Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [27,8,Mod(1,27)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(27, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("27.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 27 = 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 27.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: | \(8.43439568807\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{42}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - 42 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(6.48074\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 27.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 19.4422 | 1.71847 | 0.859233 | − | 0.511585i | \(-0.170941\pi\) | ||||
0.859233 | + | 0.511585i | \(0.170941\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 250.000 | 1.95312 | ||||||||
\(5\) | 388.844 | 1.39117 | 0.695586 | − | 0.718443i | \(-0.255145\pi\) | ||||
0.695586 | + | 0.718443i | \(0.255145\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1261.00 | −1.38954 | −0.694771 | − | 0.719231i | \(-0.744494\pi\) | ||||
−0.694771 | + | 0.719231i | \(0.744494\pi\) | |||||||
\(8\) | 2371.95 | 1.63791 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 7560.00 | 2.39068 | ||||||||
\(11\) | 1477.61 | 0.334723 | 0.167361 | − | 0.985896i | \(-0.446475\pi\) | ||||
0.167361 | + | 0.985896i | \(0.446475\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 9581.00 | 1.20951 | 0.604755 | − | 0.796412i | \(-0.293271\pi\) | ||||
0.604755 | + | 0.796412i | \(0.293271\pi\) | |||||||
\(14\) | −24516.6 | −2.38788 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 14116.0 | 0.861572 | ||||||||
\(17\) | −21230.9 | −1.04809 | −0.524043 | − | 0.851692i | \(-0.675577\pi\) | ||||
−0.524043 | + | 0.851692i | \(0.675577\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −21931.0 | −0.733535 | −0.366767 | − | 0.930313i | \(-0.619536\pi\) | ||||
−0.366767 | + | 0.930313i | \(0.619536\pi\) | |||||||
\(20\) | 97211.1 | 2.71713 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 28728.0 | 0.575209 | ||||||||
\(23\) | −85934.6 | −1.47272 | −0.736361 | − | 0.676589i | \(-0.763457\pi\) | ||||
−0.736361 | + | 0.676589i | \(0.763457\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 73075.0 | 0.935360 | ||||||||
\(26\) | 186276. | 2.07850 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −315250. | −2.71395 | ||||||||
\(29\) | −32351.9 | −0.246324 | −0.123162 | − | 0.992387i | \(-0.539303\pi\) | ||||
−0.123162 | + | 0.992387i | \(0.539303\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −50908.0 | −0.306916 | −0.153458 | − | 0.988155i | \(-0.549041\pi\) | ||||
−0.153458 | + | 0.988155i | \(0.549041\pi\) | |||||||
\(32\) | −29163.3 | −0.157330 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −412776. | −1.80110 | ||||||||
\(35\) | −490333. | −1.93309 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 246467. | 0.799931 | 0.399966 | − | 0.916530i | \(-0.369022\pi\) | ||||
0.399966 | + | 0.916530i | \(0.369022\pi\) | |||||||
\(38\) | −426387. | −1.26055 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 922320. | 2.27862 | ||||||||
\(41\) | 610952. | 1.38441 | 0.692204 | − | 0.721702i | \(-0.256640\pi\) | ||||
0.692204 | + | 0.721702i | \(0.256640\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 315512. | 0.605168 | 0.302584 | − | 0.953123i | \(-0.402151\pi\) | ||||
0.302584 | + | 0.953123i | \(0.402151\pi\) | |||||||
\(44\) | 369402. | 0.653755 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.67076e6 | −2.53082 | ||||||||
\(47\) | 425163. | 0.597327 | 0.298664 | − | 0.954358i | \(-0.403459\pi\) | ||||
0.298664 | + | 0.954358i | \(0.403459\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 766578. | 0.930829 | ||||||||
\(50\) | 1.42074e6 | 1.60738 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.39525e6 | 2.36232 | ||||||||
\(53\) | 127385. | 0.117531 | 0.0587657 | − | 0.998272i | \(-0.481283\pi\) | ||||
0.0587657 | + | 0.998272i | \(0.481283\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 574560. | 0.465657 | ||||||||
\(56\) | −2.99103e6 | −2.27595 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −628992. | −0.423299 | ||||||||
\(59\) | −964101. | −0.611140 | −0.305570 | − | 0.952170i | \(-0.598847\pi\) | ||||
−0.305570 | + | 0.952170i | \(0.598847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −497953. | −0.280888 | −0.140444 | − | 0.990089i | \(-0.544853\pi\) | ||||
−0.140444 | + | 0.990089i | \(0.544853\pi\) | |||||||
\(62\) | −989765. | −0.527425 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.37385e6 | −1.13194 | ||||||||
\(65\) | 3.72552e6 | 1.68264 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.33636e6 | 0.542828 | 0.271414 | − | 0.962463i | \(-0.412509\pi\) | ||||
0.271414 | + | 0.962463i | \(0.412509\pi\) | |||||||
\(68\) | −5.30773e6 | −2.04704 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −9.53316e6 | −3.32195 | ||||||||
\(71\) | 901964. | 0.299078 | 0.149539 | − | 0.988756i | \(-0.452221\pi\) | ||||
0.149539 | + | 0.988756i | \(0.452221\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.25079e6 | 0.978046 | 0.489023 | − | 0.872271i | \(-0.337353\pi\) | ||||
0.489023 | + | 0.872271i | \(0.337353\pi\) | |||||||
\(74\) | 4.79187e6 | 1.37465 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.48275e6 | −1.43269 | ||||||||
\(77\) | −1.86326e6 | −0.465111 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.07548e6 | 1.38639 | 0.693196 | − | 0.720749i | \(-0.256202\pi\) | ||||
0.693196 | + | 0.720749i | \(0.256202\pi\) | |||||||
\(80\) | 5.48893e6 | 1.19860 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.18783e7 | 2.37906 | ||||||||
\(83\) | 8.19171e6 | 1.57254 | 0.786269 | − | 0.617884i | \(-0.212010\pi\) | ||||
0.786269 | + | 0.617884i | \(0.212010\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.25552e6 | −1.45807 | ||||||||
\(86\) | 6.13425e6 | 1.03996 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.50482e6 | 0.548247 | ||||||||
\(89\) | −1.30407e7 | −1.96081 | −0.980404 | − | 0.196997i | \(-0.936881\pi\) | ||||
−0.980404 | + | 0.196997i | \(0.936881\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.20816e7 | −1.68066 | ||||||||
\(92\) | −2.14837e7 | −2.87641 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.26610e6 | 1.02649 | ||||||||
\(95\) | −8.52775e6 | −1.02047 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.57063e6 | 0.730981 | 0.365490 | − | 0.930815i | \(-0.380901\pi\) | ||||
0.365490 | + | 0.930815i | \(0.380901\pi\) | |||||||
\(98\) | 1.49040e7 | 1.59960 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.82688e7 | 1.82688 | ||||||||
\(101\) | −1.37657e7 | −1.32946 | −0.664728 | − | 0.747085i | \(-0.731453\pi\) | ||||
−0.664728 | + | 0.747085i | \(0.731453\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 412511. | 0.0371968 | 0.0185984 | − | 0.999827i | \(-0.494080\pi\) | ||||
0.0185984 | + | 0.999827i | \(0.494080\pi\) | |||||||
\(104\) | 2.27257e7 | 1.98107 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.47666e6 | 0.201974 | ||||||||
\(107\) | −1.01453e7 | −0.800614 | −0.400307 | − | 0.916381i | \(-0.631097\pi\) | ||||
−0.400307 | + | 0.916381i | \(0.631097\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.84661e7 | 1.36578 | 0.682891 | − | 0.730520i | \(-0.260722\pi\) | ||||
0.682891 | + | 0.730520i | \(0.260722\pi\) | |||||||
\(110\) | 1.11707e7 | 0.800215 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.78003e7 | −1.19719 | ||||||||
\(113\) | 2.05262e7 | 1.33824 | 0.669121 | − | 0.743153i | \(-0.266671\pi\) | ||||
0.669121 | + | 0.743153i | \(0.266671\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.34152e7 | −2.04881 | ||||||||
\(116\) | −8.08796e6 | −0.481101 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.87443e7 | −1.05022 | ||||||||
\(119\) | 2.67722e7 | 1.45636 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.73038e7 | −0.887961 | ||||||||
\(122\) | −9.68131e6 | −0.482697 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.27270e7 | −0.599446 | ||||||||
\(125\) | −1.96366e6 | −0.0899254 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.70206e7 | −0.737328 | −0.368664 | − | 0.929563i | \(-0.620185\pi\) | ||||
−0.368664 | + | 0.929563i | \(0.620185\pi\) | |||||||
\(128\) | −4.24200e7 | −1.78787 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.24324e7 | 2.89155 | ||||||||
\(131\) | −4.00759e6 | −0.155752 | −0.0778760 | − | 0.996963i | \(-0.524814\pi\) | ||||
−0.0778760 | + | 0.996963i | \(0.524814\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.76550e7 | 1.01928 | ||||||||
\(134\) | 2.59818e7 | 0.932831 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.03587e7 | −1.71668 | ||||||||
\(137\) | 9.85402e6 | 0.327410 | 0.163705 | − | 0.986509i | \(-0.447656\pi\) | ||||
0.163705 | + | 0.986509i | \(0.447656\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.29592e7 | −1.35676 | −0.678382 | − | 0.734710i | \(-0.737318\pi\) | ||||
−0.678382 | + | 0.734710i | \(0.737318\pi\) | |||||||
\(140\) | −1.22583e8 | −3.77557 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.75362e7 | 0.513956 | ||||||||
\(143\) | 1.41570e7 | 0.404850 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.25798e7 | −0.342679 | ||||||||
\(146\) | 6.32026e7 | 1.68074 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.16167e7 | 1.56237 | ||||||||
\(149\) | 1.90622e7 | 0.472087 | 0.236044 | − | 0.971742i | \(-0.424149\pi\) | ||||
0.236044 | + | 0.971742i | \(0.424149\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.80448e7 | 1.60833 | 0.804165 | − | 0.594405i | \(-0.202613\pi\) | ||||
0.804165 | + | 0.594405i | \(0.202613\pi\) | |||||||
\(152\) | −5.20193e7 | −1.20147 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.62260e7 | −0.799278 | ||||||||
\(155\) | −1.97953e7 | −0.426974 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.23676e7 | −0.255058 | −0.127529 | − | 0.991835i | \(-0.540705\pi\) | ||||
−0.127529 | + | 0.991835i | \(0.540705\pi\) | |||||||
\(158\) | 1.18121e8 | 2.38247 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.13400e7 | −0.218873 | ||||||||
\(161\) | 1.08364e8 | 2.04641 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.03190e7 | 0.367490 | 0.183745 | − | 0.982974i | \(-0.441178\pi\) | ||||
0.183745 | + | 0.982974i | \(0.441178\pi\) | |||||||
\(164\) | 1.52738e8 | 2.70392 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.59265e8 | 2.70235 | ||||||||
\(167\) | −8.89076e7 | −1.47717 | −0.738587 | − | 0.674159i | \(-0.764506\pi\) | ||||
−0.738587 | + | 0.674159i | \(0.764506\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.90470e7 | 0.462912 | ||||||||
\(170\) | −1.60506e8 | −2.50564 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.88780e7 | 1.18197 | ||||||||
\(173\) | −1.30135e8 | −1.91088 | −0.955441 | − | 0.295182i | \(-0.904620\pi\) | ||||
−0.955441 | + | 0.295182i | \(0.904620\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.21476e7 | −1.29972 | ||||||||
\(176\) | 2.08579e7 | 0.288388 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.53540e8 | −3.36958 | ||||||||
\(179\) | 4.09514e7 | 0.533683 | 0.266841 | − | 0.963740i | \(-0.414020\pi\) | ||||
0.266841 | + | 0.963740i | \(0.414020\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.43779e7 | 0.806979 | 0.403489 | − | 0.914984i | \(-0.367797\pi\) | ||||
0.403489 | + | 0.914984i | \(0.367797\pi\) | |||||||
\(182\) | −2.34894e8 | −2.88816 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.03833e8 | −2.41219 | ||||||||
\(185\) | 9.58373e7 | 1.11284 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.13710e7 | −0.350818 | ||||||||
\(188\) | 1.06291e8 | 1.16666 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.65798e8 | −1.75365 | ||||||||
\(191\) | −9.97479e7 | −1.03583 | −0.517913 | − | 0.855433i | \(-0.673291\pi\) | ||||
−0.517913 | + | 0.855433i | \(0.673291\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.97025e8 | 1.97274 | 0.986371 | − | 0.164539i | \(-0.0526136\pi\) | ||||
0.986371 | + | 0.164539i | \(0.0526136\pi\) | |||||||
\(194\) | 1.27748e8 | 1.25617 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.91644e8 | 1.81803 | ||||||||
\(197\) | −1.46469e8 | −1.36494 | −0.682472 | − | 0.730912i | \(-0.739095\pi\) | ||||
−0.682472 | + | 0.730912i | \(0.739095\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.26743e7 | −0.114009 | −0.0570045 | − | 0.998374i | \(-0.518155\pi\) | ||||
−0.0570045 | + | 0.998374i | \(0.518155\pi\) | |||||||
\(200\) | 1.73330e8 | 1.53204 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.67636e8 | −2.28462 | ||||||||
\(203\) | 4.07957e7 | 0.342277 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.37565e8 | 1.92595 | ||||||||
\(206\) | 8.02013e6 | 0.0639214 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.35245e8 | 1.04208 | ||||||||
\(209\) | −3.24054e7 | −0.245531 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.21343e8 | −1.62210 | −0.811051 | − | 0.584976i | \(-0.801104\pi\) | ||||
−0.811051 | + | 0.584976i | \(0.801104\pi\) | |||||||
\(212\) | 3.18464e7 | 0.229554 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.97248e8 | −1.37583 | ||||||||
\(215\) | 1.22685e8 | 0.841894 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.41950e7 | 0.426474 | ||||||||
\(218\) | 3.59021e8 | 2.34705 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.43640e8 | 0.909486 | ||||||||
\(221\) | −2.03413e8 | −1.26767 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.35957e8 | −0.820981 | −0.410491 | − | 0.911865i | \(-0.634643\pi\) | ||||
−0.410491 | + | 0.911865i | \(0.634643\pi\) | |||||||
\(224\) | 3.67750e7 | 0.218617 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.99076e8 | 2.29972 | ||||||||
\(227\) | 5.82817e7 | 0.330706 | 0.165353 | − | 0.986234i | \(-0.447124\pi\) | ||||
0.165353 | + | 0.986234i | \(0.447124\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.13523e6 | 0.0282577 | 0.0141288 | − | 0.999900i | \(-0.495503\pi\) | ||||
0.0141288 | + | 0.999900i | \(0.495503\pi\) | |||||||
\(230\) | −6.49666e8 | −3.52081 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.67370e7 | −0.403457 | ||||||||
\(233\) | −5.10755e6 | −0.0264525 | −0.0132263 | − | 0.999913i | \(-0.504210\pi\) | ||||
−0.0132263 | + | 0.999913i | \(0.504210\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.65322e8 | 0.830985 | ||||||||
\(236\) | −2.41025e8 | −1.19363 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.20511e8 | 2.50271 | ||||||||
\(239\) | 2.65911e8 | 1.25992 | 0.629961 | − | 0.776627i | \(-0.283071\pi\) | ||||
0.629961 | + | 0.776627i | \(0.283071\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.79884e8 | 0.827813 | 0.413906 | − | 0.910319i | \(-0.364164\pi\) | ||||
0.413906 | + | 0.910319i | \(0.364164\pi\) | |||||||
\(242\) | −3.36425e8 | −1.52593 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.24488e8 | −0.548610 | ||||||||
\(245\) | 2.98080e8 | 1.29494 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.10121e8 | −0.887217 | ||||||||
\(248\) | −1.20751e8 | −0.502702 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.81780e7 | −0.154534 | ||||||||
\(251\) | −9.33796e7 | −0.372730 | −0.186365 | − | 0.982481i | \(-0.559671\pi\) | ||||
−0.186365 | + | 0.982481i | \(0.559671\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.26978e8 | −0.492953 | ||||||||
\(254\) | −3.30918e8 | −1.26707 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.20886e8 | −1.94045 | ||||||||
\(257\) | 4.68071e7 | 0.172007 | 0.0860034 | − | 0.996295i | \(-0.472590\pi\) | ||||
0.0860034 | + | 0.996295i | \(0.472590\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.10795e8 | −1.11154 | ||||||||
\(260\) | 9.31380e8 | 3.28640 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.79164e7 | −0.267654 | ||||||||
\(263\) | 2.90594e8 | 0.985014 | 0.492507 | − | 0.870309i | \(-0.336081\pi\) | ||||
0.492507 | + | 0.870309i | \(0.336081\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.95331e7 | 0.163507 | ||||||||
\(266\) | 5.37674e8 | 1.75159 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.34090e8 | 1.06021 | ||||||||
\(269\) | 1.81315e8 | 0.567938 | 0.283969 | − | 0.958834i | \(-0.408349\pi\) | ||||
0.283969 | + | 0.958834i | \(0.408349\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.68408e8 | −1.73487 | −0.867437 | − | 0.497547i | \(-0.834234\pi\) | ||||
−0.867437 | + | 0.497547i | \(0.834234\pi\) | |||||||
\(272\) | −2.99695e8 | −0.903003 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.91584e8 | 0.562642 | ||||||||
\(275\) | 1.07976e8 | 0.313086 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.49241e8 | 0.704595 | 0.352298 | − | 0.935888i | \(-0.385401\pi\) | ||||
0.352298 | + | 0.935888i | \(0.385401\pi\) | |||||||
\(278\) | −8.35222e8 | −2.33155 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.16305e9 | −3.16624 | ||||||||
\(281\) | 1.31976e8 | 0.354833 | 0.177416 | − | 0.984136i | \(-0.443226\pi\) | ||||
0.177416 | + | 0.984136i | \(0.443226\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.79669e8 | 1.25802 | 0.629012 | − | 0.777395i | \(-0.283460\pi\) | ||||
0.629012 | + | 0.777395i | \(0.283460\pi\) | |||||||
\(284\) | 2.25491e8 | 0.584137 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.75243e8 | 0.695721 | ||||||||
\(287\) | −7.70411e8 | −1.92369 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.04127e7 | 0.0984863 | ||||||||
\(290\) | −2.44580e8 | −0.588882 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.12698e8 | 1.91025 | ||||||||
\(293\) | −4.76703e8 | −1.10716 | −0.553582 | − | 0.832795i | \(-0.686739\pi\) | ||||
−0.553582 | + | 0.832795i | \(0.686739\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.74885e8 | −0.850200 | ||||||||
\(296\) | 5.84608e8 | 1.31022 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.70612e8 | 0.811265 | ||||||||
\(299\) | −8.23340e8 | −1.78127 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.97861e8 | −0.840908 | ||||||||
\(302\) | 1.32294e9 | 2.76386 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.09578e8 | −0.631993 | ||||||||
\(305\) | −1.93626e8 | −0.390764 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.08731e8 | −0.214471 | −0.107236 | − | 0.994234i | \(-0.534200\pi\) | ||||
−0.107236 | + | 0.994234i | \(0.534200\pi\) | |||||||
\(308\) | −4.65816e8 | −0.908421 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.84864e8 | −0.733740 | ||||||||
\(311\) | −2.78144e8 | −0.524335 | −0.262167 | − | 0.965022i | \(-0.584437\pi\) | ||||
−0.262167 | + | 0.965022i | \(0.584437\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.31727e8 | −1.53312 | −0.766560 | − | 0.642173i | \(-0.778033\pi\) | ||||
−0.766560 | + | 0.642173i | \(0.778033\pi\) | |||||||
\(314\) | −2.40454e8 | −0.438308 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.51887e9 | 2.70780 | ||||||||
\(317\) | 8.56343e8 | 1.50987 | 0.754936 | − | 0.655798i | \(-0.227668\pi\) | ||||
0.754936 | + | 0.655798i | \(0.227668\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.78034e7 | −0.0824501 | ||||||||
\(320\) | −9.23058e8 | −1.57472 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.10683e9 | 3.51669 | ||||||||
\(323\) | 4.65615e8 | 0.768808 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.00132e8 | 1.13133 | ||||||||
\(326\) | 3.95046e8 | 0.631519 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.44915e9 | 2.26754 | ||||||||
\(329\) | −5.36130e8 | −0.830012 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.91069e7 | −0.0289596 | −0.0144798 | − | 0.999895i | \(-0.504609\pi\) | ||||
−0.0144798 | + | 0.999895i | \(0.504609\pi\) | |||||||
\(332\) | 2.04793e9 | 3.07136 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.72856e9 | −2.53847 | ||||||||
\(335\) | 5.19637e8 | 0.755167 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.42680e8 | 1.05705 | 0.528527 | − | 0.848917i | \(-0.322745\pi\) | ||||
0.528527 | + | 0.848917i | \(0.322745\pi\) | |||||||
\(338\) | 5.64739e8 | 0.795499 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.06388e9 | −2.84779 | ||||||||
\(341\) | −7.52221e7 | −0.102732 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.18329e7 | 0.0961156 | ||||||||
\(344\) | 7.48379e8 | 0.991213 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.53012e9 | −3.28379 | ||||||||
\(347\) | −58637.7 | −7.53397e−5 0 | −3.76699e−5 | − | 1.00000i | \(-0.500012\pi\) | ||||
−3.76699e−5 | 1.00000i | \(0.500012\pi\) | ||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.21859e8 | 1.03492 | 0.517462 | − | 0.855706i | \(-0.326877\pi\) | ||||
0.517462 | + | 0.855706i | \(0.326877\pi\) | |||||||
\(350\) | −1.79155e9 | −2.23353 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.30920e7 | −0.0526620 | ||||||||
\(353\) | −8.01564e6 | −0.00969899 | −0.00484950 | − | 0.999988i | \(-0.501544\pi\) | ||||
−0.00484950 | + | 0.999988i | \(0.501544\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.50724e8 | 0.416069 | ||||||||
\(356\) | −3.26017e9 | −3.82970 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.96186e8 | 0.917115 | ||||||||
\(359\) | −7.77296e8 | −0.886657 | −0.443329 | − | 0.896359i | \(-0.646203\pi\) | ||||
−0.443329 | + | 0.896359i | \(0.646203\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.12903e8 | −0.461926 | ||||||||
\(362\) | 1.25165e9 | 1.38677 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.02041e9 | −3.28255 | ||||||||
\(365\) | 1.26405e9 | 1.36063 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.92955e8 | −0.626167 | −0.313084 | − | 0.949726i | \(-0.601362\pi\) | ||||
−0.313084 | + | 0.949726i | \(0.601362\pi\) | |||||||
\(368\) | −1.21305e9 | −1.26886 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.86329e9 | 1.91238 | ||||||||
\(371\) | −1.60633e8 | −0.163315 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.77986e8 | 0.876005 | 0.438002 | − | 0.898974i | \(-0.355686\pi\) | ||||
0.438002 | + | 0.898974i | \(0.355686\pi\) | |||||||
\(374\) | −6.09921e8 | −0.602870 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.00846e9 | 0.978370 | ||||||||
\(377\) | −3.09963e8 | −0.297931 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.51623e8 | −0.143063 | −0.0715314 | − | 0.997438i | \(-0.522789\pi\) | ||||
−0.0715314 | + | 0.997438i | \(0.522789\pi\) | |||||||
\(380\) | −2.13194e9 | −1.99311 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.93932e9 | −1.78003 | ||||||||
\(383\) | 1.54017e9 | 1.40079 | 0.700397 | − | 0.713754i | \(-0.253007\pi\) | ||||
0.700397 | + | 0.713754i | \(0.253007\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.24520e8 | −0.647050 | ||||||||
\(386\) | 3.83060e9 | 3.39009 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.64266e9 | 1.42770 | ||||||||
\(389\) | −1.21574e9 | −1.04717 | −0.523585 | − | 0.851973i | \(-0.675406\pi\) | ||||
−0.523585 | + | 0.851973i | \(0.675406\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.82447e9 | 1.54354 | ||||||||
\(392\) | 1.81829e9 | 1.52462 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.84769e9 | −2.34561 | ||||||||
\(395\) | 2.36242e9 | 1.92871 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.04851e8 | −0.645578 | −0.322789 | − | 0.946471i | \(-0.604620\pi\) | ||||
−0.322789 | + | 0.946471i | \(0.604620\pi\) | |||||||
\(398\) | −2.46417e8 | −0.195921 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.03153e9 | 0.805880 | ||||||||
\(401\) | −9.50522e8 | −0.736134 | −0.368067 | − | 0.929799i | \(-0.619980\pi\) | ||||
−0.368067 | + | 0.929799i | \(0.619980\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.87750e8 | −0.371218 | ||||||||
\(404\) | −3.44143e9 | −2.59659 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.93159e8 | 0.588192 | ||||||||
\(407\) | 3.64182e8 | 0.267755 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.61635e8 | 0.116816 | 0.0584081 | − | 0.998293i | \(-0.481398\pi\) | ||||
0.0584081 | + | 0.998293i | \(0.481398\pi\) | |||||||
\(410\) | 4.61880e9 | 3.30968 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.03128e8 | 0.0726499 | ||||||||
\(413\) | 1.21573e9 | 0.849205 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.18530e9 | 2.18767 | ||||||||
\(416\) | −2.79414e8 | −0.190292 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.30034e8 | −0.421936 | ||||||||
\(419\) | 6.65427e7 | 0.0441928 | 0.0220964 | − | 0.999756i | \(-0.492966\pi\) | ||||
0.0220964 | + | 0.999756i | \(0.492966\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.04026e9 | 1.33259 | 0.666297 | − | 0.745686i | \(-0.267878\pi\) | ||||
0.666297 | + | 0.745686i | \(0.267878\pi\) | |||||||
\(422\) | −4.30341e9 | −2.78753 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.02152e8 | 0.192506 | ||||||||
\(425\) | −1.55145e9 | −0.980339 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.27919e8 | 0.390307 | ||||||||
\(428\) | −2.53634e9 | −1.56370 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.38527e9 | 1.44677 | ||||||||
\(431\) | 3.39561e8 | 0.204290 | 0.102145 | − | 0.994770i | \(-0.467429\pi\) | ||||
0.102145 | + | 0.994770i | \(0.467429\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.78104e9 | −1.64626 | −0.823132 | − | 0.567850i | \(-0.807775\pi\) | ||||
−0.823132 | + | 0.567850i | \(0.807775\pi\) | |||||||
\(434\) | 1.24809e9 | 0.732880 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.61651e9 | 2.66754 | ||||||||
\(437\) | 1.88463e9 | 1.08029 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.50331e8 | 0.254042 | 0.127021 | − | 0.991900i | \(-0.459458\pi\) | ||||
0.127021 | + | 0.991900i | \(0.459458\pi\) | |||||||
\(440\) | 1.36283e9 | 0.762705 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.95481e9 | −2.17845 | ||||||||
\(443\) | −2.30997e9 | −1.26239 | −0.631196 | − | 0.775624i | \(-0.717435\pi\) | ||||
−0.631196 | + | 0.775624i | \(0.717435\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.07079e9 | −2.72782 | ||||||||
\(446\) | −2.64330e9 | −1.41083 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.99342e9 | 1.57288 | ||||||||
\(449\) | −9.05716e8 | −0.472204 | −0.236102 | − | 0.971728i | \(-0.575870\pi\) | ||||
−0.236102 | + | 0.971728i | \(0.575870\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.02749e8 | 0.463392 | ||||||||
\(452\) | 5.13156e9 | 2.61376 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.13313e9 | 0.568307 | ||||||||
\(455\) | −4.69788e9 | −2.33809 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.37798e9 | −1.16547 | −0.582735 | − | 0.812663i | \(-0.698017\pi\) | ||||
−0.582735 | + | 0.812663i | \(0.698017\pi\) | |||||||
\(458\) | 9.98404e7 | 0.0485598 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.35380e9 | −4.00158 | ||||||||
\(461\) | −2.40725e9 | −1.14437 | −0.572187 | − | 0.820123i | \(-0.693905\pi\) | ||||
−0.572187 | + | 0.820123i | \(0.693905\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.75705e9 | 0.822719 | 0.411359 | − | 0.911473i | \(-0.365054\pi\) | ||||
0.411359 | + | 0.911473i | \(0.365054\pi\) | |||||||
\(464\) | −4.56679e8 | −0.212226 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.93021e7 | −0.0454577 | ||||||||
\(467\) | −3.08270e8 | −0.140062 | −0.0700312 | − | 0.997545i | \(-0.522310\pi\) | ||||
−0.0700312 | + | 0.997545i | \(0.522310\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.68515e9 | −0.754282 | ||||||||
\(470\) | 3.21423e9 | 1.42802 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.28680e9 | −1.00099 | ||||||||
\(473\) | 4.66203e8 | 0.202564 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.60261e9 | −0.686119 | ||||||||
\(476\) | 6.69304e9 | 2.84446 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.16990e9 | 2.16513 | ||||||||
\(479\) | 3.98618e9 | 1.65723 | 0.828614 | − | 0.559820i | \(-0.189130\pi\) | ||||
0.828614 | + | 0.559820i | \(0.189130\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.36140e9 | 0.967524 | ||||||||
\(482\) | 3.49734e9 | 1.42257 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.32596e9 | −1.73430 | ||||||||
\(485\) | 2.55495e9 | 1.01692 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.81385e9 | 1.49628 | 0.748139 | − | 0.663542i | \(-0.230948\pi\) | ||||
0.748139 | + | 0.663542i | \(0.230948\pi\) | |||||||
\(488\) | −1.18112e9 | −0.460071 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5.79533e9 | 2.22532 | ||||||||
\(491\) | −2.55705e9 | −0.974885 | −0.487442 | − | 0.873155i | \(-0.662070\pi\) | ||||
−0.487442 | + | 0.873155i | \(0.662070\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.86859e8 | 0.258169 | ||||||||
\(494\) | −4.08522e9 | −1.52465 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.18617e8 | −0.264431 | ||||||||
\(497\) | −1.13738e9 | −0.415582 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.04146e9 | −0.735510 | −0.367755 | − | 0.929923i | \(-0.619873\pi\) | ||||
−0.367755 | + | 0.929923i | \(0.619873\pi\) | |||||||
\(500\) | −4.90916e8 | −0.175635 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.81551e9 | −0.640523 | ||||||||
\(503\) | −1.57865e9 | −0.553094 | −0.276547 | − | 0.961000i | \(-0.589190\pi\) | ||||
−0.276547 | + | 0.961000i | \(0.589190\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.35272e9 | −1.84950 | ||||||||
\(506\) | −2.46873e9 | −0.847124 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.25514e9 | −1.44009 | ||||||||
\(509\) | 9.25585e8 | 0.311103 | 0.155551 | − | 0.987828i | \(-0.450285\pi\) | ||||
0.155551 | + | 0.987828i | \(0.450285\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.09925e9 | −1.35904 | ||||||||
\(512\) | −4.69742e9 | −1.54673 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.10033e8 | 0.295588 | ||||||||
\(515\) | 1.60403e8 | 0.0517471 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.28224e8 | 0.199939 | ||||||||
\(518\) | −6.04254e9 | −1.91014 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.83675e9 | 2.75601 | ||||||||
\(521\) | −8.70376e7 | −0.0269634 | −0.0134817 | − | 0.999909i | \(-0.504291\pi\) | ||||
−0.0134817 | + | 0.999909i | \(0.504291\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.76877e8 | 0.298596 | 0.149298 | − | 0.988792i | \(-0.452299\pi\) | ||||
0.149298 | + | 0.988792i | \(0.452299\pi\) | |||||||
\(524\) | −1.00190e9 | −0.304203 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.64980e9 | 1.69271 | ||||||||
\(527\) | 1.08082e9 | 0.321675 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.97993e9 | 1.16891 | ||||||||
\(530\) | 9.63034e8 | 0.280980 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.91375e9 | 1.99078 | ||||||||
\(533\) | 5.85353e9 | 1.67445 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.94496e9 | −1.11379 | ||||||||
\(536\) | 3.16978e9 | 0.889104 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.52517e9 | 0.975982 | ||||||||
\(539\) | 1.13270e9 | 0.311570 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.62833e9 | −0.442132 | −0.221066 | − | 0.975259i | \(-0.570954\pi\) | ||||
−0.221066 | + | 0.975259i | \(0.570954\pi\) | |||||||
\(542\) | −1.10511e10 | −2.98132 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.19164e8 | 0.164896 | ||||||||
\(545\) | 7.18042e9 | 1.90004 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.71898e9 | 1.23280 | 0.616400 | − | 0.787433i | \(-0.288590\pi\) | ||||
0.616400 | + | 0.787433i | \(0.288590\pi\) | |||||||
\(548\) | 2.46350e9 | 0.639472 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.09930e9 | 0.538028 | ||||||||
\(551\) | 7.09509e8 | 0.180687 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.66119e9 | −1.92645 | ||||||||
\(554\) | 4.84579e9 | 1.21082 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.07398e10 | −2.64993 | ||||||||
\(557\) | −7.69391e9 | −1.88649 | −0.943244 | − | 0.332100i | \(-0.892243\pi\) | ||||
−0.943244 | + | 0.332100i | \(0.892243\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.02292e9 | 0.731957 | ||||||||
\(560\) | −6.92154e9 | −1.66550 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.56591e9 | 0.609768 | ||||||||
\(563\) | 8.34538e9 | 1.97091 | 0.985455 | − | 0.169937i | \(-0.0543565\pi\) | ||||
0.985455 | + | 0.169937i | \(0.0543565\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.98152e9 | 1.86173 | ||||||||
\(566\) | 9.32583e9 | 2.16187 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.13941e9 | 0.489864 | ||||||||
\(569\) | 7.13067e9 | 1.62270 | 0.811348 | − | 0.584563i | \(-0.198734\pi\) | ||||
0.811348 | + | 0.584563i | \(0.198734\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.23679e8 | −0.0952381 | −0.0476191 | − | 0.998866i | \(-0.515163\pi\) | ||||
−0.0476191 | + | 0.998866i | \(0.515163\pi\) | |||||||
\(572\) | 3.53924e9 | 0.790723 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.49785e10 | −3.30580 | ||||||||
\(575\) | −6.27967e9 | −1.37753 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.22691e9 | −1.13274 | −0.566370 | − | 0.824151i | \(-0.691653\pi\) | ||||
−0.566370 | + | 0.824151i | \(0.691653\pi\) | |||||||
\(578\) | 7.85713e8 | 0.169245 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.14496e9 | −0.669294 | ||||||||
\(581\) | −1.03297e10 | −2.18511 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.88226e8 | 0.0393405 | ||||||||
\(584\) | 7.71072e9 | 1.60195 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.26817e9 | −1.90262 | ||||||||
\(587\) | −4.39679e9 | −0.897227 | −0.448614 | − | 0.893726i | \(-0.648082\pi\) | ||||
−0.448614 | + | 0.893726i | \(0.648082\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.11646e9 | 0.225134 | ||||||||
\(590\) | −7.28860e9 | −1.46104 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.47913e9 | 0.689199 | ||||||||
\(593\) | 2.18339e9 | 0.429971 | 0.214986 | − | 0.976617i | \(-0.431030\pi\) | ||||
0.214986 | + | 0.976617i | \(0.431030\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.04102e10 | 2.02605 | ||||||||
\(596\) | 4.76556e9 | 0.922045 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.60076e10 | −3.06105 | ||||||||
\(599\) | −7.69910e8 | −0.146368 | −0.0731839 | − | 0.997318i | \(-0.523316\pi\) | ||||
−0.0731839 | + | 0.997318i | \(0.523316\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.98027e9 | −0.935820 | −0.467910 | − | 0.883776i | \(-0.654993\pi\) | ||||
−0.467910 | + | 0.883776i | \(0.654993\pi\) | |||||||
\(602\) | −7.73529e9 | −1.44507 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.70112e10 | 3.14127 | ||||||||
\(605\) | −6.72850e9 | −1.23531 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.09267e9 | 1.28721 | 0.643605 | − | 0.765358i | \(-0.277438\pi\) | ||||
0.643605 | + | 0.765358i | \(0.277438\pi\) | |||||||
\(608\) | 6.39581e8 | 0.115407 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.76452e9 | −0.671515 | ||||||||
\(611\) | 4.07348e9 | 0.722473 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.27203e9 | 1.09976 | 0.549878 | − | 0.835245i | \(-0.314674\pi\) | ||||
0.549878 | + | 0.835245i | \(0.314674\pi\) | |||||||
\(614\) | −2.11397e9 | −0.368561 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.41957e9 | −0.761812 | ||||||||
\(617\) | −1.02766e10 | −1.76137 | −0.880683 | − | 0.473706i | \(-0.842916\pi\) | ||||
−0.880683 | + | 0.473706i | \(0.842916\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.95459e9 | −0.500703 | −0.250351 | − | 0.968155i | \(-0.580546\pi\) | ||||
−0.250351 | + | 0.968155i | \(0.580546\pi\) | |||||||
\(620\) | −4.94882e9 | −0.833933 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.40774e9 | −0.901051 | ||||||||
\(623\) | 1.64443e10 | 2.72463 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.47254e9 | −1.06046 | ||||||||
\(626\) | −1.61706e10 | −2.63461 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.09191e9 | −0.498159 | ||||||||
\(629\) | −5.23272e9 | −0.838398 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.81079e9 | −0.920731 | −0.460365 | − | 0.887730i | \(-0.652282\pi\) | ||||
−0.460365 | + | 0.887730i | \(0.652282\pi\) | |||||||
\(632\) | 1.44108e10 | 2.27079 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.66492e10 | 2.59466 | ||||||||
\(635\) | −6.61835e9 | −1.02575 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.34458e9 | 1.12585 | ||||||||
\(638\) | −9.29404e8 | −0.141688 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.64948e10 | −2.48723 | ||||||||
\(641\) | −1.54674e9 | −0.231961 | −0.115980 | − | 0.993252i | \(-0.537001\pi\) | ||||
−0.115980 | + | 0.993252i | \(0.537001\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.74870e9 | 0.704427 | 0.352213 | − | 0.935920i | \(-0.385429\pi\) | ||||
0.352213 | + | 0.935920i | \(0.385429\pi\) | |||||||
\(644\) | 2.70909e10 | 3.99689 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.05259e9 | 1.32117 | ||||||||
\(647\) | 5.65810e8 | 0.0821307 | 0.0410653 | − | 0.999156i | \(-0.486925\pi\) | ||||
0.0410653 | + | 0.999156i | \(0.486925\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.42456e9 | −0.204562 | ||||||||
\(650\) | 1.36121e10 | 1.94415 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.07975e9 | 0.717754 | ||||||||
\(653\) | 5.35498e9 | 0.752596 | 0.376298 | − | 0.926499i | \(-0.377197\pi\) | ||||
0.376298 | + | 0.926499i | \(0.377197\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.55833e9 | −0.216678 | ||||||||
\(656\) | 8.62420e9 | 1.19277 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.04236e10 | −1.42635 | ||||||||
\(659\) | −9.80235e9 | −1.33423 | −0.667116 | − | 0.744954i | \(-0.732471\pi\) | ||||
−0.667116 | + | 0.744954i | \(0.732471\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.26059e9 | 0.708483 | 0.354242 | − | 0.935154i | \(-0.384739\pi\) | ||||
0.354242 | + | 0.935154i | \(0.384739\pi\) | |||||||
\(662\) | −3.71480e8 | −0.0497660 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.94303e10 | 2.57568 | ||||||||
\(665\) | 1.07535e10 | 1.41799 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.78014e9 | 0.362766 | ||||||||
\(668\) | −2.22269e10 | −2.88510 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.01029e10 | 1.29773 | ||||||||
\(671\) | −7.35780e8 | −0.0940197 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.29458e10 | 1.63710 | 0.818550 | − | 0.574435i | \(-0.194778\pi\) | ||||
0.818550 | + | 0.574435i | \(0.194778\pi\) | |||||||
\(674\) | 1.44393e10 | 1.81651 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.26176e9 | 0.904125 | ||||||||
\(677\) | 5.78853e8 | 0.0716981 | 0.0358490 | − | 0.999357i | \(-0.488586\pi\) | ||||
0.0358490 | + | 0.999357i | \(0.488586\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.28556e9 | −1.01573 | ||||||||
\(680\) | −1.95817e10 | −2.38819 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.46249e9 | −0.176541 | ||||||||
\(683\) | −4.24654e9 | −0.509992 | −0.254996 | − | 0.966942i | \(-0.582074\pi\) | ||||
−0.254996 | + | 0.966942i | \(0.582074\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.83168e9 | 0.455483 | ||||||||
\(686\) | 1.39659e9 | 0.165171 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.45377e9 | 0.521396 | ||||||||
\(689\) | 1.22048e9 | 0.142155 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.36695e10 | −1.57609 | −0.788043 | − | 0.615620i | \(-0.788906\pi\) | ||||
−0.788043 | + | 0.615620i | \(0.788906\pi\) | |||||||
\(692\) | −3.25338e10 | −3.73219 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.14005e6 | −0.000129469 0 | ||||||||
\(695\) | −1.67044e10 | −1.88749 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.29711e10 | −1.45098 | ||||||||
\(698\) | 1.59788e10 | 1.77848 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.30369e10 | −2.53852 | ||||||||
\(701\) | 1.78237e9 | 0.195427 | 0.0977134 | − | 0.995215i | \(-0.468847\pi\) | ||||
0.0977134 | + | 0.995215i | \(0.468847\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.40527e9 | −0.586778 | ||||||||
\(704\) | −3.50762e9 | −0.378886 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.55842e8 | −0.0166674 | ||||||||
\(707\) | 1.73586e10 | 1.84734 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.33988e10 | 1.41190 | 0.705951 | − | 0.708261i | \(-0.250520\pi\) | ||||
0.705951 | + | 0.708261i | \(0.250520\pi\) | |||||||
\(710\) | 6.81884e9 | 0.715001 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.09318e10 | −3.21163 | ||||||||
\(713\) | 4.37476e9 | 0.452003 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.50486e9 | 0.563216 | ||||||||
\(716\) | 1.02378e10 | 1.04235 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.51124e10 | −1.52369 | ||||||||
\(719\) | 1.60918e9 | 0.161455 | 0.0807276 | − | 0.996736i | \(-0.474276\pi\) | ||||
0.0807276 | + | 0.996736i | \(0.474276\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.20176e8 | −0.0516865 | ||||||||
\(722\) | −8.02775e9 | −0.793805 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.60945e10 | 1.57613 | ||||||||
\(725\) | −2.36411e9 | −0.230401 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.11466e10 | −1.07590 | −0.537949 | − | 0.842978i | \(-0.680801\pi\) | ||||
−0.537949 | + | 0.842978i | \(0.680801\pi\) | |||||||
\(728\) | −2.86571e10 | −2.75278 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.45760e10 | 2.33820 | ||||||||
\(731\) | −6.69861e9 | −0.634269 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.02155e10 | 0.958063 | 0.479031 | − | 0.877798i | \(-0.340988\pi\) | ||||
0.479031 | + | 0.877798i | \(0.340988\pi\) | |||||||
\(734\) | −1.15284e10 | −1.07605 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.50614e9 | 0.231704 | ||||||||
\(737\) | 1.97462e9 | 0.181697 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.75748e9 | −0.160189 | −0.0800947 | − | 0.996787i | \(-0.525522\pi\) | ||||
−0.0800947 | + | 0.996787i | \(0.525522\pi\) | |||||||
\(740\) | 2.39593e10 | 2.17352 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.12306e9 | −0.280651 | ||||||||
\(743\) | 7.57290e9 | 0.677332 | 0.338666 | − | 0.940907i | \(-0.390024\pi\) | ||||
0.338666 | + | 0.940907i | \(0.390024\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.41225e9 | 0.656754 | ||||||||
\(746\) | 1.70700e10 | 1.50538 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7.84274e9 | −0.685192 | ||||||||
\(749\) | 1.27933e10 | 1.11249 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.15251e9 | −0.702347 | −0.351173 | − | 0.936310i | \(-0.614217\pi\) | ||||
−0.351173 | + | 0.936310i | \(0.614217\pi\) | |||||||
\(752\) | 6.00159e9 | 0.514641 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.02637e9 | −0.511984 | ||||||||
\(755\) | 2.64588e10 | 2.23747 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.65336e10 | −1.38526 | −0.692629 | − | 0.721294i | \(-0.743548\pi\) | ||||
−0.692629 | + | 0.721294i | \(0.743548\pi\) | |||||||
\(758\) | −2.94788e9 | −0.245848 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.02274e10 | −1.67145 | ||||||||
\(761\) | 8.94719e9 | 0.735936 | 0.367968 | − | 0.929838i | \(-0.380054\pi\) | ||||
0.367968 | + | 0.929838i | \(0.380054\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.32857e10 | −1.89781 | ||||||||
\(764\) | −2.49370e10 | −2.02310 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.99444e10 | 2.40722 | ||||||||
\(767\) | −9.23705e9 | −0.739179 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.24990e9 | −0.257708 | −0.128854 | − | 0.991664i | \(-0.541130\pi\) | ||||
−0.128854 | + | 0.991664i | \(0.541130\pi\) | |||||||
\(770\) | −1.40863e10 | −1.11193 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.92562e10 | 3.85301 | ||||||||
\(773\) | 1.48477e10 | 1.15619 | 0.578096 | − | 0.815969i | \(-0.303796\pi\) | ||||
0.578096 | + | 0.815969i | \(0.303796\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.72010e9 | −0.287077 | ||||||||
\(776\) | 1.55852e10 | 1.19728 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.36367e10 | −1.79953 | ||||||||
\(779\) | −1.33988e10 | −1.01551 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.33275e9 | 0.100108 | ||||||||
\(782\) | 3.54717e10 | 2.65252 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.08210e10 | 0.801977 | ||||||||
\(785\) | −4.80909e9 | −0.354829 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.58917e9 | −0.262472 | −0.131236 | − | 0.991351i | \(-0.541895\pi\) | ||||
−0.131236 | + | 0.991351i | \(0.541895\pi\) | |||||||
\(788\) | −3.66173e10 | −2.66590 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.59307e10 | 3.31442 | ||||||||
\(791\) | −2.58836e10 | −1.85955 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.77089e9 | −0.339737 | ||||||||
\(794\) | −1.56481e10 | −1.10940 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.16858e9 | −0.222674 | ||||||||
\(797\) | −4.27547e9 | −0.299144 | −0.149572 | − | 0.988751i | \(-0.547790\pi\) | ||||
−0.149572 | + | 0.988751i | \(0.547790\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.02659e9 | −0.626051 | ||||||||
\(800\) | −2.13111e9 | −0.147160 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.84803e10 | −1.26502 | ||||||||
\(803\) | 4.80340e9 | 0.327374 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.21366e10 | 2.84691 | ||||||||
\(806\) | −9.48294e9 | −0.637926 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.26516e10 | −2.17753 | ||||||||
\(809\) | −2.23500e10 | −1.48408 | −0.742040 | − | 0.670356i | \(-0.766142\pi\) | ||||
−0.742040 | + | 0.670356i | \(0.766142\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.46284e10 | 0.962998 | 0.481499 | − | 0.876447i | \(-0.340093\pi\) | ||||
0.481499 | + | 0.876447i | \(0.340093\pi\) | |||||||
\(812\) | 1.01989e10 | 0.668510 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.08050e9 | 0.460128 | ||||||||
\(815\) | 7.90093e9 | 0.511242 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.91949e9 | −0.443912 | ||||||||
\(818\) | 3.14254e9 | 0.200745 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.93914e10 | 3.76162 | ||||||||
\(821\) | −2.53690e10 | −1.59993 | −0.799967 | − | 0.600044i | \(-0.795150\pi\) | ||||
−0.799967 | + | 0.600044i | \(0.795150\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.42001e9 | 0.401455 | 0.200727 | − | 0.979647i | \(-0.435669\pi\) | ||||
0.200727 | + | 0.979647i | \(0.435669\pi\) | |||||||
\(824\) | 9.78456e8 | 0.0609251 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.36365e10 | 1.45933 | ||||||||
\(827\) | −1.32102e10 | −0.812157 | −0.406079 | − | 0.913838i | \(-0.633104\pi\) | ||||
−0.406079 | + | 0.913838i | \(0.633104\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.65694e10 | 1.01010 | 0.505051 | − | 0.863090i | \(-0.331474\pi\) | ||||
0.505051 | + | 0.863090i | \(0.331474\pi\) | |||||||
\(830\) | 6.19293e10 | 3.75944 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.27438e10 | −1.36909 | ||||||||
\(833\) | −1.62751e10 | −0.975590 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.45712e10 | −2.05500 | ||||||||
\(836\) | −8.10136e9 | −0.479552 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.29374e9 | 0.0759438 | ||||||||
\(839\) | 1.93141e10 | 1.12903 | 0.564517 | − | 0.825422i | \(-0.309063\pi\) | ||||
0.564517 | + | 0.825422i | \(0.309063\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.62032e10 | −0.939325 | ||||||||
\(842\) | 3.96672e10 | 2.29002 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.53359e10 | −3.16817 | ||||||||
\(845\) | 1.12948e10 | 0.643990 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.18201e10 | 1.23386 | ||||||||
\(848\) | 1.79817e9 | 0.101262 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.01636e10 | −1.68468 | ||||||||
\(851\) | −2.11800e10 | −1.17808 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.27677e9 | 0.346270 | 0.173135 | − | 0.984898i | \(-0.444610\pi\) | ||||
0.173135 | + | 0.984898i | \(0.444610\pi\) | |||||||
\(854\) | 1.22081e10 | 0.670729 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.40643e10 | −1.31134 | ||||||||
\(857\) | −4.05896e9 | −0.220284 | −0.110142 | − | 0.993916i | \(-0.535131\pi\) | ||||
−0.110142 | + | 0.993916i | \(0.535131\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.88283e10 | −1.01352 | −0.506762 | − | 0.862086i | \(-0.669158\pi\) | ||||
−0.506762 | + | 0.862086i | \(0.669158\pi\) | |||||||
\(860\) | 3.06713e10 | 1.64432 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.60183e9 | 0.351066 | ||||||||
\(863\) | 3.10346e10 | 1.64364 | 0.821822 | − | 0.569744i | \(-0.192958\pi\) | ||||
0.821822 | + | 0.569744i | \(0.192958\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.06024e10 | −2.65837 | ||||||||
\(866\) | −5.40696e10 | −2.82905 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.60487e10 | 0.832956 | ||||||||
\(869\) | 8.97719e9 | 0.464057 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.28037e10 | 0.656555 | ||||||||
\(872\) | 4.38006e10 | 2.23703 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.66414e10 | 1.85645 | ||||||||
\(875\) | 2.47618e9 | 0.124955 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.85155e10 | 1.42752 | 0.713761 | − | 0.700389i | \(-0.246990\pi\) | ||||
0.713761 | + | 0.700389i | \(0.246990\pi\) | |||||||
\(878\) | 8.75543e9 | 0.436563 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8.11049e9 | 0.401197 | ||||||||
\(881\) | −1.96153e10 | −0.966451 | −0.483225 | − | 0.875496i | \(-0.660535\pi\) | ||||
−0.483225 | + | 0.875496i | \(0.660535\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.47908e9 | 0.0722986 | 0.0361493 | − | 0.999346i | \(-0.488491\pi\) | ||||
0.0361493 | + | 0.999346i | \(0.488491\pi\) | |||||||
\(884\) | −5.08533e10 | −2.47592 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.49110e10 | −2.16938 | ||||||||
\(887\) | −1.34099e10 | −0.645195 | −0.322598 | − | 0.946536i | \(-0.604556\pi\) | ||||
−0.322598 | + | 0.946536i | \(0.604556\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.14629e10 | 1.02455 | ||||||||
\(890\) | −9.85875e10 | −4.68767 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.39891e10 | −1.60348 | ||||||||
\(893\) | −9.32424e9 | −0.438161 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.59237e10 | 0.742444 | ||||||||
\(896\) | 5.34916e10 | 2.48432 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.76091e10 | −0.811467 | ||||||||
\(899\) | 1.64697e9 | 0.0756008 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.70451e9 | −0.123183 | ||||||||
\(902\) | 1.75514e10 | 0.796324 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.86872e10 | 2.19192 | ||||||||
\(905\) | 2.50330e10 | 1.12265 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.52251e10 | 1.56757 | 0.783785 | − | 0.621032i | \(-0.213286\pi\) | ||||
0.783785 | + | 0.621032i | \(0.213286\pi\) | |||||||
\(908\) | 1.45704e10 | 0.645910 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −9.13372e10 | −4.01793 | ||||||||
\(911\) | 3.48713e10 | 1.52811 | 0.764054 | − | 0.645152i | \(-0.223206\pi\) | ||||
0.764054 | + | 0.645152i | \(0.223206\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.21041e10 | 0.526364 | ||||||||
\(914\) | −4.62331e10 | −2.00282 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.28381e9 | 0.0551907 | ||||||||
\(917\) | 5.05357e9 | 0.216424 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.34799e10 | 0.997910 | 0.498955 | − | 0.866628i | \(-0.333717\pi\) | ||||
0.498955 | + | 0.866628i | \(0.333717\pi\) | |||||||
\(920\) | −7.92592e10 | −3.35577 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.68023e10 | −1.96657 | ||||||||
\(923\) | 8.64171e9 | 0.361738 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.80106e10 | 0.748224 | ||||||||
\(926\) | 3.41610e10 | 1.41381 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.43488e8 | 0.0387542 | ||||||||
\(929\) | −1.39279e10 | −0.569943 | −0.284972 | − | 0.958536i | \(-0.591984\pi\) | ||||
−0.284972 | + | 0.958536i | \(0.591984\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.68118e10 | −0.682796 | ||||||||
\(932\) | −1.27689e9 | −0.0516651 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.99345e9 | −0.240693 | ||||||||
\(935\) | −1.21984e10 | −0.488049 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.06809e10 | 0.424148 | 0.212074 | − | 0.977254i | \(-0.431978\pi\) | ||||
0.212074 | + | 0.977254i | \(0.431978\pi\) | |||||||
\(938\) | −3.27631e10 | −1.29621 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.13305e10 | 1.62302 | ||||||||
\(941\) | 1.37831e10 | 0.539241 | 0.269621 | − | 0.962967i | \(-0.413102\pi\) | ||||
0.269621 | + | 0.962967i | \(0.413102\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.25020e10 | −2.03885 | ||||||||
\(944\) | −1.36092e10 | −0.526541 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.06403e9 | 0.348099 | ||||||||
\(947\) | 4.26474e10 | 1.63180 | 0.815901 | − | 0.578192i | \(-0.196242\pi\) | ||||
0.815901 | + | 0.578192i | \(0.196242\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.11458e10 | 1.18296 | ||||||||
\(950\) | −3.11583e10 | −1.17907 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.35023e10 | 2.38539 | ||||||||
\(953\) | −1.06780e10 | −0.399637 | −0.199819 | − | 0.979833i | \(-0.564035\pi\) | ||||
−0.199819 | + | 0.979833i | \(0.564035\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.87864e10 | −1.44101 | ||||||||
\(956\) | 6.64777e10 | 2.46078 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.75002e10 | 2.84789 | ||||||||
\(959\) | −1.24259e10 | −0.454950 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.49210e10 | −0.905802 | ||||||||
\(962\) | 4.59109e10 | 1.66266 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.49709e10 | 1.61682 | ||||||||
\(965\) | 7.66120e10 | 2.74442 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.96746e10 | 1.41098 | 0.705488 | − | 0.708721i | \(-0.250728\pi\) | ||||
0.705488 | + | 0.708721i | \(0.250728\pi\) | |||||||
\(968\) | −4.10439e10 | −1.45440 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.96740e10 | 1.74754 | ||||||||
\(971\) | −2.83156e10 | −0.992565 | −0.496282 | − | 0.868161i | \(-0.665302\pi\) | ||||
−0.496282 | + | 0.868161i | \(0.665302\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.41715e10 | 1.88528 | ||||||||
\(974\) | 7.41497e10 | 2.57130 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.02910e9 | −0.242006 | ||||||||
\(977\) | −5.38772e9 | −0.184831 | −0.0924153 | − | 0.995721i | \(-0.529459\pi\) | ||||
−0.0924153 | + | 0.995721i | \(0.529459\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.92690e10 | −0.656327 | ||||||||
\(980\) | 7.45199e10 | 2.52919 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.97146e10 | −1.67531 | ||||||||
\(983\) | −2.50997e10 | −0.842814 | −0.421407 | − | 0.906872i | \(-0.638464\pi\) | ||||
−0.421407 | + | 0.906872i | \(0.638464\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.69537e10 | −1.89887 | ||||||||
\(986\) | 1.33541e10 | 0.443654 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.25302e10 | −1.73285 | ||||||||
\(989\) | −2.71134e10 | −0.891245 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.01878e10 | −0.332524 | −0.166262 | − | 0.986082i | \(-0.553170\pi\) | ||||
−0.166262 | + | 0.986082i | \(0.553170\pi\) | |||||||
\(992\) | 1.48465e9 | 0.0482872 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.21131e10 | −0.714163 | ||||||||
\(995\) | −4.92834e9 | −0.158606 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.65762e10 | 0.529727 | 0.264864 | − | 0.964286i | \(-0.414673\pi\) | ||||
0.264864 | + | 0.964286i | \(0.414673\pi\) | |||||||
\(998\) | −3.96905e10 | −1.26395 | ||||||||
\(999\) | 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 | 27.8.a.d.1.2 | yes | 2 | |
3.2 | odd | 2 | inner | 27.8.a.d.1.1 | ✓ | 2 | |
4.3 | odd | 2 | 432.8.a.o.1.2 | 2 | |||
9.2 | odd | 6 | 81.8.c.e.28.2 | 4 | |||
9.4 | even | 3 | 81.8.c.e.55.1 | 4 | |||
9.5 | odd | 6 | 81.8.c.e.55.2 | 4 | |||
9.7 | even | 3 | 81.8.c.e.28.1 | 4 | |||
12.11 | even | 2 | 432.8.a.o.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.8.a.d.1.1 | ✓ | 2 | 3.2 | odd | 2 | inner | |
27.8.a.d.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
81.8.c.e.28.1 | 4 | 9.7 | even | 3 | |||
81.8.c.e.28.2 | 4 | 9.2 | odd | 6 | |||
81.8.c.e.55.1 | 4 | 9.4 | even | 3 | |||
81.8.c.e.55.2 | 4 | 9.5 | odd | 6 | |||
432.8.a.o.1.1 | 2 | 12.11 | even | 2 | |||
432.8.a.o.1.2 | 2 | 4.3 | odd | 2 |