Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [162,7,Mod(161,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("162.161");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(37.2687615464\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.3 | ||
Root | \(1.93185i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 162.161 |
Dual form | 162.7.b.a.161.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).
\(n\) | \(83\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.65685i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −32.0000 | −0.500000 | ||||||||
\(5\) | − 208.528i | − 1.66823i | −0.551592 | − | 0.834114i | \(-0.685980\pi\) | ||||
0.551592 | − | 0.834114i | \(-0.314020\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.19615 | 0.0122337 | 0.00611684 | − | 0.999981i | \(-0.498053\pi\) | ||||
0.00611684 | + | 0.999981i | \(0.498053\pi\) | |||||||
\(8\) | − 181.019i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1179.62 | 1.17962 | ||||||||
\(11\) | 2261.95i | 1.69944i | 0.527235 | + | 0.849719i | \(0.323229\pi\) | ||||
−0.527235 | + | 0.849719i | \(0.676771\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2840.01 | 1.29268 | 0.646338 | − | 0.763052i | \(-0.276300\pi\) | ||||
0.646338 | + | 0.763052i | \(0.276300\pi\) | |||||||
\(14\) | 23.7370i | 0.00865052i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1024.00 | 0.250000 | ||||||||
\(17\) | − 1965.86i | − 0.400134i | −0.979782 | − | 0.200067i | \(-0.935884\pi\) | ||||
0.979782 | − | 0.200067i | \(-0.0641160\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −281.295 | −0.0410111 | −0.0205056 | − | 0.999790i | \(-0.506528\pi\) | ||||
−0.0205056 | + | 0.999790i | \(0.506528\pi\) | |||||||
\(20\) | 6672.91i | 0.834114i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −12795.5 | −1.20168 | ||||||||
\(23\) | − 16744.3i | − 1.37620i | −0.725614 | − | 0.688102i | \(-0.758444\pi\) | ||||
0.725614 | − | 0.688102i | \(-0.241556\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −27859.1 | −1.78298 | ||||||||
\(26\) | 16065.5i | 0.914059i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −134.277 | −0.00611684 | ||||||||
\(29\) | − 37114.1i | − 1.52176i | −0.648895 | − | 0.760878i | \(-0.724769\pi\) | ||||
0.648895 | − | 0.760878i | \(-0.275231\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −24708.3 | −0.829389 | −0.414694 | − | 0.909961i | \(-0.636112\pi\) | ||||
−0.414694 | + | 0.909961i | \(0.636112\pi\) | |||||||
\(32\) | 5792.62i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 11120.6 | 0.282937 | ||||||||
\(35\) | − 875.017i | − 0.0204086i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −17016.7 | −0.335947 | −0.167974 | − | 0.985791i | \(-0.553722\pi\) | ||||
−0.167974 | + | 0.985791i | \(0.553722\pi\) | |||||||
\(38\) | − 1591.25i | − 0.0289993i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −37747.7 | −0.589808 | ||||||||
\(41\) | − 116236.i | − 1.68651i | −0.537516 | − | 0.843253i | \(-0.680637\pi\) | ||||
0.537516 | − | 0.843253i | \(-0.319363\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −30662.9 | −0.385662 | −0.192831 | − | 0.981232i | \(-0.561767\pi\) | ||||
−0.192831 | + | 0.981232i | \(0.561767\pi\) | |||||||
\(44\) | − 72382.5i | − 0.849719i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 94720.0 | 0.973124 | ||||||||
\(47\) | 77666.6i | 0.748068i | 0.927415 | + | 0.374034i | \(0.122026\pi\) | ||||
−0.927415 | + | 0.374034i | \(0.877974\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −117631. | −0.999850 | ||||||||
\(50\) | − 157595.i | − 1.26076i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −90880.2 | −0.646338 | ||||||||
\(53\) | − 138657.i | − 0.931354i | −0.884955 | − | 0.465677i | \(-0.845811\pi\) | ||||
0.884955 | − | 0.465677i | \(-0.154189\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 471682. | 2.83505 | ||||||||
\(56\) | − 759.585i | − 0.00432526i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 209949. | 1.07604 | ||||||||
\(59\) | 152958.i | 0.744758i | 0.928081 | + | 0.372379i | \(0.121458\pi\) | ||||
−0.928081 | + | 0.372379i | \(0.878542\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −16138.1 | −0.0710989 | −0.0355495 | − | 0.999368i | \(-0.511318\pi\) | ||||
−0.0355495 | + | 0.999368i | \(0.511318\pi\) | |||||||
\(62\) | − 139771.i | − 0.586467i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −32768.0 | −0.125000 | ||||||||
\(65\) | − 592222.i | − 2.15648i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −474667. | −1.57821 | −0.789105 | − | 0.614259i | \(-0.789455\pi\) | ||||
−0.789105 | + | 0.614259i | \(0.789455\pi\) | |||||||
\(68\) | 62907.4i | 0.200067i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4949.85 | 0.0144310 | ||||||||
\(71\) | 150338.i | 0.420043i | 0.977697 | + | 0.210021i | \(0.0673534\pi\) | ||||
−0.977697 | + | 0.210021i | \(0.932647\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 331690. | 0.852636 | 0.426318 | − | 0.904573i | \(-0.359811\pi\) | ||||
0.426318 | + | 0.904573i | \(0.359811\pi\) | |||||||
\(74\) | − 96261.2i | − 0.237551i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9001.45 | 0.0205056 | ||||||||
\(77\) | 9491.50i | 0.0207904i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −896112. | −1.81753 | −0.908764 | − | 0.417310i | \(-0.862973\pi\) | ||||
−0.908764 | + | 0.417310i | \(0.862973\pi\) | |||||||
\(80\) | − 213533.i | − 0.417057i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 657529. | 1.19254 | ||||||||
\(83\) | − 945090.i | − 1.65287i | −0.563032 | − | 0.826435i | \(-0.690365\pi\) | ||||
0.563032 | − | 0.826435i | \(-0.309635\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −409937. | −0.667514 | ||||||||
\(86\) | − 173455.i | − 0.272704i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 409457. | 0.600842 | ||||||||
\(89\) | − 790302.i | − 1.12105i | −0.828139 | − | 0.560523i | \(-0.810600\pi\) | ||||
0.828139 | − | 0.560523i | \(-0.189400\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11917.1 | 0.0158142 | ||||||||
\(92\) | 535817.i | 0.688102i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −439349. | −0.528964 | ||||||||
\(95\) | 58658.1i | 0.0684159i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.39268e6 | 1.52593 | 0.762965 | − | 0.646440i | \(-0.223743\pi\) | ||||
0.762965 | + | 0.646440i | \(0.223743\pi\) | |||||||
\(98\) | − 665424.i | − 0.707001i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 891492. | 0.891492 | ||||||||
\(101\) | − 131552.i | − 0.127683i | −0.997960 | − | 0.0638414i | \(-0.979665\pi\) | ||||
0.997960 | − | 0.0638414i | \(-0.0203352\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.93461e6 | 1.77044 | 0.885221 | − | 0.465171i | \(-0.154007\pi\) | ||||
0.885221 | + | 0.465171i | \(0.154007\pi\) | |||||||
\(104\) | − 514096.i | − 0.457030i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 784364. | 0.658567 | ||||||||
\(107\) | 621916.i | 0.507669i | 0.967248 | + | 0.253834i | \(0.0816918\pi\) | ||||
−0.967248 | + | 0.253834i | \(0.918308\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.34578e6 | −1.03919 | −0.519594 | − | 0.854413i | \(-0.673917\pi\) | ||||
−0.519594 | + | 0.854413i | \(0.673917\pi\) | |||||||
\(110\) | 2.66823e6i | 2.00468i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4296.86 | 0.00305842 | ||||||||
\(113\) | − 1.23932e6i | − 0.858914i | −0.903087 | − | 0.429457i | \(-0.858705\pi\) | ||||
0.903087 | − | 0.429457i | \(-0.141295\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.49166e6 | −2.29582 | ||||||||
\(116\) | 1.18765e6i | 0.760878i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −865259. | −0.526623 | ||||||||
\(119\) | − 8249.04i | − 0.00489511i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.34487e6 | −1.88809 | ||||||||
\(122\) | − 91290.9i | − 0.0502745i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 790666. | 0.414694 | ||||||||
\(125\) | 2.55116e6i | 1.30620i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.65297e6 | −0.806962 | −0.403481 | − | 0.914988i | \(-0.632200\pi\) | ||||
−0.403481 | + | 0.914988i | \(0.632200\pi\) | |||||||
\(128\) | − 185364.i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.35012e6 | 1.52486 | ||||||||
\(131\) | 2.66126e6i | 1.18379i | 0.806017 | + | 0.591893i | \(0.201619\pi\) | ||||
−0.806017 | + | 0.591893i | \(0.798381\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1180.36 | −0.000501717 0 | ||||||||
\(134\) | − 2.68512e6i | − 1.11596i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −355858. | −0.141469 | ||||||||
\(137\) | − 2.61015e6i | − 1.01509i | −0.861626 | − | 0.507544i | \(-0.830553\pi\) | ||||
0.861626 | − | 0.507544i | \(-0.169447\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −701321. | −0.261139 | −0.130570 | − | 0.991439i | \(-0.541681\pi\) | ||||
−0.130570 | + | 0.991439i | \(0.541681\pi\) | |||||||
\(140\) | 28000.6i | 0.0102043i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −850440. | −0.297015 | ||||||||
\(143\) | 6.42396e6i | 2.19682i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.73935e6 | −2.53864 | ||||||||
\(146\) | 1.87632e6i | 0.602904i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 544536. | 0.167974 | ||||||||
\(149\) | 4.73344e6i | 1.43093i | 0.698650 | + | 0.715464i | \(0.253785\pi\) | ||||
−0.698650 | + | 0.715464i | \(0.746215\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.73729e6 | 1.08549 | 0.542746 | − | 0.839897i | \(-0.317385\pi\) | ||||
0.542746 | + | 0.839897i | \(0.317385\pi\) | |||||||
\(152\) | 50919.9i | 0.0144996i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −53692.0 | −0.0147010 | ||||||||
\(155\) | 5.15239e6i | 1.38361i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.20662e6 | 0.828607 | 0.414303 | − | 0.910139i | \(-0.364025\pi\) | ||||
0.414303 | + | 0.910139i | \(0.364025\pi\) | |||||||
\(158\) | − 5.06918e6i | − 1.28519i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.20793e6 | 0.294904 | ||||||||
\(161\) | − 70261.6i | − 0.0168361i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −964418. | −0.222691 | −0.111345 | − | 0.993782i | \(-0.535516\pi\) | ||||
−0.111345 | + | 0.993782i | \(0.535516\pi\) | |||||||
\(164\) | 3.71954e6i | 0.843253i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.34624e6 | 1.16876 | ||||||||
\(167\) | 1.03499e6i | 0.222222i | 0.993808 | + | 0.111111i | \(0.0354410\pi\) | ||||
−0.993808 | + | 0.111111i | \(0.964559\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.23883e6 | 0.671009 | ||||||||
\(170\) | − 2.31896e6i | − 0.472004i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 981212. | 0.192831 | ||||||||
\(173\) | − 648596.i | − 0.125267i | −0.998037 | − | 0.0626334i | \(-0.980050\pi\) | ||||
0.998037 | − | 0.0626334i | \(-0.0199499\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −116901. | −0.0218125 | ||||||||
\(176\) | 2.31624e6i | 0.424860i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.47063e6 | 0.792699 | ||||||||
\(179\) | − 4.65189e6i | − 0.811092i | −0.914075 | − | 0.405546i | \(-0.867081\pi\) | ||||
0.914075 | − | 0.405546i | \(-0.132919\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.43720e6 | 0.579654 | 0.289827 | − | 0.957079i | \(-0.406402\pi\) | ||||
0.289827 | + | 0.957079i | \(0.406402\pi\) | |||||||
\(182\) | 67413.3i | 0.0111823i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.03104e6 | −0.486562 | ||||||||
\(185\) | 3.54847e6i | 0.560437i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.44668e6 | 0.680003 | ||||||||
\(188\) | − 2.48533e6i | − 0.374034i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −331820. | −0.0483774 | ||||||||
\(191\) | − 1.17509e7i | − 1.68644i | −0.537565 | − | 0.843222i | \(-0.680656\pi\) | ||||
0.537565 | − | 0.843222i | \(-0.319344\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.95599e6 | 0.967581 | 0.483790 | − | 0.875184i | \(-0.339260\pi\) | ||||
0.483790 | + | 0.875184i | \(0.339260\pi\) | |||||||
\(194\) | 7.87816e6i | 1.07900i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.76420e6 | 0.499925 | ||||||||
\(197\) | − 409645.i | − 0.0535807i | −0.999641 | − | 0.0267904i | \(-0.991471\pi\) | ||||
0.999641 | − | 0.0267904i | \(-0.00852866\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.24847e6 | −0.412212 | −0.206106 | − | 0.978530i | \(-0.566079\pi\) | ||||
−0.206106 | + | 0.978530i | \(0.566079\pi\) | |||||||
\(200\) | 5.04304e6i | 0.630380i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 744169. | 0.0902854 | ||||||||
\(203\) | − 155736.i | − 0.0186167i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.42385e7 | −2.81348 | ||||||||
\(206\) | 1.09438e7i | 1.25189i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.90817e6 | 0.323169 | ||||||||
\(209\) | − 636277.i | − 0.0696959i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.99487e6 | −0.531712 | −0.265856 | − | 0.964013i | \(-0.585655\pi\) | ||||
−0.265856 | + | 0.964013i | \(0.585655\pi\) | |||||||
\(212\) | 4.43703e6i | 0.465677i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.51809e6 | −0.358976 | ||||||||
\(215\) | 6.39408e6i | 0.643373i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −103680. | −0.0101465 | ||||||||
\(218\) | − 7.61287e6i | − 0.734817i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.50938e7 | −1.41753 | ||||||||
\(221\) | − 5.58305e6i | − 0.517243i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.68924e6 | 0.513027 | 0.256513 | − | 0.966541i | \(-0.417426\pi\) | ||||
0.256513 | + | 0.966541i | \(0.417426\pi\) | |||||||
\(224\) | 24306.7i | 0.00216263i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.01068e6 | 0.607344 | ||||||||
\(227\) | − 1.16064e7i | − 0.992246i | −0.868252 | − | 0.496123i | \(-0.834757\pi\) | ||||
0.868252 | − | 0.496123i | \(-0.165243\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.45690e6 | −0.287859 | −0.143930 | − | 0.989588i | \(-0.545974\pi\) | ||||
−0.143930 | + | 0.989588i | \(0.545974\pi\) | |||||||
\(230\) | − 1.97518e7i | − 1.62339i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.71837e6 | −0.538022 | ||||||||
\(233\) | − 1.27739e7i | − 1.00985i | −0.863164 | − | 0.504924i | \(-0.831520\pi\) | ||||
0.863164 | − | 0.504924i | \(-0.168480\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.61957e7 | 1.24795 | ||||||||
\(236\) | − 4.89464e6i | − 0.372379i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 46663.6 | 0.00346137 | ||||||||
\(239\) | − 1.29231e7i | − 0.946617i | −0.880897 | − | 0.473309i | \(-0.843060\pi\) | ||||
0.880897 | − | 0.473309i | \(-0.156940\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.28032e6 | 0.520115 | 0.260057 | − | 0.965593i | \(-0.416259\pi\) | ||||
0.260057 | + | 0.965593i | \(0.416259\pi\) | |||||||
\(242\) | − 1.89214e7i | − 1.33508i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 516419. | 0.0355495 | ||||||||
\(245\) | 2.45295e7i | 1.66798i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −798881. | −0.0530141 | ||||||||
\(248\) | 4.47268e6i | 0.293233i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.44316e7 | −0.923620 | ||||||||
\(251\) | − 1.71927e7i | − 1.08723i | −0.839334 | − | 0.543616i | \(-0.817055\pi\) | ||||
0.839334 | − | 0.543616i | \(-0.182945\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.78748e7 | 2.33878 | ||||||||
\(254\) | − 9.35059e6i | − 0.570608i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.04858e6 | 0.0625000 | ||||||||
\(257\) | − 8.01111e6i | − 0.471947i | −0.971759 | − | 0.235974i | \(-0.924172\pi\) | ||||
0.971759 | − | 0.235974i | \(-0.0758279\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −71404.8 | −0.00410987 | ||||||||
\(260\) | 1.89511e7i | 1.07824i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.50543e7 | −0.837062 | ||||||||
\(263\) | 1.68209e7i | 0.924661i | 0.886708 | + | 0.462331i | \(0.152987\pi\) | ||||
−0.886708 | + | 0.462331i | \(0.847013\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.89140e7 | −1.55371 | ||||||||
\(266\) | − 6677.11i | 0 0.000354768i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.51893e7 | 0.789105 | ||||||||
\(269\) | − 3.33514e6i | − 0.171339i | −0.996324 | − | 0.0856697i | \(-0.972697\pi\) | ||||
0.996324 | − | 0.0856697i | \(-0.0273030\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.47048e7 | −0.738840 | −0.369420 | − | 0.929263i | \(-0.620444\pi\) | ||||
−0.369420 | + | 0.929263i | \(0.620444\pi\) | |||||||
\(272\) | − 2.01304e6i | − 0.100033i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.47652e7 | 0.717776 | ||||||||
\(275\) | − 6.30160e7i | − 3.03007i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.09201e7 | −0.513790 | −0.256895 | − | 0.966439i | \(-0.582699\pi\) | ||||
−0.256895 | + | 0.966439i | \(0.582699\pi\) | |||||||
\(278\) | − 3.96727e6i | − 0.184653i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −158395. | −0.00721552 | ||||||||
\(281\) | 1.86747e7i | 0.841654i | 0.907141 | + | 0.420827i | \(0.138260\pi\) | ||||
−0.907141 | + | 0.420827i | \(0.861740\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.46255e7 | −0.645284 | −0.322642 | − | 0.946521i | \(-0.604571\pi\) | ||||
−0.322642 | + | 0.946521i | \(0.604571\pi\) | |||||||
\(284\) | − 4.81081e6i | − 0.210021i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.63394e7 | −1.55339 | ||||||||
\(287\) | − 487743.i | − 0.0206322i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.02730e7 | 0.839893 | ||||||||
\(290\) | − 4.37804e7i | − 1.79509i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.06141e7 | −0.426318 | ||||||||
\(293\) | 4.78429e7i | 1.90202i | 0.309162 | + | 0.951010i | \(0.399952\pi\) | ||||
−0.309162 | + | 0.951010i | \(0.600048\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.18960e7 | 1.24243 | ||||||||
\(296\) | 3.08036e6i | 0.118775i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.67764e7 | −1.01182 | ||||||||
\(299\) | − 4.75539e7i | − 1.77899i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −128666. | −0.00471807 | ||||||||
\(302\) | 2.11413e7i | 0.767558i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −288046. | −0.0102528 | ||||||||
\(305\) | 3.36525e6i | 0.118609i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.24782e7 | 1.46808 | 0.734042 | − | 0.679104i | \(-0.237631\pi\) | ||||
0.734042 | + | 0.679104i | \(0.237631\pi\) | |||||||
\(308\) | − 303728.i | − 0.0103952i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.91463e7 | −0.978360 | ||||||||
\(311\) | 3.09996e7i | 1.03056i | 0.857021 | + | 0.515282i | \(0.172313\pi\) | ||||
−0.857021 | + | 0.515282i | \(0.827687\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.97828e7 | −0.971254 | −0.485627 | − | 0.874166i | \(-0.661409\pi\) | ||||
−0.485627 | + | 0.874166i | \(0.661409\pi\) | |||||||
\(314\) | 1.81394e7i | 0.585913i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.86756e7 | 0.908764 | ||||||||
\(317\) | − 2.17911e6i | − 0.0684072i | −0.999415 | − | 0.0342036i | \(-0.989111\pi\) | ||||
0.999415 | − | 0.0342036i | \(-0.0108895\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.39504e7 | 2.58613 | ||||||||
\(320\) | 6.83306e6i | 0.208528i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 397459. | 0.0119049 | ||||||||
\(323\) | 552987.i | 0.0164099i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.91201e7 | −2.30482 | ||||||||
\(326\) | − 5.45557e6i | − 0.157466i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.10409e7 | −0.596270 | ||||||||
\(329\) | 325901.i | 0.00915162i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.33671e7 | 0.368598 | 0.184299 | − | 0.982870i | \(-0.440999\pi\) | ||||
0.184299 | + | 0.982870i | \(0.440999\pi\) | |||||||
\(332\) | 3.02429e7i | 0.826435i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.85480e6 | −0.157135 | ||||||||
\(335\) | 9.89816e7i | 2.63281i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.45488e7 | 1.16398 | 0.581991 | − | 0.813195i | \(-0.302274\pi\) | ||||
0.581991 | + | 0.813195i | \(0.302274\pi\) | |||||||
\(338\) | 1.83216e7i | 0.474475i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.31180e7 | 0.333757 | ||||||||
\(341\) | − 5.58891e7i | − 1.40950i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −987272. | −0.0244655 | ||||||||
\(344\) | 5.55057e6i | 0.136352i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.66902e6 | 0.0885771 | ||||||||
\(347\) | 2.08986e7i | 0.500182i | 0.968222 | + | 0.250091i | \(0.0804605\pi\) | ||||
−0.968222 | + | 0.250091i | \(0.919540\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.45154e7 | 1.51770 | 0.758852 | − | 0.651263i | \(-0.225761\pi\) | ||||
0.758852 | + | 0.651263i | \(0.225761\pi\) | |||||||
\(350\) | − 661293.i | − 0.0154237i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.31026e7 | −0.300421 | ||||||||
\(353\) | 4.20921e6i | 0.0956923i | 0.998855 | + | 0.0478461i | \(0.0152357\pi\) | ||||
−0.998855 | + | 0.0478461i | \(0.984764\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.13497e7 | 0.700727 | ||||||||
\(356\) | 2.52897e7i | 0.560523i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.63151e7 | 0.573529 | ||||||||
\(359\) | 5.61320e7i | 1.21319i | 0.795012 | + | 0.606593i | \(0.207464\pi\) | ||||
−0.795012 | + | 0.606593i | \(0.792536\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.69668e7 | −0.998318 | ||||||||
\(362\) | 1.94437e7i | 0.409877i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −381347. | −0.00790709 | ||||||||
\(365\) | − 6.91668e7i | − 1.42239i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.35103e7 | 0.677922 | 0.338961 | − | 0.940800i | \(-0.389925\pi\) | ||||
0.338961 | + | 0.940800i | \(0.389925\pi\) | |||||||
\(368\) | − 1.71461e7i | − 0.344051i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.00732e7 | −0.396289 | ||||||||
\(371\) | − 581827.i | − 0.0113939i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.22777e7 | 0.429283 | 0.214642 | − | 0.976693i | \(-0.431142\pi\) | ||||
0.214642 | + | 0.976693i | \(0.431142\pi\) | |||||||
\(374\) | 2.51542e7i | 0.480835i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.40592e7 | 0.264482 | ||||||||
\(377\) | − 1.05404e8i | − 1.96714i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.72205e7 | 1.41845 | 0.709226 | − | 0.704981i | \(-0.249044\pi\) | ||||
0.709226 | + | 0.704981i | \(0.249044\pi\) | |||||||
\(380\) | − 1.87706e6i | − 0.0342080i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.64733e7 | 1.19250 | ||||||||
\(383\) | 3.32594e7i | 0.591996i | 0.955189 | + | 0.295998i | \(0.0956521\pi\) | ||||
−0.955189 | + | 0.295998i | \(0.904348\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.97925e6 | 0.0346831 | ||||||||
\(386\) | 3.93490e7i | 0.684183i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.45656e7 | −0.762965 | ||||||||
\(389\) | 1.50959e7i | 0.256454i | 0.991745 | + | 0.128227i | \(0.0409286\pi\) | ||||
−0.991745 | + | 0.128227i | \(0.959071\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.29169e7 | −0.550666 | ||||||||
\(392\) | 2.12936e7i | 0.353500i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.31730e6 | 0.0378873 | ||||||||
\(395\) | 1.86865e8i | 3.03205i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.91350e7 | −1.42455 | −0.712273 | − | 0.701902i | \(-0.752334\pi\) | ||||
−0.712273 | + | 0.701902i | \(0.752334\pi\) | |||||||
\(398\) | − 1.83761e7i | − 0.291478i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.85277e7 | −0.445746 | ||||||||
\(401\) | 1.12043e8i | 1.73761i | 0.495158 | + | 0.868803i | \(0.335110\pi\) | ||||
−0.495158 | + | 0.868803i | \(0.664890\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.01718e7 | −1.07213 | ||||||||
\(404\) | 4.20966e6i | 0.0638414i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 880978. | 0.0131640 | ||||||||
\(407\) | − 3.84911e7i | − 0.570922i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.67941e7 | −0.976266 | −0.488133 | − | 0.872769i | \(-0.662322\pi\) | ||||
−0.488133 | + | 0.872769i | \(0.662322\pi\) | |||||||
\(410\) | − 1.37113e8i | − 1.98943i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.19075e7 | −0.885221 | ||||||||
\(413\) | 641833.i | 0.00911113i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.97078e8 | −2.75736 | ||||||||
\(416\) | 1.64511e7i | 0.228515i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.59933e6 | 0.0492824 | ||||||||
\(419\) | − 4.73571e7i | − 0.643789i | −0.946776 | − | 0.321894i | \(-0.895680\pi\) | ||||
0.946776 | − | 0.321894i | \(-0.104320\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.61569e7 | 0.886602 | 0.443301 | − | 0.896373i | \(-0.353807\pi\) | ||||
0.443301 | + | 0.896373i | \(0.353807\pi\) | |||||||
\(422\) | − 2.82552e7i | − 0.375977i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.50996e7 | −0.329283 | ||||||||
\(425\) | 5.47671e7i | 0.713432i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −67717.9 | −0.000869801 0 | ||||||||
\(428\) | − 1.99013e7i | − 0.253834i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.61704e7 | −0.454933 | ||||||||
\(431\) | 9.06666e7i | 1.13244i | 0.824254 | + | 0.566221i | \(0.191595\pi\) | ||||
−0.824254 | + | 0.566221i | \(0.808405\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −699414. | −0.00861530 | −0.00430765 | − | 0.999991i | \(-0.501371\pi\) | ||||
−0.00430765 | + | 0.999991i | \(0.501371\pi\) | |||||||
\(434\) | − 586502.i | − 0.00717464i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.30649e7 | 0.519594 | ||||||||
\(437\) | 4.71009e6i | 0.0564397i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.57296e7 | −0.304116 | −0.152058 | − | 0.988372i | \(-0.548590\pi\) | ||||
−0.152058 | + | 0.988372i | \(0.548590\pi\) | |||||||
\(440\) | − 8.53835e7i | − 1.00234i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.15825e7 | 0.365746 | ||||||||
\(443\) | − 165578.i | − 0.00190455i | −1.00000 | 0.000952273i | \(-0.999697\pi\) | |||||
1.00000 | 0.000952273i | \(-0.000303118\pi\) | ||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.64801e8 | −1.87016 | ||||||||
\(446\) | 3.21832e7i | 0.362765i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −137500. | −0.00152921 | ||||||||
\(449\) | 4.30456e7i | 0.475542i | 0.971321 | + | 0.237771i | \(0.0764169\pi\) | ||||
−0.971321 | + | 0.237771i | \(0.923583\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.62920e8 | 2.86611 | ||||||||
\(452\) | 3.96584e7i | 0.429457i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.56556e7 | 0.701624 | ||||||||
\(455\) | − 2.48506e6i | − 0.0263816i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.35491e8 | −1.41959 | −0.709793 | − | 0.704411i | \(-0.751211\pi\) | ||||
−0.709793 | + | 0.704411i | \(0.751211\pi\) | |||||||
\(458\) | − 1.95552e7i | − 0.203547i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.11733e8 | 1.14791 | ||||||||
\(461\) | − 3.20349e7i | − 0.326980i | −0.986545 | − | 0.163490i | \(-0.947725\pi\) | ||||
0.986545 | − | 0.163490i | \(-0.0522751\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.29333e8 | 1.30306 | 0.651532 | − | 0.758621i | \(-0.274127\pi\) | ||||
0.651532 | + | 0.758621i | \(0.274127\pi\) | |||||||
\(464\) | − 3.80048e7i | − 0.380439i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.22602e7 | 0.714071 | ||||||||
\(467\) | − 8.49294e7i | − 0.833887i | −0.908932 | − | 0.416944i | \(-0.863101\pi\) | ||||
0.908932 | − | 0.416944i | \(-0.136899\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.99178e6 | −0.0193073 | ||||||||
\(470\) | 9.16168e7i | 0.882432i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.76883e7 | 0.263312 | ||||||||
\(473\) | − 6.93579e7i | − 0.655410i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.83664e6 | 0.0731222 | ||||||||
\(476\) | 263969.i | 0.00244755i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.31043e7 | 0.669360 | ||||||||
\(479\) | − 1.15719e8i | − 1.05292i | −0.850199 | − | 0.526461i | \(-0.823518\pi\) | ||||
0.850199 | − | 0.526461i | \(-0.176482\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.83277e7 | −0.434271 | ||||||||
\(482\) | 4.11837e7i | 0.367777i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.07036e8 | 0.944046 | ||||||||
\(485\) | − 2.90412e8i | − 2.54560i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.52839e7 | 0.392064 | 0.196032 | − | 0.980597i | \(-0.437194\pi\) | ||||
0.196032 | + | 0.980597i | \(0.437194\pi\) | |||||||
\(488\) | 2.92131e6i | 0.0251373i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.38760e8 | −1.17944 | ||||||||
\(491\) | − 2.04312e8i | − 1.72603i | −0.505175 | − | 0.863017i | \(-0.668572\pi\) | ||||
0.505175 | − | 0.863017i | \(-0.331428\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.29611e7 | −0.608906 | ||||||||
\(494\) | − 4.51915e6i | − 0.0374866i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.53013e7 | −0.207347 | ||||||||
\(497\) | 630841.i | 0.00513867i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.92990e7 | −0.235804 | −0.117902 | − | 0.993025i | \(-0.537617\pi\) | ||||
−0.117902 | + | 0.993025i | \(0.537617\pi\) | |||||||
\(500\) | − 8.16373e7i | − 0.653098i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.72564e7 | 0.768789 | ||||||||
\(503\) | 1.64834e8i | 1.29522i | 0.761973 | + | 0.647609i | \(0.224231\pi\) | ||||
−0.761973 | + | 0.647609i | \(0.775769\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.74323e7 | −0.213004 | ||||||||
\(506\) | 2.14252e8i | 1.65376i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.28949e7 | 0.403481 | ||||||||
\(509\) | 1.67339e8i | 1.26895i | 0.772944 | + | 0.634474i | \(0.218783\pi\) | ||||
−0.772944 | + | 0.634474i | \(0.781217\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.39182e6 | 0.0104309 | ||||||||
\(512\) | 5.93164e6i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.53177e7 | 0.333717 | ||||||||
\(515\) | − 4.03421e8i | − 2.95350i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.75678e8 | −1.27130 | ||||||||
\(518\) | − 403927.i | − 0.00290612i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.07204e8 | −0.762430 | ||||||||
\(521\) | 6.01419e7i | 0.425270i | 0.977132 | + | 0.212635i | \(0.0682045\pi\) | ||||
−0.977132 | + | 0.212635i | \(0.931796\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.09251e8 | 0.763698 | 0.381849 | − | 0.924225i | \(-0.375287\pi\) | ||||
0.381849 | + | 0.924225i | \(0.375287\pi\) | |||||||
\(524\) | − 8.51602e7i | − 0.591893i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.51535e7 | −0.653834 | ||||||||
\(527\) | 4.85731e7i | 0.331867i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.32335e8 | −0.893940 | ||||||||
\(530\) | − 1.63562e8i | − 1.09864i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 37771.5 | 0.000250859 0 | ||||||||
\(533\) | − 3.30110e8i | − 2.18011i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.29687e8 | 0.846907 | ||||||||
\(536\) | 8.59239e7i | 0.557981i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.88664e7 | 0.121155 | ||||||||
\(539\) | − 2.66077e8i | − 1.69918i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.52159e7 | 0.285561 | 0.142781 | − | 0.989754i | \(-0.454396\pi\) | ||||
0.142781 | + | 0.989754i | \(0.454396\pi\) | |||||||
\(542\) | − 8.31827e7i | − 0.522439i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.13875e7 | 0.0707343 | ||||||||
\(545\) | 2.80633e8i | 1.73360i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.11451e7 | 0.312494 | 0.156247 | − | 0.987718i | \(-0.450060\pi\) | ||||
0.156247 | + | 0.987718i | \(0.450060\pi\) | |||||||
\(548\) | 8.35248e7i | 0.507544i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.56473e8 | 2.14258 | ||||||||
\(551\) | 1.04400e7i | 0.0624089i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.76022e6 | −0.0222351 | ||||||||
\(554\) | − 6.17732e7i | − 0.363304i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.24423e7 | 0.130570 | ||||||||
\(557\) | 2.43306e7i | 0.140795i | 0.997519 | + | 0.0703974i | \(0.0224267\pi\) | ||||
−0.997519 | + | 0.0703974i | \(0.977573\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.70827e7 | −0.498536 | ||||||||
\(560\) | − 896018.i | − 0.00510214i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.05640e8 | −0.595139 | ||||||||
\(563\) | − 1.44398e8i | − 0.809166i | −0.914501 | − | 0.404583i | \(-0.867417\pi\) | ||||
0.914501 | − | 0.404583i | \(-0.132583\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.58434e8 | −1.43286 | ||||||||
\(566\) | − 8.27342e7i | − 0.456284i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.72141e7 | 0.148508 | ||||||||
\(569\) | 8.31553e7i | 0.451391i | 0.974198 | + | 0.225696i | \(0.0724655\pi\) | ||||
−0.974198 | + | 0.225696i | \(0.927534\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.26080e8 | −1.21438 | −0.607188 | − | 0.794558i | \(-0.707703\pi\) | ||||
−0.607188 | + | 0.794558i | \(0.707703\pi\) | |||||||
\(572\) | − 2.05567e8i | − 1.09841i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.75909e6 | 0.0145892 | ||||||||
\(575\) | 4.66481e8i | 2.45375i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.11006e7 | 0.213954 | 0.106977 | − | 0.994261i | \(-0.465883\pi\) | ||||
0.106977 | + | 0.994261i | \(0.465883\pi\) | |||||||
\(578\) | 1.14681e8i | 0.593894i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.47659e8 | 1.26932 | ||||||||
\(581\) | − 3.96574e6i | − 0.0202207i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.13636e8 | 1.58278 | ||||||||
\(584\) | − 6.00423e7i | − 0.301452i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.70640e8 | −1.34493 | ||||||||
\(587\) | 1.14693e8i | 0.567052i | 0.958965 | + | 0.283526i | \(0.0915042\pi\) | ||||
−0.958965 | + | 0.283526i | \(0.908496\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.95034e6 | 0.0340142 | ||||||||
\(590\) | 1.80431e8i | 0.878528i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.74251e7 | −0.0839868 | ||||||||
\(593\) | − 2.90487e8i | − 1.39304i | −0.717539 | − | 0.696518i | \(-0.754731\pi\) | ||||
0.717539 | − | 0.696518i | \(-0.245269\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.72016e6 | −0.00816616 | ||||||||
\(596\) | − 1.51470e8i | − 0.715464i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.69005e8 | 1.25793 | ||||||||
\(599\) | − 3.57152e8i | − 1.66178i | −0.556439 | − | 0.830888i | \(-0.687833\pi\) | ||||
0.556439 | − | 0.830888i | \(-0.312167\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.40094e7 | −0.386994 | −0.193497 | − | 0.981101i | \(-0.561983\pi\) | ||||
−0.193497 | + | 0.981101i | \(0.561983\pi\) | |||||||
\(602\) | − 727845.i | − 0.00333618i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.19593e8 | −0.542746 | ||||||||
\(605\) | 6.97500e8i | 3.14977i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.16287e7 | 0.230847 | 0.115424 | − | 0.993316i | \(-0.463177\pi\) | ||||
0.115424 | + | 0.993316i | \(0.463177\pi\) | |||||||
\(608\) | − 1.62944e6i | − 0.00724981i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.90368e7 | −0.0838694 | ||||||||
\(611\) | 2.20574e8i | 0.967009i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.44326e7 | 0.192895 | 0.0964473 | − | 0.995338i | \(-0.469252\pi\) | ||||
0.0964473 | + | 0.995338i | \(0.469252\pi\) | |||||||
\(614\) | 2.40293e8i | 1.03809i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.71814e6 | 0.00735051 | ||||||||
\(617\) | 1.65408e8i | 0.704208i | 0.935961 | + | 0.352104i | \(0.114534\pi\) | ||||
−0.935961 | + | 0.352104i | \(0.885466\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.68162e8 | 1.13064 | 0.565320 | − | 0.824871i | \(-0.308753\pi\) | ||||
0.565320 | + | 0.824871i | \(0.308753\pi\) | |||||||
\(620\) | − 1.64876e8i | − 0.691805i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.75360e8 | −0.728718 | ||||||||
\(623\) | − 3.31623e6i | − 0.0137145i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.66915e7 | 0.396049 | ||||||||
\(626\) | − 1.68477e8i | − 0.686780i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.02612e8 | −0.414303 | ||||||||
\(629\) | 3.34525e7i | 0.134424i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.13998e8 | 0.453741 | 0.226871 | − | 0.973925i | \(-0.427151\pi\) | ||||
0.226871 | + | 0.973925i | \(0.427151\pi\) | |||||||
\(632\) | 1.62214e8i | 0.642593i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.23269e7 | 0.0483712 | ||||||||
\(635\) | 3.44691e8i | 1.34620i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.34074e8 | −1.29248 | ||||||||
\(638\) | 4.74895e8i | 1.82867i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.86536e7 | −0.147452 | ||||||||
\(641\) | − 3.65639e7i | − 0.138828i | −0.997588 | − | 0.0694142i | \(-0.977887\pi\) | ||||
0.997588 | − | 0.0694142i | \(-0.0221130\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.82268e8 | −1.06177 | −0.530883 | − | 0.847445i | \(-0.678140\pi\) | ||||
−0.530883 | + | 0.847445i | \(0.678140\pi\) | |||||||
\(644\) | 2.24837e6i | 0.00841803i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.12817e6 | −0.0116036 | ||||||||
\(647\) | − 1.45187e8i | − 0.536062i | −0.963410 | − | 0.268031i | \(-0.913627\pi\) | ||||
0.963410 | − | 0.268031i | \(-0.0863729\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.45983e8 | −1.26567 | ||||||||
\(650\) | − 4.47571e8i | − 1.62975i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.08614e7 | 0.111345 | ||||||||
\(653\) | − 9.91905e7i | − 0.356230i | −0.984010 | − | 0.178115i | \(-0.943000\pi\) | ||||
0.984010 | − | 0.178115i | \(-0.0569999\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.54948e8 | 1.97482 | ||||||||
\(656\) | − 1.19025e8i | − 0.421627i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.84357e6 | −0.00647117 | ||||||||
\(659\) | − 1.69578e8i | − 0.592535i | −0.955105 | − | 0.296268i | \(-0.904258\pi\) | ||||
0.955105 | − | 0.296268i | \(-0.0957420\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.38050e8 | 1.86302 | 0.931511 | − | 0.363713i | \(-0.118491\pi\) | ||||
0.931511 | + | 0.363713i | \(0.118491\pi\) | |||||||
\(662\) | 7.56157e7i | 0.260638i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.71080e8 | −0.584378 | ||||||||
\(665\) | 246138.i | 0 0.000836978i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.21449e8 | −2.09425 | ||||||||
\(668\) | − 3.31198e7i | − 0.111111i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.59924e8 | −1.86168 | ||||||||
\(671\) | − 3.65036e7i | − 0.120828i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.85365e7 | −0.126423 | −0.0632116 | − | 0.998000i | \(-0.520134\pi\) | ||||
−0.0632116 | + | 0.998000i | \(0.520134\pi\) | |||||||
\(674\) | 2.52006e8i | 0.823060i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.03643e8 | −0.335504 | ||||||||
\(677\) | 1.90802e8i | 0.614916i | 0.951562 | + | 0.307458i | \(0.0994784\pi\) | ||||
−0.951562 | + | 0.307458i | \(0.900522\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.84388e6 | 0.0186677 | ||||||||
\(680\) | 7.42066e7i | 0.236002i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.16156e8 | 0.996664 | ||||||||
\(683\) | 5.45896e8i | 1.71336i | 0.515850 | + | 0.856679i | \(0.327476\pi\) | ||||
−0.515850 | + | 0.856679i | \(0.672524\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.44291e8 | −1.69340 | ||||||||
\(686\) | − 5.58486e6i | − 0.0172997i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.13988e7 | −0.0964156 | ||||||||
\(689\) | − 3.93788e8i | − 1.20394i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.70447e8 | −0.516601 | −0.258301 | − | 0.966065i | \(-0.583162\pi\) | ||||
−0.258301 | + | 0.966065i | \(0.583162\pi\) | |||||||
\(692\) | 2.07551e7i | 0.0626334i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.18220e8 | −0.353682 | ||||||||
\(695\) | 1.46245e8i | 0.435640i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.28503e8 | −0.674828 | ||||||||
\(698\) | 3.64954e8i | 1.07318i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.74084e6 | 0.0109062 | ||||||||
\(701\) | 8.02305e7i | 0.232909i | 0.993196 | + | 0.116454i | \(0.0371529\pi\) | ||||
−0.993196 | + | 0.116454i | \(0.962847\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.78673e6 | 0.0137776 | ||||||||
\(704\) | − 7.41197e7i | − 0.212430i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.38109e7 | −0.0676647 | ||||||||
\(707\) | − 552011.i | − 0.00156203i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.01132e8 | 1.12551 | 0.562754 | − | 0.826625i | \(-0.309742\pi\) | ||||
0.562754 | + | 0.826625i | \(0.309742\pi\) | |||||||
\(710\) | 1.77341e8i | 0.495489i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.43060e8 | −0.396349 | ||||||||
\(713\) | 4.13723e8i | 1.14141i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.33958e9 | 3.66480 | ||||||||
\(716\) | 1.48860e8i | 0.405546i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.17531e8 | −0.857852 | ||||||||
\(719\) | 1.02302e8i | 0.275232i | 0.990486 | + | 0.137616i | \(0.0439439\pi\) | ||||
−0.990486 | + | 0.137616i | \(0.956056\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.11792e6 | 0.0216590 | ||||||||
\(722\) | − 2.65684e8i | − 0.705917i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.09990e8 | −0.289827 | ||||||||
\(725\) | 1.03397e9i | 2.71327i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.87675e8 | −1.52944 | −0.764722 | − | 0.644360i | \(-0.777124\pi\) | ||||
−0.764722 | + | 0.644360i | \(0.777124\pi\) | |||||||
\(728\) | − 2.15723e6i | − 0.00559115i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.91266e8 | 1.00578 | ||||||||
\(731\) | 6.02788e7i | 0.154317i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.12015e8 | −0.284424 | −0.142212 | − | 0.989836i | \(-0.545421\pi\) | ||||
−0.142212 | + | 0.989836i | \(0.545421\pi\) | |||||||
\(734\) | 1.89563e8i | 0.479363i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.69933e7 | 0.243281 | ||||||||
\(737\) | − 1.07367e9i | − 2.68207i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.86968e8 | 1.70217 | 0.851086 | − | 0.525027i | \(-0.175945\pi\) | ||||
0.851086 | + | 0.525027i | \(0.175945\pi\) | |||||||
\(740\) | − 1.13551e8i | − 0.280218i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.29131e6 | 0.00805670 | ||||||||
\(743\) | − 5.57615e8i | − 1.35946i | −0.733460 | − | 0.679732i | \(-0.762096\pi\) | ||||
0.733460 | − | 0.679732i | \(-0.237904\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.87057e8 | 2.38711 | ||||||||
\(746\) | 1.26022e8i | 0.303549i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.42294e8 | −0.340001 | ||||||||
\(749\) | 2.60966e6i | 0.00621066i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.04996e8 | 0.956160 | 0.478080 | − | 0.878316i | \(-0.341333\pi\) | ||||
0.478080 | + | 0.878316i | \(0.341333\pi\) | |||||||
\(752\) | 7.95306e7i | 0.187017i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.96257e8 | 1.39098 | ||||||||
\(755\) | − 7.79332e8i | − 1.81085i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.51769e8 | 1.50247 | 0.751235 | − | 0.660035i | \(-0.229458\pi\) | ||||
0.751235 | + | 0.660035i | \(0.229458\pi\) | |||||||
\(758\) | 4.36825e8i | 1.00300i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.06182e7 | 0.0241887 | ||||||||
\(761\) | − 3.11208e8i | − 0.706149i | −0.935595 | − | 0.353074i | \(-0.885136\pi\) | ||||
0.935595 | − | 0.353074i | \(-0.114864\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.64709e6 | −0.0127131 | ||||||||
\(764\) | 3.76030e8i | 0.843222i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.88144e8 | −0.418604 | ||||||||
\(767\) | 4.34401e8i | 0.962730i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.37211e8 | −0.961417 | −0.480708 | − | 0.876880i | \(-0.659620\pi\) | ||||
−0.480708 | + | 0.876880i | \(0.659620\pi\) | |||||||
\(770\) | 1.11963e7i | 0.0245247i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.22592e8 | −0.483790 | ||||||||
\(773\) | 5.41906e7i | 0.117324i | 0.998278 | + | 0.0586619i | \(0.0186834\pi\) | ||||
−0.998278 | + | 0.0586619i | \(0.981317\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.88352e8 | 1.47879 | ||||||||
\(776\) | − 2.52101e8i | − 0.539498i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.53951e7 | −0.181340 | ||||||||
\(779\) | 3.26966e7i | 0.0691656i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.40057e8 | −0.713837 | ||||||||
\(782\) | − 1.86206e8i | − 0.389380i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.20455e8 | −0.249963 | ||||||||
\(785\) | − 6.68671e8i | − 1.38230i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.02320e7 | −0.0825367 | −0.0412684 | − | 0.999148i | \(-0.513140\pi\) | ||||
−0.0412684 | + | 0.999148i | \(0.513140\pi\) | |||||||
\(788\) | 1.31086e7i | 0.0267904i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.05707e9 | −2.14398 | ||||||||
\(791\) | − 5.20039e6i | − 0.0105077i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.58323e7 | −0.0919078 | ||||||||
\(794\) | − 5.04223e8i | − 1.00731i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.03951e8 | 0.206106 | ||||||||
\(797\) | − 8.94029e7i | − 0.176594i | −0.996094 | − | 0.0882972i | \(-0.971857\pi\) | ||||
0.996094 | − | 0.0882972i | \(-0.0281425\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.52682e8 | 0.299327 | ||||||||
\(800\) | − 1.61377e8i | − 0.315190i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.33810e8 | −1.22867 | ||||||||
\(803\) | 7.50266e8i | 1.44900i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.46515e7 | −0.0280864 | ||||||||
\(806\) | − 3.96952e8i | − 0.758111i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.38134e7 | −0.0451427 | ||||||||
\(809\) | 7.82985e8i | 1.47879i | 0.673270 | + | 0.739397i | \(0.264889\pi\) | ||||
−0.673270 | + | 0.739397i | \(0.735111\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.76238e6 | −0.0126776 | −0.00633880 | − | 0.999980i | \(-0.502018\pi\) | ||||
−0.00633880 | + | 0.999980i | \(0.502018\pi\) | |||||||
\(812\) | 4.98357e6i | 0.00930834i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.17738e8 | 0.403703 | ||||||||
\(815\) | 2.01109e8i | 0.371499i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.62532e6 | 0.0158165 | ||||||||
\(818\) | − 3.77844e8i | − 0.690324i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.75631e8 | 1.40674 | ||||||||
\(821\) | − 2.93295e7i | − 0.0530000i | −0.999649 | − | 0.0265000i | \(-0.991564\pi\) | ||||
0.999649 | − | 0.0265000i | \(-0.00843619\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.90952e8 | −1.59829 | −0.799144 | − | 0.601140i | \(-0.794713\pi\) | ||||
−0.799144 | + | 0.601140i | \(0.794713\pi\) | |||||||
\(824\) | − 3.50202e8i | − 0.625946i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.63076e6 | −0.00644254 | ||||||||
\(827\) | 4.36886e8i | 0.772417i | 0.922411 | + | 0.386209i | \(0.126216\pi\) | ||||
−0.922411 | + | 0.386209i | \(0.873784\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.08489e8 | 0.365948 | 0.182974 | − | 0.983118i | \(-0.441428\pi\) | ||||
0.182974 | + | 0.983118i | \(0.441428\pi\) | |||||||
\(830\) | − 1.11484e9i | − 1.94975i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −9.30614e7 | −0.161584 | ||||||||
\(833\) | 2.31247e8i | 0.400074i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.15825e8 | 0.370718 | ||||||||
\(836\) | 2.03609e7i | 0.0348480i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.67892e8 | 0.455227 | ||||||||
\(839\) | − 1.11428e9i | − 1.88672i | −0.331767 | − | 0.943361i | \(-0.607645\pi\) | ||||
0.331767 | − | 0.943361i | \(-0.392355\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.82634e8 | −1.31574 | ||||||||
\(842\) | 3.74240e8i | 0.626922i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.59836e8 | 0.265856 | ||||||||
\(845\) | − 6.75389e8i | − 1.11940i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.40356e7 | −0.0230983 | ||||||||
\(848\) | − 1.41985e8i | − 0.232839i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.09809e8 | −0.504473 | ||||||||
\(851\) | 2.84933e8i | 0.462332i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.03808e7 | −0.113399 | −0.0566993 | − | 0.998391i | \(-0.518058\pi\) | ||||
−0.0566993 | + | 0.998391i | \(0.518058\pi\) | |||||||
\(854\) | − 383071.i | 0 0.000615043i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.12579e8 | 0.179488 | ||||||||
\(857\) | − 1.58916e8i | − 0.252479i | −0.992000 | − | 0.126240i | \(-0.959709\pi\) | ||||
0.992000 | − | 0.126240i | \(-0.0402908\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.14241e8 | 0.495774 | 0.247887 | − | 0.968789i | \(-0.420264\pi\) | ||||
0.247887 | + | 0.968789i | \(0.420264\pi\) | |||||||
\(860\) | − 2.04611e8i | − 0.321686i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.12888e8 | −0.800757 | ||||||||
\(863\) | − 3.90351e8i | − 0.607328i | −0.952779 | − | 0.303664i | \(-0.901790\pi\) | ||||
0.952779 | − | 0.303664i | \(-0.0982101\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.35251e8 | −0.208974 | ||||||||
\(866\) | − 3.95648e6i | − 0.00609194i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.31776e6 | 0.00507324 | ||||||||
\(869\) | − 2.02696e9i | − 3.08878i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.34806e9 | −2.04011 | ||||||||
\(872\) | 2.43612e8i | 0.367408i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.66443e7 | −0.0399089 | ||||||||
\(875\) | 1.07051e7i | 0.0159796i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.15579e9 | −1.71349 | −0.856745 | − | 0.515741i | \(-0.827517\pi\) | ||||
−0.856745 | + | 0.515741i | \(0.827517\pi\) | |||||||
\(878\) | − 1.45549e8i | − 0.215043i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.83002e8 | 0.708763 | ||||||||
\(881\) | − 7.82859e8i | − 1.14487i | −0.819951 | − | 0.572434i | \(-0.805999\pi\) | ||||
0.819951 | − | 0.572434i | \(-0.194001\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.01047e9 | 1.46772 | 0.733860 | − | 0.679300i | \(-0.237717\pi\) | ||||
0.733860 | + | 0.679300i | \(0.237717\pi\) | |||||||
\(884\) | 1.78658e8i | 0.258622i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 936650. | 0.00134672 | ||||||||
\(887\) | − 3.28343e8i | − 0.470498i | −0.971935 | − | 0.235249i | \(-0.924410\pi\) | ||||
0.971935 | − | 0.235249i | \(-0.0755905\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.93610e6 | −0.00987211 | ||||||||
\(890\) | − 9.32253e8i | − 1.32240i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.82056e8 | −0.256513 | ||||||||
\(893\) | − 2.18473e7i | − 0.0306791i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.70051e8 | −1.35309 | ||||||||
\(896\) | − 777815.i | − 0.00108131i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.43502e8 | −0.336259 | ||||||||
\(899\) | 9.17028e8i | 1.26213i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.72580e8 | −0.372666 | ||||||||
\(902\) | 1.48730e9i | 2.02665i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.24342e8 | −0.303672 | ||||||||
\(905\) | − 7.16753e8i | − 0.966994i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.15438e8 | 0.288736 | 0.144368 | − | 0.989524i | \(-0.453885\pi\) | ||||
0.144368 | + | 0.989524i | \(0.453885\pi\) | |||||||
\(908\) | 3.71404e8i | 0.496123i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.40576e7 | 0.0186546 | ||||||||
\(911\) | 7.52234e8i | 0.994942i | 0.867481 | + | 0.497471i | \(0.165738\pi\) | ||||
−0.867481 | + | 0.497471i | \(0.834262\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.13775e9 | 2.80895 | ||||||||
\(914\) | − 7.66452e8i | − 1.00380i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.10621e8 | 0.143930 | ||||||||
\(917\) | 1.11670e7i | 0.0144820i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.81968e8 | 0.878653 | 0.439327 | − | 0.898327i | \(-0.355217\pi\) | ||||
0.439327 | + | 0.898327i | \(0.355217\pi\) | |||||||
\(920\) | 6.32058e8i | 0.811696i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.81217e8 | 0.231210 | ||||||||
\(923\) | 4.26961e8i | 0.542979i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.74072e8 | 0.598989 | ||||||||
\(926\) | 7.31617e8i | 0.921406i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.14988e8 | 0.269011 | ||||||||
\(929\) | 1.11639e8i | 0.139242i | 0.997574 | + | 0.0696208i | \(0.0221789\pi\) | ||||
−0.997574 | + | 0.0696208i | \(0.977821\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.30892e7 | 0.0410050 | ||||||||
\(932\) | 4.08765e8i | 0.504924i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.80433e8 | 0.589647 | ||||||||
\(935\) | − 9.27259e8i | − 1.13440i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.66443e8 | 0.931668 | 0.465834 | − | 0.884872i | \(-0.345754\pi\) | ||||
0.465834 | + | 0.884872i | \(0.345754\pi\) | |||||||
\(938\) | − 1.12672e7i | − 0.0136523i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5.18263e8 | −0.623974 | ||||||||
\(941\) | 5.32996e8i | 0.639669i | 0.947473 | + | 0.319834i | \(0.103627\pi\) | ||||
−0.947473 | + | 0.319834i | \(0.896373\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.94628e9 | −2.32098 | ||||||||
\(944\) | 1.56629e8i | 0.186189i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.92348e8 | 0.463445 | ||||||||
\(947\) | 3.13628e7i | 0.0369288i | 0.999830 | + | 0.0184644i | \(0.00587773\pi\) | ||||
−0.999830 | + | 0.0184644i | \(0.994122\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.42001e8 | 1.10218 | ||||||||
\(950\) | 4.43308e7i | 0.0517052i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.49324e6 | −0.00173068 | ||||||||
\(953\) | 6.21244e8i | 0.717767i | 0.933382 | + | 0.358883i | \(0.116842\pi\) | ||||
−0.933382 | + | 0.358883i | \(0.883158\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.45040e9 | −2.81337 | ||||||||
\(956\) | 4.13541e8i | 0.473309i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.54603e8 | 0.744529 | ||||||||
\(959\) | − 1.09526e7i | − 0.0124183i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.77002e8 | −0.312114 | ||||||||
\(962\) | − 2.73383e8i | − 0.307076i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.32970e8 | −0.260057 | ||||||||
\(965\) | − 1.45052e9i | − 1.61415i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.29984e8 | −0.696707 | −0.348354 | − | 0.937363i | \(-0.613259\pi\) | ||||
−0.348354 | + | 0.937363i | \(0.613259\pi\) | |||||||
\(968\) | 6.05486e8i | 0.667541i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.64282e9 | 1.80001 | ||||||||
\(971\) | 1.38333e8i | 0.151101i | 0.997142 | + | 0.0755507i | \(0.0240715\pi\) | ||||
−0.997142 | + | 0.0755507i | \(0.975929\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.94285e6 | −0.00319470 | ||||||||
\(974\) | 2.56165e8i | 0.277231i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.65254e7 | −0.0177747 | ||||||||
\(977\) | 8.23975e8i | 0.883549i | 0.897126 | + | 0.441774i | \(0.145651\pi\) | ||||
−0.897126 | + | 0.441774i | \(0.854349\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.78763e9 | 1.90515 | ||||||||
\(980\) | − 7.84944e8i | − 0.833989i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.15576e9 | 1.22049 | ||||||||
\(983\) | − 1.28601e9i | − 1.35389i | −0.736032 | − | 0.676947i | \(-0.763303\pi\) | ||||
0.736032 | − | 0.676947i | \(-0.236697\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.54226e7 | −0.0893849 | ||||||||
\(986\) | − 4.12730e8i | − 0.430562i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.55642e7 | 0.0265070 | ||||||||
\(989\) | 5.13428e8i | 0.530751i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.70244e8 | −0.174924 | −0.0874621 | − | 0.996168i | \(-0.527876\pi\) | ||||
−0.0874621 | + | 0.996168i | \(0.527876\pi\) | |||||||
\(992\) | − 1.43126e8i | − 0.146617i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.56858e6 | −0.00363359 | ||||||||
\(995\) | 6.77399e8i | 0.687663i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.01078e8 | −0.707426 | −0.353713 | − | 0.935354i | \(-0.615081\pi\) | ||||
−0.353713 | + | 0.935354i | \(0.615081\pi\) | |||||||
\(998\) | − 1.65740e8i | − 0.166738i | ||||||||
\(999\) | 0 | 0 |
(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 | 162.7.b.a.161.3 | yes | 4 | |
3.2 | odd | 2 | inner | 162.7.b.a.161.2 | ✓ | 4 | |
9.2 | odd | 6 | 162.7.d.f.53.1 | 8 | |||
9.4 | even | 3 | 162.7.d.f.107.1 | 8 | |||
9.5 | odd | 6 | 162.7.d.f.107.4 | 8 | |||
9.7 | even | 3 | 162.7.d.f.53.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
162.7.b.a.161.2 | ✓ | 4 | 3.2 | odd | 2 | inner | |
162.7.b.a.161.3 | yes | 4 | 1.1 | even | 1 | trivial | |
162.7.d.f.53.1 | 8 | 9.2 | odd | 6 | |||
162.7.d.f.53.4 | 8 | 9.7 | even | 3 | |||
162.7.d.f.107.1 | 8 | 9.4 | even | 3 | |||
162.7.d.f.107.4 | 8 | 9.5 | odd | 6 |