Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,9,Mod(42,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.42");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.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: | \(17.5172802326\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.12 | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.9.b.b.42.17 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 8.15532i | − | 0.509708i | −0.966980 | − | 0.254854i | \(-0.917973\pi\) | ||
0.966980 | − | 0.254854i | \(-0.0820273\pi\) | |||||||
\(3\) | 11.7848i | 0.145491i | 0.997351 | + | 0.0727457i | \(0.0231762\pi\) | ||||
−0.997351 | + | 0.0727457i | \(0.976824\pi\) | |||||||
\(4\) | 189.491 | 0.740198 | ||||||||
\(5\) | − | 1153.14i | − | 1.84503i | −0.385962 | − | 0.922515i | \(-0.626130\pi\) | ||
0.385962 | − | 0.922515i | \(-0.373870\pi\) | |||||||
\(6\) | 96.1089 | 0.0741581 | ||||||||
\(7\) | 1566.67i | 0.652506i | 0.945282 | + | 0.326253i | \(0.105786\pi\) | ||||
−0.945282 | + | 0.326253i | \(0.894214\pi\) | |||||||
\(8\) | − | 3633.12i | − | 0.886992i | ||||||
\(9\) | 6422.12 | 0.978832 | ||||||||
\(10\) | −9404.25 | −0.940425 | ||||||||
\(11\) | −10047.4 | −0.686253 | −0.343127 | − | 0.939289i | \(-0.611486\pi\) | ||||
−0.343127 | + | 0.939289i | \(0.611486\pi\) | |||||||
\(12\) | 2233.11i | 0.107693i | ||||||||
\(13\) | −1635.86 | −0.0572760 | −0.0286380 | − | 0.999590i | \(-0.509117\pi\) | ||||
−0.0286380 | + | 0.999590i | \(0.509117\pi\) | |||||||
\(14\) | 12776.7 | 0.332587 | ||||||||
\(15\) | 13589.6 | 0.268436 | ||||||||
\(16\) | 18880.4 | 0.288092 | ||||||||
\(17\) | 25926.9 | 0.310424 | 0.155212 | − | 0.987881i | \(-0.450394\pi\) | ||||
0.155212 | + | 0.987881i | \(0.450394\pi\) | |||||||
\(18\) | − | 52374.4i | − | 0.498918i | ||||||
\(19\) | − | 167816.i | − | 1.28771i | −0.765147 | − | 0.643855i | \(-0.777334\pi\) | ||
0.765147 | − | 0.643855i | \(-0.222666\pi\) | |||||||
\(20\) | − | 218510.i | − | 1.36569i | ||||||
\(21\) | −18462.9 | −0.0949341 | ||||||||
\(22\) | 81940.1i | 0.349789i | ||||||||
\(23\) | −225426. | −0.805551 | −0.402775 | − | 0.915299i | \(-0.631954\pi\) | ||||
−0.402775 | + | 0.915299i | \(0.631954\pi\) | |||||||
\(24\) | 42815.6 | 0.129050 | ||||||||
\(25\) | −939115. | −2.40413 | ||||||||
\(26\) | 13341.0i | 0.0291940i | ||||||||
\(27\) | 153004.i | 0.287903i | ||||||||
\(28\) | 296869.i | 0.482984i | ||||||||
\(29\) | − | 829628.i | − | 1.17298i | −0.809956 | − | 0.586491i | \(-0.800509\pi\) | ||
0.809956 | − | 0.586491i | \(-0.199491\pi\) | |||||||
\(30\) | − | 110827.i | − | 0.136824i | ||||||
\(31\) | −803727. | −0.870285 | −0.435143 | − | 0.900362i | \(-0.643302\pi\) | ||||
−0.435143 | + | 0.900362i | \(0.643302\pi\) | |||||||
\(32\) | − | 1.08405e6i | − | 1.03383i | ||||||
\(33\) | − | 118407.i | − | 0.0998440i | ||||||
\(34\) | − | 211442.i | − | 0.158225i | ||||||
\(35\) | 1.80659e6 | 1.20389 | ||||||||
\(36\) | 1.21693e6 | 0.724530 | ||||||||
\(37\) | − | 267963.i | − | 0.142978i | −0.997441 | − | 0.0714889i | \(-0.977225\pi\) | ||
0.997441 | − | 0.0714889i | \(-0.0227751\pi\) | |||||||
\(38\) | −1.36859e6 | −0.656356 | ||||||||
\(39\) | − | 19278.3i | − | 0.00833317i | ||||||
\(40\) | −4.18951e6 | −1.63653 | ||||||||
\(41\) | 2.02467e6 | 0.716503 | 0.358252 | − | 0.933625i | \(-0.383373\pi\) | ||||
0.358252 | + | 0.933625i | \(0.383373\pi\) | |||||||
\(42\) | 150571.i | 0.0483886i | ||||||||
\(43\) | −1.99883e6 | + | 2.77361e6i | −0.584658 | + | 0.811280i | ||||
\(44\) | −1.90390e6 | −0.507964 | ||||||||
\(45\) | − | 7.40562e6i | − | 1.80597i | ||||||
\(46\) | 1.83842e6i | 0.410595i | ||||||||
\(47\) | 6.67489e6 | 1.36789 | 0.683947 | − | 0.729531i | \(-0.260262\pi\) | ||||
0.683947 | + | 0.729531i | \(0.260262\pi\) | |||||||
\(48\) | 222502.i | 0.0419149i | ||||||||
\(49\) | 3.31036e6 | 0.574236 | ||||||||
\(50\) | 7.65878e6i | 1.22540i | ||||||||
\(51\) | 305544.i | 0.0451640i | ||||||||
\(52\) | −309980. | −0.0423956 | ||||||||
\(53\) | 1.35151e7 | 1.71284 | 0.856420 | − | 0.516280i | \(-0.172684\pi\) | ||||
0.856420 | + | 0.516280i | \(0.172684\pi\) | |||||||
\(54\) | 1.24779e6 | 0.146746 | ||||||||
\(55\) | 1.15861e7i | 1.26616i | ||||||||
\(56\) | 5.69189e6 | 0.578768 | ||||||||
\(57\) | 1.97768e6 | 0.187351 | ||||||||
\(58\) | −6.76588e6 | −0.597878 | ||||||||
\(59\) | −1.38645e7 | −1.14419 | −0.572093 | − | 0.820188i | \(-0.693869\pi\) | ||||
−0.572093 | + | 0.820188i | \(0.693869\pi\) | |||||||
\(60\) | 2.57510e6 | 0.198696 | ||||||||
\(61\) | 2.78916e6i | 0.201444i | 0.994915 | + | 0.100722i | \(0.0321153\pi\) | ||||
−0.994915 | + | 0.100722i | \(0.967885\pi\) | |||||||
\(62\) | 6.55465e6i | 0.443591i | ||||||||
\(63\) | 1.00613e7i | 0.638694i | ||||||||
\(64\) | −4.00743e6 | −0.238862 | ||||||||
\(65\) | 1.88638e6i | 0.105676i | ||||||||
\(66\) | −965648. | −0.0508912 | ||||||||
\(67\) | −2.07321e6 | −0.102883 | −0.0514416 | − | 0.998676i | \(-0.516382\pi\) | ||||
−0.0514416 | + | 0.998676i | \(0.516382\pi\) | |||||||
\(68\) | 4.91291e6 | 0.229775 | ||||||||
\(69\) | − | 2.65660e6i | − | 0.117201i | ||||||
\(70\) | − | 1.47333e7i | − | 0.613633i | ||||||
\(71\) | 3.64571e7i | 1.43466i | 0.696733 | + | 0.717330i | \(0.254636\pi\) | ||||
−0.696733 | + | 0.717330i | \(0.745364\pi\) | |||||||
\(72\) | − | 2.33323e7i | − | 0.868217i | ||||||
\(73\) | 2.21335e7i | 0.779396i | 0.920943 | + | 0.389698i | \(0.127421\pi\) | ||||
−0.920943 | + | 0.389698i | \(0.872579\pi\) | |||||||
\(74\) | −2.18533e6 | −0.0728769 | ||||||||
\(75\) | − | 1.10673e7i | − | 0.349781i | ||||||
\(76\) | − | 3.17995e7i | − | 0.953161i | ||||||
\(77\) | − | 1.57410e7i | − | 0.447785i | ||||||
\(78\) | −157221. | −0.00424748 | ||||||||
\(79\) | −2.21707e7 | −0.569209 | −0.284605 | − | 0.958645i | \(-0.591862\pi\) | ||||
−0.284605 | + | 0.958645i | \(0.591862\pi\) | |||||||
\(80\) | − | 2.17718e7i | − | 0.531538i | ||||||
\(81\) | 4.03324e7 | 0.936945 | ||||||||
\(82\) | − | 1.65118e7i | − | 0.365207i | ||||||
\(83\) | 1.20032e7 | 0.252922 | 0.126461 | − | 0.991972i | \(-0.459638\pi\) | ||||
0.126461 | + | 0.991972i | \(0.459638\pi\) | |||||||
\(84\) | −3.49854e6 | −0.0702700 | ||||||||
\(85\) | − | 2.98974e7i | − | 0.572741i | ||||||
\(86\) | 2.26196e7 | + | 1.63011e7i | 0.413516 | + | 0.298004i | ||||
\(87\) | 9.77700e6 | 0.170659 | ||||||||
\(88\) | 3.65035e7i | 0.608701i | ||||||||
\(89\) | − | 4.53594e7i | − | 0.722949i | −0.932382 | − | 0.361474i | \(-0.882274\pi\) | ||
0.932382 | − | 0.361474i | \(-0.117726\pi\) | |||||||
\(90\) | −6.03952e7 | −0.920519 | ||||||||
\(91\) | − | 2.56285e6i | − | 0.0373729i | ||||||
\(92\) | −4.27162e7 | −0.596267 | ||||||||
\(93\) | − | 9.47177e6i | − | 0.126619i | ||||||
\(94\) | − | 5.44359e7i | − | 0.697226i | ||||||
\(95\) | −1.93516e8 | −2.37586 | ||||||||
\(96\) | 1.27754e7 | 0.150414 | ||||||||
\(97\) | 1.49594e8 | 1.68977 | 0.844884 | − | 0.534950i | \(-0.179669\pi\) | ||||
0.844884 | + | 0.534950i | \(0.179669\pi\) | |||||||
\(98\) | − | 2.69970e7i | − | 0.292692i | ||||||
\(99\) | −6.45258e7 | −0.671727 | ||||||||
\(100\) | −1.77954e8 | −1.77954 | ||||||||
\(101\) | 5.23322e7 | 0.502902 | 0.251451 | − | 0.967870i | \(-0.419092\pi\) | ||||
0.251451 | + | 0.967870i | \(0.419092\pi\) | |||||||
\(102\) | 2.49181e6 | 0.0230204 | ||||||||
\(103\) | −3.20839e7 | −0.285061 | −0.142531 | − | 0.989790i | \(-0.545524\pi\) | ||||
−0.142531 | + | 0.989790i | \(0.545524\pi\) | |||||||
\(104\) | 5.94327e6i | 0.0508034i | ||||||||
\(105\) | 2.12903e7i | 0.175156i | ||||||||
\(106\) | − | 1.10220e8i | − | 0.873047i | ||||||
\(107\) | 1.76389e8 | 1.34566 | 0.672830 | − | 0.739797i | \(-0.265078\pi\) | ||||
0.672830 | + | 0.739797i | \(0.265078\pi\) | |||||||
\(108\) | 2.89928e7i | 0.213105i | ||||||||
\(109\) | 1.39197e8 | 0.986104 | 0.493052 | − | 0.870000i | \(-0.335881\pi\) | ||||
0.493052 | + | 0.870000i | \(0.335881\pi\) | |||||||
\(110\) | 9.44886e7 | 0.645370 | ||||||||
\(111\) | 3.15790e6 | 0.0208021 | ||||||||
\(112\) | 2.95793e7i | 0.187982i | ||||||||
\(113\) | 8.95103e7i | 0.548984i | 0.961589 | + | 0.274492i | \(0.0885096\pi\) | ||||
−0.961589 | + | 0.274492i | \(0.911490\pi\) | |||||||
\(114\) | − | 1.61286e7i | − | 0.0954941i | ||||||
\(115\) | 2.59949e8i | 1.48627i | ||||||||
\(116\) | − | 1.57207e8i | − | 0.868239i | ||||||
\(117\) | −1.05057e7 | −0.0560636 | ||||||||
\(118\) | 1.13070e8i | 0.583201i | ||||||||
\(119\) | 4.06188e7i | 0.202553i | ||||||||
\(120\) | − | 4.93725e7i | − | 0.238101i | ||||||
\(121\) | −1.13408e8 | −0.529056 | ||||||||
\(122\) | 2.27465e7 | 0.102678 | ||||||||
\(123\) | 2.38603e7i | 0.104245i | ||||||||
\(124\) | −1.52299e8 | −0.644184 | ||||||||
\(125\) | 6.32487e8i | 2.59067i | ||||||||
\(126\) | 8.20533e7 | 0.325547 | ||||||||
\(127\) | −6.38872e7 | −0.245583 | −0.122792 | − | 0.992432i | \(-0.539185\pi\) | ||||
−0.122792 | + | 0.992432i | \(0.539185\pi\) | |||||||
\(128\) | − | 2.44836e8i | − | 0.912085i | ||||||
\(129\) | −3.26864e7 | − | 2.35558e7i | −0.118034 | − | 0.0850627i | ||||
\(130\) | 1.53840e7 | 0.0538638 | ||||||||
\(131\) | 2.45176e8i | 0.832517i | 0.909246 | + | 0.416258i | \(0.136659\pi\) | ||||
−0.909246 | + | 0.416258i | \(0.863341\pi\) | |||||||
\(132\) | − | 2.24371e7i | − | 0.0739044i | ||||||
\(133\) | 2.62911e8 | 0.840239 | ||||||||
\(134\) | 1.69077e7i | 0.0524404i | ||||||||
\(135\) | 1.76435e8 | 0.531190 | ||||||||
\(136\) | − | 9.41956e7i | − | 0.275344i | ||||||
\(137\) | − | 4.58018e8i | − | 1.30017i | −0.759861 | − | 0.650085i | \(-0.774733\pi\) | ||
0.759861 | − | 0.650085i | \(-0.225267\pi\) | |||||||
\(138\) | −2.16655e7 | −0.0597381 | ||||||||
\(139\) | 5.84939e8 | 1.56694 | 0.783468 | − | 0.621433i | \(-0.213449\pi\) | ||||
0.783468 | + | 0.621433i | \(0.213449\pi\) | |||||||
\(140\) | 3.42332e8 | 0.891119 | ||||||||
\(141\) | 7.86623e7i | 0.199017i | ||||||||
\(142\) | 2.97320e8 | 0.731257 | ||||||||
\(143\) | 1.64362e7 | 0.0393058 | ||||||||
\(144\) | 1.21252e8 | 0.281993 | ||||||||
\(145\) | −9.56680e8 | −2.16419 | ||||||||
\(146\) | 1.80506e8 | 0.397264 | ||||||||
\(147\) | 3.90119e7i | 0.0835464i | ||||||||
\(148\) | − | 5.07766e7i | − | 0.105832i | ||||||
\(149\) | − | 7.73760e8i | − | 1.56986i | −0.619584 | − | 0.784930i | \(-0.712699\pi\) | ||
0.619584 | − | 0.784930i | \(-0.287301\pi\) | |||||||
\(150\) | −9.02573e7 | −0.178286 | ||||||||
\(151\) | − | 1.68887e7i | − | 0.0324855i | −0.999868 | − | 0.0162427i | \(-0.994830\pi\) | ||
0.999868 | − | 0.0162427i | \(-0.00517045\pi\) | |||||||
\(152\) | −6.09694e8 | −1.14219 | ||||||||
\(153\) | 1.66506e8 | 0.303853 | ||||||||
\(154\) | −1.28373e8 | −0.228239 | ||||||||
\(155\) | 9.26812e8i | 1.60570i | ||||||||
\(156\) | − | 3.65306e6i | − | 0.00616820i | ||||||
\(157\) | 1.03371e9i | 1.70138i | 0.525665 | + | 0.850692i | \(0.323816\pi\) | ||||
−0.525665 | + | 0.850692i | \(0.676184\pi\) | |||||||
\(158\) | 1.80810e8i | 0.290130i | ||||||||
\(159\) | 1.59273e8i | 0.249203i | ||||||||
\(160\) | −1.25007e9 | −1.90746 | ||||||||
\(161\) | − | 3.53168e8i | − | 0.525627i | ||||||
\(162\) | − | 3.28924e8i | − | 0.477568i | ||||||
\(163\) | − | 9.59746e8i | − | 1.35958i | −0.733405 | − | 0.679792i | \(-0.762070\pi\) | ||
0.733405 | − | 0.679792i | \(-0.237930\pi\) | |||||||
\(164\) | 3.83656e8 | 0.530354 | ||||||||
\(165\) | −1.36540e8 | −0.184215 | ||||||||
\(166\) | − | 9.78902e7i | − | 0.128916i | ||||||
\(167\) | 3.88487e8 | 0.499471 | 0.249736 | − | 0.968314i | \(-0.419656\pi\) | ||||
0.249736 | + | 0.968314i | \(0.419656\pi\) | |||||||
\(168\) | 6.70778e7i | 0.0842058i | ||||||||
\(169\) | −8.13055e8 | −0.996719 | ||||||||
\(170\) | −2.43823e8 | −0.291930 | ||||||||
\(171\) | − | 1.07773e9i | − | 1.26045i | ||||||
\(172\) | −3.78759e8 | + | 5.25573e8i | −0.432763 | + | 0.600508i | ||||
\(173\) | 8.26563e8 | 0.922765 | 0.461383 | − | 0.887201i | \(-0.347354\pi\) | ||||
0.461383 | + | 0.887201i | \(0.347354\pi\) | |||||||
\(174\) | − | 7.97346e7i | − | 0.0869861i | ||||||
\(175\) | − | 1.47128e9i | − | 1.56871i | ||||||
\(176\) | −1.89699e8 | −0.197704 | ||||||||
\(177\) | − | 1.63391e8i | − | 0.166469i | ||||||
\(178\) | −3.69921e8 | −0.368492 | ||||||||
\(179\) | − | 4.45921e8i | − | 0.434356i | −0.976132 | − | 0.217178i | \(-0.930315\pi\) | ||
0.976132 | − | 0.217178i | \(-0.0696852\pi\) | |||||||
\(180\) | − | 1.40330e9i | − | 1.33678i | ||||||
\(181\) | −9.84597e7 | −0.0917369 | −0.0458685 | − | 0.998947i | \(-0.514606\pi\) | ||||
−0.0458685 | + | 0.998947i | \(0.514606\pi\) | |||||||
\(182\) | −2.09008e7 | −0.0190493 | ||||||||
\(183\) | −3.28698e7 | −0.0293084 | ||||||||
\(184\) | 8.19000e8i | 0.714517i | ||||||||
\(185\) | −3.09000e8 | −0.263798 | ||||||||
\(186\) | −7.72453e7 | −0.0645387 | ||||||||
\(187\) | −2.60499e8 | −0.213029 | ||||||||
\(188\) | 1.26483e9 | 1.01251 | ||||||||
\(189\) | −2.39706e8 | −0.187859 | ||||||||
\(190\) | 1.57818e9i | 1.21100i | ||||||||
\(191\) | 1.95755e9i | 1.47088i | 0.677587 | + | 0.735442i | \(0.263026\pi\) | ||||
−0.677587 | + | 0.735442i | \(0.736974\pi\) | |||||||
\(192\) | − | 4.72268e7i | − | 0.0347523i | ||||||
\(193\) | 8.96951e8 | 0.646457 | 0.323228 | − | 0.946321i | \(-0.395232\pi\) | ||||
0.323228 | + | 0.946321i | \(0.395232\pi\) | |||||||
\(194\) | − | 1.21999e9i | − | 0.861287i | ||||||
\(195\) | −2.22306e7 | −0.0153749 | ||||||||
\(196\) | 6.27282e8 | 0.425048 | ||||||||
\(197\) | −9.47778e8 | −0.629277 | −0.314638 | − | 0.949212i | \(-0.601883\pi\) | ||||
−0.314638 | + | 0.949212i | \(0.601883\pi\) | |||||||
\(198\) | 5.26229e8i | 0.342384i | ||||||||
\(199\) | − | 2.15162e9i | − | 1.37200i | −0.727602 | − | 0.686000i | \(-0.759365\pi\) | ||
0.727602 | − | 0.686000i | \(-0.240635\pi\) | |||||||
\(200\) | 3.41192e9i | 2.13245i | ||||||||
\(201\) | − | 2.44324e7i | − | 0.0149686i | ||||||
\(202\) | − | 4.26786e8i | − | 0.256333i | ||||||
\(203\) | 1.29975e9 | 0.765378 | ||||||||
\(204\) | 5.78977e7i | 0.0334303i | ||||||||
\(205\) | − | 2.33473e9i | − | 1.32197i | ||||||
\(206\) | 2.61654e8i | 0.145298i | ||||||||
\(207\) | −1.44771e9 | −0.788499 | ||||||||
\(208\) | −3.08856e7 | −0.0165007 | ||||||||
\(209\) | 1.68612e9i | 0.883696i | ||||||||
\(210\) | 1.73630e8 | 0.0892784 | ||||||||
\(211\) | 2.26160e9i | 1.14100i | 0.821298 | + | 0.570500i | \(0.193250\pi\) | ||||
−0.821298 | + | 0.570500i | \(0.806750\pi\) | |||||||
\(212\) | 2.56099e9 | 1.26784 | ||||||||
\(213\) | −4.29640e8 | −0.208731 | ||||||||
\(214\) | − | 1.43851e9i | − | 0.685894i | ||||||
\(215\) | 3.19836e9 | + | 2.30494e9i | 1.49684 | + | 1.07871i | ||||
\(216\) | 5.55880e8 | 0.255368 | ||||||||
\(217\) | − | 1.25917e9i | − | 0.567866i | ||||||
\(218\) | − | 1.13519e9i | − | 0.502624i | ||||||
\(219\) | −2.60839e8 | −0.113395 | ||||||||
\(220\) | 2.19547e9i | 0.937208i | ||||||||
\(221\) | −4.24128e7 | −0.0177798 | ||||||||
\(222\) | − | 2.57537e7i | − | 0.0106030i | ||||||
\(223\) | − | 2.14578e9i | − | 0.867692i | −0.900987 | − | 0.433846i | \(-0.857156\pi\) | ||
0.900987 | − | 0.433846i | \(-0.142844\pi\) | |||||||
\(224\) | 1.69835e9 | 0.674583 | ||||||||
\(225\) | −6.03111e9 | −2.35324 | ||||||||
\(226\) | 7.29986e8 | 0.279821 | ||||||||
\(227\) | 4.15632e9i | 1.56533i | 0.622445 | + | 0.782664i | \(0.286139\pi\) | ||||
−0.622445 | + | 0.782664i | \(0.713861\pi\) | |||||||
\(228\) | 3.74751e8 | 0.138677 | ||||||||
\(229\) | 4.21103e9 | 1.53125 | 0.765625 | − | 0.643287i | \(-0.222430\pi\) | ||||
0.765625 | + | 0.643287i | \(0.222430\pi\) | |||||||
\(230\) | 2.11996e9 | 0.757561 | ||||||||
\(231\) | 1.85505e8 | 0.0651488 | ||||||||
\(232\) | −3.01414e9 | −1.04043 | ||||||||
\(233\) | 4.28129e9i | 1.45262i | 0.687369 | + | 0.726309i | \(0.258766\pi\) | ||||
−0.687369 | + | 0.726309i | \(0.741234\pi\) | |||||||
\(234\) | 8.56772e7i | 0.0285760i | ||||||||
\(235\) | − | 7.69711e9i | − | 2.52381i | ||||||
\(236\) | −2.62720e9 | −0.846925 | ||||||||
\(237\) | − | 2.61278e8i | − | 0.0828151i | ||||||
\(238\) | 3.31260e8 | 0.103243 | ||||||||
\(239\) | −5.77453e9 | −1.76980 | −0.884901 | − | 0.465778i | \(-0.845774\pi\) | ||||
−0.884901 | + | 0.465778i | \(0.845774\pi\) | |||||||
\(240\) | 2.56576e8 | 0.0773342 | ||||||||
\(241\) | 5.53206e9i | 1.63991i | 0.572431 | + | 0.819953i | \(0.306001\pi\) | ||||
−0.572431 | + | 0.819953i | \(0.693999\pi\) | |||||||
\(242\) | 9.24878e8i | 0.269664i | ||||||||
\(243\) | 1.47917e9i | 0.424221i | ||||||||
\(244\) | 5.28521e8i | 0.149109i | ||||||||
\(245\) | − | 3.81731e9i | − | 1.05948i | ||||||
\(246\) | 1.94588e8 | 0.0531345 | ||||||||
\(247\) | 2.74523e8i | 0.0737549i | ||||||||
\(248\) | 2.92004e9i | 0.771936i | ||||||||
\(249\) | 1.41456e8i | 0.0367979i | ||||||||
\(250\) | 5.15814e9 | 1.32048 | ||||||||
\(251\) | −2.90089e9 | −0.730865 | −0.365432 | − | 0.930838i | \(-0.619079\pi\) | ||||
−0.365432 | + | 0.930838i | \(0.619079\pi\) | |||||||
\(252\) | 1.90653e9i | 0.472760i | ||||||||
\(253\) | 2.26496e9 | 0.552812 | ||||||||
\(254\) | 5.21020e8i | 0.125176i | ||||||||
\(255\) | 3.52336e8 | 0.0833289 | ||||||||
\(256\) | −3.02262e9 | −0.703758 | ||||||||
\(257\) | − | 4.03352e9i | − | 0.924596i | −0.886725 | − | 0.462298i | \(-0.847025\pi\) | ||
0.886725 | − | 0.462298i | \(-0.152975\pi\) | |||||||
\(258\) | −1.92105e8 | + | 2.66568e8i | −0.0433571 | + | 0.0601630i | ||||
\(259\) | 4.19810e8 | 0.0932939 | ||||||||
\(260\) | 3.57452e8i | 0.0782211i | ||||||||
\(261\) | − | 5.32797e9i | − | 1.14815i | ||||||
\(262\) | 1.99949e9 | 0.424340 | ||||||||
\(263\) | 5.82399e8i | 0.121730i | 0.998146 | + | 0.0608650i | \(0.0193859\pi\) | ||||
−0.998146 | + | 0.0608650i | \(0.980614\pi\) | |||||||
\(264\) | −4.30187e8 | −0.0885609 | ||||||||
\(265\) | − | 1.55849e10i | − | 3.16024i | ||||||
\(266\) | − | 2.14413e9i | − | 0.428276i | ||||||
\(267\) | 5.34552e8 | 0.105183 | ||||||||
\(268\) | −3.92855e8 | −0.0761540 | ||||||||
\(269\) | −3.25850e9 | −0.622313 | −0.311156 | − | 0.950359i | \(-0.600716\pi\) | ||||
−0.311156 | + | 0.950359i | \(0.600716\pi\) | |||||||
\(270\) | − | 1.43888e9i | − | 0.270751i | ||||||
\(271\) | 2.65797e9 | 0.492802 | 0.246401 | − | 0.969168i | \(-0.420752\pi\) | ||||
0.246401 | + | 0.969168i | \(0.420752\pi\) | |||||||
\(272\) | 4.89510e8 | 0.0894305 | ||||||||
\(273\) | 3.02027e7 | 0.00543744 | ||||||||
\(274\) | −3.73528e9 | −0.662706 | ||||||||
\(275\) | 9.43569e9 | 1.64984 | ||||||||
\(276\) | − | 5.03402e8i | − | 0.0867518i | ||||||
\(277\) | 2.12193e9i | 0.360422i | 0.983628 | + | 0.180211i | \(0.0576780\pi\) | ||||
−0.983628 | + | 0.180211i | \(0.942322\pi\) | |||||||
\(278\) | − | 4.77036e9i | − | 0.798679i | ||||||
\(279\) | −5.16163e9 | −0.851863 | ||||||||
\(280\) | − | 6.56356e9i | − | 1.06784i | ||||||
\(281\) | −5.91486e9 | −0.948679 | −0.474339 | − | 0.880342i | \(-0.657313\pi\) | ||||
−0.474339 | + | 0.880342i | \(0.657313\pi\) | |||||||
\(282\) | 6.41516e8 | 0.101440 | ||||||||
\(283\) | −6.44035e9 | −1.00407 | −0.502035 | − | 0.864847i | \(-0.667415\pi\) | ||||
−0.502035 | + | 0.864847i | \(0.667415\pi\) | |||||||
\(284\) | 6.90829e9i | 1.06193i | ||||||||
\(285\) | − | 2.28054e9i | − | 0.345668i | ||||||
\(286\) | − | 1.34042e8i | − | 0.0200345i | ||||||
\(287\) | 3.17198e9i | 0.467523i | ||||||||
\(288\) | − | 6.96192e9i | − | 1.01195i | ||||||
\(289\) | −6.30355e9 | −0.903637 | ||||||||
\(290\) | 7.80203e9i | 1.10310i | ||||||||
\(291\) | 1.76294e9i | 0.245847i | ||||||||
\(292\) | 4.19409e9i | 0.576908i | ||||||||
\(293\) | 9.16798e9 | 1.24395 | 0.621976 | − | 0.783037i | \(-0.286330\pi\) | ||||
0.621976 | + | 0.783037i | \(0.286330\pi\) | |||||||
\(294\) | 3.18155e8 | 0.0425842 | ||||||||
\(295\) | 1.59878e10i | 2.11106i | ||||||||
\(296\) | −9.73543e8 | −0.126820 | ||||||||
\(297\) | − | 1.53729e9i | − | 0.197575i | ||||||
\(298\) | −6.31026e9 | −0.800170 | ||||||||
\(299\) | 3.68766e8 | 0.0461387 | ||||||||
\(300\) | − | 2.09715e9i | − | 0.258907i | ||||||
\(301\) | −4.34532e9 | − | 3.13150e9i | −0.529365 | − | 0.381493i | ||||
\(302\) | −1.37733e8 | −0.0165581 | ||||||||
\(303\) | 6.16725e8i | 0.0731680i | ||||||||
\(304\) | − | 3.16842e9i | − | 0.370979i | ||||||
\(305\) | 3.21630e9 | 0.371670 | ||||||||
\(306\) | − | 1.35791e9i | − | 0.154876i | ||||||
\(307\) | −6.19557e9 | −0.697474 | −0.348737 | − | 0.937221i | \(-0.613389\pi\) | ||||
−0.348737 | + | 0.937221i | \(0.613389\pi\) | |||||||
\(308\) | − | 2.98277e9i | − | 0.331449i | ||||||
\(309\) | − | 3.78102e8i | − | 0.0414740i | ||||||
\(310\) | 7.55845e9 | 0.818438 | ||||||||
\(311\) | 4.05221e8 | 0.0433162 | 0.0216581 | − | 0.999765i | \(-0.493105\pi\) | ||||
0.0216581 | + | 0.999765i | \(0.493105\pi\) | |||||||
\(312\) | −7.00403e7 | −0.00739145 | ||||||||
\(313\) | 7.98641e9i | 0.832098i | 0.909342 | + | 0.416049i | \(0.136586\pi\) | ||||
−0.909342 | + | 0.416049i | \(0.863414\pi\) | |||||||
\(314\) | 8.43028e9 | 0.867208 | ||||||||
\(315\) | 1.16021e10 | 1.17841 | ||||||||
\(316\) | −4.20115e9 | −0.421328 | ||||||||
\(317\) | 1.01939e10 | 1.00949 | 0.504745 | − | 0.863268i | \(-0.331586\pi\) | ||||
0.504745 | + | 0.863268i | \(0.331586\pi\) | |||||||
\(318\) | 1.29892e9 | 0.127021 | ||||||||
\(319\) | 8.33563e9i | 0.804963i | ||||||||
\(320\) | 4.62115e9i | 0.440707i | ||||||||
\(321\) | 2.07871e9i | 0.195782i | ||||||||
\(322\) | −2.88020e9 | −0.267916 | ||||||||
\(323\) | − | 4.35094e9i | − | 0.399736i | ||||||
\(324\) | 7.64262e9 | 0.693525 | ||||||||
\(325\) | 1.53626e9 | 0.137699 | ||||||||
\(326\) | −7.82703e9 | −0.692990 | ||||||||
\(327\) | 1.64040e9i | 0.143470i | ||||||||
\(328\) | − | 7.35586e9i | − | 0.635533i | ||||||
\(329\) | 1.04573e10i | 0.892560i | ||||||||
\(330\) | 1.11353e9i | 0.0938958i | ||||||||
\(331\) | 1.22332e9i | 0.101913i | 0.998701 | + | 0.0509565i | \(0.0162270\pi\) | ||||
−0.998701 | + | 0.0509565i | \(0.983773\pi\) | |||||||
\(332\) | 2.27450e9 | 0.187212 | ||||||||
\(333\) | − | 1.72089e9i | − | 0.139951i | ||||||
\(334\) | − | 3.16823e9i | − | 0.254584i | ||||||
\(335\) | 2.39071e9i | 0.189823i | ||||||||
\(336\) | −3.48586e8 | −0.0273497 | ||||||||
\(337\) | −7.58634e9 | −0.588183 | −0.294092 | − | 0.955777i | \(-0.595017\pi\) | ||||
−0.294092 | + | 0.955777i | \(0.595017\pi\) | |||||||
\(338\) | 6.63072e9i | 0.508035i | ||||||||
\(339\) | −1.05486e9 | −0.0798724 | ||||||||
\(340\) | − | 5.66529e9i | − | 0.423942i | ||||||
\(341\) | 8.07539e9 | 0.597236 | ||||||||
\(342\) | −8.78925e9 | −0.642462 | ||||||||
\(343\) | 1.42177e10i | 1.02720i | ||||||||
\(344\) | 1.00768e10 | + | 7.26198e9i | 0.719599 | + | 0.518587i | ||||
\(345\) | −3.06345e9 | −0.216239 | ||||||||
\(346\) | − | 6.74088e9i | − | 0.470341i | ||||||
\(347\) | − | 7.28005e9i | − | 0.502130i | −0.967970 | − | 0.251065i | \(-0.919219\pi\) | ||
0.967970 | − | 0.251065i | \(-0.0807809\pi\) | |||||||
\(348\) | 1.85265e9 | 0.126321 | ||||||||
\(349\) | 2.15740e9i | 0.145422i | 0.997353 | + | 0.0727108i | \(0.0231650\pi\) | ||||
−0.997353 | + | 0.0727108i | \(0.976835\pi\) | |||||||
\(350\) | −1.19988e10 | −0.799584 | ||||||||
\(351\) | − | 2.50292e8i | − | 0.0164899i | ||||||
\(352\) | 1.08920e10i | 0.709473i | ||||||||
\(353\) | −1.82199e10 | −1.17340 | −0.586701 | − | 0.809804i | \(-0.699574\pi\) | ||||
−0.586701 | + | 0.809804i | \(0.699574\pi\) | |||||||
\(354\) | −1.33250e9 | −0.0848507 | ||||||||
\(355\) | 4.20403e10 | 2.64699 | ||||||||
\(356\) | − | 8.59519e9i | − | 0.535125i | ||||||
\(357\) | −4.78685e8 | −0.0294698 | ||||||||
\(358\) | −3.63663e9 | −0.221394 | ||||||||
\(359\) | 2.80903e10 | 1.69114 | 0.845569 | − | 0.533867i | \(-0.179262\pi\) | ||||
0.845569 | + | 0.533867i | \(0.179262\pi\) | |||||||
\(360\) | −2.69055e10 | −1.60188 | ||||||||
\(361\) | −1.11785e10 | −0.658197 | ||||||||
\(362\) | 8.02971e8i | 0.0467590i | ||||||||
\(363\) | − | 1.33649e9i | − | 0.0769732i | ||||||
\(364\) | − | 4.85636e8i | − | 0.0276634i | ||||||
\(365\) | 2.55231e10 | 1.43801 | ||||||||
\(366\) | 2.68063e8i | 0.0149387i | ||||||||
\(367\) | 1.01135e10 | 0.557491 | 0.278746 | − | 0.960365i | \(-0.410081\pi\) | ||||
0.278746 | + | 0.960365i | \(0.410081\pi\) | |||||||
\(368\) | −4.25613e9 | −0.232072 | ||||||||
\(369\) | 1.30027e10 | 0.701336 | ||||||||
\(370\) | 2.52000e9i | 0.134460i | ||||||||
\(371\) | 2.11737e10i | 1.11764i | ||||||||
\(372\) | − | 1.79481e9i | − | 0.0937232i | ||||||
\(373\) | − | 3.73566e10i | − | 1.92989i | −0.262452 | − | 0.964945i | \(-0.584531\pi\) | ||
0.262452 | − | 0.964945i | \(-0.415469\pi\) | |||||||
\(374\) | 2.12445e9i | 0.108583i | ||||||||
\(375\) | −7.45374e9 | −0.376920 | ||||||||
\(376\) | − | 2.42507e10i | − | 1.21331i | ||||||
\(377\) | 1.35715e9i | 0.0671837i | ||||||||
\(378\) | 1.95488e9i | 0.0957529i | ||||||||
\(379\) | −1.85816e10 | −0.900590 | −0.450295 | − | 0.892880i | \(-0.648681\pi\) | ||||
−0.450295 | + | 0.892880i | \(0.648681\pi\) | |||||||
\(380\) | −3.66694e10 | −1.75861 | ||||||||
\(381\) | − | 7.52898e8i | − | 0.0357303i | ||||||
\(382\) | 1.59644e10 | 0.749721 | ||||||||
\(383\) | − | 3.19636e10i | − | 1.48546i | −0.669591 | − | 0.742730i | \(-0.733531\pi\) | ||
0.669591 | − | 0.742730i | \(-0.266469\pi\) | |||||||
\(384\) | 2.88534e9 | 0.132701 | ||||||||
\(385\) | −1.81516e10 | −0.826176 | ||||||||
\(386\) | − | 7.31493e9i | − | 0.329504i | ||||||
\(387\) | −1.28367e10 | + | 1.78124e10i | −0.572282 | + | 0.794107i | ||||
\(388\) | 2.83467e10 | 1.25076 | ||||||||
\(389\) | − | 1.02069e10i | − | 0.445753i | −0.974847 | − | 0.222877i | \(-0.928455\pi\) | ||
0.974847 | − | 0.222877i | \(-0.0715447\pi\) | |||||||
\(390\) | 1.81298e8i | 0.00783672i | ||||||||
\(391\) | −5.84460e9 | −0.250062 | ||||||||
\(392\) | − | 1.20269e10i | − | 0.509343i | ||||||
\(393\) | −2.88935e9 | −0.121124 | ||||||||
\(394\) | 7.72944e9i | 0.320747i | ||||||||
\(395\) | 2.55660e10i | 1.05021i | ||||||||
\(396\) | −1.22270e10 | −0.497211 | ||||||||
\(397\) | −1.37116e10 | −0.551982 | −0.275991 | − | 0.961160i | \(-0.589006\pi\) | ||||
−0.275991 | + | 0.961160i | \(0.589006\pi\) | |||||||
\(398\) | −1.75472e10 | −0.699319 | ||||||||
\(399\) | 3.09836e9i | 0.122248i | ||||||||
\(400\) | −1.77308e10 | −0.692611 | ||||||||
\(401\) | −4.03228e10 | −1.55946 | −0.779729 | − | 0.626118i | \(-0.784643\pi\) | ||||
−0.779729 | + | 0.626118i | \(0.784643\pi\) | |||||||
\(402\) | −1.99254e8 | −0.00762963 | ||||||||
\(403\) | 1.31478e9 | 0.0498465 | ||||||||
\(404\) | 9.91647e9 | 0.372247 | ||||||||
\(405\) | − | 4.65090e10i | − | 1.72869i | ||||||
\(406\) | − | 1.05999e10i | − | 0.390119i | ||||||
\(407\) | 2.69235e9i | 0.0981190i | ||||||||
\(408\) | 1.11008e9 | 0.0400601 | ||||||||
\(409\) | 4.14921e10i | 1.48276i | 0.671083 | + | 0.741382i | \(0.265829\pi\) | ||||
−0.671083 | + | 0.741382i | \(0.734171\pi\) | |||||||
\(410\) | −1.90405e10 | −0.673818 | ||||||||
\(411\) | 5.39765e9 | 0.189164 | ||||||||
\(412\) | −6.07960e9 | −0.211002 | ||||||||
\(413\) | − | 2.17211e10i | − | 0.746589i | ||||||
\(414\) | 1.18066e10i | 0.401904i | ||||||||
\(415\) | − | 1.38415e10i | − | 0.466648i | ||||||
\(416\) | 1.77336e9i | 0.0592139i | ||||||||
\(417\) | 6.89339e9i | 0.227976i | ||||||||
\(418\) | 1.37508e10 | 0.450426 | ||||||||
\(419\) | 2.11727e10i | 0.686941i | 0.939164 | + | 0.343470i | \(0.111602\pi\) | ||||
−0.939164 | + | 0.343470i | \(0.888398\pi\) | |||||||
\(420\) | 4.03432e9i | 0.129650i | ||||||||
\(421\) | − | 9.68981e8i | − | 0.0308451i | −0.999881 | − | 0.0154226i | \(-0.995091\pi\) | ||
0.999881 | − | 0.0154226i | \(-0.00490935\pi\) | |||||||
\(422\) | 1.84440e10 | 0.581576 | ||||||||
\(423\) | 4.28669e10 | 1.33894 | ||||||||
\(424\) | − | 4.91021e10i | − | 1.51928i | ||||||
\(425\) | −2.43483e10 | −0.746300 | ||||||||
\(426\) | 3.50385e9i | 0.106392i | ||||||||
\(427\) | −4.36969e9 | −0.131443 | ||||||||
\(428\) | 3.34240e10 | 0.996056 | ||||||||
\(429\) | 1.93697e8i | 0.00571866i | ||||||||
\(430\) | 1.87975e10 | − | 2.60837e10i | 0.549827 | − | 0.762948i | ||||
\(431\) | 2.61536e10 | 0.757917 | 0.378959 | − | 0.925414i | \(-0.376282\pi\) | ||||
0.378959 | + | 0.925414i | \(0.376282\pi\) | |||||||
\(432\) | 2.88876e9i | 0.0829425i | ||||||||
\(433\) | 3.22035e10i | 0.916118i | 0.888922 | + | 0.458059i | \(0.151455\pi\) | ||||
−0.888922 | + | 0.458059i | \(0.848545\pi\) | |||||||
\(434\) | −1.02690e10 | −0.289446 | ||||||||
\(435\) | − | 1.12743e10i | − | 0.314871i | ||||||
\(436\) | 2.63765e10 | 0.729912 | ||||||||
\(437\) | 3.78300e10i | 1.03732i | ||||||||
\(438\) | 2.12722e9i | 0.0577985i | ||||||||
\(439\) | −1.53021e10 | −0.411997 | −0.205998 | − | 0.978552i | \(-0.566044\pi\) | ||||
−0.205998 | + | 0.978552i | \(0.566044\pi\) | |||||||
\(440\) | 4.20938e10 | 1.12307 | ||||||||
\(441\) | 2.12595e10 | 0.562081 | ||||||||
\(442\) | 3.45890e8i | 0.00906251i | ||||||||
\(443\) | 3.37252e10 | 0.875669 | 0.437834 | − | 0.899056i | \(-0.355746\pi\) | ||||
0.437834 | + | 0.899056i | \(0.355746\pi\) | |||||||
\(444\) | 5.98392e8 | 0.0153976 | ||||||||
\(445\) | −5.23059e10 | −1.33386 | ||||||||
\(446\) | −1.74995e10 | −0.442269 | ||||||||
\(447\) | 9.11861e9 | 0.228401 | ||||||||
\(448\) | − | 6.27831e9i | − | 0.155859i | ||||||
\(449\) | − | 2.28762e10i | − | 0.562859i | −0.959582 | − | 0.281429i | \(-0.909192\pi\) | ||
0.959582 | − | 0.281429i | \(-0.0908085\pi\) | |||||||
\(450\) | 4.91856e10i | 1.19947i | ||||||||
\(451\) | −2.03427e10 | −0.491703 | ||||||||
\(452\) | 1.69614e10i | 0.406357i | ||||||||
\(453\) | 1.99030e8 | 0.00472636 | ||||||||
\(454\) | 3.38961e10 | 0.797859 | ||||||||
\(455\) | −2.95533e9 | −0.0689541 | ||||||||
\(456\) | − | 7.18513e9i | − | 0.166179i | ||||||
\(457\) | 3.74308e10i | 0.858152i | 0.903268 | + | 0.429076i | \(0.141161\pi\) | ||||
−0.903268 | + | 0.429076i | \(0.858839\pi\) | |||||||
\(458\) | − | 3.43423e10i | − | 0.780490i | ||||||
\(459\) | 3.96691e9i | 0.0893720i | ||||||||
\(460\) | 4.92579e10i | 1.10013i | ||||||||
\(461\) | −8.15419e10 | −1.80542 | −0.902708 | − | 0.430254i | \(-0.858424\pi\) | ||||
−0.902708 | + | 0.430254i | \(0.858424\pi\) | |||||||
\(462\) | − | 1.51285e9i | − | 0.0332068i | ||||||
\(463\) | 2.57195e10i | 0.559679i | 0.960047 | + | 0.279840i | \(0.0902813\pi\) | ||||
−0.960047 | + | 0.279840i | \(0.909719\pi\) | |||||||
\(464\) | − | 1.56637e10i | − | 0.337926i | ||||||
\(465\) | −1.09223e10 | −0.233616 | ||||||||
\(466\) | 3.49153e10 | 0.740410 | ||||||||
\(467\) | − | 5.31933e10i | − | 1.11838i | −0.829040 | − | 0.559190i | \(-0.811112\pi\) | ||
0.829040 | − | 0.559190i | \(-0.188888\pi\) | |||||||
\(468\) | −1.99073e9 | −0.0414982 | ||||||||
\(469\) | − | 3.24803e9i | − | 0.0671320i | ||||||
\(470\) | −6.27724e10 | −1.28640 | ||||||||
\(471\) | −1.21821e10 | −0.247537 | ||||||||
\(472\) | 5.03715e10i | 1.01488i | ||||||||
\(473\) | 2.00831e10 | − | 2.78676e10i | 0.401223 | − | 0.556744i | ||||
\(474\) | −2.13081e9 | −0.0422115 | ||||||||
\(475\) | 1.57598e11i | 3.09583i | ||||||||
\(476\) | 7.69689e9i | 0.149930i | ||||||||
\(477\) | 8.67957e10 | 1.67658 | ||||||||
\(478\) | 4.70931e10i | 0.902082i | ||||||||
\(479\) | 2.65359e10 | 0.504071 | 0.252036 | − | 0.967718i | \(-0.418900\pi\) | ||||
0.252036 | + | 0.967718i | \(0.418900\pi\) | |||||||
\(480\) | − | 1.47318e10i | − | 0.277518i | ||||||
\(481\) | 4.38351e8i | 0.00818920i | ||||||||
\(482\) | 4.51158e10 | 0.835873 | ||||||||
\(483\) | 4.16201e9 | 0.0764742 | ||||||||
\(484\) | −2.14897e10 | −0.391606 | ||||||||
\(485\) | − | 1.72503e11i | − | 3.11767i | ||||||
\(486\) | 1.20631e10 | 0.216228 | ||||||||
\(487\) | 7.74386e10 | 1.37671 | 0.688354 | − | 0.725375i | \(-0.258334\pi\) | ||||
0.688354 | + | 0.725375i | \(0.258334\pi\) | |||||||
\(488\) | 1.01334e10 | 0.178679 | ||||||||
\(489\) | 1.13104e10 | 0.197808 | ||||||||
\(490\) | −3.11314e10 | −0.540026 | ||||||||
\(491\) | − | 8.99438e10i | − | 1.54755i | −0.633459 | − | 0.773776i | \(-0.718366\pi\) | ||
0.633459 | − | 0.773776i | \(-0.281634\pi\) | |||||||
\(492\) | 4.52131e9i | 0.0771620i | ||||||||
\(493\) | − | 2.15097e10i | − | 0.364122i | ||||||
\(494\) | 2.23882e9 | 0.0375934 | ||||||||
\(495\) | 7.44075e10i | 1.23936i | ||||||||
\(496\) | −1.51747e10 | −0.250722 | ||||||||
\(497\) | −5.71162e10 | −0.936125 | ||||||||
\(498\) | 1.15362e9 | 0.0187562 | ||||||||
\(499\) | − | 4.06147e10i | − | 0.655059i | −0.944841 | − | 0.327530i | \(-0.893784\pi\) | ||
0.944841 | − | 0.327530i | \(-0.106216\pi\) | |||||||
\(500\) | 1.19850e11i | 1.91761i | ||||||||
\(501\) | 4.57824e9i | 0.0726688i | ||||||||
\(502\) | 2.36577e10i | 0.372527i | ||||||||
\(503\) | 6.63800e10i | 1.03697i | 0.855087 | + | 0.518484i | \(0.173503\pi\) | ||||
−0.855087 | + | 0.518484i | \(0.826497\pi\) | |||||||
\(504\) | 3.65540e10 | 0.566517 | ||||||||
\(505\) | − | 6.03465e10i | − | 0.927869i | ||||||
\(506\) | − | 1.84714e10i | − | 0.281772i | ||||||
\(507\) | − | 9.58169e9i | − | 0.145014i | ||||||
\(508\) | −1.21060e10 | −0.181780 | ||||||||
\(509\) | −2.27423e10 | −0.338815 | −0.169408 | − | 0.985546i | \(-0.554185\pi\) | ||||
−0.169408 | + | 0.985546i | \(0.554185\pi\) | |||||||
\(510\) | − | 2.87341e9i | − | 0.0424734i | ||||||
\(511\) | −3.46758e10 | −0.508561 | ||||||||
\(512\) | − | 3.80276e10i | − | 0.553374i | ||||||
\(513\) | 2.56764e10 | 0.370736 | ||||||||
\(514\) | −3.28947e10 | −0.471274 | ||||||||
\(515\) | 3.69973e10i | 0.525946i | ||||||||
\(516\) | −6.19377e9 | − | 4.46361e9i | −0.0873688 | − | 0.0629633i | ||||
\(517\) | −6.70655e10 | −0.938723 | ||||||||
\(518\) | − | 3.42368e9i | − | 0.0475526i | ||||||
\(519\) | 9.74088e9i | 0.134254i | ||||||||
\(520\) | 6.85345e9 | 0.0937337 | ||||||||
\(521\) | − | 1.10812e11i | − | 1.50396i | −0.659189 | − | 0.751978i | \(-0.729100\pi\) | ||
0.659189 | − | 0.751978i | \(-0.270900\pi\) | |||||||
\(522\) | −4.34513e10 | −0.585222 | ||||||||
\(523\) | 8.07121e10i | 1.07878i | 0.842057 | + | 0.539389i | \(0.181345\pi\) | ||||
−0.842057 | + | 0.539389i | \(0.818655\pi\) | |||||||
\(524\) | 4.64586e10i | 0.616227i | ||||||||
\(525\) | 1.73388e10 | 0.228234 | ||||||||
\(526\) | 4.74965e9 | 0.0620467 | ||||||||
\(527\) | −2.08382e10 | −0.270157 | ||||||||
\(528\) | − | 2.23557e9i | − | 0.0287642i | ||||||
\(529\) | −2.74940e10 | −0.351088 | ||||||||
\(530\) | −1.27100e11 | −1.61080 | ||||||||
\(531\) | −8.90396e10 | −1.11997 | ||||||||
\(532\) | 4.98193e10 | 0.621943 | ||||||||
\(533\) | −3.31207e9 | −0.0410384 | ||||||||
\(534\) | − | 4.35944e9i | − | 0.0536125i | ||||||
\(535\) | − | 2.03401e11i | − | 2.48278i | ||||||
\(536\) | 7.53223e9i | 0.0912567i | ||||||||
\(537\) | 5.25509e9 | 0.0631950 | ||||||||
\(538\) | 2.65741e10i | 0.317198i | ||||||||
\(539\) | −3.32606e10 | −0.394071 | ||||||||
\(540\) | 3.34328e10 | 0.393186 | ||||||||
\(541\) | 2.03972e10 | 0.238112 | 0.119056 | − | 0.992888i | \(-0.462013\pi\) | ||||
0.119056 | + | 0.992888i | \(0.462013\pi\) | |||||||
\(542\) | − | 2.16766e10i | − | 0.251185i | ||||||
\(543\) | − | 1.16033e9i | − | 0.0133469i | ||||||
\(544\) | − | 2.81062e10i | − | 0.320927i | ||||||
\(545\) | − | 1.60514e11i | − | 1.81939i | ||||||
\(546\) | − | 2.46312e8i | − | 0.00277150i | ||||||
\(547\) | 1.36264e11 | 1.52206 | 0.761029 | − | 0.648718i | \(-0.224695\pi\) | ||||
0.761029 | + | 0.648718i | \(0.224695\pi\) | |||||||
\(548\) | − | 8.67902e10i | − | 0.962384i | ||||||
\(549\) | 1.79123e10i | 0.197180i | ||||||||
\(550\) | − | 7.69511e10i | − | 0.840938i | ||||||
\(551\) | −1.39225e11 | −1.51046 | ||||||||
\(552\) | −9.65176e9 | −0.103956 | ||||||||
\(553\) | − | 3.47342e10i | − | 0.371412i | ||||||
\(554\) | 1.73050e10 | 0.183710 | ||||||||
\(555\) | − | 3.64151e9i | − | 0.0383804i | ||||||
\(556\) | 1.10840e11 | 1.15984 | ||||||||
\(557\) | 1.43090e11 | 1.48658 | 0.743290 | − | 0.668970i | \(-0.233264\pi\) | ||||
0.743290 | + | 0.668970i | \(0.233264\pi\) | |||||||
\(558\) | 4.20947e10i | 0.434201i | ||||||||
\(559\) | 3.26980e9 | − | 4.53723e9i | 0.0334868 | − | 0.0464669i | ||||
\(560\) | 3.41091e10 | 0.346831 | ||||||||
\(561\) | − | 3.06993e9i | − | 0.0309940i | ||||||
\(562\) | 4.82376e10i | 0.483549i | ||||||||
\(563\) | −1.55272e11 | −1.54546 | −0.772731 | − | 0.634734i | \(-0.781110\pi\) | ||||
−0.772731 | + | 0.634734i | \(0.781110\pi\) | |||||||
\(564\) | 1.49058e10i | 0.147312i | ||||||||
\(565\) | 1.03218e11 | 1.01289 | ||||||||
\(566\) | 5.25231e10i | 0.511782i | ||||||||
\(567\) | 6.31874e10i | 0.611362i | ||||||||
\(568\) | 1.32453e11 | 1.27253 | ||||||||
\(569\) | −1.98849e11 | −1.89703 | −0.948515 | − | 0.316732i | \(-0.897414\pi\) | ||||
−0.948515 | + | 0.316732i | \(0.897414\pi\) | |||||||
\(570\) | −1.85986e10 | −0.176189 | ||||||||
\(571\) | 1.76753e10i | 0.166273i | 0.996538 | + | 0.0831367i | \(0.0264938\pi\) | ||||
−0.996538 | + | 0.0831367i | \(0.973506\pi\) | |||||||
\(572\) | 3.11451e9 | 0.0290941 | ||||||||
\(573\) | −2.30693e10 | −0.214001 | ||||||||
\(574\) | 2.58685e10 | 0.238300 | ||||||||
\(575\) | 2.11701e11 | 1.93665 | ||||||||
\(576\) | −2.57362e10 | −0.233805 | ||||||||
\(577\) | − | 6.20468e10i | − | 0.559779i | −0.960032 | − | 0.279889i | \(-0.909702\pi\) | ||
0.960032 | − | 0.279889i | \(-0.0902978\pi\) | |||||||
\(578\) | 5.14075e10i | 0.460591i | ||||||||
\(579\) | 1.05704e10i | 0.0940540i | ||||||||
\(580\) | −1.81282e11 | −1.60193 | ||||||||
\(581\) | 1.88051e10i | 0.165033i | ||||||||
\(582\) | 1.43773e10 | 0.125310 | ||||||||
\(583\) | −1.35792e11 | −1.17544 | ||||||||
\(584\) | 8.04136e10 | 0.691318 | ||||||||
\(585\) | 1.21146e10i | 0.103439i | ||||||||
\(586\) | − | 7.47679e10i | − | 0.634051i | ||||||
\(587\) | 1.47391e11i | 1.24142i | 0.784039 | + | 0.620712i | \(0.213156\pi\) | ||||
−0.784039 | + | 0.620712i | \(0.786844\pi\) | |||||||
\(588\) | 7.39239e9i | 0.0618409i | ||||||||
\(589\) | 1.34878e11i | 1.12068i | ||||||||
\(590\) | 1.30386e11 | 1.07602 | ||||||||
\(591\) | − | 1.11694e10i | − | 0.0915544i | ||||||
\(592\) | − | 5.05925e9i | − | 0.0411907i | ||||||
\(593\) | 5.54340e10i | 0.448289i | 0.974556 | + | 0.224144i | \(0.0719587\pi\) | ||||
−0.974556 | + | 0.224144i | \(0.928041\pi\) | |||||||
\(594\) | −1.25371e10 | −0.100705 | ||||||||
\(595\) | 4.68393e10 | 0.373717 | ||||||||
\(596\) | − | 1.46620e11i | − | 1.16201i | ||||||
\(597\) | 2.53565e10 | 0.199614 | ||||||||
\(598\) | − | 3.00740e9i | − | 0.0235173i | ||||||
\(599\) | −1.08881e11 | −0.845759 | −0.422880 | − | 0.906186i | \(-0.638981\pi\) | ||||
−0.422880 | + | 0.906186i | \(0.638981\pi\) | |||||||
\(600\) | −4.02088e10 | −0.310253 | ||||||||
\(601\) | − | 1.15997e10i | − | 0.0889098i | −0.999011 | − | 0.0444549i | \(-0.985845\pi\) | ||
0.999011 | − | 0.0444549i | \(-0.0141551\pi\) | |||||||
\(602\) | −2.55384e10 | + | 3.54374e10i | −0.194450 | + | 0.269821i | ||||
\(603\) | −1.33144e10 | −0.100705 | ||||||||
\(604\) | − | 3.20026e9i | − | 0.0240457i | ||||||
\(605\) | 1.30776e11i | 0.976124i | ||||||||
\(606\) | 5.02959e9 | 0.0372943 | ||||||||
\(607\) | 1.26228e11i | 0.929825i | 0.885357 | + | 0.464912i | \(0.153914\pi\) | ||||
−0.885357 | + | 0.464912i | \(0.846086\pi\) | |||||||
\(608\) | −1.81921e11 | −1.33128 | ||||||||
\(609\) | 1.53173e10i | 0.111356i | ||||||||
\(610\) | − | 2.62300e10i | − | 0.189443i | ||||||
\(611\) | −1.09192e10 | −0.0783475 | ||||||||
\(612\) | 3.15513e10 | 0.224911 | ||||||||
\(613\) | −3.92822e10 | −0.278198 | −0.139099 | − | 0.990278i | \(-0.544421\pi\) | ||||
−0.139099 | + | 0.990278i | \(0.544421\pi\) | |||||||
\(614\) | 5.05269e10i | 0.355508i | ||||||||
\(615\) | 2.75144e10 | 0.192335 | ||||||||
\(616\) | −5.71889e10 | −0.397181 | ||||||||
\(617\) | −8.85815e10 | −0.611227 | −0.305613 | − | 0.952156i | \(-0.598862\pi\) | ||||
−0.305613 | + | 0.952156i | \(0.598862\pi\) | |||||||
\(618\) | −3.08355e9 | −0.0211396 | ||||||||
\(619\) | 2.85485e11 | 1.94456 | 0.972278 | − | 0.233827i | \(-0.0751249\pi\) | ||||
0.972278 | + | 0.233827i | \(0.0751249\pi\) | |||||||
\(620\) | 1.75622e11i | 1.18854i | ||||||||
\(621\) | − | 3.44910e10i | − | 0.231921i | ||||||
\(622\) | − | 3.30471e9i | − | 0.0220786i | ||||||
\(623\) | 7.10631e10 | 0.471728 | ||||||||
\(624\) | − | 3.63981e8i | − | 0.00240072i | ||||||
\(625\) | 3.62507e11 | 2.37572 | ||||||||
\(626\) | 6.51318e10 | 0.424127 | ||||||||
\(627\) | −1.98706e10 | −0.128570 | ||||||||
\(628\) | 1.95879e11i | 1.25936i | ||||||||
\(629\) | − | 6.94746e9i | − | 0.0443837i | ||||||
\(630\) | − | 9.46192e10i | − | 0.600644i | ||||||
\(631\) | − | 2.01760e11i | − | 1.27268i | −0.771409 | − | 0.636339i | \(-0.780448\pi\) | ||
0.771409 | − | 0.636339i | \(-0.219552\pi\) | |||||||
\(632\) | 8.05490e10i | 0.504884i | ||||||||
\(633\) | −2.66525e10 | −0.166006 | ||||||||
\(634\) | − | 8.31343e10i | − | 0.514545i | ||||||
\(635\) | 7.36711e10i | 0.453108i | ||||||||
\(636\) | 3.01808e10i | 0.184460i | ||||||||
\(637\) | −5.41528e9 | −0.0328899 | ||||||||
\(638\) | 6.79798e10 | 0.410296 | ||||||||
\(639\) | 2.34132e11i | 1.40429i | ||||||||
\(640\) | −2.82331e11 | −1.68282 | ||||||||
\(641\) | − | 2.00339e11i | − | 1.18668i | −0.804952 | − | 0.593340i | \(-0.797809\pi\) | ||
0.804952 | − | 0.593340i | \(-0.202191\pi\) | |||||||
\(642\) | 1.69525e10 | 0.0997917 | ||||||||
\(643\) | −2.88308e10 | −0.168660 | −0.0843302 | − | 0.996438i | \(-0.526875\pi\) | ||||
−0.0843302 | + | 0.996438i | \(0.526875\pi\) | |||||||
\(644\) | − | 6.69220e10i | − | 0.389068i | ||||||
\(645\) | −2.71632e10 | + | 3.76921e10i | −0.156943 | + | 0.217777i | ||||
\(646\) | −3.54833e10 | −0.203748 | ||||||||
\(647\) | 2.38176e10i | 0.135919i | 0.997688 | + | 0.0679596i | \(0.0216489\pi\) | ||||
−0.997688 | + | 0.0679596i | \(0.978351\pi\) | |||||||
\(648\) | − | 1.46532e11i | − | 0.831063i | ||||||
\(649\) | 1.39303e11 | 0.785202 | ||||||||
\(650\) | − | 1.25287e10i | − | 0.0701863i | ||||||
\(651\) | 1.48391e10 | 0.0826197 | ||||||||
\(652\) | − | 1.81863e11i | − | 1.00636i | ||||||
\(653\) | 4.13167e10i | 0.227234i | 0.993525 | + | 0.113617i | \(0.0362437\pi\) | ||||
−0.993525 | + | 0.113617i | \(0.963756\pi\) | |||||||
\(654\) | 1.33780e10 | 0.0731276 | ||||||||
\(655\) | 2.82723e11 | 1.53602 | ||||||||
\(656\) | 3.82265e10 | 0.206419 | ||||||||
\(657\) | 1.42144e11i | 0.762898i | ||||||||
\(658\) | 8.52829e10 | 0.454944 | ||||||||
\(659\) | 7.00111e10 | 0.371215 | 0.185607 | − | 0.982624i | \(-0.440575\pi\) | ||||
0.185607 | + | 0.982624i | \(0.440575\pi\) | |||||||
\(660\) | −2.58731e10 | −0.136356 | ||||||||
\(661\) | −1.97163e11 | −1.03281 | −0.516403 | − | 0.856346i | \(-0.672729\pi\) | ||||
−0.516403 | + | 0.856346i | \(0.672729\pi\) | |||||||
\(662\) | 9.97659e9 | 0.0519458 | ||||||||
\(663\) | − | 4.99826e8i | − | 0.00258681i | ||||||
\(664\) | − | 4.36092e10i | − | 0.224339i | ||||||
\(665\) | − | 3.03174e11i | − | 1.55027i | ||||||
\(666\) | −1.40344e10 | −0.0713342 | ||||||||
\(667\) | 1.87020e11i | 0.944897i | ||||||||
\(668\) | 7.36146e10 | 0.369708 | ||||||||
\(669\) | 2.52876e10 | 0.126242 | ||||||||
\(670\) | 1.94970e10 | 0.0967540 | ||||||||
\(671\) | − | 2.80239e10i | − | 0.138242i | ||||||
\(672\) | 2.00148e10i | 0.0981461i | ||||||||
\(673\) | 3.14113e11i | 1.53118i | 0.643331 | + | 0.765588i | \(0.277552\pi\) | ||||
−0.643331 | + | 0.765588i | \(0.722448\pi\) | |||||||
\(674\) | 6.18690e10i | 0.299801i | ||||||||
\(675\) | − | 1.43688e11i | − | 0.692158i | ||||||
\(676\) | −1.54066e11 | −0.737770 | ||||||||
\(677\) | 2.15963e11i | 1.02808i | 0.857767 | + | 0.514038i | \(0.171851\pi\) | ||||
−0.857767 | + | 0.514038i | \(0.828149\pi\) | |||||||
\(678\) | 8.60274e9i | 0.0407116i | ||||||||
\(679\) | 2.34364e11i | 1.10258i | ||||||||
\(680\) | −1.08621e11 | −0.508017 | ||||||||
\(681\) | −4.89814e10 | −0.227742 | ||||||||
\(682\) | − | 6.58574e10i | − | 0.304416i | ||||||
\(683\) | −1.59874e11 | −0.734674 | −0.367337 | − | 0.930088i | \(-0.619730\pi\) | ||||
−0.367337 | + | 0.930088i | \(0.619730\pi\) | |||||||
\(684\) | − | 2.04220e11i | − | 0.932984i | ||||||
\(685\) | −5.28160e11 | −2.39885 | ||||||||
\(686\) | 1.15950e11 | 0.523571 | ||||||||
\(687\) | 4.96261e10i | 0.222784i | ||||||||
\(688\) | −3.77386e10 | + | 5.23667e10i | −0.168435 | + | 0.233723i | ||||
\(689\) | −2.21088e10 | −0.0981046 | ||||||||
\(690\) | 2.49834e10i | 0.110219i | ||||||||
\(691\) | − | 3.44476e11i | − | 1.51094i | −0.655183 | − | 0.755470i | \(-0.727409\pi\) | ||
0.655183 | − | 0.755470i | \(-0.272591\pi\) | |||||||
\(692\) | 1.56626e11 | 0.683029 | ||||||||
\(693\) | − | 1.01090e11i | − | 0.438306i | ||||||
\(694\) | −5.93711e10 | −0.255940 | ||||||||
\(695\) | − | 6.74518e11i | − | 2.89104i | ||||||
\(696\) | − | 3.55210e10i | − | 0.151373i | ||||||
\(697\) | 5.24934e10 | 0.222420 | ||||||||
\(698\) | 1.75943e10 | 0.0741225 | ||||||||
\(699\) | −5.04542e10 | −0.211343 | ||||||||
\(700\) | − | 2.78794e11i | − | 1.16116i | ||||||
\(701\) | 3.62423e10 | 0.150087 | 0.0750437 | − | 0.997180i | \(-0.476090\pi\) | ||||
0.0750437 | + | 0.997180i | \(0.476090\pi\) | |||||||
\(702\) | −2.04121e9 | −0.00840505 | ||||||||
\(703\) | −4.49685e10 | −0.184114 | ||||||||
\(704\) | 4.02644e10 | 0.163920 | ||||||||
\(705\) | 9.07089e10 | 0.367192 | ||||||||
\(706\) | 1.48589e11i | 0.598092i | ||||||||
\(707\) | 8.19871e10i | 0.328147i | ||||||||
\(708\) | − | 3.09610e10i | − | 0.123220i | ||||||
\(709\) | −2.60959e11 | −1.03273 | −0.516365 | − | 0.856368i | \(-0.672715\pi\) | ||||
−0.516365 | + | 0.856368i | \(0.672715\pi\) | |||||||
\(710\) | − | 3.42852e11i | − | 1.34919i | ||||||
\(711\) | −1.42383e11 | −0.557160 | ||||||||
\(712\) | −1.64796e11 | −0.641250 | ||||||||
\(713\) | 1.81181e11 | 0.701059 | ||||||||
\(714\) | 3.90383e9i | 0.0150210i | ||||||||
\(715\) | − | 1.89533e10i | − | 0.0725204i | ||||||
\(716\) | − | 8.44978e10i | − | 0.321509i | ||||||
\(717\) | − | 6.80517e10i | − | 0.257491i | ||||||
\(718\) | − | 2.29086e11i | − | 0.861985i | ||||||
\(719\) | 2.99391e11 | 1.12027 | 0.560135 | − | 0.828402i | \(-0.310749\pi\) | ||||
0.560135 | + | 0.828402i | \(0.310749\pi\) | |||||||
\(720\) | − | 1.39821e11i | − | 0.520286i | ||||||
\(721\) | − | 5.02648e10i | − | 0.186004i | ||||||
\(722\) | 9.11646e10i | 0.335488i | ||||||||
\(723\) | −6.51943e10 | −0.238592 | ||||||||
\(724\) | −1.86572e10 | −0.0679035 | ||||||||
\(725\) | 7.79116e11i | 2.82000i | ||||||||
\(726\) | −1.08995e10 | −0.0392338 | ||||||||
\(727\) | 2.92370e11i | 1.04664i | 0.852138 | + | 0.523318i | \(0.175306\pi\) | ||||
−0.852138 | + | 0.523318i | \(0.824694\pi\) | |||||||
\(728\) | −9.31113e9 | −0.0331495 | ||||||||
\(729\) | 2.47189e11 | 0.875224 | ||||||||
\(730\) | − | 2.08149e11i | − | 0.732964i | ||||||
\(731\) | −5.18234e10 | + | 7.19110e10i | −0.181492 | + | 0.251841i | ||||
\(732\) | −6.22851e9 | −0.0216940 | ||||||||
\(733\) | 1.93990e11i | 0.671992i | 0.941863 | + | 0.335996i | \(0.109073\pi\) | ||||
−0.941863 | + | 0.335996i | \(0.890927\pi\) | |||||||
\(734\) | − | 8.24790e10i | − | 0.284157i | ||||||
\(735\) | 4.49863e10 | 0.154146 | ||||||||
\(736\) | 2.44374e11i | 0.832806i | ||||||||
\(737\) | 2.08305e10 | 0.0706040 | ||||||||
\(738\) | − | 1.06041e11i | − | 0.357476i | ||||||
\(739\) | − | 3.15121e11i | − | 1.05657i | −0.849066 | − | 0.528287i | \(-0.822834\pi\) | ||
0.849066 | − | 0.528287i | \(-0.177166\pi\) | |||||||
\(740\) | −5.85527e10 | −0.195263 | ||||||||
\(741\) | −3.23520e9 | −0.0107307 | ||||||||
\(742\) | 1.72678e11 | 0.569669 | ||||||||
\(743\) | 2.35524e11i | 0.772821i | 0.922327 | + | 0.386411i | \(0.126285\pi\) | ||||
−0.922327 | + | 0.386411i | \(0.873715\pi\) | |||||||
\(744\) | −3.44121e10 | −0.112310 | ||||||||
\(745\) | −8.92256e11 | −2.89644 | ||||||||
\(746\) | −3.04655e11 | −0.983679 | ||||||||
\(747\) | 7.70862e10 | 0.247568 | ||||||||
\(748\) | −4.93621e10 | −0.157684 | ||||||||
\(749\) | 2.76342e11i | 0.878052i | ||||||||
\(750\) | 6.07876e10i | 0.192119i | ||||||||
\(751\) | − | 4.32289e11i | − | 1.35898i | −0.733683 | − | 0.679492i | \(-0.762200\pi\) | ||
0.733683 | − | 0.679492i | \(-0.237800\pi\) | |||||||
\(752\) | 1.26024e11 | 0.394079 | ||||||||
\(753\) | − | 3.41865e10i | − | 0.106335i | ||||||
\(754\) | 1.10680e10 | 0.0342440 | ||||||||
\(755\) | −1.94751e10 | −0.0599366 | ||||||||
\(756\) | −4.54220e10 | −0.139053 | ||||||||
\(757\) | 1.51060e11i | 0.460007i | 0.973190 | + | 0.230004i | \(0.0738738\pi\) | ||||
−0.973190 | + | 0.230004i | \(0.926126\pi\) | |||||||
\(758\) | 1.51539e11i | 0.459037i | ||||||||
\(759\) | 2.66921e10i | 0.0804294i | ||||||||
\(760\) | 7.03065e11i | 2.10737i | ||||||||
\(761\) | − | 1.99597e11i | − | 0.595135i | −0.954701 | − | 0.297568i | \(-0.903825\pi\) | ||
0.954701 | − | 0.297568i | \(-0.0961754\pi\) | |||||||
\(762\) | −6.14012e9 | −0.0182120 | ||||||||
\(763\) | 2.18075e11i | 0.643439i | ||||||||
\(764\) | 3.70937e11i | 1.08875i | ||||||||
\(765\) | − | 1.92005e11i | − | 0.560617i | ||||||
\(766\) | −2.60674e11 | −0.757150 | ||||||||
\(767\) | 2.26804e10 | 0.0655344 | ||||||||
\(768\) | − | 3.56210e10i | − | 0.102391i | ||||||
\(769\) | 2.01782e11 | 0.577002 | 0.288501 | − | 0.957480i | \(-0.406843\pi\) | ||||
0.288501 | + | 0.957480i | \(0.406843\pi\) | |||||||
\(770\) | 1.48032e11i | 0.421108i | ||||||||
\(771\) | 4.75343e10 | 0.134521 | ||||||||
\(772\) | 1.69964e11 | 0.478506 | ||||||||
\(773\) | − | 2.36295e11i | − | 0.661816i | −0.943663 | − | 0.330908i | \(-0.892645\pi\) | ||
0.943663 | − | 0.330908i | \(-0.107355\pi\) | |||||||
\(774\) | 1.45266e11 | + | 1.04687e11i | 0.404762 | + | 0.291696i | ||||
\(775\) | 7.54792e11 | 2.09228 | ||||||||
\(776\) | − | 5.43493e11i | − | 1.49881i | ||||||
\(777\) | 4.94737e9i | 0.0135735i | ||||||||
\(778\) | −8.32403e10 | −0.227204 | ||||||||
\(779\) | − | 3.39771e11i | − | 0.922648i | ||||||
\(780\) | −4.21250e9 | −0.0113805 | ||||||||
\(781\) | − | 3.66301e11i | − | 0.984541i | ||||||
\(782\) | 4.76646e10i | 0.127459i | ||||||||
\(783\) | 1.26936e11 | 0.337705 | ||||||||
\(784\) | 6.25008e10 | 0.165433 | ||||||||
\(785\) | 1.19202e12 | 3.13910 | ||||||||
\(786\) | 2.35636e10i | 0.0617379i | ||||||||
\(787\) | 1.73669e11 | 0.452714 | 0.226357 | − | 0.974044i | \(-0.427318\pi\) | ||||
0.226357 | + | 0.974044i | \(0.427318\pi\) | |||||||
\(788\) | −1.79595e11 | −0.465790 | ||||||||
\(789\) | −6.86346e9 | −0.0177107 | ||||||||
\(790\) | 2.08499e11 | 0.535299 | ||||||||
\(791\) | −1.40233e11 | −0.358215 | ||||||||
\(792\) | 2.34430e11i | 0.595817i | ||||||||
\(793\) | − | 4.56268e9i | − | 0.0115379i | ||||||
\(794\) | 1.11822e11i | 0.281350i | ||||||||
\(795\) | 1.83665e11 | 0.459788 | ||||||||
\(796\) | − | 4.07713e11i | − | 1.01555i | ||||||
\(797\) | 3.04355e11 | 0.754305 | 0.377153 | − | 0.926151i | \(-0.376903\pi\) | ||||
0.377153 | + | 0.926151i | \(0.376903\pi\) | |||||||
\(798\) | 2.52681e10 | 0.0623105 | ||||||||
\(799\) | 1.73059e11 | 0.424627 | ||||||||
\(800\) | 1.01805e12i | 2.48548i | ||||||||
\(801\) | − | 2.91304e11i | − | 0.707645i | ||||||
\(802\) | 3.28846e11i | 0.794867i | ||||||||
\(803\) | − | 2.22385e11i | − | 0.534863i | ||||||
\(804\) | − | 4.62972e9i | − | 0.0110798i | ||||||
\(805\) | −4.07253e11 | −0.969797 | ||||||||
\(806\) | − | 1.07225e10i | − | 0.0254071i | ||||||
\(807\) | − | 3.84008e10i | − | 0.0905412i | ||||||
\(808\) | − | 1.90129e11i | − | 0.446070i | ||||||
\(809\) | −4.38947e11 | −1.02475 | −0.512375 | − | 0.858762i | \(-0.671234\pi\) | ||||
−0.512375 | + | 0.858762i | \(0.671234\pi\) | |||||||
\(810\) | −3.79296e11 | −0.881127 | ||||||||
\(811\) | 3.98119e11i | 0.920300i | 0.887841 | + | 0.460150i | \(0.152204\pi\) | ||||
−0.887841 | + | 0.460150i | \(0.847796\pi\) | |||||||
\(812\) | 2.46291e11 | 0.566531 | ||||||||
\(813\) | 3.13236e10i | 0.0716984i | ||||||||
\(814\) | 2.19569e10 | 0.0500120 | ||||||||
\(815\) | −1.10672e12 | −2.50847 | ||||||||
\(816\) | 5.76878e9i | 0.0130114i | ||||||||
\(817\) | 4.65454e11 | + | 3.35435e11i | 1.04469 | + | 0.752870i | ||||
\(818\) | 3.38381e11 | 0.755776 | ||||||||
\(819\) | − | 1.64589e10i | − | 0.0365818i | ||||||
\(820\) | − | 4.42410e11i | − | 0.978520i | ||||||
\(821\) | 6.38892e11 | 1.40623 | 0.703113 | − | 0.711078i | \(-0.251793\pi\) | ||||
0.703113 | + | 0.711078i | \(0.251793\pi\) | |||||||
\(822\) | − | 4.40196e10i | − | 0.0964181i | ||||||
\(823\) | −4.24621e11 | −0.925555 | −0.462777 | − | 0.886475i | \(-0.653147\pi\) | ||||
−0.462777 | + | 0.886475i | \(0.653147\pi\) | |||||||
\(824\) | 1.16565e11i | 0.252847i | ||||||||
\(825\) | 1.11198e11i | 0.240038i | ||||||||
\(826\) | −1.77143e11 | −0.380542 | ||||||||
\(827\) | −4.42513e11 | −0.946029 | −0.473014 | − | 0.881055i | \(-0.656834\pi\) | ||||
−0.473014 | + | 0.881055i | \(0.656834\pi\) | |||||||
\(828\) | −2.74328e11 | −0.583646 | ||||||||
\(829\) | 7.03831e11i | 1.49022i | 0.666941 | + | 0.745110i | \(0.267603\pi\) | ||||
−0.666941 | + | 0.745110i | \(0.732397\pi\) | |||||||
\(830\) | −1.12881e11 | −0.237854 | ||||||||
\(831\) | −2.50065e10 | −0.0524383 | ||||||||
\(832\) | 6.55560e9 | 0.0136810 | ||||||||
\(833\) | 8.58273e10 | 0.178257 | ||||||||
\(834\) | 5.62178e10 | 0.116201 | ||||||||
\(835\) | − | 4.47981e11i | − | 0.921539i | ||||||
\(836\) | 3.19504e11i | 0.654110i | ||||||||
\(837\) | − | 1.22973e11i | − | 0.250558i | ||||||
\(838\) | 1.72670e11 | 0.350139 | ||||||||
\(839\) | 6.70095e11i | 1.35235i | 0.736742 | + | 0.676174i | \(0.236363\pi\) | ||||
−0.736742 | + | 0.676174i | \(0.763637\pi\) | |||||||
\(840\) | 7.73503e10 | 0.155362 | ||||||||
\(841\) | −1.88036e11 | −0.375886 | ||||||||
\(842\) | −7.90235e9 | −0.0157220 | ||||||||
\(843\) | − | 6.97055e10i | − | 0.138025i | ||||||
\(844\) | 4.28552e11i | 0.844566i | ||||||||
\(845\) | 9.37569e11i | 1.83898i | ||||||||
\(846\) | − | 3.49594e11i | − | 0.682468i | ||||||
\(847\) | − | 1.77672e11i | − | 0.345212i | ||||||
\(848\) | 2.55171e11 | 0.493455 | ||||||||
\(849\) | − | 7.58983e10i | − | 0.146084i | ||||||
\(850\) | 1.98569e11i | 0.380395i | ||||||||
\(851\) | 6.04060e10i | 0.115176i | ||||||||
\(852\) | −8.14129e10 | −0.154502 | ||||||||
\(853\) | 1.64190e11 | 0.310134 | 0.155067 | − | 0.987904i | \(-0.450441\pi\) | ||||
0.155067 | + | 0.987904i | \(0.450441\pi\) | |||||||
\(854\) | 3.56362e10i | 0.0669977i | ||||||||
\(855\) | −1.24278e12 | −2.32557 | ||||||||
\(856\) | − | 6.40841e11i | − | 1.19359i | ||||||
\(857\) | 4.86990e11 | 0.902811 | 0.451406 | − | 0.892319i | \(-0.350923\pi\) | ||||
0.451406 | + | 0.892319i | \(0.350923\pi\) | |||||||
\(858\) | 1.57966e9 | 0.00291485 | ||||||||
\(859\) | − | 9.50663e11i | − | 1.74604i | −0.487685 | − | 0.873020i | \(-0.662158\pi\) | ||
0.487685 | − | 0.873020i | \(-0.337842\pi\) | |||||||
\(860\) | 6.06060e11 | + | 4.36764e11i | 1.10796 | + | 0.798460i | ||||
\(861\) | −3.73812e10 | −0.0680206 | ||||||||
\(862\) | − | 2.13291e11i | − | 0.386316i | ||||||
\(863\) | − | 3.36337e11i | − | 0.606361i | −0.952933 | − | 0.303181i | \(-0.901951\pi\) | ||
0.952933 | − | 0.303181i | \(-0.0980486\pi\) | |||||||
\(864\) | 1.65864e11 | 0.297644 | ||||||||
\(865\) | − | 9.53145e11i | − | 1.70253i | ||||||
\(866\) | 2.62630e11 | 0.466952 | ||||||||
\(867\) | − | 7.42862e10i | − | 0.131471i | ||||||
\(868\) | − | 2.38601e11i | − | 0.420334i | ||||||
\(869\) | 2.22759e11 | 0.390622 | ||||||||
\(870\) | −9.19454e10 | −0.160492 | ||||||||
\(871\) | 3.39149e9 | 0.00589274 | ||||||||
\(872\) | − | 5.05718e11i | − | 0.874666i | ||||||
\(873\) | 9.60710e11 | 1.65400 | ||||||||
\(874\) | 3.08516e11 | 0.528728 | ||||||||
\(875\) | −9.90897e11 | −1.69043 | ||||||||
\(876\) | −4.94265e10 | −0.0839351 | ||||||||
\(877\) | 1.41500e11 | 0.239199 | 0.119599 | − | 0.992822i | \(-0.461839\pi\) | ||||
0.119599 | + | 0.992822i | \(0.461839\pi\) | |||||||
\(878\) | 1.24794e11i | 0.209998i | ||||||||
\(879\) | 1.08043e11i | 0.180984i | ||||||||
\(880\) | 2.18751e11i | 0.364769i | ||||||||
\(881\) | −1.16281e12 | −1.93022 | −0.965108 | − | 0.261853i | \(-0.915666\pi\) | ||||
−0.965108 | + | 0.261853i | \(0.915666\pi\) | |||||||
\(882\) | − | 1.73378e11i | − | 0.286497i | ||||||
\(883\) | −8.93632e11 | −1.46999 | −0.734997 | − | 0.678070i | \(-0.762817\pi\) | ||||
−0.734997 | + | 0.678070i | \(0.762817\pi\) | |||||||
\(884\) | −8.03683e9 | −0.0131606 | ||||||||
\(885\) | −1.88413e11 | −0.307141 | ||||||||
\(886\) | − | 2.75040e11i | − | 0.446335i | ||||||
\(887\) | − | 7.54758e11i | − | 1.21931i | −0.792668 | − | 0.609653i | \(-0.791309\pi\) | ||
0.792668 | − | 0.609653i | \(-0.208691\pi\) | |||||||
\(888\) | − | 1.14730e10i | − | 0.0184513i | ||||||
\(889\) | − | 1.00090e11i | − | 0.160245i | ||||||
\(890\) | 4.26571e11i | 0.679879i | ||||||||
\(891\) | −4.05237e11 | −0.642982 | ||||||||
\(892\) | − | 4.06605e11i | − | 0.642264i | ||||||
\(893\) | − | 1.12015e12i | − | 1.76145i | ||||||
\(894\) | − | 7.43652e10i | − | 0.116418i | ||||||
\(895\) | −5.14210e11 | −0.801399 | ||||||||
\(896\) | 3.83576e11 | 0.595141 | ||||||||
\(897\) | 4.34583e9i | 0.00671279i | ||||||||
\(898\) | −1.86563e11 | −0.286893 | ||||||||
\(899\) | 6.66794e11i | 1.02083i | ||||||||
\(900\) | −1.14284e12 | −1.74187 | ||||||||
\(901\) | 3.50405e11 | 0.531706 | ||||||||
\(902\) | 1.65901e11i | 0.250625i | ||||||||
\(903\) | 3.69041e10 | − | 5.12087e10i | 0.0555039 | − | 0.0770181i | ||||
\(904\) | 3.25202e11 | 0.486944 | ||||||||
\(905\) | 1.13538e11i | 0.169257i | ||||||||
\(906\) | − | 1.62316e9i | − | 0.00240906i | ||||||
\(907\) | 9.46310e10 | 0.139831 | 0.0699156 | − | 0.997553i | \(-0.477727\pi\) | ||||
0.0699156 | + | 0.997553i | \(0.477727\pi\) | |||||||
\(908\) | 7.87583e11i | 1.15865i | ||||||||
\(909\) | 3.36084e11 | 0.492257 | ||||||||
\(910\) | 2.41017e10i | 0.0351464i | ||||||||
\(911\) | − | 2.97419e11i | − | 0.431813i | −0.976414 | − | 0.215907i | \(-0.930729\pi\) | ||
0.976414 | − | 0.215907i | \(-0.0692707\pi\) | |||||||
\(912\) | 3.73393e10 | 0.0539742 | ||||||||
\(913\) | −1.20602e11 | −0.173568 | ||||||||
\(914\) | 3.05260e11 | 0.437406 | ||||||||
\(915\) | 3.79035e10i | 0.0540749i | ||||||||
\(916\) | 7.97951e11 | 1.13343 | ||||||||
\(917\) | −3.84109e11 | −0.543222 | ||||||||
\(918\) | 3.23514e10 | 0.0455536 | ||||||||
\(919\) | −1.79265e11 | −0.251324 | −0.125662 | − | 0.992073i | \(-0.540105\pi\) | ||||
−0.125662 | + | 0.992073i | \(0.540105\pi\) | |||||||
\(920\) | 9.44425e11 | 1.31831 | ||||||||
\(921\) | − | 7.30136e10i | − | 0.101476i | ||||||
\(922\) | 6.65000e11i | 0.920234i | ||||||||
\(923\) | − | 5.96387e10i | − | 0.0821716i | ||||||
\(924\) | 3.51514e10 | 0.0482230 | ||||||||
\(925\) | 2.51648e11i | 0.343738i | ||||||||
\(926\) | 2.09751e11 | 0.285273 | ||||||||
\(927\) | −2.06046e11 | −0.279027 | ||||||||
\(928\) | −8.99361e11 | −1.21267 | ||||||||
\(929\) | − | 1.07215e12i | − | 1.43943i | −0.694268 | − | 0.719716i | \(-0.744272\pi\) | ||
0.694268 | − | 0.719716i | \(-0.255728\pi\) | |||||||
\(930\) | 8.90749e10i | 0.119076i | ||||||||
\(931\) | − | 5.55530e11i | − | 0.739449i | ||||||
\(932\) | 8.11265e11i | 1.07522i | ||||||||
\(933\) | 4.77545e9i | 0.00630214i | ||||||||
\(934\) | −4.33808e11 | −0.570047 | ||||||||
\(935\) | 3.00393e11i | 0.393046i | ||||||||
\(936\) | 3.81684e10i | 0.0497280i | ||||||||
\(937\) | 4.41660e11i | 0.572967i | 0.958085 | + | 0.286483i | \(0.0924863\pi\) | ||||
−0.958085 | + | 0.286483i | \(0.907514\pi\) | |||||||
\(938\) | −2.64888e10 | −0.0342177 | ||||||||
\(939\) | −9.41183e10 | −0.121063 | ||||||||
\(940\) | − | 1.45853e12i | − | 1.86812i | ||||||
\(941\) | −2.82461e11 | −0.360246 | −0.180123 | − | 0.983644i | \(-0.557650\pi\) | ||||
−0.180123 | + | 0.983644i | \(0.557650\pi\) | |||||||
\(942\) | 9.93492e10i | 0.126171i | ||||||||
\(943\) | −4.56413e11 | −0.577180 | ||||||||
\(944\) | −2.61767e11 | −0.329631 | ||||||||
\(945\) | 2.76415e11i | 0.346605i | ||||||||
\(946\) | −2.27269e11 | − | 1.63784e11i | −0.283776 | − | 0.204507i | ||||
\(947\) | 1.21007e12 | 1.50457 | 0.752283 | − | 0.658840i | \(-0.228952\pi\) | ||||
0.752283 | + | 0.658840i | \(0.228952\pi\) | |||||||
\(948\) | − | 4.95098e10i | − | 0.0612996i | ||||||
\(949\) | − | 3.62073e10i | − | 0.0446407i | ||||||
\(950\) | 1.28526e12 | 1.57797 | ||||||||
\(951\) | 1.20133e11i | 0.146872i | ||||||||
\(952\) | 1.47573e11 | 0.179663 | ||||||||
\(953\) | 1.30519e12i | 1.58234i | 0.611594 | + | 0.791172i | \(0.290529\pi\) | ||||
−0.611594 | + | 0.791172i | \(0.709471\pi\) | |||||||
\(954\) | − | 7.07847e11i | − | 0.854567i | ||||||
\(955\) | 2.25733e12 | 2.71383 | ||||||||
\(956\) | −1.09422e12 | −1.31000 | ||||||||
\(957\) | −9.82338e10 | −0.117115 | ||||||||
\(958\) | − | 2.16409e11i | − | 0.256929i | ||||||
\(959\) | 7.17562e11 | 0.848369 | ||||||||
\(960\) | −5.44593e10 | −0.0641191 | ||||||||
\(961\) | −2.06914e11 | −0.242603 | ||||||||
\(962\) | 3.57489e9 | 0.00417409 | ||||||||
\(963\) | 1.13279e12 | 1.31718 | ||||||||
\(964\) | 1.04828e12i | 1.21386i | ||||||||
\(965\) | − | 1.03431e12i | − | 1.19273i | ||||||
\(966\) | − | 3.39426e10i | − | 0.0389795i | ||||||
\(967\) | −8.47293e11 | −0.969009 | −0.484505 | − | 0.874789i | \(-0.661000\pi\) | ||||
−0.484505 | + | 0.874789i | \(0.661000\pi\) | |||||||
\(968\) | 4.12024e11i | 0.469269i | ||||||||
\(969\) | 5.12750e10 | 0.0581582 | ||||||||
\(970\) | −1.40682e12 | −1.58910 | ||||||||
\(971\) | −2.58446e11 | −0.290732 | −0.145366 | − | 0.989378i | \(-0.546436\pi\) | ||||
−0.145366 | + | 0.989378i | \(0.546436\pi\) | |||||||
\(972\) | 2.80288e11i | 0.314007i | ||||||||
\(973\) | 9.16404e11i | 1.02243i | ||||||||
\(974\) | − | 6.31537e11i | − | 0.701718i | ||||||
\(975\) | 1.81045e10i | 0.0200340i | ||||||||
\(976\) | 5.26604e10i | 0.0580344i | ||||||||
\(977\) | 1.24467e12 | 1.36608 | 0.683038 | − | 0.730383i | \(-0.260658\pi\) | ||||
0.683038 | + | 0.730383i | \(0.260658\pi\) | |||||||
\(978\) | − | 9.22401e10i | − | 0.100824i | ||||||
\(979\) | 4.55746e11i | 0.496126i | ||||||||
\(980\) | − | 7.23346e11i | − | 0.784227i | ||||||
\(981\) | 8.93937e11 | 0.965230 | ||||||||
\(982\) | −7.33521e11 | −0.788799 | ||||||||
\(983\) | − | 3.78960e11i | − | 0.405862i | −0.979193 | − | 0.202931i | \(-0.934953\pi\) | ||
0.979193 | − | 0.202931i | \(-0.0650468\pi\) | |||||||
\(984\) | 8.66874e10 | 0.0924646 | ||||||||
\(985\) | 1.09292e12i | 1.16103i | ||||||||
\(986\) | −1.75418e11 | −0.185595 | ||||||||
\(987\) | −1.23238e11 | −0.129860 | ||||||||
\(988\) | 5.20195e10i | 0.0545932i | ||||||||
\(989\) | 4.50588e11 | − | 6.25243e11i | 0.470971 | − | 0.653527i | ||||
\(990\) | 6.06817e11 | 0.631709 | ||||||||
\(991\) | 1.16005e12i | 1.20277i | 0.798958 | + | 0.601387i | \(0.205385\pi\) | ||||
−0.798958 | + | 0.601387i | \(0.794615\pi\) | |||||||
\(992\) | 8.71283e11i | 0.899731i | ||||||||
\(993\) | −1.44166e10 | −0.0148275 | ||||||||
\(994\) | 4.65801e11i | 0.477150i | ||||||||
\(995\) | −2.48113e12 | −2.53138 | ||||||||
\(996\) | 2.68046e10i | 0.0272378i | ||||||||
\(997\) | 1.30049e12i | 1.31622i | 0.752924 | + | 0.658108i | \(0.228643\pi\) | ||||
−0.752924 | + | 0.658108i | \(0.771357\pi\) | |||||||
\(998\) | −3.31226e11 | −0.333889 | ||||||||
\(999\) | 4.09994e10 | 0.0411638 |
(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 | 43.9.b.b.42.12 | ✓ | 28 | |
43.42 | odd | 2 | inner | 43.9.b.b.42.17 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.9.b.b.42.12 | ✓ | 28 | 1.1 | even | 1 | trivial | |
43.9.b.b.42.17 | yes | 28 | 43.42 | odd | 2 | inner |