Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [84,12,Mod(5,84)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(84, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("84.5");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 84.k (of order \(6\), degree \(2\), 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: | \(64.5408271670\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 5.2 | ||
Character | \(\chi\) | \(=\) | 84.5 |
Dual form | 84.12.k.b.17.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(43\) | \(73\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −416.405 | + | 61.2712i | −0.989347 | + | 0.145576i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3914.60 | − | 6780.29i | 0.560212 | − | 0.970316i | −0.437265 | − | 0.899333i | \(-0.644053\pi\) |
0.997477 | − | 0.0709836i | \(-0.0226138\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −44460.5 | − | 768.569i | −0.999851 | − | 0.0172840i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 169639. | − | 51027.2i | 0.957615 | − | 0.288050i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 650650. | − | 375653.i | 1.21811 | − | 0.703278i | 0.253599 | − | 0.967309i | \(-0.418385\pi\) |
0.964514 | + | 0.264031i | \(0.0850522\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.53606e6i | 1.14741i | 0.819060 | + | 0.573707i | \(0.194495\pi\) | ||||
−0.819060 | + | 0.573707i | \(0.805505\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.21462e6 | + | 3.06320e6i | −0.412990 | + | 1.04153i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.13310e6 | + | 1.96259e6i | 0.193553 | + | 0.335243i | 0.946425 | − | 0.322924i | \(-0.104666\pi\) |
−0.752872 | + | 0.658166i | \(0.771332\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.29343e7 | − | 7.46761e6i | −1.19839 | − | 0.691890i | −0.238192 | − | 0.971218i | \(-0.576555\pi\) |
−0.960196 | + | 0.279328i | \(0.909888\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.85607e7 | − | 2.40411e6i | 0.991715 | − | 0.128454i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.98810e7 | + | 2.87988e7i | 1.61597 | + | 0.932978i | 0.987949 | + | 0.154778i | \(0.0494663\pi\) |
0.628016 | + | 0.778200i | \(0.283867\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.23417e6 | − | 1.07979e7i | −0.127676 | − | 0.221141i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −6.75118e7 | + | 3.16420e7i | −0.905481 | + | 0.424387i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.09792e8i | − | 0.993987i | −0.867754 | − | 0.496993i | \(-0.834437\pi\) | ||
0.867754 | − | 0.496993i | \(-0.165563\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.32191e8 | + | 7.63203e7i | −0.829299 | + | 0.478796i | −0.853613 | − | 0.520908i | \(-0.825593\pi\) |
0.0243135 | + | 0.999704i | \(0.492260\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.47917e8 | + | 1.96290e8i | −1.10276 | + | 0.873114i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.79256e8 | + | 2.98446e8i | −0.576900 | + | 0.960489i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.09464e8 | + | 5.36007e8i | −0.733670 | + | 1.27075i | 0.221635 | + | 0.975130i | \(0.428861\pi\) |
−0.955304 | + | 0.295624i | \(0.904473\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.41164e7 | − | 6.39623e8i | −0.167036 | − | 1.13519i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.72560e8 | 0.771809 | 0.385905 | − | 0.922539i | \(-0.373889\pi\) | ||||
0.385905 | + | 0.922539i | \(0.373889\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.55328e8 | 0.472333 | 0.236166 | − | 0.971713i | \(-0.424109\pi\) | ||||
0.236166 | + | 0.971713i | \(0.424109\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.18088e8 | − | 1.34995e9i | 0.256968 | − | 1.09056i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.65090e8 | + | 4.59150e8i | −0.168599 | + | 0.292022i | −0.937928 | − | 0.346831i | \(-0.887258\pi\) |
0.769328 | + | 0.638854i | \(0.220591\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.97615e9 | + | 6.83419e7i | 0.999403 | + | 0.0345628i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.92078e8 | − | 7.47803e8i | −0.240294 | − | 0.303495i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.33336e9 | − | 1.92452e9i | 1.09488 | − | 0.632128i | 0.160006 | − | 0.987116i | \(-0.448849\pi\) |
0.934871 | + | 0.354988i | \(0.115515\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.88213e9i | − | 1.57594i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.84344e9 | + | 2.31705e9i | 1.28634 | + | 0.510063i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.62559e9 | − | 6.27971e9i | −0.660227 | − | 1.14355i | −0.980556 | − | 0.196240i | \(-0.937127\pi\) |
0.320329 | − | 0.947306i | \(-0.396206\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.36594e9 | + | 1.94333e9i | 0.510261 | + | 0.294599i | 0.732941 | − | 0.680292i | \(-0.238147\pi\) |
−0.222680 | + | 0.974892i | \(0.571480\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.58144e9 | + | 2.13832e9i | −0.962451 | + | 0.271456i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.04149e10 | + | 6.01307e9i | 1.11335 | + | 0.642796i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.95833e8 | + | 6.85604e8i | 0.0358180 | + | 0.0620386i | 0.883379 | − | 0.468660i | \(-0.155263\pi\) |
−0.847561 | + | 0.530698i | \(0.821930\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.25352e10 | − | 8.93569e9i | −1.73457 | − | 0.687794i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.32309e10i | − | 1.52808i | −0.645171 | − | 0.764039i | \(-0.723214\pi\) | ||
0.645171 | − | 0.764039i | \(-0.276786\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.11716e10 | − | 1.22234e10i | 1.19530 | − | 0.690109i | 0.235799 | − | 0.971802i | \(-0.424229\pi\) |
0.959504 | + | 0.281693i | \(0.0908961\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.25754e9 | + | 4.11432e9i | 0.158508 | + | 0.200199i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.92169e10 | + | 1.62017e10i | −1.23009 | + | 0.682119i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.91219e10 | − | 3.31201e10i | 0.699169 | − | 1.21100i | −0.269586 | − | 0.962976i | \(-0.586887\pi\) |
0.968755 | − | 0.248020i | \(-0.0797798\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.61735e10 | − | 1.73124e10i | 0.834054 | − | 0.551683i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.31403e10 | 0.644822 | 0.322411 | − | 0.946600i | \(-0.395507\pi\) | ||||
0.322411 | + | 0.946600i | \(0.395507\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.77425e10 | 0.433722 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.72707e9 | + | 4.57178e10i | 0.144701 | + | 0.983398i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.17781e9 | − | 8.96823e9i | 0.0982881 | − | 0.170240i | −0.812688 | − | 0.582699i | \(-0.801997\pi\) |
0.910976 | + | 0.412459i | \(0.135330\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.18057e9 | − | 6.82941e10i | 0.0198319 | − | 1.14724i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.03685e10 | − | 3.98796e10i | 0.750763 | − | 0.594421i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.01265e11 | + | 5.84655e10i | −1.34270 | + | 0.775210i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 2.68038e10i | − | 0.316922i | −0.987365 | − | 0.158461i | \(-0.949347\pi\) | ||
0.987365 | − | 0.158461i | \(-0.0506532\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.12069e10 | − | 9.69262e10i | 0.963905 | − | 1.02435i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.56936e9 | + | 1.65746e10i | 0.0905974 | + | 0.156919i | 0.907763 | − | 0.419484i | \(-0.137789\pi\) |
−0.817165 | + | 0.576403i | \(0.804456\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.09296e10 | + | 3.51777e10i | 0.517874 | + | 0.298994i | 0.736064 | − | 0.676912i | \(-0.236682\pi\) |
−0.218191 | + | 0.975906i | \(0.570015\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.63570e10 | − | 1.35258e11i | 0.430930 | − | 1.03424i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.24209e11 | − | 1.29447e11i | −1.54541 | − | 0.892241i | −0.998483 | − | 0.0550581i | \(-0.982466\pi\) |
−0.546923 | − | 0.837183i | \(-0.684201\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.10453e10 | + | 1.23054e11i | 0.442272 | + | 0.766038i | 0.997858 | − | 0.0654214i | \(-0.0208391\pi\) |
−0.555585 | + | 0.831459i | \(0.687506\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.60204e10 | − | 2.42157e11i | 0.540863 | − | 1.36402i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2.71376e11i | − | 1.38561i | −0.721126 | − | 0.692804i | \(-0.756375\pi\) | ||
0.721126 | − | 0.692804i | \(-0.243625\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.90529e11 | − | 2.25472e11i | 1.81057 | − | 1.04533i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.83810e10 | + | 2.60576e11i | 0.330513 | + | 1.09878i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.88698e10 | − | 8.81284e10i | −0.187729 | − | 0.338538i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.39575e11 | − | 2.41750e11i | 0.489200 | − | 0.847320i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.38417e11 | + | 3.50815e10i | −0.763587 | + | 0.112357i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.84668e11 | 0.834323 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.47094e11 | −1.73799 | −0.868994 | − | 0.494823i | \(-0.835233\pi\) | ||||
−0.868994 | + | 0.494823i | \(0.835233\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.89601e11 | + | 2.78985e10i | −0.467301 | + | 0.0687603i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.04238e11 | + | 3.53751e11i | −0.462535 | + | 0.801135i | −0.999087 | − | 0.0427331i | \(-0.986393\pi\) |
0.536551 | + | 0.843868i | \(0.319727\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.69325e11 | + | 3.41955e11i | 1.18625 | + | 0.712499i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.97404e10 | + | 5.81616e11i | −0.0954714 | + | 1.11635i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.62000e11 | − | 3.24471e11i | 0.994885 | − | 0.574397i | 0.0881541 | − | 0.996107i | \(-0.471903\pi\) |
0.906731 | + | 0.421710i | \(0.138570\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2.15022e11i | − | 0.351480i | −0.984437 | − | 0.175740i | \(-0.943768\pi\) | ||
0.984437 | − | 0.175740i | \(-0.0562318\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.22521e10 | − | 2.07434e11i | 0.124292 | − | 0.313455i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.77026e11 | + | 9.99439e11i | 0.806952 | + | 1.39768i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.44420e11 | − | 4.29791e11i | −0.964481 | − | 0.556844i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.27064e11 | + | 9.26230e10i | −0.993787 | + | 0.111294i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.06652e11 | + | 6.15753e10i | 0.118972 | + | 0.0686882i | 0.558305 | − | 0.829636i | \(-0.311452\pi\) |
−0.439333 | + | 0.898324i | \(0.644785\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.05755e10 | − | 8.75993e10i | −0.0524284 | − | 0.0908087i | 0.838620 | − | 0.544717i | \(-0.183363\pi\) |
−0.891049 | + | 0.453908i | \(0.850029\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.92363e11 | + | 2.75111e11i | 0.281916 | + | 0.265281i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.19505e12i | 1.07291i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.87323e12 | + | 1.08151e12i | −1.56726 | + | 0.904861i | −0.570778 | + | 0.821104i | \(0.693358\pi\) |
−0.996486 | + | 0.0837566i | \(0.973308\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.27011e12 | + | 1.00562e12i | −0.991191 | + | 0.784781i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.19560e12 | − | 1.31875e12i | −1.59960 | − | 0.960769i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.53517e11 | − | 2.65900e11i | 0.104502 | − | 0.181003i | −0.809032 | − | 0.587764i | \(-0.800008\pi\) |
0.913535 | + | 0.406761i | \(0.133342\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.60405e11 | + | 2.44935e12i | 0.229419 | + | 1.55915i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.44797e12 | 0.862620 | 0.431310 | − | 0.902204i | \(-0.358052\pi\) | ||||
0.431310 | + | 0.902204i | \(0.358052\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.67326e11 | −0.316560 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.57521e12 | − | 6.06795e11i | −1.34689 | − | 0.317368i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.89441e11 | − | 3.28121e11i | 0.0929436 | − | 0.160983i | −0.815805 | − | 0.578327i | \(-0.803706\pi\) |
0.908748 | + | 0.417344i | \(0.137039\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.68875e11 | + | 4.84871e11i | 0.123834 | + | 0.223315i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.89448e12 | + | 2.39276e12i | 0.819666 | + | 1.03525i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.35250e12 | − | 1.93557e12i | 1.36357 | − | 0.787258i | 0.373473 | − | 0.927641i | \(-0.378167\pi\) |
0.990097 | + | 0.140383i | \(0.0448335\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.58201e11i | 0.0987931i | 0.998779 | + | 0.0493965i | \(0.0157298\pi\) | ||||
−0.998779 | + | 0.0493965i | \(0.984270\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.52066e12 | − | 6.02975e11i | −0.547712 | − | 0.217179i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.42286e12 | + | 4.19651e12i | 0.822022 | + | 1.42378i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.47450e12 | + | 8.51305e11i | 0.471538 | + | 0.272243i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.02593e12 | − | 1.35493e12i | 0.912681 | − | 0.408674i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.10868e12 | − | 1.79480e12i | −0.884896 | − | 0.510895i | −0.0126261 | − | 0.999920i | \(-0.504019\pi\) |
−0.872269 | + | 0.489026i | \(0.837352\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.03325e10 | + | 1.78964e10i | 0.00277742 | + | 0.00481063i | 0.867411 | − | 0.497593i | \(-0.165783\pi\) |
−0.864633 | + | 0.502403i | \(0.832449\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.70526e12 | − | 1.86573e12i | −1.19507 | − | 0.473870i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.88985e12i | − | 0.453799i | −0.973918 | − | 0.226900i | \(-0.927141\pi\) | ||
0.973918 | − | 0.226900i | \(-0.0728589\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.13197e12 | + | 1.80825e12i | −0.711420 | + | 0.410739i | −0.811587 | − | 0.584232i | \(-0.801396\pi\) |
0.100167 | + | 0.994971i | \(0.468062\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.06835e11 | − | 2.61235e11i | −0.0444677 | − | 0.0561634i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.43825e10 | + | 4.88139e12i | −0.0171800 | + | 0.993838i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.24135e12 | − | 3.88213e12i | 0.432377 | − | 0.748899i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.93127e12 | + | 2.34010e12i | 1.81622 | + | 0.427955i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.12209e13 | −1.94636 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.86782e11 | −0.162431 | −0.0812153 | − | 0.996697i | \(-0.525880\pi\) | ||||
−0.0812153 | + | 0.996697i | \(0.525880\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.42339e12 | + | 9.67346e12i | 0.222451 | + | 1.51180i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.78243e12 | − | 3.08726e12i | 0.264607 | − | 0.458312i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.93592e12 | − | 3.29164e12i | 0.837451 | − | 0.464391i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.06701e12 | + | 6.38710e12i | −1.08211 | + | 0.856764i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.01465e12 | + | 1.74051e12i | −0.384663 | + | 0.222085i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.51241e13i | − | 1.83651i | −0.395995 | − | 0.918253i | \(-0.629600\pi\) | ||
0.395995 | − | 0.918253i | \(-0.370400\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.60854e12 | − | 1.51363e12i | −0.185964 | − | 0.174991i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.95720e11 | − | 1.37823e12i | −0.0876230 | − | 0.151767i | 0.818883 | − | 0.573961i | \(-0.194594\pi\) |
−0.906506 | + | 0.422193i | \(0.861260\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.17063e13 | − | 6.75866e12i | −1.22836 | − | 0.709194i | −0.261673 | − | 0.965156i | \(-0.584274\pi\) |
−0.966687 | + | 0.255962i | \(0.917608\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.11734e13 | − | 8.53660e12i | 1.11768 | − | 0.853924i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.15987e12 | − | 6.69654e11i | −0.110651 | − | 0.0638841i | 0.443653 | − | 0.896198i | \(-0.353682\pi\) |
−0.554304 | + | 0.832314i | \(0.687015\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.07545e12 | + | 3.59478e12i | 0.188903 | + | 0.327189i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.93314e12 | + | 1.49630e13i | −0.515429 | + | 1.29988i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.95527e13i | 1.62187i | 0.585133 | + | 0.810937i | \(0.301042\pi\) | ||||
−0.585133 | + | 0.810937i | \(0.698958\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.34554e13 | − | 7.76848e12i | 1.06611 | − | 0.615520i | 0.138996 | − | 0.990293i | \(-0.455613\pi\) |
0.927117 | + | 0.374773i | \(0.122279\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.83802e12 | + | 8.81264e12i | −0.744857 | + | 0.667224i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.19920e12 | − | 1.31313e13i | 0.593414 | − | 0.950374i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.14707e13 | − | 1.98679e13i | 0.793884 | − | 1.37505i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.63574e12 | + | 1.41784e12i | −0.637953 | + | 0.0938706i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.50746e11 | −0.0475650 | −0.0237825 | − | 0.999717i | \(-0.507571\pi\) | ||||
−0.0237825 | + | 0.999717i | \(0.507571\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.32735e13 | 2.62457 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.38807e12 | + | 1.08711e12i | −0.429102 | + | 0.0631395i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.73516e12 | − | 1.51297e13i | 0.486003 | − | 0.841782i | −0.513868 | − | 0.857869i | \(-0.671788\pi\) |
0.999871 | + | 0.0160879i | \(0.00512115\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.41709e13 | − | 2.35933e13i | 0.755524 | − | 1.25788i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.60237e12 | − | 1.86249e13i | −0.286318 | − | 0.951857i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.34132e13 | − | 1.92911e13i | 1.63742 | − | 0.945367i | 0.655708 | − | 0.755014i | \(-0.272370\pi\) |
0.981716 | − | 0.190353i | \(-0.0609633\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3.01349e13i | − | 1.41650i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.60657e12 | + | 4.05166e12i | −0.0724582 | + | 0.182735i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.63697e13 | − | 2.83532e13i | −0.708604 | − | 1.22734i | −0.965375 | − | 0.260866i | \(-0.915992\pi\) |
0.256771 | − | 0.966472i | \(-0.417342\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.95405e12 | − | 4.01492e12i | −0.289006 | − | 0.166858i | 0.348488 | − | 0.937313i | \(-0.386695\pi\) |
−0.637493 | + | 0.770456i | \(0.720029\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.69287e12 | + | 2.85103e13i | 0.147390 | + | 1.13791i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.11252e12 | − | 4.68377e12i | −0.311047 | − | 0.179583i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.06811e13 | + | 1.85002e13i | 0.393529 | + | 0.681613i | 0.992912 | − | 0.118850i | \(-0.0379207\pi\) |
−0.599383 | + | 0.800462i | \(0.704587\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.85302e13 | + | 1.96922e13i | −0.656232 | + | 0.697382i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.08162e13i | 0.708789i | 0.935096 | + | 0.354394i | \(0.115313\pi\) | ||||
−0.935096 | + | 0.354394i | \(0.884687\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.91344e12 | − | 4.56883e12i | 0.259143 | − | 0.149617i | −0.364800 | − | 0.931086i | \(-0.618863\pi\) |
0.623944 | + | 0.781469i | \(0.285529\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.85850e13 | − | 3.05499e13i | 1.21555 | − | 0.962417i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.54563e13 | − | 4.40052e11i | −0.771694 | − | 0.0133399i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.45681e13 | − | 2.52327e13i | 0.425075 | − | 0.736251i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.64230e12 | + | 1.11612e13i | 0.0461362 | + | 0.313546i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.99193e12 | −0.107997 | −0.0539984 | − | 0.998541i | \(-0.517197\pi\) | ||||
−0.0539984 | + | 0.998541i | \(0.517197\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.67710e13 | −1.47947 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.20402e13 | + | 4.59489e13i | −0.804516 | + | 1.15376i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.42368e13 | + | 7.66203e13i | −1.07051 | + | 1.85418i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.02441e13 | − | 3.49951e11i | −0.472262 | − | 0.00816378i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.00028e12 | − | 6.31542e12i | −0.112476 | − | 0.142059i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.63526e13 | − | 1.52147e13i | 0.571709 | − | 0.330076i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.76589e13i | − | 0.369575i | −0.982779 | − | 0.184787i | \(-0.940840\pi\) | ||
0.982779 | − | 0.184787i | \(-0.0591597\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.75268e13 | − | 1.09149e13i | −0.555883 | − | 0.220419i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.93664e12 | + | 1.20146e13i | 0.135197 | + | 0.234168i | 0.925673 | − | 0.378325i | \(-0.123500\pi\) |
−0.790476 | + | 0.612493i | \(0.790167\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.92739e13 | + | 2.26748e13i | 0.738941 | + | 0.426628i | 0.821684 | − | 0.569943i | \(-0.193035\pi\) |
−0.0827432 | + | 0.996571i | \(0.526368\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.51799e13 | + | 5.97750e13i | −0.275779 | + | 1.08595i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.12138e13 | + | 2.95683e13i | 0.898589 | + | 0.518801i | 0.876742 | − | 0.480961i | \(-0.159712\pi\) |
0.0218470 | + | 0.999761i | \(0.493045\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.12436e13 | − | 7.14360e13i | −0.699049 | − | 1.21079i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.01293e14 | + | 4.01649e13i | 1.65883 | + | 0.657762i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.38462e13i | − | 0.535668i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.65862e13 | − | 9.57607e12i | 0.253740 | − | 0.146497i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.71233e13 | − | 4.68873e13i | −0.549078 | − | 0.693493i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.21389e13 | − | 2.02103e13i | 0.173621 | − | 0.289065i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.21737e13 | + | 5.57265e13i | −0.445090 | + | 0.770918i | −0.998058 | − | 0.0622840i | \(-0.980162\pi\) |
0.552969 | + | 0.833202i | \(0.313495\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.51461e13 | + | 1.06719e14i | −0.336533 | + | 1.42823i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.19812e12 | 0.0802627 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.15966e13 | 1.02260 | 0.511302 | − | 0.859401i | \(-0.329163\pi\) | ||||
0.511302 | + | 0.859401i | \(0.329163\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.66276e13 | + | 1.13002e14i | 0.201711 | + | 1.37085i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.73399e13 | + | 9.93156e13i | −0.673454 | + | 1.16646i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.78079e13 | − | 4.55732e12i | −0.998656 | − | 0.0518313i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.48803e14 | + | 1.17816e14i | −1.63910 | + | 1.29777i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.00571e13 | + | 1.15800e13i | −0.214021 | + | 0.123565i | −0.603179 | − | 0.797606i | \(-0.706099\pi\) |
0.389158 | + | 0.921171i | \(0.372766\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 3.68983e12i | − | 0.0381475i | −0.999818 | − | 0.0190738i | \(-0.993928\pi\) | ||
0.999818 | − | 0.0190738i | \(-0.00607173\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.86040e13 | − | 1.03702e14i | −0.486948 | − | 1.03896i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.76110e13 | − | 4.78237e13i | −0.268115 | − | 0.464389i | 0.700260 | − | 0.713888i | \(-0.253067\pi\) |
−0.968375 | + | 0.249499i | \(0.919734\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.57512e14 | − | 9.09398e13i | −1.48272 | − | 0.856048i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.57493e13 | + | 3.37028e13i | 0.235012 | + | 0.307603i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.88317e13 | + | 5.12870e13i | 0.786228 | + | 0.453929i | 0.838633 | − | 0.544697i | \(-0.183355\pi\) |
−0.0524051 | + | 0.998626i | \(0.516689\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.32853e13 | + | 9.22928e13i | 0.457423 | + | 0.792279i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.33072e13 | + | 1.09218e14i | −0.360640 | + | 0.909509i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 1.91400e14i | − | 1.54643i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.58521e13 | − | 3.22462e13i | 0.437901 | − | 0.252822i | −0.264806 | − | 0.964302i | \(-0.585308\pi\) |
0.702707 | + | 0.711480i | \(0.251975\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.71284e13 | − | 2.92162e13i | 0.739096 | − | 0.222320i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.49682e14 | + | 8.30031e13i | −1.10564 | + | 0.613109i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.05428e14 | − | 1.82606e14i | 0.756060 | − | 1.30953i | −0.188785 | − | 0.982018i | \(-0.560455\pi\) |
0.944845 | − | 0.327516i | \(-0.106212\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.18537e14 | + | 1.74420e13i | −0.825435 | + | 0.121457i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.68647e14 | 1.14051 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.35546e13 | −0.417476 | −0.208738 | − | 0.977972i | \(-0.566936\pi\) | ||||
−0.208738 | + | 0.977972i | \(0.566936\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.69453e14 | − | 3.96482e13i | 1.71947 | − | 0.253009i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.87687e13 | − | 8.44699e13i | 0.302377 | − | 0.523732i | −0.674297 | − | 0.738460i | \(-0.735553\pi\) |
0.976674 | + | 0.214729i | \(0.0688867\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.52082e12 | + | 2.61522e14i | −0.0272385 | + | 1.57571i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.72413e13 | − | 2.32341e13i | 0.452313 | − | 0.136056i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.76559e13 | + | 3.90612e13i | −0.385109 | + | 0.222343i | −0.680039 | − | 0.733176i | \(-0.738037\pi\) |
0.294930 | + | 0.955519i | \(0.404704\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.30528e14i | 0.722321i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.33710e13 | − | 1.59817e14i | 0.340982 | − | 0.859934i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.49709e14 | − | 2.59304e14i | −0.783366 | − | 1.35683i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.05457e13 | + | 4.07296e13i | 0.359023 | + | 0.207282i | 0.668652 | − | 0.743575i | \(-0.266871\pi\) |
−0.309629 | + | 0.950857i | \(0.600205\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.58022e14 | − | 1.07508e14i | −1.27734 | − | 0.532219i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.30748e14 | + | 7.54872e13i | 0.629709 | + | 0.363563i | 0.780639 | − | 0.624982i | \(-0.214894\pi\) |
−0.150930 | + | 0.988544i | \(0.548227\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.17233e14 | − | 2.03053e14i | −0.549378 | − | 0.951550i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.49242e13 | − | 2.45235e14i | −0.0680594 | − | 1.11836i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.65004e14i | 2.06390i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.98507e13 | − | 2.30078e13i | 0.172170 | − | 0.0994024i | −0.411439 | − | 0.911437i | \(-0.634974\pi\) |
0.583609 | + | 0.812035i | \(0.301640\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.14139e14 | + | 1.69545e14i | −0.900668 | + | 0.713109i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.56369e14 | + | 2.81986e14i | 0.640363 | + | 1.15479i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.05852e13 | − | 1.56898e14i | 0.361237 | − | 0.625682i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.31746e13 | + | 8.95360e13i | 0.0511670 | + | 0.347736i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.64676e14 | 1.37953 | 0.689763 | − | 0.724035i | \(-0.257715\pi\) | ||||
0.689763 | + | 0.724035i | \(0.257715\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.46037e13 | 0.164369 | 0.0821844 | − | 0.996617i | \(-0.473810\pi\) | ||||
0.0821844 | + | 0.996617i | \(0.473810\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.15404e13 | + | 9.14164e13i | −0.0773360 | + | 0.328210i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.41279e13 | − | 2.44702e13i | 0.0494239 | − | 0.0856048i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.48158e14 | − | 8.89882e13i | −0.505093 | − | 0.303375i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.01513e14 | − | 3.80816e14i | −1.00182 | − | 1.26532i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.45964e14 | − | 1.42007e14i | 0.796610 | − | 0.459923i | −0.0456743 | − | 0.998956i | \(-0.514544\pi\) |
0.842284 | + | 0.539033i | \(0.181210\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.58726e14i | 1.44834i | 0.689623 | + | 0.724169i | \(0.257776\pi\) | ||||
−0.689623 | + | 0.724169i | \(0.742224\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.36314e14 | + | 1.33355e14i | 1.03527 | + | 0.410506i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.30117e14 | − | 7.44984e14i | −1.29104 | − | 2.23614i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.20636e14 | + | 6.96493e13i | 0.353120 | + | 0.203874i | 0.666059 | − | 0.745899i | \(-0.267980\pi\) |
−0.312938 | + | 0.949773i | \(0.601313\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.38718e14 | − | 8.92438e13i | 0.966999 | − | 0.254780i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.37215e14 | − | 3.10161e14i | −1.49599 | − | 0.863708i | −0.495997 | − | 0.868324i | \(-0.665197\pi\) |
−0.999989 | + | 0.00461656i | \(0.998530\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.05381e13 | − | 7.02141e13i | −0.110124 | − | 0.190741i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.81830e13 | − | 1.91056e13i | −0.127703 | − | 0.0506371i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.84911e14i | 0.736807i | 0.929666 | + | 0.368404i | \(0.120096\pi\) | ||||
−0.929666 | + | 0.368404i | \(0.879904\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.72536e14 | − | 2.15084e14i | 0.940151 | − | 0.542797i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.64272e13 | + | 3.33779e13i | 0.0650895 | + | 0.0822090i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.58432e14 | − | 2.75349e14i | −1.10208 | − | 0.661943i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.73713e14 | − | 3.00879e14i | 0.407654 | − | 0.706078i | −0.586972 | − | 0.809607i | \(-0.699680\pi\) |
0.994626 | + | 0.103529i | \(0.0330135\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.38598e14 | − | 9.66443e13i | −0.317531 | − | 0.221415i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.60458e14 | −0.358928 | −0.179464 | − | 0.983765i | \(-0.557436\pi\) | ||||
−0.179464 | + | 0.983765i | \(0.557436\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.22098e14 | 0.921972 | 0.460986 | − | 0.887408i | \(-0.347496\pi\) | ||||
0.460986 | + | 0.887408i | \(0.347496\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.32224e13 | − | 4.97626e14i | −0.156190 | − | 1.06148i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.32028e13 | − | 7.48294e13i | 0.0900055 | − | 0.155894i | −0.817508 | − | 0.575918i | \(-0.804645\pi\) |
0.907513 | + | 0.420024i | \(0.137978\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.70720e13 | − | 3.07865e13i | −0.0347404 | − | 0.0626484i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.13755e14 | − | 5.65120e14i | 1.41884 | − | 1.12338i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.96259e14 | − | 1.71045e14i | 0.575355 | − | 0.332181i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.86217e14i | 0.353350i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.67264e14 | − | 4.96565e14i | 0.866386 | − | 0.920715i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.38068e14 | + | 9.31961e14i | 0.974971 | + | 1.68870i | 0.680031 | + | 0.733184i | \(0.261967\pi\) |
0.294941 | + | 0.955516i | \(0.404700\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.23341e14 | − | 4.75356e14i | −1.45808 | − | 0.841824i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.95060e14 | + | 4.14605e14i | 1.72242 | + | 0.717671i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.81738e14 | − | 1.04926e14i | −0.307514 | − | 0.177544i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.41751e14 | + | 9.38341e14i | 0.896171 | + | 1.55221i | 0.832349 | + | 0.554252i | \(0.186996\pi\) |
0.0638218 | + | 0.997961i | \(0.479671\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.76333e13 | + | 1.20128e14i | −0.0770393 | + | 0.194288i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 4.73703e14i | − | 0.749131i | −0.927200 | − | 0.374565i | \(-0.877792\pi\) | ||
0.927200 | − | 0.374565i | \(-0.122208\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.15476e14 | − | 1.24405e14i | 0.333227 | − | 0.192389i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.00149e14 | − | 9.97837e14i | −0.453950 | − | 1.50914i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.78545e13 | + | 1.03286e15i | −0.0264112 | + | 1.52785i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.91573e14 | + | 5.05019e14i | −0.421885 | + | 0.730726i | −0.996124 | − | 0.0879620i | \(-0.971965\pi\) |
0.574239 | + | 0.818688i | \(0.305298\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.02942e14 | + | 8.87190e13i | −0.853431 | + | 0.125577i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.37096e15 | −1.89845 | −0.949227 | − | 0.314592i | \(-0.898132\pi\) | ||||
−0.949227 | + | 0.314592i | \(0.898132\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.49841e14 | 0.203015 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.36237e14 | − | 3.47608e13i | 0.313188 | − | 0.0460835i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.55389e14 | − | 2.69141e14i | 0.201591 | − | 0.349166i | −0.747450 | − | 0.664318i | \(-0.768722\pi\) |
0.949041 | + | 0.315152i | \(0.102055\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.50695e14 | + | 5.27188e14i | −1.20705 | + | 0.669346i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.10951e15 | + | 9.48862e13i | 1.37875 | + | 0.117912i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.77031e14 | − | 2.75414e14i | 0.580238 | − | 0.335001i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.98328e14i | 0.474288i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.87796e13 | + | 1.48238e14i | −0.0685182 | + | 0.172798i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.38465e14 | − | 2.39828e14i | −0.158027 | − | 0.273711i | 0.776130 | − | 0.630573i | \(-0.217180\pi\) |
−0.934157 | + | 0.356862i | \(0.883847\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.74025e14 | − | 5.62353e14i | −1.08846 | − | 0.628420i | −0.155291 | − | 0.987869i | \(-0.549631\pi\) |
−0.933165 | + | 0.359449i | \(0.882965\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.41670e14 | − | 1.85428e14i | −0.155025 | − | 0.202908i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.99570e14 | − | 1.72957e14i | −0.321026 | − | 0.185344i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.18234e15 | + | 2.04787e15i | 1.24090 | + | 2.14930i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.35477e14 | − | 8.80278e14i | −0.961642 | − | 0.904899i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.79488e14i | 0.885585i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.75538e15 | + | 1.01347e15i | −1.73151 | + | 0.999689i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.27740e15 | + | 1.01139e15i | −1.23444 | + | 0.977374i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.31145e15 | − | 6.97878e14i | 1.24169 | − | 0.660757i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.40956e14 | + | 5.90554e14i | −0.316311 | + | 0.547866i | −0.979715 | − | 0.200395i | \(-0.935778\pi\) |
0.663405 | + | 0.748261i | \(0.269111\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.58203e13 | − | 1.07516e14i | −0.0143819 | − | 0.0977406i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.11246e15 | 0.991066 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.13043e15 | −0.986992 | −0.493496 | − | 0.869748i | \(-0.664281\pi\) | ||||
−0.493496 | + | 0.869748i | \(0.664281\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.70156e14 | + | 1.57909e14i | 0.573493 | + | 0.135132i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.19882e14 | + | 1.42008e15i | −0.687729 | + | 1.19118i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.75624e14 | + | 1.45784e15i | −0.719995 | + | 1.19873i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.26601e15 | − | 1.59900e15i | −1.02053 | − | 1.28895i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.14154e15 | − | 6.59067e14i | 0.902167 | − | 0.520866i | 0.0242644 | − | 0.999706i | \(-0.492276\pi\) |
0.877903 | + | 0.478839i | \(0.158942\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.99412e14i | 0.541961i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.66150e14 | − | 2.64143e14i | −0.506147 | − | 0.200698i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.07279e15 | + | 1.85812e15i | 0.799313 | + | 1.38445i | 0.920064 | + | 0.391767i | \(0.128136\pi\) |
−0.120752 | + | 0.992683i | \(0.538531\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.84001e15 | − | 1.06233e15i | −1.34448 | − | 0.776235i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.17699e15 | + | 7.49601e14i | −0.843465 | + | 0.537185i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.09271e14 | − | 6.30877e13i | −0.0768047 | − | 0.0443432i | 0.461106 | − | 0.887345i | \(-0.347453\pi\) |
−0.537911 | + | 0.843002i | \(0.680786\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.35236e14 | + | 1.44667e15i | 0.575851 | + | 0.997404i | 0.995949 | + | 0.0899247i | \(0.0286626\pi\) |
−0.420097 | + | 0.907479i | \(0.638004\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.40444e15 | + | 5.56889e14i | 0.949843 | + | 0.376633i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 7.18147e14i | − | 0.476475i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.56393e15 | + | 1.48029e15i | −1.66893 | + | 0.963560i | −0.700720 | + | 0.713436i | \(0.747138\pi\) |
−0.968214 | + | 0.250124i | \(0.919529\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.39905e12 | − | 6.81908e12i | −0.00344814 | − | 0.00435505i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.02883e15 | − | 1.77849e13i | −0.644726 | − | 0.0111451i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.44590e15 | − | 2.50438e15i | 0.889123 | − | 1.54001i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.07361e15 | + | 4.88604e14i | 1.25132 | + | 0.294849i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.56255e15 | 0.925386 | 0.462693 | − | 0.886519i | \(-0.346883\pi\) | ||||
0.462693 | + | 0.886519i | \(0.346883\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.27972e15 | 1.32510 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.15794e14 | + | 7.86944e14i | 0.0660623 | + | 0.448965i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.24512e14 | + | 5.62072e14i | −0.181731 | + | 0.314768i | −0.942470 | − | 0.334290i | \(-0.891504\pi\) |
0.760739 | + | 0.649058i | \(0.224837\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.88842e14 | − | 1.36364e13i | −0.433657 | − | 0.00749644i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.19337e15 | − | 9.44862e14i | 0.644048 | − | 0.509929i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.60010e15 | − | 9.23818e14i | 0.847812 | − | 0.489485i | −0.0120998 | − | 0.999927i | \(-0.503852\pi\) |
0.859912 | + | 0.510442i | \(0.170518\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 9.66604e14i | − | 0.502851i | −0.967877 | − | 0.251425i | \(-0.919101\pi\) | ||
0.967877 | − | 0.251425i | \(-0.0808993\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.02133e14 | + | 9.61066e13i | 0.0521701 | + | 0.0490917i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.09276e15 | − | 1.89271e15i | −0.548112 | − | 0.949358i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.62928e15 | + | 9.40663e14i | 0.802522 | + | 0.463336i | 0.844352 | − | 0.535788i | \(-0.179986\pi\) |
−0.0418303 | + | 0.999125i | \(0.513319\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.63952e14 | − | 2.03781e15i | −0.127682 | − | 0.985752i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.05282e14 | − | 4.07195e14i | −0.335071 | − | 0.193453i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.18489e14 | − | 2.05229e14i | −0.0552898 | − | 0.0957647i | 0.837056 | − | 0.547118i | \(-0.184275\pi\) |
−0.892346 | + | 0.451353i | \(0.850942\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.95444e14 | + | 1.75387e15i | −0.318749 | + | 0.803865i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1.98091e15i | − | 0.891859i | −0.895068 | − | 0.445929i | \(-0.852873\pi\) | ||
0.895068 | − | 0.445929i | \(-0.147127\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.51866e15 | − | 1.45415e15i | 1.11396 | − | 0.643146i | 0.174109 | − | 0.984726i | \(-0.444295\pi\) |
0.939853 | + | 0.341580i | \(0.110962\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.27881e15 | − | 3.65928e14i | −1.85917 | − | 0.158998i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.37101e14 | + | 3.94752e14i | −0.101216 | + | 0.168516i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.41877e15 | − | 2.45737e15i | 0.595074 | − | 1.03070i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.67244e15 | − | 6.87520e14i | 1.92563 | − | 0.283344i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.40261e15 | −0.568015 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.45914e15 | 0.580678 | 0.290339 | − | 0.956924i | \(-0.406232\pi\) | ||||
0.290339 | + | 0.956924i | \(0.406232\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.10901e14 | − | 6.04614e13i | 0.160700 | − | 0.0236460i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.53311e15 | + | 4.38748e15i | −0.973642 | + | 1.68640i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.04977e14 | + | 3.03548e15i | −0.0396578 | + | 1.14673i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.18541e15 | − | 3.94086e15i | −0.440163 | − | 1.46331i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.05736e15 | + | 2.34252e15i | −1.48090 | + | 0.854995i | −0.999766 | − | 0.0216541i | \(-0.993107\pi\) |
−0.481130 | + | 0.876649i | \(0.659773\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.55663e14i | 0.0558503i | 0.999610 | + | 0.0279252i | \(0.00889001\pi\) | ||||
−0.999610 | + | 0.0279252i | \(0.991110\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.53052e14 | + | 1.39476e15i | −0.195069 | + | 0.491950i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.82203e14 | − | 1.00841e15i | −0.201884 | − | 0.349673i | 0.747252 | − | 0.664541i | \(-0.231373\pi\) |
−0.949135 | + | 0.314868i | \(0.898040\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.71799e15 | − | 2.72393e15i | −1.60846 | − | 0.928646i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.27006e15 | + | 1.73435e15i | −0.760925 | + | 0.581357i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.02620e15 | − | 5.92478e14i | −0.338229 | − | 0.195276i | 0.321260 | − | 0.946991i | \(-0.395894\pi\) |
−0.659488 | + | 0.751715i | \(0.729227\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.59902e15 | + | 2.76959e15i | 0.518236 | + | 0.897611i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.96779e15 | − | 3.15390e15i | 0.945854 | − | 1.00517i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 3.09117e15i | − | 0.968843i | −0.874835 | − | 0.484422i | \(-0.839030\pi\) | ||
0.874835 | − | 0.484422i | \(-0.160970\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.36474e15 | − | 7.87932e14i | 0.420670 | − | 0.242874i | −0.274694 | − | 0.961532i | \(-0.588577\pi\) |
0.695364 | + | 0.718658i | \(0.255243\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.14867e15 | − | 9.09468e14i | 0.348235 | − | 0.275717i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.54723e15 | − | 2.52157e15i | 1.35590 | − | 0.751887i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.16187e15 | − | 5.47652e15i | 0.927368 | − | 1.60625i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.26671e14 | + | 6.29774e15i | 0.267351 | + | 1.81694i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.92007e15 | 0.828741 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.57612e15 | −0.719256 | −0.359628 | − | 0.933096i | \(-0.617096\pi\) | ||||
−0.359628 | + | 0.933096i | \(0.617096\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.62547e14 | + | 5.31724e14i | 0.209457 | + | 0.146055i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.50799e14 | − | 6.07601e14i | 0.0948026 | − | 0.164203i | −0.814724 | − | 0.579849i | \(-0.803111\pi\) |
0.909526 | + | 0.415647i | \(0.136445\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.06006e13 | + | 1.19171e15i | −0.00547767 | + | 0.316874i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.15787e14 | + | 5.25145e14i | 0.108783 | + | 0.137395i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.03080e15 | + | 5.95135e14i | −0.265377 | + | 0.153215i | −0.626785 | − | 0.779193i | \(-0.715629\pi\) |
0.361408 | + | 0.932408i | \(0.382296\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 5.08069e15i | − | 1.28714i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.28868e15 | + | 2.09707e15i | 1.31852 | + | 0.522819i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.95618e15 | + | 5.12025e15i | 0.725312 | + | 1.25628i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.26662e15 | − | 2.46334e15i | −1.03028 | − | 0.594832i | −0.113215 | − | 0.993571i | \(-0.536115\pi\) |
−0.917065 | + | 0.398738i | \(0.869448\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.12960e15 | + | 4.23929e15i | −0.981465 | + | 1.00753i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.45791e15 | − | 8.41724e14i | −0.341047 | − | 0.196903i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.48768e14 | + | 1.12370e15i | 0.149386 | + | 0.258744i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.24008e14 | + | 2.07780e14i | 0.118772 | + | 0.0470955i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1.31638e15i | − | 0.293719i | −0.989157 | − | 0.146860i | \(-0.953083\pi\) | ||
0.989157 | − | 0.146860i | \(-0.0469166\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.00539e15 | − | 4.62191e15i | 1.75844 | − | 1.01524i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.08448e15 | − | 1.36972e15i | −0.234521 | − | 0.296204i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.12720e14 | − | 7.44271e14i | −0.0878716 | − | 0.158462i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.86327e15 | − | 4.95932e15i | 0.600216 | − | 1.03960i | −0.392572 | − | 0.919721i | \(-0.628415\pi\) |
0.992788 | − | 0.119883i | \(-0.0382520\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.55379e15 | − | 6.59419e15i | 0.320707 | − | 1.36106i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.79173e15 | −1.78683 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.03532e15 | 1.80826 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.19802e15 | − | 8.14182e15i | −0.236106 | − | 1.60460i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.94175e14 | − | 6.82732e14i | 0.0765034 | − | 0.132508i | −0.825236 | − | 0.564789i | \(-0.808958\pi\) |
0.901739 | + | 0.432281i | \(0.142291\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.68193e15 | − | 1.61085e15i | −0.512628 | − | 0.307901i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.12691e15 | + | 4.05926e15i | −0.965150 | + | 0.764164i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.18552e15 | + | 6.84460e14i | −0.219811 | + | 0.126908i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.07902e16i | 1.97056i | 0.170952 | + | 0.985279i | \(0.445316\pi\) | ||||
−0.170952 | + | 0.985279i | \(0.554684\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.55663e15 | − | 4.27241e15i | 0.639791 | − | 0.768549i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.15932e14 | + | 8.93621e14i | 0.0914212 | + | 0.158346i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.87209e15 | − | 3.39025e15i | −1.02499 | − | 0.591779i | −0.109446 | − | 0.993993i | \(-0.534908\pi\) |
−0.915546 | + | 0.402213i | \(0.868241\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.60961e15 | + | 5.97031e15i | −0.448741 | + | 1.02664i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.15098e14 | + | 2.97392e14i | 0.0872607 | + | 0.0503800i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.13087e15 | + | 7.15488e15i | 0.689441 | + | 1.19415i | 0.972019 | + | 0.234903i | \(0.0754771\pi\) |
−0.282578 | + | 0.959244i | \(0.591190\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.55913e15 | + | 8.97589e15i | −0.585253 | + | 1.47597i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.13253e16i | − | 1.83489i | −0.397861 | − | 0.917446i | \(-0.630247\pi\) | ||
0.397861 | − | 0.917446i | \(-0.369753\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.34997e14 | − | 4.82086e14i | 0.133299 | − | 0.0769600i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.92549e15 | − | 1.18079e15i | 0.617492 | − | 0.185741i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.86897e15 | + | 5.92761e15i | 1.52975 | + | 0.918818i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.24618e15 | − | 9.08665e15i | 0.801353 | − | 1.38798i | −0.117373 | − | 0.993088i | \(-0.537447\pi\) |
0.918726 | − | 0.394896i | \(-0.129219\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.12614e14 | − | 4.59991e13i | 0.0470583 | − | 0.00692432i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.91932e14 | −0.117484 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.94582e15 | −0.284495 | −0.142248 | − | 0.989831i | \(-0.545433\pi\) | ||||
−0.142248 | + | 0.989831i | \(0.545433\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.80193e16 | + | 2.65142e15i | −2.59661 | + | 0.382075i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.28327e15 | + | 2.22269e15i | −0.182265 | + | 0.315692i | −0.942652 | − | 0.333779i | \(-0.891676\pi\) |
0.760386 | + | 0.649471i | \(0.225010\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.06413e15 | − | 5.52565e15i | −0.428966 | − | 0.773568i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.00982e15 | − | 9.05353e14i | 0.415339 | − | 0.124934i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.64603e15 | − | 5.56914e15i | 1.31212 | − | 0.757554i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 9.14883e14i | − | 0.122679i | −0.998117 | − | 0.0613396i | \(-0.980463\pi\) | ||
0.998117 | − | 0.0613396i | \(-0.0195373\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.71034e15 | + | 6.83531e15i | −0.358282 | + | 0.903564i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.12136e15 | − | 1.94225e15i | −0.146136 | − | 0.253115i | 0.783660 | − | 0.621190i | \(-0.213350\pi\) |
−0.929796 | + | 0.368075i | \(0.880017\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.64820e15 | + | 9.51587e14i | 0.211763 | + | 0.122261i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.45523e15 | + | 1.06926e16i | −0.564358 | + | 1.35447i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.40566e15 | − | 4.27566e15i | −0.924927 | − | 0.534007i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.72676e15 | − | 1.51152e16i | −1.07466 | − | 1.86137i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.47402e15 | + | 7.41224e15i | 0.421836 | + | 0.900036i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.69347e16i | 2.02766i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.84798e15 | − | 1.64428e15i | 0.336260 | − | 0.194140i | −0.322357 | − | 0.946618i | \(-0.604475\pi\) |
0.658617 | + | 0.752478i | \(0.271142\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.27314e16 | + | 1.00802e16i | −1.48236 | + | 1.17367i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.08571e14 | + | 1.20655e16i | −0.0239488 | + | 1.38540i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.98507e15 | + | 5.17029e15i | −0.338028 | + | 0.585481i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.84640e15 | + | 1.25483e16i | 0.206209 | + | 1.40141i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.63390e15 | 1.06116 | 0.530580 | − | 0.847635i | \(-0.321974\pi\) | ||||
0.530580 | + | 0.847635i | \(0.321974\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.20149e15 | −0.130531 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.20733e14 | − | 1.78557e15i | 0.0450845 | − | 0.191336i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.18354e15 | − | 1.59064e16i | 0.970677 | − | 1.68126i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.75364e16 | + | 9.72444e15i | −1.82836 | + | 1.01388i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.55366e15 | + | 1.08034e16i | 0.879727 | + | 1.11111i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.02037e14 | − | 1.16646e14i | 0.0204981 | − | 0.0118346i | −0.489716 | − | 0.871882i | \(-0.662900\pi\) |
0.510214 | + | 0.860047i | \(0.329566\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.17182e15i | − | 0.217375i | −0.994076 | − | 0.108688i | \(-0.965335\pi\) | ||
0.994076 | − | 0.108688i | \(-0.0346648\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.14170e15 | + | 1.24575e15i | 0.310218 | + | 0.123008i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.20192e15 | − | 2.08179e15i | −0.117087 | − | 0.202801i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.88934e15 | − | 3.40021e15i | −0.566038 | − | 0.326802i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.28459e15 | − | 1.16456e16i | −0.311472 | − | 1.10433i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.15578e15 | − | 6.67291e14i | −0.108141 | − | 0.0624350i | 0.444954 | − | 0.895553i | \(-0.353220\pi\) |
−0.553095 | + | 0.833118i | \(0.686553\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.66232e15 | + | 8.07538e15i | 0.430431 | + | 0.745528i | 0.996910 | − | 0.0785478i | \(-0.0250283\pi\) |
−0.566480 | + | 0.824076i | \(0.691695\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.66507e15 | + | 1.45328e15i | 0.333877 | + | 0.132389i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.85920e16i | 1.67127i | 0.549286 | + | 0.835634i | \(0.314900\pi\) | ||||
−0.549286 | + | 0.835634i | \(0.685100\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.07899e14 | − | 1.20030e14i | 0.0184417 | − | 0.0106473i | −0.490751 | − | 0.871300i | \(-0.663277\pi\) |
0.509193 | + | 0.860653i | \(0.329944\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.58119e15 | − | 7.04912e15i | −0.488563 | − | 0.617063i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.10504e15 | + | 3.95579e15i | 0.181850 | + | 0.341732i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.66824e15 | − | 9.81767e15i | 0.483250 | − | 0.837014i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.50951e15 | − | 9.33529e15i | 0.547719 | − | 0.785485i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.34331e16 | 1.11554 | 0.557770 | − | 0.829996i | \(-0.311657\pi\) | ||||
0.557770 | + | 0.829996i | \(0.311657\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.46290e14 | 0.0119905 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.27543e15 | − | 8.66796e15i | −0.103183 | − | 0.701238i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.22086e15 | + | 3.84664e15i | −0.177341 | + | 0.307163i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.39136e15 | + | 1.06411e16i | −0.503772 | + | 0.838738i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.01526e15 | + | 2.38735e15i | −0.234602 | + | 0.185748i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.08728e16 | + | 1.78244e16i | −2.37117 | + | 1.36900i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.09188e16i | 1.58605i | 0.609190 | + | 0.793025i | \(0.291495\pi\) | ||||
−0.609190 | + | 0.793025i | \(0.708505\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.41952e16 | + | 1.50853e16i | −1.06249 | + | 1.12912i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.09388e15 | − | 1.05549e16i | −0.450297 | − | 0.779938i | 0.548107 | − | 0.836408i | \(-0.315349\pi\) |
−0.998404 | + | 0.0564703i | \(0.982015\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.03889e15 | − | 4.06391e15i | −0.513502 | − | 0.296470i | 0.220770 | − | 0.975326i | \(-0.429143\pi\) |
−0.734272 | + | 0.678856i | \(0.762476\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.06271e16 | − | 1.37650e15i | 0.765415 | − | 0.0991423i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.06283e15 | − | 3.50038e15i | −0.431138 | − | 0.248917i | 0.268694 | − | 0.963226i | \(-0.413408\pi\) |
−0.699831 | + | 0.714308i | \(0.746741\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.48317e15 | − | 2.56892e15i | −0.104136 | − | 0.180369i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.52019e15 | + | 1.13996e16i | −0.313366 | + | 0.790289i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 2.87328e16i | − | 1.96684i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.05313e15 | + | 6.08025e14i | −0.0711839 | + | 0.0410981i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.36773e15 | − | 4.54696e15i | −0.0912894 | − | 0.303489i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.26565e16 | − | 2.18787e14i | −0.834198 | − | 0.0144204i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.35218e15 | + | 9.27025e15i | −0.348364 | + | 0.603384i | −0.985959 | − | 0.166988i | \(-0.946596\pi\) |
0.637595 | + | 0.770372i | \(0.279929\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.66226e15 | − | 2.44591e14i | 0.106846 | − | 0.0157218i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.55605e16 | −0.987772 | −0.493886 | − | 0.869527i | \(-0.664424\pi\) | ||||
−0.493886 | + | 0.869527i | \(0.664424\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.61350e16 | 1.01155 | 0.505773 | − | 0.862667i | \(-0.331208\pi\) | ||||
0.505773 | + | 0.862667i | \(0.331208\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.36397e16 | − | 3.47843e15i | 1.46371 | − | 0.215375i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.60498e15 | + | 9.70811e15i | −0.342763 | + | 0.593683i | −0.984945 | − | 0.172869i | \(-0.944696\pi\) |
0.642182 | + | 0.766552i | \(0.278029\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.87701e16 | + | 4.97336e14i | 1.73773 | + | 0.0300393i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.05263e16 | − | 2.10965e16i | 0.627986 | − | 1.25858i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.85750e15 | − | 3.95918e15i | 0.404094 | − | 0.233304i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 3.03079e16i | − | 1.76413i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.37258e16 | − | 3.46155e16i | 0.789184 | − | 1.99027i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.37933e15 | + | 1.45134e16i | 0.475917 | + | 0.824312i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.55406e15 | + | 4.36134e15i | 0.423833 | + | 0.244700i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.45119e15 | − | 1.09466e15i | 0.468420 | − | 0.0606732i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.75068e15 | + | 1.01076e15i | 0.0958605 | + | 0.0553451i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.28904e15 | − | 7.42884e15i | −0.232017 | − | 0.401866i | 0.726384 | − | 0.687289i | \(-0.241199\pi\) |
−0.958402 | + | 0.285423i | \(0.907866\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.46909e15 | + | 2.32340e15i | 0.131958 | + | 0.124172i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 2.86298e16i | − | 1.51171i | −0.654741 | − | 0.755854i | \(-0.727222\pi\) | ||
0.654741 | − | 0.755854i | \(-0.272778\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.50563e16 | − | 8.69274e15i | 0.785467 | − | 0.453489i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.00411e16 | + | 7.95013e15i | −0.517567 | + | 0.409787i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.35241e15 | − | 1.55710e16i | 0.476313 | − | 0.793020i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.45902e15 | − | 4.25915e15i | 0.123745 | − | 0.214332i | −0.797497 | − | 0.603323i | \(-0.793843\pi\) |
0.921242 | + | 0.388991i | \(0.127176\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.08198e15 | + | 7.35325e15i | 0.0538012 | + | 0.365638i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.56841e16 | 1.75334 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.71700e15 | 0.374687 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.21310e16 | + | 2.85843e15i | 0.582049 | + | 0.137148i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.72223e15 | + | 4.71505e15i | −0.129074 | + | 0.223563i | −0.923318 | − | 0.384036i | \(-0.874534\pi\) |
0.794244 | + | 0.607599i | \(0.207867\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.50497e16 | − | 1.56410e16i | −1.17376 | − | 0.732896i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.62460e15 | − | 4.57793e15i | −0.167846 | − | 0.211992i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.15442e16 | − | 6.66504e15i | 0.528323 | − | 0.305027i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.60283e16i | − | 1.17728i | −0.808397 | − | 0.588638i | \(-0.799664\pi\) | ||
0.808397 | − | 0.588638i | \(-0.200336\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.77431e16 | − | 7.03552e15i | −0.793176 | − | 0.314511i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.09386e15 | + | 8.82283e15i | 0.225063 | + | 0.389821i | 0.956338 | − | 0.292262i | \(-0.0944078\pi\) |
−0.731275 | + | 0.682082i | \(0.761075\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.85599e16 | + | 1.64891e16i | 1.24722 | + | 0.720081i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.65849e15 | − | 2.58207e16i | 0.114752 | − | 1.11453i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.34755e16 | − | 7.78009e15i | −0.574937 | − | 0.331940i | 0.184182 | − | 0.982892i | \(-0.441037\pi\) |
−0.759119 | + | 0.650952i | \(0.774370\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.87759e16 | + | 3.25209e16i | 0.791841 | + | 1.37151i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.31374e16 | − | 9.17445e15i | −0.964541 | − | 0.382461i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.14850e16i | 0.473281i | 0.971597 | + | 0.236641i | \(0.0760464\pi\) | ||||
−0.971597 | + | 0.236641i | \(0.923954\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.43385e16 | + | 1.40518e16i | −0.991459 | + | 0.572419i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.15510e16 | + | 2.72192e16i | 0.867864 | + | 1.09613i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.52362e16 | + | 1.39942e16i | −1.00466 | + | 0.557116i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.05467e15 | + | 1.82675e15i | −0.0415087 | + | 0.0718951i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.46399e16 | − | 1.05185e16i | −1.73692 | − | 0.409269i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.61791e14 | 0.00622377 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.18286e16 | −0.830194 | −0.415097 | − | 0.909777i | \(-0.636252\pi\) | ||||
−0.415097 | + | 0.909777i | \(0.636252\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.07380e15 | + | 1.40937e16i | 0.0779804 | + | 0.529962i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.93013e15 | − | 1.20033e16i | 0.257653 | − | 0.446268i | −0.707960 | − | 0.706253i | \(-0.750384\pi\) |
0.965613 | + | 0.259985i | \(0.0837175\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.65259e14 | + | 9.55997e15i | −0.00607497 | + | 0.351428i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.31985e15 | + | 5.00378e15i | −0.229711 | + | 0.181875i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.38113e16 | − | 1.37474e16i | 0.855781 | − | 0.494085i | −0.00681620 | − | 0.999977i | \(-0.502170\pi\) |
0.862597 | + | 0.505891i | \(0.168836\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 7.78024e15i | − | 0.276496i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.83311e16 | + | 1.72495e16i | 0.644184 | + | 0.606173i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.23017e15 | − | 3.86277e15i | −0.0774987 | − | 0.134232i | 0.824671 | − | 0.565612i | \(-0.191360\pi\) |
−0.902170 | + | 0.431380i | \(0.858027\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.28138e16 | − | 7.39802e15i | −0.440329 | − | 0.254224i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.81640e15 | + | 9.15942e15i | −0.129691 | + | 0.311260i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.27122e16 | + | 1.31129e16i | 0.763273 | + | 0.440676i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.26211e15 | + | 7.38220e15i | 0.141651 | + | 0.245347i | 0.928119 | − | 0.372285i | \(-0.121426\pi\) |
−0.786467 | + | 0.617632i | \(0.788092\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.98286e15 | − | 2.51761e16i | 0.328121 | − | 0.827500i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.83142e16i | 0.920403i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.07346e15 | − | 6.19763e14i | 0.0345114 | − | 0.0199252i | −0.482645 | − | 0.875816i | \(-0.660324\pi\) |
0.517156 | + | 0.855891i | \(0.326991\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.93216e15 | − | 4.59789e16i | 0.125032 | − | 1.46200i |
(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 | 84.12.k.b.5.2 | ✓ | 56 | |
3.2 | odd | 2 | inner | 84.12.k.b.5.9 | yes | 56 | |
7.3 | odd | 6 | inner | 84.12.k.b.17.9 | yes | 56 | |
21.17 | even | 6 | inner | 84.12.k.b.17.2 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.12.k.b.5.2 | ✓ | 56 | 1.1 | even | 1 | trivial | |
84.12.k.b.5.9 | yes | 56 | 3.2 | odd | 2 | inner | |
84.12.k.b.17.2 | yes | 56 | 21.17 | even | 6 | inner | |
84.12.k.b.17.9 | yes | 56 | 7.3 | odd | 6 | inner |