.492700\pi\) | ||||
0.0229301 | + | 0.999737i | \(0.492700\pi\) | |||||||
\(258\) | 4.77745 | 0.297431 | ||||||||
\(259\) | −0.487359 | −0.0302830 | ||||||||
\(260\) | 4.12492 | 0.255817 | ||||||||
\(261\) | −6.77745 | −0.419513 | ||||||||
\(262\) | −17.5549 | −1.08454 | ||||||||
\(263\) | 6.47231 | 0.399100 | 0.199550 | − | 0.979888i | \(-0.436052\pi\) | ||||
0.199550 | + | 0.979888i | \(0.436052\pi\) | |||||||
\(264\) | −5.20750 | −0.320500 | ||||||||
\(265\) | −7.67781 | −0.471644 | ||||||||
\(266\) | 0.209592 | 0.0128509 | ||||||||
\(267\) | 16.7051 | 1.02234 | ||||||||
\(268\) | −1.19045 | −0.0727183 | ||||||||
\(269\) | −0.810958 | −0.0494450 | −0.0247225 | − | 0.999694i | \(-0.507870\pi\) | ||||
−0.0247225 | + | 0.999694i | \(0.507870\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | 17.4403 | 1.05942 | 0.529711 | − | 0.848178i | \(-0.322300\pi\) | ||||
0.529711 | + | 0.848178i | \(0.322300\pi\) | |||||||
\(272\) | 3.67781 | 0.223000 | ||||||||
\(273\) | 2.01032 | 0.121670 | ||||||||
\(274\) | −21.2498 | −1.28374 | ||||||||
\(275\) | −5.20750 | −0.314024 | ||||||||
\(276\) | 7.31537 | 0.440334 | ||||||||
\(277\) | −1.46007 | −0.0877272 | −0.0438636 | − | 0.999038i | \(-0.513967\pi\) | ||||
−0.0438636 | + | 0.999038i | \(0.513967\pi\) | |||||||
\(278\) | −15.4082 | −0.924122 | ||||||||
\(279\) | 7.80273 | 0.467137 | ||||||||
\(280\) | 0.487359 | 0.0291253 | ||||||||
\(281\) | −12.1249 | −0.723312 | −0.361656 | − | 0.932312i | \(-0.617789\pi\) | ||||
−0.361656 | + | 0.932312i | \(0.617789\pi\) | |||||||
\(282\) | 3.52969 | 0.210190 | ||||||||
\(283\) | 19.5652 | 1.16303 | 0.581516 | − | 0.813535i | \(-0.302460\pi\) | ||||
0.581516 | + | 0.813535i | \(0.302460\pi\) | |||||||
\(284\) | 8.58018 | 0.509140 | ||||||||
\(285\) | 0.430057 | 0.0254744 | ||||||||
\(286\) | −21.4805 | −1.27017 | ||||||||
\(287\) | −4.77745 | −0.282004 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −3.47372 | −0.204336 | ||||||||
\(290\) | −6.77745 | −0.397985 | ||||||||
\(291\) | −7.16726 | −0.420152 | ||||||||
\(292\) | −7.15020 | −0.418434 | ||||||||
\(293\) | −17.5126 | −1.02310 | −0.511550 | − | 0.859254i | \(-0.670928\pi\) | ||||
−0.511550 | + | 0.859254i | \(0.670928\pi\) | |||||||
\(294\) | −6.76248 | −0.394396 | ||||||||
\(295\) | −0.974718 | −0.0567503 | ||||||||
\(296\) | −1.00000 | −0.0581238 | ||||||||
\(297\) | −5.20750 | −0.302170 | ||||||||
\(298\) | −3.47913 | −0.201541 | ||||||||
\(299\) | 30.1753 | 1.74508 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 2.32833 | 0.134203 | ||||||||
\(302\) | −17.7304 | −1.02027 | ||||||||
\(303\) | −13.7454 | −0.789654 | ||||||||
\(304\) | 0.430057 | 0.0246655 | ||||||||
\(305\) | −14.5229 | −0.831577 | ||||||||
\(306\) | 3.67781 | 0.210246 | ||||||||
\(307\) | −0.364444 | −0.0207999 | −0.0104000 | − | 0.999946i | \(-0.503310\pi\) | ||||
−0.0104000 | + | 0.999946i | \(0.503310\pi\) | |||||||
\(308\) | −2.53792 | −0.144612 | ||||||||
\(309\) | −3.52969 | −0.200797 | ||||||||
\(310\) | 7.80273 | 0.443165 | ||||||||
\(311\) | −15.1583 | −0.859551 | −0.429776 | − | 0.902936i | \(-0.641407\pi\) | ||||
−0.429776 | + | 0.902936i | \(0.641407\pi\) | |||||||
\(312\) | 4.12492 | 0.233528 | ||||||||
\(313\) | −14.7201 | −0.832032 | −0.416016 | − | 0.909357i | \(-0.636574\pi\) | ||||
−0.416016 | + | 0.909357i | \(0.636574\pi\) | |||||||
\(314\) | 11.8533 | 0.668920 | ||||||||
\(315\) | 0.487359 | 0.0274596 | ||||||||
\(316\) | 4.00000 | 0.225018 | ||||||||
\(317\) | −0.942615 | −0.0529426 | −0.0264713 | − | 0.999650i | \(-0.508427\pi\) | ||||
−0.0264713 | + | 0.999650i | \(0.508427\pi\) | |||||||
\(318\) | −7.67781 | −0.430550 | ||||||||
\(319\) | 35.2936 | 1.97606 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 7.09964 | 0.396263 | ||||||||
\(322\) | 3.56521 | 0.198681 | ||||||||
\(323\) | 1.58167 | 0.0880063 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 4.12492 | 0.228809 | ||||||||
\(326\) | 5.89354 | 0.326413 | ||||||||
\(327\) | 16.4321 | 0.908695 | ||||||||
\(328\) | −9.80273 | −0.541265 | ||||||||
\(329\) | 1.72023 | 0.0948392 | ||||||||
\(330\) | −5.20750 | −0.286664 | ||||||||
\(331\) | 15.8600 | 0.871746 | 0.435873 | − | 0.900008i | \(-0.356440\pi\) | ||||
0.435873 | + | 0.900008i | \(0.356440\pi\) | |||||||
\(332\) | −16.5399 | −0.907747 | ||||||||
\(333\) | −1.00000 | −0.0547997 | ||||||||
\(334\) | 24.8362 | 1.35897 | ||||||||
\(335\) | −1.19045 | −0.0650413 | ||||||||
\(336\) | 0.487359 | 0.0265876 | ||||||||
\(337\) | 16.9549 | 0.923594 | 0.461797 | − | 0.886986i | \(-0.347205\pi\) | ||||
0.461797 | + | 0.886986i | \(0.347205\pi\) | |||||||
\(338\) | 4.01497 | 0.218385 | ||||||||
\(339\) | −1.22255 | −0.0664000 | ||||||||
\(340\) | 3.67781 | 0.199457 | ||||||||
\(341\) | −40.6327 | −2.20039 | ||||||||
\(342\) | 0.430057 | 0.0232548 | ||||||||
\(343\) | −6.70727 | −0.362158 | ||||||||
\(344\) | 4.77745 | 0.257583 | ||||||||
\(345\) | 7.31537 | 0.393846 | ||||||||
\(346\) | −19.9276 | −1.07132 | ||||||||
\(347\) | −5.44029 | −0.292050 | −0.146025 | − | 0.989281i | \(-0.546648\pi\) | ||||
−0.146025 | + | 0.989281i | \(0.546648\pi\) | |||||||
\(348\) | −6.77745 | −0.363309 | ||||||||
\(349\) | 23.1262 | 1.23792 | 0.618960 | − | 0.785423i | \(-0.287554\pi\) | ||||
0.618960 | + | 0.785423i | \(0.287554\pi\) | |||||||
\(350\) | 0.487359 | 0.0260504 | ||||||||
\(351\) | 4.12492 | 0.220172 | ||||||||
\(352\) | −5.20750 | −0.277561 | ||||||||
\(353\) | 24.7638 | 1.31804 | 0.659022 | − | 0.752123i | \(-0.270970\pi\) | ||||
0.659022 | + | 0.752123i | \(0.270970\pi\) | |||||||
\(354\) | −0.974718 | −0.0518057 | ||||||||
\(355\) | 8.58018 | 0.455388 | ||||||||
\(356\) | 16.7051 | 0.885368 | ||||||||
\(357\) | 1.79241 | 0.0948646 | ||||||||
\(358\) | −4.33034 | −0.228865 | ||||||||
\(359\) | −17.5549 | −0.926512 | −0.463256 | − | 0.886225i | \(-0.653319\pi\) | ||||
−0.463256 | + | 0.886225i | \(0.653319\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −18.8151 | −0.990266 | ||||||||
\(362\) | −0.0505645 | −0.00265761 | ||||||||
\(363\) | 16.1181 | 0.845981 | ||||||||
\(364\) | 2.01032 | 0.105369 | ||||||||
\(365\) | −7.15020 | −0.374259 | ||||||||
\(366\) | −14.5229 | −0.759123 | ||||||||
\(367\) | −8.17331 | −0.426644 | −0.213322 | − | 0.976982i | \(-0.568428\pi\) | ||||
−0.213322 | + | 0.976982i | \(0.568428\pi\) | |||||||
\(368\) | 7.31537 | 0.381340 | ||||||||
\(369\) | −9.80273 | −0.510310 | ||||||||
\(370\) | −1.00000 | −0.0519875 | ||||||||
\(371\) | −3.74185 | −0.194267 | ||||||||
\(372\) | 7.80273 | 0.404553 | ||||||||
\(373\) | −6.00000 | −0.310668 | −0.155334 | − | 0.987862i | \(-0.549645\pi\) | ||||
−0.155334 | + | 0.987862i | \(0.549645\pi\) | |||||||
\(374\) | −19.1522 | −0.990337 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 3.52969 | 0.182030 | ||||||||
\(377\) | −27.9564 | −1.43983 | ||||||||
\(378\) | 0.487359 | 0.0250670 | ||||||||
\(379\) | 26.1993 | 1.34577 | 0.672883 | − | 0.739749i | \(-0.265056\pi\) | ||||
0.672883 | + | 0.739749i | \(0.265056\pi\) | |||||||
\(380\) | 0.430057 | 0.0220615 | ||||||||
\(381\) | 15.5652 | 0.797430 | ||||||||
\(382\) | −4.37276 | −0.223730 | ||||||||
\(383\) | −5.87508 | −0.300203 | −0.150101 | − | 0.988671i | \(-0.547960\pi\) | ||||
−0.150101 | + | 0.988671i | \(0.547960\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −2.53792 | −0.129345 | ||||||||
\(386\) | −2.47031 | −0.125735 | ||||||||
\(387\) | 4.77745 | 0.242851 | ||||||||
\(388\) | −7.16726 | −0.363862 | ||||||||
\(389\) | 33.8368 | 1.71560 | 0.857798 | − | 0.513987i | \(-0.171832\pi\) | ||||
0.857798 | + | 0.513987i | \(0.171832\pi\) | |||||||
\(390\) | 4.12492 | 0.208873 | ||||||||
\(391\) | 26.9045 | 1.36062 | ||||||||
\(392\) | −6.76248 | −0.341557 | ||||||||
\(393\) | −17.5549 | −0.885527 | ||||||||
\(394\) | −13.3154 | −0.670819 | ||||||||
\(395\) | 4.00000 | 0.201262 | ||||||||
\(396\) | −5.20750 | −0.261687 | ||||||||
\(397\) | −1.75016 | −0.0878380 | −0.0439190 | − | 0.999035i | \(-0.513984\pi\) | ||||
−0.0439190 | + | 0.999035i | \(0.513984\pi\) | |||||||
\(398\) | 21.4403 | 1.07470 | ||||||||
\(399\) | 0.209592 | 0.0104927 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 24.7051 | 1.23371 | 0.616857 | − | 0.787075i | \(-0.288406\pi\) | ||||
0.616857 | + | 0.787075i | \(0.288406\pi\) | |||||||
\(402\) | −1.19045 | −0.0593743 | ||||||||
\(403\) | 32.1856 | 1.60328 | ||||||||
\(404\) | −13.7454 | −0.683861 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −3.30305 | −0.163928 | ||||||||
\(407\) | 5.20750 | 0.258126 | ||||||||
\(408\) | 3.67781 | 0.182079 | ||||||||
\(409\) | 6.75899 | 0.334210 | 0.167105 | − | 0.985939i | \(-0.446558\pi\) | ||||
0.167105 | + | 0.985939i | \(0.446558\pi\) | |||||||
\(410\) | −9.80273 | −0.484122 | ||||||||
\(411\) | −21.2498 | −1.04817 | ||||||||
\(412\) | −3.52969 | −0.173896 | ||||||||
\(413\) | −0.475037 | −0.0233751 | ||||||||
\(414\) | 7.31537 | 0.359531 | ||||||||
\(415\) | −16.5399 | −0.811913 | ||||||||
\(416\) | 4.12492 | 0.202241 | ||||||||
\(417\) | −15.4082 | −0.754542 | ||||||||
\(418\) | −2.23952 | −0.109539 | ||||||||
\(419\) | 12.2143 | 0.596709 | 0.298354 | − | 0.954455i | \(-0.403562\pi\) | ||||
0.298354 | + | 0.954455i | \(0.403562\pi\) | |||||||
\(420\) | 0.487359 | 0.0237807 | ||||||||
\(421\) | −8.91942 | −0.434706 | −0.217353 | − | 0.976093i | \(-0.569742\pi\) | ||||
−0.217353 | + | 0.976093i | \(0.569742\pi\) | |||||||
\(422\) | 13.9679 | 0.679947 | ||||||||
\(423\) | 3.52969 | 0.171620 | ||||||||
\(424\) | −7.67781 | −0.372867 | ||||||||
\(425\) | 3.67781 | 0.178400 | ||||||||
\(426\) | 8.58018 | 0.415711 | ||||||||
\(427\) | −7.07785 | −0.342521 | ||||||||
\(428\) | 7.09964 | 0.343174 | ||||||||
\(429\) | −21.4805 | −1.03709 | ||||||||
\(430\) | 4.77745 | 0.230389 | ||||||||
\(431\) | 4.98704 | 0.240217 | 0.120109 | − | 0.992761i | \(-0.461676\pi\) | ||||
0.120109 | + | 0.992761i | \(0.461676\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 15.4805 | 0.743947 | 0.371974 | − | 0.928243i | \(-0.378681\pi\) | ||||
0.371974 | + | 0.928243i | \(0.378681\pi\) | |||||||
\(434\) | 3.80273 | 0.182537 | ||||||||
\(435\) | −6.77745 | −0.324954 | ||||||||
\(436\) | 16.4321 | 0.786953 | ||||||||
\(437\) | 3.14603 | 0.150495 | ||||||||
\(438\) | −7.15020 | −0.341650 | ||||||||
\(439\) | −21.4929 | −1.02580 | −0.512899 | − | 0.858449i | \(-0.671429\pi\) | ||||
−0.512899 | + | 0.858449i | \(0.671429\pi\) | |||||||
\(440\) | −5.20750 | −0.248258 | ||||||||
\(441\) | −6.76248 | −0.322023 | ||||||||
\(442\) | 15.1707 | 0.721595 | ||||||||
\(443\) | −32.4355 | −1.54106 | −0.770528 | − | 0.637406i | \(-0.780007\pi\) | ||||
−0.770528 | + | 0.637406i | \(0.780007\pi\) | |||||||
\(444\) | −1.00000 | −0.0474579 | ||||||||
\(445\) | 16.7051 | 0.791898 | ||||||||
\(446\) | −22.4335 | −1.06226 | ||||||||
\(447\) | −3.47913 | −0.164557 | ||||||||
\(448\) | 0.487359 | 0.0230255 | ||||||||
\(449\) | 15.8348 | 0.747292 | 0.373646 | − | 0.927571i | \(-0.378108\pi\) | ||||
0.373646 | + | 0.927571i | \(0.378108\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 51.0478 | 2.40374 | ||||||||
\(452\) | −1.22255 | −0.0575040 | ||||||||
\(453\) | −17.7304 | −0.833046 | ||||||||
\(454\) | 23.8368 | 1.11872 | ||||||||
\(455\) | 2.01032 | 0.0942451 | ||||||||
\(456\) | 0.430057 | 0.0201393 | ||||||||
\(457\) | −29.4470 | −1.37747 | −0.688737 | − | 0.725011i | \(-0.741834\pi\) | ||||
−0.688737 | + | 0.725011i | \(0.741834\pi\) | |||||||
\(458\) | 10.2157 | 0.477350 | ||||||||
\(459\) | 3.67781 | 0.171665 | ||||||||
\(460\) | 7.31537 | 0.341081 | ||||||||
\(461\) | 18.4975 | 0.861515 | 0.430757 | − | 0.902468i | \(-0.358246\pi\) | ||||
0.430757 | + | 0.902468i | \(0.358246\pi\) | |||||||
\(462\) | −2.53792 | −0.118075 | ||||||||
\(463\) | −7.46549 | −0.346951 | −0.173475 | − | 0.984838i | \(-0.555500\pi\) | ||||
−0.173475 | + | 0.984838i | \(0.555500\pi\) | |||||||
\(464\) | −6.77745 | −0.314635 | ||||||||
\(465\) | 7.80273 | 0.361843 | ||||||||
\(466\) | 2.07576 | 0.0961579 | ||||||||
\(467\) | 33.3917 | 1.54519 | 0.772593 | − | 0.634902i | \(-0.218960\pi\) | ||||
0.772593 | + | 0.634902i | \(0.218960\pi\) | |||||||
\(468\) | 4.12492 | 0.190674 | ||||||||
\(469\) | −0.580177 | −0.0267901 | ||||||||
\(470\) | 3.52969 | 0.162813 | ||||||||
\(471\) | 11.8533 | 0.546171 | ||||||||
\(472\) | −0.974718 | −0.0448650 | ||||||||
\(473\) | −24.8786 | −1.14392 | ||||||||
\(474\) | 4.00000 | 0.183726 | ||||||||
\(475\) | 0.430057 | 0.0197324 | ||||||||
\(476\) | 1.79241 | 0.0821551 | ||||||||
\(477\) | −7.67781 | −0.351543 | ||||||||
\(478\) | −28.2683 | −1.29296 | ||||||||
\(479\) | 26.7051 | 1.22019 | 0.610094 | − | 0.792329i | \(-0.291132\pi\) | ||||
0.610094 | + | 0.792329i | \(0.291132\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | −4.12492 | −0.188080 | ||||||||
\(482\) | 20.4491 | 0.931432 | ||||||||
\(483\) | 3.56521 | 0.162223 | ||||||||
\(484\) | 16.1181 | 0.732641 | ||||||||
\(485\) | −7.16726 | −0.325448 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −1.61437 | −0.0731539 | −0.0365770 | − | 0.999331i | \(-0.511645\pi\) | ||||
−0.0365770 | + | 0.999331i | \(0.511645\pi\) | |||||||
\(488\) | −14.5229 | −0.657420 | ||||||||
\(489\) | 5.89354 | 0.266515 | ||||||||
\(490\) | −6.76248 | −0.305498 | ||||||||
\(491\) | 1.40477 | 0.0633966 | 0.0316983 | − | 0.999497i | \(-0.489908\pi\) | ||||
0.0316983 | + | 0.999497i | \(0.489908\pi\) | |||||||
\(492\) | −9.80273 | −0.441941 | ||||||||
\(493\) | −24.9262 | −1.12262 | ||||||||
\(494\) | 1.77395 | 0.0798138 | ||||||||
\(495\) | −5.20750 | −0.234060 | ||||||||
\(496\) | 7.80273 | 0.350353 | ||||||||
\(497\) | 4.18163 | 0.187572 | ||||||||
\(498\) | −16.5399 | −0.741172 | ||||||||
\(499\) | −9.98495 | −0.446988 | −0.223494 | − | 0.974705i | \(-0.571746\pi\) | ||||
−0.223494 | + | 0.974705i | \(0.571746\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 24.8362 | 1.10960 | ||||||||
\(502\) | −19.3092 | −0.861813 | ||||||||
\(503\) | −20.8300 | −0.928765 | −0.464382 | − | 0.885635i | \(-0.653724\pi\) | ||||
−0.464382 | + | 0.885635i | \(0.653724\pi\) | |||||||
\(504\) | 0.487359 | 0.0217087 | ||||||||
\(505\) | −13.7454 | −0.611663 | ||||||||
\(506\) | −38.0948 | −1.69352 | ||||||||
\(507\) | 4.01497 | 0.178311 | ||||||||
\(508\) | 15.5652 | 0.690595 | ||||||||
\(509\) | 26.5816 | 1.17821 | 0.589104 | − | 0.808057i | \(-0.299481\pi\) | ||||
0.589104 | + | 0.808057i | \(0.299481\pi\) | |||||||
\(510\) | 3.67781 | 0.162856 | ||||||||
\(511\) | −3.48471 | −0.154155 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0.430057 | 0.0189875 | ||||||||
\(514\) | 0.735194 | 0.0324280 | ||||||||
\(515\) | −3.52969 | −0.155537 | ||||||||
\(516\) | 4.77745 | 0.210315 | ||||||||
\(517\) | −18.3809 | −0.808391 | ||||||||
\(518\) | −0.487359 | −0.0214133 | ||||||||
\(519\) | −19.9276 | −0.874727 | ||||||||
\(520\) | 4.12492 | 0.180890 | ||||||||
\(521\) | −9.91733 | −0.434486 | −0.217243 | − | 0.976118i | \(-0.569706\pi\) | ||||
−0.217243 | + | 0.976118i | \(0.569706\pi\) | |||||||
\(522\) | −6.77745 | −0.296641 | ||||||||
\(523\) | 5.61910 | 0.245706 | 0.122853 | − | 0.992425i | \(-0.460796\pi\) | ||||
0.122853 | + | 0.992425i | \(0.460796\pi\) | |||||||
\(524\) | −17.5549 | −0.766889 | ||||||||
\(525\) | 0.487359 | 0.0212701 | ||||||||
\(526\) | 6.47231 | 0.282206 | ||||||||
\(527\) | 28.6970 | 1.25006 | ||||||||
\(528\) | −5.20750 | −0.226628 | ||||||||
\(529\) | 30.5146 | 1.32672 | ||||||||
\(530\) | −7.67781 | −0.333503 | ||||||||
\(531\) | −0.974718 | −0.0422991 | ||||||||
\(532\) | 0.209592 | 0.00908697 | ||||||||
\(533\) | −40.4355 | −1.75145 | ||||||||
\(534\) | 16.7051 | 0.722900 | ||||||||
\(535\) | 7.09964 | 0.306944 | ||||||||
\(536\) | −1.19045 | −0.0514196 | ||||||||
\(537\) | −4.33034 | −0.186868 | ||||||||
\(538\) | −0.810958 | −0.0349629 | ||||||||
\(539\) | 35.2156 | 1.51685 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | −0.315288 | −0.0135553 | −0.00677764 | − | 0.999977i | \(-0.502157\pi\) | ||||
−0.00677764 | + | 0.999977i | \(0.502157\pi\) | |||||||
\(542\) | 17.4403 | 0.749125 | ||||||||
\(543\) | −0.0505645 | −0.00216993 | ||||||||
\(544\) | 3.67781 | 0.157685 | ||||||||
\(545\) | 16.4321 | 0.703872 | ||||||||
\(546\) | 2.01032 | 0.0860336 | ||||||||
\(547\) | 22.1133 | 0.945496 | 0.472748 | − | 0.881198i | \(-0.343262\pi\) | ||||
0.472748 | + | 0.881198i | \(0.343262\pi\) | |||||||
\(548\) | −21.2498 | −0.907745 | ||||||||
\(549\) | −14.5229 | −0.619821 | ||||||||
\(550\) | −5.20750 | −0.222049 | ||||||||
\(551\) | −2.91469 | −0.124170 | ||||||||
\(552\) | 7.31537 | 0.311363 | ||||||||
\(553\) | 1.94944 | 0.0828984 | ||||||||
\(554\) | −1.46007 | −0.0620325 | ||||||||
\(555\) | −1.00000 | −0.0424476 | ||||||||
\(556\) | −15.4082 | −0.653453 | ||||||||
\(557\) | 24.9611 | 1.05763 | 0.528817 | − | 0.848736i | \(-0.322636\pi\) | ||||
0.528817 | + | 0.848736i | \(0.322636\pi\) | |||||||
\(558\) | 7.80273 | 0.330316 | ||||||||
\(559\) | 19.7066 | 0.833500 | ||||||||
\(560\) | 0.487359 | 0.0205947 | ||||||||
\(561\) | −19.1522 | −0.808607 | ||||||||
\(562\) | −12.1249 | −0.511459 | ||||||||
\(563\) | −29.0642 | −1.22491 | −0.612455 | − | 0.790505i | \(-0.709818\pi\) | ||||
−0.612455 | + | 0.790505i | \(0.709818\pi\) | |||||||
\(564\) | 3.52969 | 0.148627 | ||||||||
\(565\) | −1.22255 | −0.0514332 | ||||||||
\(566\) | 19.5652 | 0.822387 | ||||||||
\(567\) | 0.487359 | 0.0204671 | ||||||||
\(568\) | 8.58018 | 0.360016 | ||||||||
\(569\) | 34.5740 | 1.44942 | 0.724709 | − | 0.689055i | \(-0.241974\pi\) | ||||
0.724709 | + | 0.689055i | \(0.241974\pi\) | |||||||
\(570\) | 0.430057 | 0.0180131 | ||||||||
\(571\) | −40.4539 | −1.69294 | −0.846472 | − | 0.532433i | \(-0.821278\pi\) | ||||
−0.846472 | + | 0.532433i | \(0.821278\pi\) | |||||||
\(572\) | −21.4805 | −0.898146 | ||||||||
\(573\) | −4.37276 | −0.182674 | ||||||||
\(574\) | −4.77745 | −0.199407 | ||||||||
\(575\) | 7.31537 | 0.305072 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −15.5803 | −0.648615 | −0.324307 | − | 0.945952i | \(-0.605131\pi\) | ||||
−0.324307 | + | 0.945952i | \(0.605131\pi\) | |||||||
\(578\) | −3.47372 | −0.144488 | ||||||||
\(579\) | −2.47031 | −0.102662 | ||||||||
\(580\) | −6.77745 | −0.281418 | ||||||||
\(581\) | −8.06088 | −0.334422 | ||||||||
\(582\) | −7.16726 | −0.297092 | ||||||||
\(583\) | 39.9822 | 1.65589 | ||||||||
\(584\) | −7.15020 | −0.295877 | ||||||||
\(585\) | 4.12492 | 0.170544 | ||||||||
\(586\) | −17.5126 | −0.723441 | ||||||||
\(587\) | 25.6717 | 1.05958 | 0.529792 | − | 0.848128i | \(-0.322270\pi\) | ||||
0.529792 | + | 0.848128i | \(0.322270\pi\) | |||||||
\(588\) | −6.76248 | −0.278880 | ||||||||
\(589\) | 3.35562 | 0.138266 | ||||||||
\(590\) | −0.974718 | −0.0401285 | ||||||||
\(591\) | −13.3154 | −0.547721 | ||||||||
\(592\) | −1.00000 | −0.0410997 | ||||||||
\(593\) | 22.9399 | 0.942028 | 0.471014 | − | 0.882126i | \(-0.343888\pi\) | ||||
0.471014 | + | 0.882126i | \(0.343888\pi\) | |||||||
\(594\) | −5.20750 | −0.213666 | ||||||||
\(595\) | 1.79241 | 0.0734818 | ||||||||
\(596\) | −3.47913 | −0.142511 | ||||||||
\(597\) | 21.4403 | 0.877493 | ||||||||
\(598\) | 30.1753 | 1.23396 | ||||||||
\(599\) | −10.9583 | −0.447742 | −0.223871 | − | 0.974619i | \(-0.571869\pi\) | ||||
−0.223871 | + | 0.974619i | \(0.571869\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | 38.0123 | 1.55055 | 0.775277 | − | 0.631621i | \(-0.217610\pi\) | ||||
0.775277 | + | 0.631621i | \(0.217610\pi\) | |||||||
\(602\) | 2.32833 | 0.0948957 | ||||||||
\(603\) | −1.19045 | −0.0484789 | ||||||||
\(604\) | −17.7304 | −0.721439 | ||||||||
\(605\) | 16.1181 | 0.655294 | ||||||||
\(606\) | −13.7454 | −0.558370 | ||||||||
\(607\) | −5.16509 | −0.209644 | −0.104822 | − | 0.994491i | \(-0.533427\pi\) | ||||
−0.104822 | + | 0.994491i | \(0.533427\pi\) | |||||||
\(608\) | 0.430057 | 0.0174411 | ||||||||
\(609\) | −3.30305 | −0.133846 | ||||||||
\(610\) | −14.5229 | −0.588014 | ||||||||
\(611\) | 14.5597 | 0.589023 | ||||||||
\(612\) | 3.67781 | 0.148667 | ||||||||
\(613\) | 35.6075 | 1.43817 | 0.719086 | − | 0.694921i | \(-0.244561\pi\) | ||||
0.719086 | + | 0.694921i | \(0.244561\pi\) | |||||||
\(614\) | −0.364444 | −0.0147078 | ||||||||
\(615\) | −9.80273 | −0.395284 | ||||||||
\(616\) | −2.53792 | −0.102256 | ||||||||
\(617\) | 32.0799 | 1.29149 | 0.645745 | − | 0.763553i | \(-0.276547\pi\) | ||||
0.645745 | + | 0.763553i | \(0.276547\pi\) | |||||||
\(618\) | −3.52969 | −0.141985 | ||||||||
\(619\) | 24.6628 | 0.991283 | 0.495642 | − | 0.868527i | \(-0.334933\pi\) | ||||
0.495642 | + | 0.868527i | \(0.334933\pi\) | |||||||
\(620\) | 7.80273 | 0.313365 | ||||||||
\(621\) | 7.31537 | 0.293556 | ||||||||
\(622\) | −15.1583 | −0.607794 | ||||||||
\(623\) | 8.14138 | 0.326177 | ||||||||
\(624\) | 4.12492 | 0.165129 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −14.7201 | −0.588335 | ||||||||
\(627\) | −2.23952 | −0.0894380 | ||||||||
\(628\) | 11.8533 | 0.472998 | ||||||||
\(629\) | −3.67781 | −0.146644 | ||||||||
\(630\) | 0.487359 | 0.0194168 | ||||||||
\(631\) | 8.89205 | 0.353987 | 0.176993 | − | 0.984212i | \(-0.443363\pi\) | ||||
0.176993 | + | 0.984212i | \(0.443363\pi\) | |||||||
\(632\) | 4.00000 | 0.159111 | ||||||||
\(633\) | 13.9679 | 0.555174 | ||||||||
\(634\) | −0.942615 | −0.0374360 | ||||||||
\(635\) | 15.5652 | 0.617687 | ||||||||
\(636\) | −7.67781 | −0.304445 | ||||||||
\(637\) | −27.8947 | −1.10523 | ||||||||
\(638\) | 35.2936 | 1.39729 | ||||||||
\(639\) | 8.58018 | 0.339427 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 41.5775 | 1.64221 | 0.821107 | − | 0.570774i | \(-0.193357\pi\) | ||||
0.821107 | + | 0.570774i | \(0.193357\pi\) | |||||||
\(642\) | 7.09964 | 0.280200 | ||||||||
\(643\) | 43.1522 | 1.70176 | 0.850878 | − | 0.525363i | \(-0.176070\pi\) | ||||
0.850878 | + | 0.525363i | \(0.176070\pi\) | |||||||
\(644\) | 3.56521 | 0.140489 | ||||||||
\(645\) | 4.77745 | 0.188112 | ||||||||
\(646\) | 1.58167 | 0.0622299 | ||||||||
\(647\) | −15.4641 | −0.607956 | −0.303978 | − | 0.952679i | \(-0.598315\pi\) | ||||
−0.303978 | + | 0.952679i | \(0.598315\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 5.07585 | 0.199244 | ||||||||
\(650\) | 4.12492 | 0.161793 | ||||||||
\(651\) | 3.80273 | 0.149041 | ||||||||
\(652\) | 5.89354 | 0.230809 | ||||||||
\(653\) | 17.3556 | 0.679178 | 0.339589 | − | 0.940574i | \(-0.389712\pi\) | ||||
0.339589 | + | 0.940574i | \(0.389712\pi\) | |||||||
\(654\) | 16.4321 | 0.642544 | ||||||||
\(655\) | −17.5549 | −0.685926 | ||||||||
\(656\) | −9.80273 | −0.382732 | ||||||||
\(657\) | −7.15020 | −0.278956 | ||||||||
\(658\) | 1.72023 | 0.0670615 | ||||||||
\(659\) | −15.3509 | −0.597986 | −0.298993 | − | 0.954255i | \(-0.596651\pi\) | ||||
−0.298993 | + | 0.954255i | \(0.596651\pi\) | |||||||
\(660\) | −5.20750 | −0.202702 | ||||||||
\(661\) | −23.8218 | −0.926560 | −0.463280 | − | 0.886212i | \(-0.653328\pi\) | ||||
−0.463280 | + | 0.886212i | \(0.653328\pi\) | |||||||
\(662\) | 15.8600 | 0.616418 | ||||||||
\(663\) | 15.1707 | 0.589180 | ||||||||
\(664\) | −16.5399 | −0.641874 | ||||||||
\(665\) | 0.209592 | 0.00812763 | ||||||||
\(666\) | −1.00000 | −0.0387492 | ||||||||
\(667\) | −49.5795 | −1.91973 | ||||||||
\(668\) | 24.8362 | 0.960940 | ||||||||
\(669\) | −22.4335 | −0.867328 | ||||||||
\(670\) | −1.19045 | −0.0459911 | ||||||||
\(671\) | 75.6279 | 2.91958 | ||||||||
\(672\) | 0.487359 | 0.0188003 | ||||||||
\(673\) | −37.3523 | −1.43983 | −0.719913 | − | 0.694065i | \(-0.755818\pi\) | ||||
−0.719913 | + | 0.694065i | \(0.755818\pi\) | |||||||
\(674\) | 16.9549 | 0.653080 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 4.01497 | 0.154422 | ||||||||
\(677\) | 40.0143 | 1.53788 | 0.768938 | − | 0.639324i | \(-0.220786\pi\) | ||||
0.768938 | + | 0.639324i | \(0.220786\pi\) | |||||||
\(678\) | −1.22255 | −0.0469519 | ||||||||
\(679\) | −3.49303 | −0.134050 | ||||||||
\(680\) | 3.67781 | 0.141038 | ||||||||
\(681\) | 23.8368 | 0.913430 | ||||||||
\(682\) | −40.6327 | −1.55591 | ||||||||
\(683\) | 7.25948 | 0.277776 | 0.138888 | − | 0.990308i | \(-0.455647\pi\) | ||||
0.138888 | + | 0.990308i | \(0.455647\pi\) | |||||||
\(684\) | 0.430057 | 0.0164436 | ||||||||
\(685\) | −21.2498 | −0.811911 | ||||||||
\(686\) | −6.70727 | −0.256085 | ||||||||
\(687\) | 10.2157 | 0.389755 | ||||||||
\(688\) | 4.77745 | 0.182138 | ||||||||
\(689\) | −31.6703 | −1.20654 | ||||||||
\(690\) | 7.31537 | 0.278491 | ||||||||
\(691\) | 7.91733 | 0.301190 | 0.150595 | − | 0.988596i | \(-0.451881\pi\) | ||||
0.150595 | + | 0.988596i | \(0.451881\pi\) | |||||||
\(692\) | −19.9276 | −0.757536 | ||||||||
\(693\) | −2.53792 | −0.0964077 | ||||||||
\(694\) | −5.44029 | −0.206511 | ||||||||
\(695\) | −15.4082 | −0.584466 | ||||||||
\(696\) | −6.77745 | −0.256898 | ||||||||
\(697\) | −36.0526 | −1.36559 | ||||||||
\(698\) | 23.1262 | 0.875341 | ||||||||
\(699\) | 2.07576 | 0.0785126 | ||||||||
\(700\) | 0.487359 | 0.0184204 | ||||||||
\(701\) | −39.1303 | −1.47793 | −0.738965 | − | 0.673744i | \(-0.764685\pi\) | ||||
−0.738965 | + | 0.673744i | \(0.764685\pi\) | |||||||
\(702\) | 4.12492 | 0.155685 | ||||||||
\(703\) | −0.430057 | −0.0162199 | ||||||||
\(704\) | −5.20750 | −0.196265 | ||||||||
\(705\) | 3.52969 | 0.132936 | ||||||||
\(706\) | 24.7638 | 0.931998 | ||||||||
\(707\) | −6.69896 | −0.251940 | ||||||||
\(708\) | −0.974718 | −0.0366321 | ||||||||
\(709\) | −40.6478 | −1.52656 | −0.763280 | − | 0.646068i | \(-0.776412\pi\) | ||||
−0.763280 | + | 0.646068i | \(0.776412\pi\) | |||||||
\(710\) | 8.58018 | 0.322008 | ||||||||
\(711\) | 4.00000 | 0.150012 | ||||||||
\(712\) | 16.7051 | 0.626050 | ||||||||
\(713\) | 57.0799 | 2.13766 | ||||||||
\(714\) | 1.79241 | 0.0670794 | ||||||||
\(715\) | −21.4805 | −0.803327 | ||||||||
\(716\) | −4.33034 | −0.161832 | ||||||||
\(717\) | −28.2683 | −1.05570 | ||||||||
\(718\) | −17.5549 | −0.655143 | ||||||||
\(719\) | −34.9147 | −1.30210 | −0.651049 | − | 0.759036i | \(-0.725671\pi\) | ||||
−0.651049 | + | 0.759036i | \(0.725671\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | −1.72023 | −0.0640646 | ||||||||
\(722\) | −18.8151 | −0.700224 | ||||||||
\(723\) | 20.4491 | 0.760511 | ||||||||
\(724\) | −0.0505645 | −0.00187922 | ||||||||
\(725\) | −6.77745 | −0.251708 | ||||||||
\(726\) | 16.1181 | 0.598199 | ||||||||
\(727\) | −16.1741 | −0.599863 | −0.299932 | − | 0.953961i | \(-0.596964\pi\) | ||||
−0.299932 | + | 0.953961i | \(0.596964\pi\) | |||||||
\(728\) | 2.01032 | 0.0745073 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −7.15020 | −0.264641 | ||||||||
\(731\) | 17.5705 | 0.649870 | ||||||||
\(732\) | −14.5229 | −0.536781 | ||||||||
\(733\) | 50.0895 | 1.85010 | 0.925049 | − | 0.379848i | \(-0.124024\pi\) | ||||
0.925049 | + | 0.379848i | \(0.124024\pi\) | |||||||
\(734\) | −8.17331 | −0.301683 | ||||||||
\(735\) | −6.76248 | −0.249438 | ||||||||
\(736\) | 7.31537 | 0.269648 | ||||||||
\(737\) | 6.19928 | 0.228353 | ||||||||
\(738\) | −9.80273 | −0.360843 | ||||||||
\(739\) | −4.01846 | −0.147822 | −0.0739108 | − | 0.997265i | \(-0.523548\pi\) | ||||
−0.0739108 | + | 0.997265i | \(0.523548\pi\) | |||||||
\(740\) | −1.00000 | −0.0367607 | ||||||||
\(741\) | 1.77395 | 0.0651677 | ||||||||
\(742\) | −3.74185 | −0.137368 | ||||||||
\(743\) | −14.4382 | −0.529686 | −0.264843 | − | 0.964292i | \(-0.585320\pi\) | ||||
−0.264843 | + | 0.964292i | \(0.585320\pi\) | |||||||
\(744\) | 7.80273 | 0.286062 | ||||||||
\(745\) | −3.47913 | −0.127465 | ||||||||
\(746\) | −6.00000 | −0.219676 | ||||||||
\(747\) | −16.5399 | −0.605164 | ||||||||
\(748\) | −19.1522 | −0.700274 | ||||||||
\(749\) | 3.46007 | 0.126428 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | 25.0088 | 0.912585 | 0.456292 | − | 0.889830i | \(-0.349177\pi\) | ||||
0.456292 | + | 0.889830i | \(0.349177\pi\) | |||||||
\(752\) | 3.52969 | 0.128715 | ||||||||
\(753\) | −19.3092 | −0.703667 | ||||||||
\(754\) | −27.9564 | −1.01811 | ||||||||
\(755\) | −17.7304 | −0.645275 | ||||||||
\(756\) | 0.487359 | 0.0177251 | ||||||||
\(757\) | −16.4049 | −0.596245 | −0.298122 | − | 0.954528i | \(-0.596360\pi\) | ||||
−0.298122 | + | 0.954528i | \(0.596360\pi\) | |||||||
\(758\) | 26.1993 | 0.951601 | ||||||||
\(759\) | −38.0948 | −1.38275 | ||||||||
\(760\) | 0.430057 | 0.0155998 | ||||||||
\(761\) | 19.3877 | 0.702804 | 0.351402 | − | 0.936225i | \(-0.385705\pi\) | ||||
0.351402 | + | 0.936225i | \(0.385705\pi\) | |||||||
\(762\) | 15.5652 | 0.563868 | ||||||||
\(763\) | 8.00831 | 0.289920 | ||||||||
\(764\) | −4.37276 | −0.158201 | ||||||||
\(765\) | 3.67781 | 0.132971 | ||||||||
\(766\) | −5.87508 | −0.212275 | ||||||||
\(767\) | −4.02063 | −0.145177 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 14.1693 | 0.510960 | 0.255480 | − | 0.966814i | \(-0.417767\pi\) | ||||
0.255480 | + | 0.966814i | \(0.417767\pi\) | |||||||
\(770\) | −2.53792 | −0.0914604 | ||||||||
\(771\) | 0.735194 | 0.0264774 | ||||||||
\(772\) | −2.47031 | −0.0889082 | ||||||||
\(773\) | −9.58367 | −0.344701 | −0.172350 | − | 0.985036i | \(-0.555136\pi\) | ||||
−0.172350 | + | 0.985036i | \(0.555136\pi\) | |||||||
\(774\) | 4.77745 | 0.171722 | ||||||||
\(775\) | 7.80273 | 0.280282 | ||||||||
\(776\) | −7.16726 | −0.257289 | ||||||||
\(777\) | −0.487359 | −0.0174839 | ||||||||
\(778\) | 33.8368 | 1.21311 | ||||||||
\(779\) | −4.21573 | −0.151044 | ||||||||
\(780\) | 4.12492 | 0.147696 | ||||||||
\(781\) | −44.6813 | −1.59882 | ||||||||
\(782\) | 26.9045 | 0.962104 | ||||||||
\(783\) | −6.77745 | −0.242206 | ||||||||
\(784\) | −6.76248 | −0.241517 | ||||||||
\(785\) | 11.8533 | 0.423062 | ||||||||
\(786\) | −17.5549 | −0.626162 | ||||||||
\(787\) | 2.47921 | 0.0883744 | 0.0441872 | − | 0.999023i | \(-0.485930\pi\) | ||||
0.0441872 | + | 0.999023i | \(0.485930\pi\) | |||||||
\(788\) | −13.3154 | −0.474340 | ||||||||
\(789\) | 6.47231 | 0.230420 | ||||||||
\(790\) | 4.00000 | 0.142314 | ||||||||
\(791\) | −0.595822 | −0.0211850 | ||||||||
\(792\) | −5.20750 | −0.185041 | ||||||||
\(793\) | −59.9057 | −2.12731 | ||||||||
\(794\) | −1.75016 | −0.0621108 | ||||||||
\(795\) | −7.67781 | −0.272304 | ||||||||
\(796\) | 21.4403 | 0.759931 | ||||||||
\(797\) | −47.0961 | −1.66823 | −0.834116 | − | 0.551590i | \(-0.814021\pi\) | ||||
−0.834116 | + | 0.551590i | \(0.814021\pi\) | |||||||
\(798\) | 0.209592 | 0.00741948 | ||||||||
\(799\) | 12.9815 | 0.459254 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 16.7051 | 0.590246 | ||||||||
\(802\) | 24.7051 | 0.872367 | ||||||||
\(803\) | 37.2347 | 1.31398 | ||||||||
\(804\) | −1.19045 | −0.0419840 | ||||||||
\(805\) | 3.56521 | 0.125657 | ||||||||
\(806\) | 32.1856 | 1.13369 | ||||||||
\(807\) | −0.810958 | −0.0285471 | ||||||||
\(808\) | −13.7454 | −0.483562 | ||||||||
\(809\) | 36.6409 | 1.28823 | 0.644113 | − | 0.764931i | \(-0.277227\pi\) | ||||
0.644113 | + | 0.764931i | \(0.277227\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | 12.4997 | 0.438923 | 0.219462 | − | 0.975621i | \(-0.429570\pi\) | ||||
0.219462 | + | 0.975621i | \(0.429570\pi\) | |||||||
\(812\) | −3.30305 | −0.115914 | ||||||||
\(813\) | 17.4403 | 0.611658 | ||||||||
\(814\) | 5.20750 | 0.182523 | ||||||||
\(815\) | 5.89354 | 0.206442 | ||||||||
\(816\) | 3.67781 | 0.128749 | ||||||||
\(817\) | 2.05457 | 0.0718805 | ||||||||
\(818\) | 6.75899 | 0.236322 | ||||||||
\(819\) | 2.01032 | 0.0702461 | ||||||||
\(820\) | −9.80273 | −0.342326 | ||||||||
\(821\) | −11.7351 | −0.409558 | −0.204779 | − | 0.978808i | \(-0.565648\pi\) | ||||
−0.204779 | + | 0.978808i | \(0.565648\pi\) | |||||||
\(822\) | −21.2498 | −0.741170 | ||||||||
\(823\) | 40.5058 | 1.41194 | 0.705972 | − | 0.708240i | \(-0.250510\pi\) | ||||
0.705972 | + | 0.708240i | \(0.250510\pi\) | |||||||
\(824\) | −3.52969 | −0.122963 | ||||||||
\(825\) | −5.20750 | −0.181302 | ||||||||
\(826\) | −0.475037 | −0.0165287 | ||||||||
\(827\) | −6.51115 | −0.226415 | −0.113207 | − | 0.993571i | \(-0.536112\pi\) | ||||
−0.113207 | + | 0.993571i | \(0.536112\pi\) | |||||||
\(828\) | 7.31537 | 0.254227 | ||||||||
\(829\) | 11.0422 | 0.383510 | 0.191755 | − | 0.981443i | \(-0.438582\pi\) | ||||
0.191755 | + | 0.981443i | \(0.438582\pi\) | |||||||
\(830\) | −16.5399 | −0.574109 | ||||||||
\(831\) | −1.46007 | −0.0506493 | ||||||||
\(832\) | 4.12492 | 0.143006 | ||||||||
\(833\) | −24.8711 | −0.861733 | ||||||||
\(834\) | −15.4082 | −0.533542 | ||||||||
\(835\) | 24.8362 | 0.859491 | ||||||||
\(836\) | −2.23952 | −0.0774555 | ||||||||
\(837\) | 7.80273 | 0.269702 | ||||||||
\(838\) | 12.2143 | 0.421937 | ||||||||
\(839\) | 3.12641 | 0.107936 | 0.0539679 | − | 0.998543i | \(-0.482813\pi\) | ||||
0.0539679 | + | 0.998543i | \(0.482813\pi\) | |||||||
\(840\) | 0.487359 | 0.0168155 | ||||||||
\(841\) | 16.9338 | 0.583924 | ||||||||
\(842\) | −8.91942 | −0.307384 | ||||||||
\(843\) | −12.1249 | −0.417604 | ||||||||
\(844\) | 13.9679 | 0.480795 | ||||||||
\(845\) | 4.01497 | 0.138119 | ||||||||
\(846\) | 3.52969 | 0.121353 | ||||||||
\(847\) | 7.85530 | 0.269911 | ||||||||
\(848\) | −7.67781 | −0.263657 | ||||||||
\(849\) | 19.5652 | 0.671476 | ||||||||
\(850\) | 3.67781 | 0.126148 | ||||||||
\(851\) | −7.31537 | −0.250768 | ||||||||
\(852\) | 8.58018 | 0.293952 | ||||||||
\(853\) | −8.98503 | −0.307642 | −0.153821 | − | 0.988099i | \(-0.549158\pi\) | ||||
−0.153821 | + | 0.988099i | \(0.549158\pi\) | |||||||
\(854\) | −7.07785 | −0.242199 | ||||||||
\(855\) | 0.430057 | 0.0147076 | ||||||||
\(856\) | 7.09964 | 0.242661 | ||||||||
\(857\) | 5.59314 | 0.191058 | 0.0955290 | − | 0.995427i | \(-0.469546\pi\) | ||||
0.0955290 | + | 0.995427i | \(0.469546\pi\) | |||||||
\(858\) | −21.4805 | −0.733334 | ||||||||
\(859\) | −18.8110 | −0.641822 | −0.320911 | − | 0.947109i | \(-0.603989\pi\) | ||||
−0.320911 | + | 0.947109i | \(0.603989\pi\) | |||||||
\(860\) | 4.77745 | 0.162910 | ||||||||
\(861\) | −4.77745 | −0.162815 | ||||||||
\(862\) | 4.98704 | 0.169859 | ||||||||
\(863\) | −29.8116 | −1.01480 | −0.507400 | − | 0.861711i | \(-0.669393\pi\) | ||||
−0.507400 | + | 0.861711i | \(0.669393\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −19.9276 | −0.677560 | ||||||||
\(866\) | 15.4805 | 0.526050 | ||||||||
\(867\) | −3.47372 | −0.117974 | ||||||||
\(868\) | 3.80273 | 0.129073 | ||||||||
\(869\) | −20.8300 | −0.706610 | ||||||||
\(870\) | −6.77745 | −0.229777 | ||||||||
\(871\) | −4.91051 | −0.166386 | ||||||||
\(872\) | 16.4321 | 0.556460 | ||||||||
\(873\) | −7.16726 | −0.242575 | ||||||||
\(874\) | 3.14603 | 0.106416 | ||||||||
\(875\) | 0.487359 | 0.0164757 | ||||||||
\(876\) | −7.15020 | −0.241583 | ||||||||
\(877\) | −9.96806 | −0.336598 | −0.168299 | − | 0.985736i | \(-0.553827\pi\) | ||||
−0.168299 | + | 0.985736i | \(0.553827\pi\) | |||||||
\(878\) | −21.4929 | −0.725349 | ||||||||
\(879\) | −17.5126 | −0.590687 | ||||||||
\(880\) | −5.20750 | −0.175545 | ||||||||
\(881\) | 27.7387 | 0.934540 | 0.467270 | − | 0.884115i | \(-0.345238\pi\) | ||||
0.467270 | + | 0.884115i | \(0.345238\pi\) | |||||||
\(882\) | −6.76248 | −0.227705 | ||||||||
\(883\) | 7.79659 | 0.262376 | 0.131188 | − | 0.991358i | \(-0.458121\pi\) | ||||
0.131188 | + | 0.991358i | \(0.458121\pi\) | |||||||
\(884\) | 15.1707 | 0.510245 | ||||||||
\(885\) | −0.974718 | −0.0327648 | ||||||||
\(886\) | −32.4355 | −1.08969 | ||||||||
\(887\) | 19.1536 | 0.643115 | 0.321558 | − | 0.946890i | \(-0.395794\pi\) | ||||
0.321558 | + | 0.946890i | \(0.395794\pi\) | |||||||
\(888\) | −1.00000 | −0.0335578 | ||||||||
\(889\) | 7.58584 | 0.254421 | ||||||||
\(890\) | 16.7051 | 0.559956 | ||||||||
\(891\) | −5.20750 | −0.174458 | ||||||||
\(892\) | −22.4335 | −0.751128 | ||||||||
\(893\) | 1.51797 | 0.0507969 | ||||||||
\(894\) | −3.47913 | −0.116360 | ||||||||
\(895\) | −4.33034 | −0.144747 | ||||||||
\(896\) | 0.487359 | 0.0162815 | ||||||||
\(897\) | 30.1753 | 1.00752 | ||||||||
\(898\) | 15.8348 | 0.528415 | ||||||||
\(899\) | −52.8826 | −1.76373 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −28.2375 | −0.940728 | ||||||||
\(902\) | 51.0478 | 1.69970 | ||||||||
\(903\) | 2.32833 | 0.0774820 | ||||||||
\(904\) | −1.22255 | −0.0406615 | ||||||||
\(905\) | −0.0505645 | −0.00168082 | ||||||||
\(906\) | −17.7304 | −0.589052 | ||||||||
\(907\) | 1.34530 | 0.0446700 | 0.0223350 | − | 0.999751i | \(-0.492890\pi\) | ||||
0.0223350 | + | 0.999751i | \(0.492890\pi\) | |||||||
\(908\) | 23.8368 | 0.791053 | ||||||||
\(909\) | −13.7454 | −0.455907 | ||||||||
\(910\) | 2.01032 | 0.0666413 | ||||||||
\(911\) | 2.95826 | 0.0980116 | 0.0490058 | − | 0.998798i | \(-0.484395\pi\) | ||||
0.0490058 | + | 0.998798i | \(0.484395\pi\) | |||||||
\(912\) | 0.430057 | 0.0142406 | ||||||||
\(913\) | 86.1317 | 2.85054 | ||||||||
\(914\) | −29.4470 | −0.974021 | ||||||||
\(915\) | −14.5229 | −0.480111 | ||||||||
\(916\) | 10.2157 | 0.337537 | ||||||||
\(917\) | −8.55553 | −0.282529 | ||||||||
\(918\) | 3.67781 | 0.121386 | ||||||||
\(919\) | 16.0504 | 0.529454 | 0.264727 | − | 0.964323i | \(-0.414718\pi\) | ||||
0.264727 | + | 0.964323i | \(0.414718\pi\) | |||||||
\(920\) | 7.31537 | 0.241181 | ||||||||
\(921\) | −0.364444 | −0.0120088 | ||||||||
\(922\) | 18.4975 | 0.609183 | ||||||||
\(923\) | 35.3925 | 1.16496 | ||||||||
\(924\) | −2.53792 | −0.0834915 | ||||||||
\(925\) | −1.00000 | −0.0328798 | ||||||||
\(926\) | −7.46549 | −0.245331 | ||||||||
\(927\) | −3.52969 | −0.115930 | ||||||||
\(928\) | −6.77745 | −0.222481 | ||||||||
\(929\) | −2.20009 | −0.0721825 | −0.0360913 | − | 0.999348i | \(-0.511491\pi\) | ||||
−0.0360913 | + | 0.999348i | \(0.511491\pi\) | |||||||
\(930\) | 7.80273 | 0.255862 | ||||||||
\(931\) | −2.90825 | −0.0953141 | ||||||||
\(932\) | 2.07576 | 0.0679939 | ||||||||
\(933\) | −15.1583 | −0.496262 | ||||||||
\(934\) | 33.3917 | 1.09261 | ||||||||
\(935\) | −19.1522 | −0.626344 | ||||||||
\(936\) | 4.12492 | 0.134827 | ||||||||
\(937\) | −15.9030 | −0.519530 | −0.259765 | − | 0.965672i | \(-0.583645\pi\) | ||||
−0.259765 | + | 0.965672i | \(0.583645\pi\) | |||||||
\(938\) | −0.580177 | −0.0189434 | ||||||||
\(939\) | −14.7201 | −0.480374 | ||||||||
\(940\) | 3.52969 | 0.115126 | ||||||||
\(941\) | 50.0021 | 1.63002 | 0.815011 | − | 0.579446i | \(-0.196731\pi\) | ||||
0.815011 | + | 0.579446i | \(0.196731\pi\) | |||||||
\(942\) | 11.8533 | 0.386201 | ||||||||
\(943\) | −71.7106 | −2.33522 | ||||||||
\(944\) | −0.974718 | −0.0317244 | ||||||||
\(945\) | 0.487359 | 0.0158538 | ||||||||
\(946\) | −24.8786 | −0.808872 | ||||||||
\(947\) | 8.11677 | 0.263760 | 0.131880 | − | 0.991266i | \(-0.457899\pi\) | ||||
0.131880 | + | 0.991266i | \(0.457899\pi\) | |||||||
\(948\) | 4.00000 | 0.129914 | ||||||||
\(949\) | −29.4940 | −0.957416 | ||||||||
\(950\) | 0.430057 | 0.0139529 | ||||||||
\(951\) | −0.942615 | −0.0305664 | ||||||||
\(952\) | 1.79241 | 0.0580924 | ||||||||
\(953\) | −34.2451 | −1.10931 | −0.554654 | − | 0.832081i | \(-0.687149\pi\) | ||||
−0.554654 | + | 0.832081i | \(0.687149\pi\) | |||||||
\(954\) | −7.67781 | −0.248578 | ||||||||
\(955\) | −4.37276 | −0.141499 | ||||||||
\(956\) | −28.2683 | −0.914262 | ||||||||
\(957\) | 35.2936 | 1.14088 | ||||||||
\(958\) | 26.7051 | 0.862803 | ||||||||
\(959\) | −10.3563 | −0.334421 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | 29.8826 | 0.963954 | ||||||||
\(962\) | −4.12492 | −0.132993 | ||||||||
\(963\) | 7.09964 | 0.228783 | ||||||||
\(964\) | 20.4491 | 0.658622 | ||||||||
\(965\) | −2.47031 | −0.0795219 | ||||||||
\(966\) | 3.56521 | 0.114709 | ||||||||
\(967\) | −7.49960 | −0.241171 | −0.120585 | − | 0.992703i | \(-0.538477\pi\) | ||||
−0.120585 | + | 0.992703i | \(0.538477\pi\) | |||||||
\(968\) | 16.1181 | 0.518055 | ||||||||
\(969\) | 1.58167 | 0.0508105 | ||||||||
\(970\) | −7.16726 | −0.230127 | ||||||||
\(971\) | 55.6327 | 1.78534 | 0.892669 | − | 0.450714i | \(-0.148830\pi\) | ||||
0.892669 | + | 0.450714i | \(0.148830\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −7.50932 | −0.240738 | ||||||||
\(974\) | −1.61437 | −0.0517277 | ||||||||
\(975\) | 4.12492 | 0.132103 | ||||||||
\(976\) | −14.5229 | −0.464866 | ||||||||
\(977\) | 33.1685 | 1.06115 | 0.530577 | − | 0.847637i | \(-0.321975\pi\) | ||||
0.530577 | + | 0.847637i | \(0.321975\pi\) | |||||||
\(978\) | 5.89354 | 0.188455 | ||||||||
\(979\) | −86.9919 | −2.78027 | ||||||||
\(980\) | −6.76248 | −0.216020 | ||||||||
\(981\) | 16.4321 | 0.524635 | ||||||||
\(982\) | 1.40477 | 0.0448282 | ||||||||
\(983\) | 55.2178 | 1.76117 | 0.880587 | − | 0.473884i | \(-0.157148\pi\) | ||||
0.880587 | + | 0.473884i | \(0.157148\pi\) | |||||||
\(984\) | −9.80273 | −0.312500 | ||||||||
\(985\) | −13.3154 | −0.424263 | ||||||||
\(986\) | −24.9262 | −0.793811 | ||||||||
\(987\) | 1.72023 | 0.0547555 | ||||||||
\(988\) | 1.77395 | 0.0564369 | ||||||||
\(989\) | 34.9488 | 1.11131 | ||||||||
\(990\) | −5.20750 | −0.165505 | ||||||||
\(991\) | −36.7815 | −1.16840 | −0.584201 | − | 0.811609i | \(-0.698592\pi\) | ||||
−0.584201 | + | 0.811609i | \(0.698592\pi\) | |||||||
\(992\) | 7.80273 | 0.247737 | ||||||||
\(993\) | 15.8600 | 0.503303 | ||||||||
\(994\) | 4.18163 | 0.132633 | ||||||||
\(995\) | 21.4403 | 0.679703 | ||||||||
\(996\) | −16.5399 | −0.524088 | ||||||||
\(997\) | −42.5058 | −1.34617 | −0.673086 | − | 0.739564i | \(-0.735032\pi\) | ||||
−0.673086 | + | 0.739564i | \(0.735032\pi\) | |||||||
\(998\) | −9.98495 | −0.316068 | ||||||||
\(999\) | −1.00000 | −0.0316386 |
(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 | 1110.2.a.s.1.2 | ✓ | 4 | |
3.2 | odd | 2 | 3330.2.a.bj.1.2 | 4 | |||
4.3 | odd | 2 | 8880.2.a.cg.1.3 | 4 | |||
5.4 | even | 2 | 5550.2.a.cj.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.a.s.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
3330.2.a.bj.1.2 | 4 | 3.2 | odd | 2 | |||
5550.2.a.cj.1.3 | 4 | 5.4 | even | 2 | |||
8880.2.a.cg.1.3 | 4 | 4.3 | odd | 2 |