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 | 5.20 | ||
Character | \(\chi\) | \(=\) | 84.5 |
Dual form | 84.12.k.b.17.20 |
$q$-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 | ||||||||
\(3\) | 204.376 | − | 367.937i | 0.485583 | − | 0.874190i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1631.25 | − | 2825.41i | 0.233445 | − | 0.404339i | −0.725374 | − | 0.688355i | \(-0.758333\pi\) |
0.958820 | + | 0.284015i | \(0.0916667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 25977.5 | − | 36090.1i | 0.584195 | − | 0.811613i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −93607.5 | − | 150395.i | −0.528417 | − | 0.848985i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −759895. | + | 438726.i | −1.42264 | + | 0.821359i | −0.996524 | − | 0.0833111i | \(-0.973450\pi\) |
−0.426112 | + | 0.904670i | \(0.640117\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.65981e6i | 1.98684i | 0.114545 | + | 0.993418i | \(0.463459\pi\) | ||||
−0.114545 | + | 0.993418i | \(0.536541\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −706181. | − | 1.17764e6i | −0.240112 | − | 0.400416i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.28810e6 | + | 9.15925e6i | 0.903296 | + | 1.56455i | 0.823188 | + | 0.567769i | \(0.192193\pi\) |
0.0801082 | + | 0.996786i | \(0.474473\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −45948.9 | − | 26528.6i | −0.00425726 | − | 0.00245793i | 0.497870 | − | 0.867252i | \(-0.334116\pi\) |
−0.502127 | + | 0.864794i | \(0.667449\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.96969e6 | − | 1.69340e7i | −0.425829 | − | 0.904804i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.42309e6 | − | 1.39897e6i | −0.0784994 | − | 0.0453216i | 0.460237 | − | 0.887796i | \(-0.347765\pi\) |
−0.538736 | + | 0.842475i | \(0.681098\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.90921e7 | + | 3.30685e7i | 0.391007 | + | 0.677243i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7.44670e7 | + | 3.70442e6i | −0.998765 | + | 0.0496843i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.08750e7i | 0.822726i | 0.911472 | + | 0.411363i | \(0.134947\pi\) | ||||
−0.911472 | + | 0.411363i | \(0.865053\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.33162e7 | + | 3.65556e7i | −0.397215 | + | 0.229332i | −0.685282 | − | 0.728278i | \(-0.740321\pi\) |
0.288067 | + | 0.957610i | \(0.406988\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.11853e6 | + | 3.69258e8i | 0.0272158 | + | 1.64249i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.95935e7 | − | 1.32269e8i | −0.191789 | − | 0.425680i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.19975e8 | − | 3.81008e8i | 0.521511 | − | 0.903284i | −0.478176 | − | 0.878264i | \(-0.658702\pi\) |
0.999687 | − | 0.0250199i | \(-0.00796490\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.78641e8 | + | 5.43602e8i | 1.73687 | + | 0.964775i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.27550e8 | −1.11554 | −0.557768 | − | 0.829997i | \(-0.688342\pi\) | ||||
−0.557768 | + | 0.829997i | \(0.688342\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.38417e8 | −0.454790 | −0.227395 | − | 0.973803i | \(-0.573021\pi\) | ||||
−0.227395 | + | 0.973803i | \(0.573021\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.77624e8 | + | 1.91475e7i | −0.466634 | + | 0.0154683i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.36570e8 | + | 1.44898e9i | −0.532064 | + | 0.921562i | 0.467235 | + | 0.884133i | \(0.345250\pi\) |
−0.999299 | + | 0.0374289i | \(0.988083\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.27667e8 | − | 1.87506e9i | −0.317432 | − | 0.948281i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.45078e9 | − | 7.37485e7i | 1.80634 | − | 0.0299307i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.20646e9 | − | 1.85125e9i | 1.05319 | − | 0.608062i | 0.129652 | − | 0.991560i | \(-0.458614\pi\) |
0.923542 | + | 0.383497i | \(0.125281\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.86268e9i | 0.766970i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.91517e7 | + | 1.14845e7i | −0.00421596 | + | 0.00252813i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.94646e9 | − | 6.83546e9i | −0.718656 | − | 1.24475i | −0.961532 | − | 0.274692i | \(-0.911424\pi\) |
0.242876 | − | 0.970057i | \(-0.421909\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.69398e9 | + | 3.86477e9i | 1.01478 | + | 0.585882i | 0.912587 | − | 0.408883i | \(-0.134082\pi\) |
0.102190 | + | 0.994765i | \(0.467415\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.85947e9 | − | 5.28578e8i | −0.997746 | − | 0.0671021i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.51504e9 | + | 4.33881e9i | 0.803356 | + | 0.463818i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.55459e9 | + | 7.88877e9i | 0.412133 | + | 0.713835i | 0.995123 | − | 0.0986441i | \(-0.0314506\pi\) |
−0.582990 | + | 0.812480i | \(0.698117\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00995e9 | + | 6.05626e8i | −0.0777377 | + | 0.0466160i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.04217e9i | 0.397440i | 0.980056 | + | 0.198720i | \(0.0636784\pi\) | ||||
−0.980056 | + | 0.198720i | \(0.936322\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.57592e10 | − | 1.48721e10i | 1.45431 | − | 0.839646i | 0.455588 | − | 0.890191i | \(-0.349429\pi\) |
0.998722 | + | 0.0505448i | \(0.0160958\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.60691e10 | − | 2.66261e8i | 0.781906 | − | 0.0129560i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.90650e9 | + | 3.88217e10i | −0.164471 | + | 1.63446i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.45666e9 | + | 1.11833e10i | −0.236080 | + | 0.408902i | −0.959586 | − | 0.281416i | \(-0.909196\pi\) |
0.723506 | + | 0.690318i | \(0.242529\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.38563e10 | + | 2.81562e10i | −0.441550 | + | 0.897237i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.05047e10 | −1.12869 | −0.564346 | − | 0.825538i | \(-0.690872\pi\) | ||||
−0.564346 | + | 0.825538i | \(0.690872\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.45048e10 | 0.843481 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.34362e10 | + | 1.85727e10i | 0.719219 | + | 0.399502i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.20949e10 | + | 3.82694e10i | −0.419417 | + | 0.726452i | −0.995881 | − | 0.0906709i | \(-0.971099\pi\) |
0.576464 | + | 0.817123i | \(0.304432\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.59928e10 | + | 6.90951e10i | 1.61254 | + | 1.16070i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.09810e8 | + | 3.07675e10i | 0.00759893 | + | 0.458601i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.49908e8 | + | 8.65496e7i | −0.00198768 | + | 0.00114759i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.96326e8i | − | 0.00468606i | −0.999997 | − | 0.00234303i | \(-0.999254\pi\) | ||
0.999997 | − | 0.00234303i | \(-0.000745810\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.37114e11 | + | 7.32164e10i | 1.44907 | + | 0.773776i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.42870e10 | + | 1.11348e11i | 0.608633 | + | 1.05418i | 0.991466 | + | 0.130366i | \(0.0416153\pi\) |
−0.382832 | + | 0.923818i | \(0.625051\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.70529e10 | + | 9.84548e9i | 0.144941 | + | 0.0836820i | 0.570717 | − | 0.821147i | \(-0.306665\pi\) |
−0.425776 | + | 0.904829i | \(0.639999\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.08461e10 | − | 5.10602e9i | −0.465255 | − | 0.0390428i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.25780e11 | − | 7.26194e10i | −0.866967 | − | 0.500543i | −0.000627646 | − | 1.00000i | \(-0.500200\pi\) |
−0.866339 | + | 0.499456i | \(0.833533\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.79034e10 | + | 4.83301e10i | 0.173705 | + | 0.300865i | 0.939712 | − | 0.341966i | \(-0.111093\pi\) |
−0.766008 | + | 0.642831i | \(0.777760\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.52290e10 | − | 1.58806e11i | −0.536405 | − | 0.894520i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2.81459e10i | − | 0.143709i | −0.997415 | − | 0.0718545i | \(-0.977108\pi\) | ||
0.997415 | − | 0.0718545i | \(-0.0228917\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.90532e9 | + | 4.56414e9i | −0.0366506 | + | 0.0211602i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.00022e11 | − | 2.48978e11i | 1.68679 | − | 1.04988i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.67930e11 | + | 4.70862e10i | 1.79751 | + | 0.180878i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.42304e11 | − | 4.19683e11i | 0.849262 | − | 1.47096i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.69132e11 | + | 3.04486e11i | −0.541685 | + | 0.975190i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.83878e11 | 0.832005 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.16856e11 | −1.11961 | −0.559803 | − | 0.828626i | \(-0.689123\pi\) | ||||
−0.559803 | + | 0.828626i | \(0.689123\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.96021e10 | + | 1.61310e11i | −0.220838 | + | 0.397573i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.70325e11 | + | 6.41422e11i | −0.838670 | + | 1.45262i | 0.0523376 | + | 0.998629i | \(0.483333\pi\) |
−0.891007 | + | 0.453989i | \(0.850001\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.15106e9 | + | 9.69156e8i | −0.00448196 | + | 0.00201934i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.11008e11 | + | 2.16442e11i | −0.213068 | + | 0.415438i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.57867e11 | + | 2.06615e11i | −0.633517 | + | 0.365761i | −0.782113 | − | 0.623137i | \(-0.785858\pi\) |
0.148596 | + | 0.988898i | \(0.452525\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.15488e11i | 1.49648i | 0.663427 | + | 0.748241i | \(0.269101\pi\) | ||||
−0.663427 | + | 0.748241i | \(0.730899\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.62158e11 | + | 6.03942e11i | 0.547259 | + | 0.912620i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.16693e12 | − | 2.02118e12i | −1.63191 | − | 2.82654i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.56759e11 | + | 1.48240e11i | 0.332660 | + | 0.192062i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.18184e11 | − | 1.52277e11i | −0.983118 | − | 0.182973i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.77109e11 | + | 3.90929e11i | 0.755326 | + | 0.436088i | 0.827615 | − | 0.561296i | \(-0.189697\pi\) |
−0.0722892 | + | 0.997384i | \(0.523030\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.78532e11 | − | 4.82432e11i | −0.288737 | − | 0.500107i | 0.684772 | − | 0.728758i | \(-0.259902\pi\) |
−0.973508 | + | 0.228651i | \(0.926569\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.82501e11 | − | 1.65268e12i | 0.850966 | − | 1.59362i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.38525e11i | 0.214146i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.73937e11 | + | 3.31363e11i | −0.480193 | + | 0.277240i | −0.720497 | − | 0.693458i | \(-0.756086\pi\) |
0.240304 | + | 0.970698i | \(0.422753\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.58178e10 | − | 1.55813e12i | −0.0201482 | − | 1.21596i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.13435e11 | + | 5.11078e10i | −0.0826426 | + | 0.0372345i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.01748e10 | + | 5.22643e10i | −0.0205406 | + | 0.0355773i | −0.876113 | − | 0.482106i | \(-0.839872\pi\) |
0.855572 | + | 0.517683i | \(0.173205\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.05329e12 | + | 5.85065e11i | 0.670478 | + | 0.372428i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.58050e11 | −0.213306 | −0.106653 | − | 0.994296i | \(-0.534013\pi\) | ||||
−0.106653 | + | 0.994296i | \(0.534013\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.28242e12 | −2.94752 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.11391e8 | + | 9.39377e9i | 0.000162865 | + | 0.00491317i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.20251e12 | − | 2.08281e12i | 0.589979 | − | 1.02187i | −0.404256 | − | 0.914646i | \(-0.632469\pi\) |
0.994235 | − | 0.107227i | \(-0.0341972\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.68941e12 | + | 1.70000e11i | 0.778084 | + | 0.0782960i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.32158e12 | + | 5.50378e10i | −1.43712 | + | 0.0238127i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.32135e12 | − | 7.62882e11i | 0.537435 | − | 0.310288i | −0.206604 | − | 0.978425i | \(-0.566241\pi\) |
0.744039 | + | 0.668136i | \(0.232908\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.19711e12i | − | 0.840660i | −0.907371 | − | 0.420330i | \(-0.861914\pi\) | ||
0.907371 | − | 0.420330i | \(-0.138086\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.79008e12 | − | 1.67309e12i | 1.00493 | − | 0.602614i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.17668e11 | − | 1.24304e12i | −0.243489 | − | 0.421735i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.03679e12 | − | 4.64004e12i | −2.57012 | − | 1.48386i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.80077e12 | + | 2.78376e12i | −0.543149 | + | 0.839636i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.47282e12 | + | 2.58238e12i | 1.27320 | + | 0.735084i | 0.975590 | − | 0.219602i | \(-0.0704759\pi\) |
0.297614 | + | 0.954686i | \(0.403809\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.50501e11 | − | 4.33881e11i | −0.0673357 | − | 0.116629i | 0.830392 | − | 0.557180i | \(-0.188117\pi\) |
−0.897728 | + | 0.440551i | \(0.854783\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.13230e12 | − | 1.87831e12i | 0.795561 | − | 0.477064i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 5.68212e12i | − | 1.36441i | −0.731159 | − | 0.682207i | \(-0.761020\pi\) | ||
0.731159 | − | 0.682207i | \(-0.238980\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.60888e12 | + | 2.66094e12i | −1.04690 | + | 0.604426i | −0.921779 | − | 0.387716i | \(-0.873264\pi\) |
−0.125118 | + | 0.992142i | \(0.539931\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.83342e12 | − | 6.35189e10i | 0.824153 | − | 0.0136560i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.27969e12 | + | 2.36070e12i | 0.667735 | + | 0.480632i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.34994e12 | + | 2.33817e12i | −0.260416 | + | 0.451055i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.64210e10 | + | 4.95375e11i | 0.00300305 | + | 0.0905935i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.65551e10 | 0.00807538 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.35994e12 | 0.553067 | 0.276534 | − | 0.961004i | \(-0.410814\pi\) | ||||
0.276534 | + | 0.961004i | \(0.410814\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.22313e12 | + | 1.23488e12i | 0.347438 | + | 0.192990i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.15167e11 | + | 1.23871e12i | −0.106169 | + | 0.183889i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.25499e11 | + | 3.23471e12i | −0.0459220 | + | 0.456360i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.07408e11 | − | 1.25173e13i | −0.0278217 | − | 1.67906i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.43619e13 | + | 1.40653e13i | −3.10851 | + | 1.79470i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.63453e12i | 0.441338i | 0.975349 | + | 0.220669i | \(0.0708240\pi\) | ||||
−0.975349 | + | 0.220669i | \(0.929176\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.18618e12 | − | 5.96682e12i | 0.368354 | − | 0.689826i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.30101e12 | − | 9.18162e12i | −0.583736 | − | 1.01106i | −0.995032 | − | 0.0995583i | \(-0.968257\pi\) |
0.411296 | − | 0.911502i | \(-0.365076\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.22823e13 | + | 7.09120e12i | 1.28880 | + | 0.744088i | 0.978440 | − | 0.206531i | \(-0.0662175\pi\) |
0.310359 | + | 0.950620i | \(0.399551\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.34855e13 | + | 9.37158e12i | 1.34897 | + | 0.937448i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.32964e13 | + | 7.67668e12i | 1.26846 | + | 0.732345i | 0.974696 | − | 0.223533i | \(-0.0717590\pi\) |
0.293763 | + | 0.955878i | \(0.405092\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.72931e12 | + | 4.72730e12i | 0.248416 | + | 0.430269i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.79514e12 | + | 4.66123e12i | 0.242822 | + | 0.404935i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.82714e12i | 0.483356i | 0.970356 | + | 0.241678i | \(0.0776978\pi\) | ||||
−0.970356 | + | 0.241678i | \(0.922302\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.36416e13 | + | 7.87599e12i | −1.08087 | + | 0.624039i | −0.931130 | − | 0.364687i | \(-0.881176\pi\) |
−0.149736 | + | 0.988726i | \(0.547843\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.52780e12 | + | 1.08527e13i | 0.569946 | + | 0.821682i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.32169e12 | − | 1.28528e12i | −0.457530 | − | 0.0930214i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.05611e10 | − | 1.22215e11i | 0.00488351 | − | 0.00845849i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.27820e12 | + | 1.49031e13i | −0.548074 | + | 0.986692i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.58946e13 | 1.64061 | 0.820303 | − | 0.571930i | \(-0.193805\pi\) | ||||
0.820303 | + | 0.571930i | \(0.193805\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.45506e12 | 0.148901 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.05197e12 | − | 1.26956e13i | 0.409581 | − | 0.737363i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.04076e12 | + | 8.73086e12i | −0.280456 | + | 0.485763i | −0.971497 | − | 0.237052i | \(-0.923819\pi\) |
0.691041 | + | 0.722815i | \(0.257152\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.03622e12 | − | 1.78365e13i | −0.428453 | − | 0.950960i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.36671e13 | − | 8.50658e12i | 0.698482 | − | 0.434743i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.95406e13 | − | 1.12818e13i | 0.957593 | − | 0.552866i | 0.0621613 | − | 0.998066i | \(-0.480201\pi\) |
0.895431 | + | 0.445200i | \(0.146867\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.20794e13i | − | 0.567797i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.56505e12 | + | 1.59509e13i | 0.431395 | + | 0.719403i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.22091e12 | − | 3.84672e12i | −0.0961375 | − | 0.166515i | 0.813945 | − | 0.580942i | \(-0.197316\pi\) |
−0.910083 | + | 0.414426i | \(0.863982\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.91238e13 | − | 1.10411e13i | −0.794771 | − | 0.458861i | 0.0468683 | − | 0.998901i | \(-0.485076\pi\) |
−0.841640 | + | 0.540040i | \(0.818409\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.50413e13 | − | 2.11979e13i | 1.79770 | − | 0.846052i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.90160e13 | − | 1.67524e13i | −1.11252 | − | 0.642314i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.42979e13 | + | 2.47647e13i | 0.526786 | + | 0.912420i | 0.999513 | + | 0.0312111i | \(0.00993640\pi\) |
−0.472727 | + | 0.881209i | \(0.656730\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.14247e13 | + | 6.10057e12i | 0.404595 | + | 0.216046i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.38668e13i | 0.472163i | 0.971733 | + | 0.236082i | \(0.0758633\pi\) | ||||
−0.971733 | + | 0.236082i | \(0.924137\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.23338e12 | + | 4.17620e12i | −0.236873 | + | 0.136759i | −0.613739 | − | 0.789509i | \(-0.710335\pi\) |
0.376866 | + | 0.926268i | \(0.377002\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.20703e9 | + | 7.28454e10i | 3.80253e−5 | + | 0.00229486i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.14977e13 | + | 2.98664e13i | −0.651690 | + | 0.905383i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.87920e13 | + | 6.71896e13i | −1.13189 | + | 1.96049i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.45823e11 | − | 8.09997e10i | −0.00409651 | − | 0.00227547i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.14544e11 | −0.0220365 | −0.0110182 | − | 0.999939i | \(-0.503507\pi\) | ||||
−0.0110182 | + | 0.999939i | \(0.503507\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.57506e13 | −0.671068 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.49619e13 | − | 3.54856e13i | 1.38007 | − | 0.891028i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.72100e12 | − | 6.44495e12i | 0.0900467 | − | 0.155965i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.13890e13 | + | 1.58225e13i | −0.265686 | + | 0.369114i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.41079e13 | − | 8.96556e11i | 1.21710 | − | 0.0201671i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.18391e13 | − | 1.26088e13i | 0.473790 | − | 0.273543i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 5.50636e13i | − | 1.15240i | −0.817308 | − | 0.576201i | \(-0.804535\pi\) | ||
0.817308 | − | 0.576201i | \(-0.195465\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.10772e12 | − | 4.26219e12i | 0.143535 | − | 0.0860718i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.23497e12 | − | 1.25313e13i | −0.141011 | − | 0.244239i | 0.786866 | − | 0.617123i | \(-0.211702\pi\) |
−0.927878 | + | 0.372884i | \(0.878369\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.34098e13 | − | 1.35156e13i | −0.440457 | − | 0.254298i | 0.263335 | − | 0.964705i | \(-0.415178\pi\) |
−0.703791 | + | 0.710407i | \(0.748511\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.43142e13 | + | 2.13439e13i | −0.260051 | + | 0.387763i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.72992e13 | − | 3.30817e13i | −1.00536 | − | 0.580446i | −0.0955321 | − | 0.995426i | \(-0.530455\pi\) |
−0.909831 | + | 0.414980i | \(0.863789\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.98692e13 | − | 6.90554e13i | −0.675754 | − | 1.17044i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.24259e13 | + | 3.14375e13i | −0.858555 | + | 0.514838i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 5.61144e11i | − | 0.00888096i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.79559e13 | + | 5.07814e13i | −1.34557 | + | 0.776866i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.34852e13 | − | 3.89145e11i | 0.347361 | − | 0.00575571i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.05619e13 | + | 6.78328e13i | 0.437123 | + | 0.970202i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.38852e12 | + | 5.86909e12i | −0.0468766 | + | 0.0811927i | −0.888512 | − | 0.458854i | \(-0.848260\pi\) |
0.841635 | + | 0.540047i | \(0.181593\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.78930e13 | + | 2.58205e12i | −1.04245 | + | 0.0345558i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.97187e13 | 0.384842 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.68257e13 | −0.712165 | −0.356082 | − | 0.934455i | \(-0.615888\pi\) | ||||
−0.356082 | + | 0.934455i | \(0.615888\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.03559e13 | − | 5.75236e12i | −0.125629 | − | 0.0697827i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.20758e13 | − | 5.55569e13i | 0.376728 | − | 0.652512i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.39764e13 | − | 2.60568e13i | −0.955080 | − | 0.296349i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.36522e10 | + | 3.84146e12i | 0.000701145 | + | 0.0423147i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.78016e13 | − | 5.64658e13i | 1.04360 | − | 0.602522i | 0.122749 | − | 0.992438i | \(-0.460829\pi\) |
0.920851 | + | 0.389915i | \(0.127496\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.15743e14i | 1.19661i | 0.801268 | + | 0.598306i | \(0.204159\pi\) | ||||
−0.801268 | + | 0.598306i | \(0.795841\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.85305e12 | − | 1.98068e14i | −0.0987147 | − | 1.98438i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.59576e13 | + | 7.96010e13i | 0.446269 | + | 0.772961i | 0.998140 | − | 0.0609690i | \(-0.0194191\pi\) |
−0.551870 | + | 0.833930i | \(0.686086\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.70716e13 | + | 9.85628e12i | 0.160701 | + | 0.0927805i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.12959e14 | − | 1.62545e14i | 1.03097 | − | 1.48354i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.24544e10 | + | 4.76051e10i | 0.000729784 | + | 0.000421341i | 0.500365 | − | 0.865815i | \(-0.333199\pi\) |
−0.499635 | + | 0.866236i | \(0.666533\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.82437e13 | − | 1.00881e14i | −0.499988 | − | 0.866004i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.04896e14 | − | 1.74926e14i | −0.873515 | − | 1.45669i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 9.70403e13i | − | 0.784046i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.12170e13 | − | 6.47613e12i | 0.0879454 | − | 0.0507753i | −0.455382 | − | 0.890296i | \(-0.650497\pi\) |
0.543328 | + | 0.839521i | \(0.317164\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.74650e13 | + | 1.24460e14i | 0.589468 | + | 0.947072i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.64839e13 | − | 1.63812e14i | 0.121760 | − | 1.21001i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.87774e11 | − | 1.53767e12i | 0.00636655 | − | 0.0110272i | −0.862825 | − | 0.505503i | \(-0.831307\pi\) |
0.869191 | + | 0.494476i | \(0.164640\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.80179e13 | − | 1.04449e14i | 0.404008 | − | 0.727331i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.41710e14 | −1.63462 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.73701e14 | −1.79788 | −0.898942 | − | 0.438068i | \(-0.855663\pi\) | ||||
−0.898942 | + | 0.438068i | \(0.855663\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.51955e13 | + | 1.53376e14i | −0.543662 | + | 0.978749i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.61001e13 | + | 4.52066e13i | −0.161826 | + | 0.280291i | −0.935524 | − | 0.353264i | \(-0.885072\pi\) |
0.773698 | + | 0.633555i | \(0.218405\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.03315e14 | + | 7.43653e13i | 0.622483 | + | 0.448060i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.10391e13 | + | 6.59358e13i | 0.240319 | + | 0.386110i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.17356e14 | − | 1.25490e14i | 1.23722 | − | 0.714312i | 0.268699 | − | 0.963224i | \(-0.413406\pi\) |
0.968526 | + | 0.248912i | \(0.0800731\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2.95916e13i | − | 0.163755i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.60317e14 | + | 2.67348e14i | 0.862621 | + | 1.43852i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.10648e13 | + | 3.64854e13i | 0.110223 | + | 0.190913i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.84470e13 | + | 5.68384e13i | 0.501020 | + | 0.289264i | 0.729134 | − | 0.684370i | \(-0.239923\pi\) |
−0.228115 | + | 0.973634i | \(0.573256\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.30380e10 | + | 9.89526e11i | −0.000411080 | + | 0.00489865i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.35237e14 | − | 7.80794e13i | −0.651333 | − | 0.376047i | 0.137634 | − | 0.990483i | \(-0.456050\pi\) |
−0.788967 | + | 0.614436i | \(0.789384\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.72310e13 | − | 1.68409e14i | −0.455646 | − | 0.789201i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.69497e13 | + | 8.50795e13i | 0.259710 | + | 0.387992i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.86034e14i | 1.71339i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.13142e14 | − | 1.23057e14i | 0.920853 | − | 0.531655i | 0.0369461 | − | 0.999317i | \(-0.488237\pi\) |
0.883907 | + | 0.467662i | \(0.154904\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.88148e12 | + | 1.73899e14i | 0.0121195 | + | 0.731422i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.49212e14 | − | 3.51400e13i | −1.43009 | − | 0.143905i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.60732e13 | + | 1.14442e14i | −0.263488 | + | 0.456375i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.36842e14 | + | 1.87104e14i | 1.30821 | + | 0.726667i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.70620e14 | 0.645436 | 0.322718 | − | 0.946495i | \(-0.395404\pi\) | ||||
0.322718 | + | 0.946495i | \(0.395404\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.48151e14 | 0.914459 | 0.457230 | − | 0.889349i | \(-0.348842\pi\) | ||||
0.457230 | + | 0.889349i | \(0.348842\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.96229e14 | − | 9.81960e12i | 1.06354 | − | 0.0352551i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.01922e14 | + | 3.49739e14i | −0.706389 | + | 1.22350i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.13373e14 | − | 1.41190e14i | 1.06834 | − | 0.481337i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.82156e14 | + | 1.62741e13i | −3.26336 | + | 0.0540732i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.28149e14 | + | 7.39868e13i | −0.415040 | + | 0.239624i | −0.692953 | − | 0.720983i | \(-0.743691\pi\) |
0.277913 | + | 0.960606i | \(0.410357\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.44844e14i | 1.08878i | 0.838833 | + | 0.544388i | \(0.183238\pi\) | ||||
−0.838833 | + | 0.544388i | \(0.816762\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.07018e14 | − | 6.41742e13i | 0.329433 | − | 0.197547i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.42255e10 | + | 1.28562e11i | 0.000222795 | + | 0.000385892i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.65935e14 | + | 1.53538e14i | 0.778433 | + | 0.449428i | 0.835875 | − | 0.548920i | \(-0.184961\pi\) |
−0.0574417 | + | 0.998349i | \(0.518294\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.23246e14 | + | 2.69918e14i | −0.637339 | + | 0.770583i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.35932e14 | + | 1.93951e14i | 0.935473 | + | 0.540095i | 0.888538 | − | 0.458803i | \(-0.151721\pi\) |
0.0469344 | + | 0.998898i | \(0.485055\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.20844e13 | + | 1.24854e14i | 0.195822 | + | 0.339174i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.82222e14 | − | 1.69237e14i | 0.747997 | − | 0.448542i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.54077e13i | 0.220873i | 0.993883 | + | 0.110436i | \(0.0352248\pi\) | ||||
−0.993883 | + | 0.110436i | \(0.964775\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.28851e14 | − | 3.63067e14i | 1.58700 | − | 0.916255i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.34430e14 | + | 3.88445e12i | −0.577394 | + | 0.00956730i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.51810e14 | − | 1.58507e14i | 0.845757 | − | 0.381054i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.59878e13 | + | 2.76916e13i | −0.0375188 | + | 0.0649844i | −0.884175 | − | 0.467156i | \(-0.845279\pi\) |
0.846656 | + | 0.532140i | \(0.178612\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.27718e14 | − | 6.62473e14i | −0.979915 | − | 1.51774i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.97115e13 | −0.0440924 | −0.0220462 | − | 0.999757i | \(-0.507018\pi\) | ||||
−0.0220462 | + | 0.999757i | \(0.507018\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.41121e14 | 0.308246 | 0.154123 | − | 0.988052i | \(-0.450745\pi\) | ||||
0.154123 | + | 0.988052i | \(0.450745\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.77622e13 | + | 4.87490e13i | 0.187205 | + | 0.103986i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.74550e13 | + | 1.51476e14i | −0.182197 | + | 0.315575i | −0.942628 | − | 0.333844i | \(-0.891654\pi\) |
0.760431 | + | 0.649418i | \(0.224988\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.03023e14 | + | 4.05549e13i | 0.820124 | + | 0.0825264i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.62123e12 | + | 2.78895e14i | 0.00918634 | + | 0.554403i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.33151e14 | − | 1.92345e14i | 0.647000 | − | 0.373546i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 2.02595e12i | − | 0.00384427i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.78568e14 | − | 3.08945e14i | −1.07276 | − | 0.572835i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.69560e14 | − | 4.66892e14i | −0.488439 | − | 0.846001i | 0.511473 | − | 0.859300i | \(-0.329100\pi\) |
−0.999912 | + | 0.0132984i | \(0.995767\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.01341e15 | + | 5.85091e14i | 1.79468 | + | 1.03616i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.37896e12 | + | 5.21820e13i | −0.00757987 | + | 0.0903258i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.11978e12 | − | 6.46506e11i | −0.00189476 | − | 0.00109394i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.61066e14 | − | 2.78974e14i | −0.266437 | − | 0.461482i | 0.701502 | − | 0.712667i | \(-0.252513\pi\) |
−0.967939 | + | 0.251185i | \(0.919180\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.30629e13 | + | 2.17840e13i | 0.0211272 | + | 0.0352321i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 3.22865e14i | − | 0.510590i | −0.966863 | − | 0.255295i | \(-0.917827\pi\) | ||
0.966863 | − | 0.255295i | \(-0.0821726\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.32346e14 | + | 4.80555e14i | −1.28720 | + | 0.743165i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.30533e14 | − | 2.67969e14i | 0.651146 | − | 0.405280i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.18062e14 | + | 1.56960e14i | 0.322568 | + | 0.232183i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.45306e13 | − | 4.24882e13i | 0.0354940 | − | 0.0614774i | −0.847733 | − | 0.530424i | \(-0.822033\pi\) |
0.883227 | + | 0.468946i | \(0.155366\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.31771e13 | + | 1.31740e14i | −0.103578 | + | 0.186470i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.47454e14 | −0.204189 | −0.102095 | − | 0.994775i | \(-0.532554\pi\) | ||||
−0.102095 | + | 0.994775i | \(0.532554\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.19473e14 | 0.568331 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.07960e15 | + | 1.94360e15i | −1.43127 | + | 2.57669i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.25926e14 | + | 1.25734e15i | −0.941769 | + | 1.63119i | −0.179675 | + | 0.983726i | \(0.557505\pi\) |
−0.762094 | + | 0.647466i | \(0.775829\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.32424e14 | − | 1.31599e15i | 0.168133 | − | 1.67085i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.51995e12 | + | 1.80529e12i | 0.00437413 | + | 0.00224338i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.56349e13 | − | 3.21209e13i | 0.0676718 | − | 0.0390704i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.46810e15i | − | 1.74806i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.20578e14 | − | 8.68127e14i | −0.606828 | − | 1.01196i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.76153e14 | + | 3.05106e14i | 0.201040 | + | 0.348212i | 0.948864 | − | 0.315686i | \(-0.102234\pi\) |
−0.747824 | + | 0.663897i | \(0.768901\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.80071e14 | + | 3.92639e14i | 0.759968 | + | 0.438768i | 0.829284 | − | 0.558827i | \(-0.188748\pi\) |
−0.0693165 | + | 0.997595i | \(0.522082\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.07825e14 | − | 5.86852e14i | 0.446270 | − | 0.642174i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.69644e14 | − | 3.86619e14i | −0.717606 | − | 0.414310i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.72491e14 | − | 8.18378e14i | −0.495892 | − | 0.858910i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.58602e14 | + | 1.23338e15i | −0.677023 | + | 1.26788i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 2.20113e15i | − | 2.21639i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.10359e14 | + | 2.36921e14i | −0.404779 | + | 0.233699i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.06393e13 | − | 6.42088e14i | −0.0102814 | − | 0.620492i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.29960e15 | + | 1.14948e15i | 1.23047 | + | 1.08833i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.72954e14 | + | 9.92386e14i | −0.531539 | + | 0.920652i | 0.467783 | + | 0.883843i | \(0.345053\pi\) |
−0.999322 | + | 0.0368093i | \(0.988281\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.08399e14 | − | 4.49038e14i | −0.734897 | − | 0.408211i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.82070e14 | 0.162202 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.25038e14 | −0.109172 | −0.0545860 | − | 0.998509i | \(-0.517384\pi\) | ||||
−0.0545860 | + | 0.998509i | \(0.517384\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.53644e13 | − | 1.36851e15i | −0.0388211 | − | 1.17112i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.41079e12 | − | 4.17561e12i | 0.00202220 | − | 0.00350256i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.35877e14 | + | 5.23534e14i | 0.193954 | + | 0.430484i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.04033e14 | + | 1.00087e13i | −0.486911 | + | 0.00806801i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.97890e14 | − | 4.02927e14i | 0.551548 | − | 0.318437i | −0.198198 | − | 0.980162i | \(-0.563509\pi\) |
0.749746 | + | 0.661725i | \(0.230176\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.16611e15i | − | 0.903593i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.34977e15 | + | 2.00871e15i | −2.54519 | + | 1.52624i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.08538e15 | − | 1.87993e15i | −0.808696 | − | 1.40070i | −0.913767 | − | 0.406238i | \(-0.866840\pi\) |
0.105071 | − | 0.994465i | \(-0.466493\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.95237e13 | − | 4.59130e13i | −0.0581072 | − | 0.0335482i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.56210e14 | + | 1.23150e15i | 0.470258 | + | 0.882529i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.83451e13 | + | 2.79121e13i | 0.0339809 | + | 0.0196189i | 0.516894 | − | 0.856049i | \(-0.327088\pi\) |
−0.482913 | + | 0.875668i | \(0.660421\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.45388e14 | + | 4.25025e14i | 0.169182 | + | 0.293032i | 0.938133 | − | 0.346276i | \(-0.112554\pi\) |
−0.768950 | + | 0.639309i | \(0.779221\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.86429e15 | − | 1.11794e15i | 1.26085 | − | 0.756077i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 1.06837e14i | − | 0.0708842i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.36955e14 | − | 4.25481e14i | 0.479705 | − | 0.276958i | −0.240589 | − | 0.970627i | \(-0.577340\pi\) |
0.720293 | + | 0.693670i | \(0.244007\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.10837e14 | + | 3.49353e12i | −0.134653 | + | 0.00223117i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.05221e15 | + | 1.46182e15i | −0.659376 | + | 0.916062i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.62438e15 | + | 2.81351e15i | −0.998875 | + | 1.73010i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.09287e13 | − | 1.53637e15i | −0.0307330 | − | 0.927126i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.10431e15 | 1.24624 | 0.623119 | − | 0.782127i | \(-0.285865\pi\) | ||||
0.623119 | + | 0.782127i | \(0.285865\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.87908e12 | 0.00225473 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.09066e15 | − | 1.16129e15i | −1.19276 | − | 0.662537i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.75597e14 | − | 1.17017e15i | 0.378344 | − | 0.655311i | −0.612478 | − | 0.790488i | \(-0.709827\pi\) |
0.990821 | + | 0.135177i | \(0.0431603\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.96348e14 | − | 1.24528e15i | 0.492758 | − | 0.684581i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.71099e13 | + | 2.23961e15i | 0.0200277 | + | 1.20869i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.17424e14 | + | 1.83265e14i | −0.168187 | + | 0.0971029i | −0.581731 | − | 0.813381i | \(-0.697624\pi\) |
0.413544 | + | 0.910484i | \(0.364291\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 2.62688e15i | − | 1.36657i | −0.730153 | − | 0.683284i | \(-0.760551\pi\) | ||
0.730153 | − | 0.683284i | \(-0.239449\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.60089e14 | − | 1.42344e15i | 0.388257 | − | 0.727098i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.90517e14 | − | 1.36922e15i | −0.396512 | − | 0.686780i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.72128e14 | + | 3.88053e14i | 0.331066 | + | 0.191141i | 0.656314 | − | 0.754488i | \(-0.272115\pi\) |
−0.325248 | + | 0.945629i | \(0.605448\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.53888e15 | − | 7.24245e14i | 0.744405 | − | 0.350341i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.85401e15 | − | 2.22512e15i | −1.83099 | − | 1.05712i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.82208e14 | − | 1.52803e15i | −0.411660 | − | 0.713015i | 0.583412 | − | 0.812177i | \(-0.301717\pi\) |
−0.995071 | + | 0.0991611i | \(0.968384\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.84401e14 | + | 9.74559e14i | 0.267854 | + | 0.446678i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.98087e15i | 0.891841i | 0.895073 | + | 0.445920i | \(0.147124\pi\) | ||||
−0.895073 | + | 0.445920i | \(0.852876\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.46694e14 | − | 3.73369e14i | 0.286022 | − | 0.165135i | −0.350124 | − | 0.936703i | \(-0.613861\pi\) |
0.636147 | + | 0.771568i | \(0.280527\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.85623e14 | + | 9.52011e13i | 0.0806542 | + | 0.0413655i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.07179e14 | + | 1.79155e15i | 0.344577 | + | 0.764794i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.69157e14 | + | 8.12604e14i | −0.196779 | + | 0.340831i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.51477e12 | − | 1.71293e13i | 0.00392127 | − | 0.00705942i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.65299e15 | 1.88432 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.48659e15 | −0.989561 | −0.494780 | − | 0.869018i | \(-0.664751\pi\) | ||||
−0.494780 | + | 0.869018i | \(0.664751\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.86693e14 | − | 1.23624e15i | 0.268560 | − | 0.483486i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.79995e14 | + | 1.17779e15i | −0.261367 | + | 0.452701i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.98730e15 | − | 1.66948e15i | 1.88408 | − | 0.630686i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.08712e14 | − | 5.65592e14i | 0.337421 | − | 0.210014i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.75339e14 | − | 4.47642e14i | 0.282991 | − | 0.163385i | −0.351786 | − | 0.936081i | \(-0.614425\pi\) |
0.634777 | + | 0.772696i | \(0.281092\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.33450e15i | 0.478806i | 0.970920 | + | 0.239403i | \(0.0769518\pi\) | ||||
−0.970920 | + | 0.239403i | \(0.923048\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.09602e14 | + | 5.16298e14i | 0.109201 | + | 0.182105i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.26317e14 | + | 9.11608e14i | 0.182505 | + | 0.316108i | 0.942733 | − | 0.333549i | \(-0.108246\pi\) |
−0.760228 | + | 0.649656i | \(0.774913\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.99778e15 | + | 3.46282e15i | 2.04477 | + | 1.18055i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.12365e15 | + | 7.80862e14i | 0.376646 | + | 0.261745i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.22024e15 | − | 7.04504e14i | −0.402181 | − | 0.232199i | 0.285244 | − | 0.958455i | \(-0.407925\pi\) |
−0.687425 | + | 0.726256i | \(0.741259\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.20818e15 | + | 2.09264e15i | 0.391567 | + | 0.678214i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.64795e15 | − | 2.48192e15i | −1.48133 | − | 0.791003i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.56604e15i | 1.11768i | 0.829276 | + | 0.558839i | \(0.188753\pi\) | ||||
−0.829276 | + | 0.558839i | \(0.811247\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.80721e15 | + | 2.77545e15i | −1.48179 | + | 0.855509i | −0.999787 | − | 0.0206627i | \(-0.993422\pi\) |
−0.481999 | + | 0.876172i | \(0.660089\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.96157e14 | + | 1.18382e16i | 0.0594675 | + | 3.58891i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.70654e11 | + | 7.65855e12i | −0.000229795 | + | 0.00228364i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.27131e14 | − | 2.20198e14i | 0.0372873 | − | 0.0645835i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.33727e15 | + | 7.42811e14i | 0.385813 | + | 0.214306i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.78230e15 | −1.92488 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.15970e15 | −0.323790 | −0.161895 | − | 0.986808i | \(-0.551761\pi\) | ||||
−0.161895 | + | 0.986808i | \(0.551761\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.54423e15 | − | 2.39179e15i | −0.424172 | − | 0.656980i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.90351e14 | − | 3.29697e14i | 0.0514419 | − | 0.0891000i | −0.839158 | − | 0.543888i | \(-0.816952\pi\) |
0.890600 | + | 0.454788i | \(0.150285\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.43034e13 | − | 1.02955e13i | −0.00380327 | − | 0.00273757i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.46165e15 | + | 7.39286e13i | −1.16731 | + | 0.0193421i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.96367e15 | + | 1.71108e15i | −0.762985 | + | 0.440509i | −0.830366 | − | 0.557218i | \(-0.811869\pi\) |
0.0673816 | + | 0.997727i | \(0.478536\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.34816e15i | 0.341541i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.11933e15 | − | 3.06984e15i | 1.27629 | − | 0.765338i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.92397e15 | + | 8.52857e15i | 1.20812 | + | 2.09252i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.71666e15 | + | 3.87787e15i | 1.62190 | + | 0.936405i | 0.986411 | + | 0.164296i | \(0.0525351\pi\) |
0.635490 | + | 0.772109i | \(0.280798\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.20427e15 | − | 3.04648e15i | 1.47454 | − | 0.724046i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.58663e15 | + | 1.49339e15i | 0.605086 | + | 0.349347i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.37617e15 | − | 7.57974e15i | −1.00766 | − | 1.74532i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.54200e15 | − | 3.32330e15i | 1.25615 | − | 0.753260i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 4.96728e15i | − | 1.10833i | −0.832407 | − | 0.554165i | \(-0.813038\pi\) | ||
0.832407 | − | 0.554165i | \(-0.186962\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.02152e13 | + | 1.16713e13i | −0.00444042 | + | 0.00256368i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.29715e15 | − | 3.80633e13i | 0.496763 | − | 0.00823126i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.68859e15 | + | 5.72424e14i | 1.21115 | + | 0.121874i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.86753e14 | + | 1.18949e15i | −0.143961 | + | 0.249348i | −0.928985 | − | 0.370117i | \(-0.879317\pi\) |
0.785024 | + | 0.619466i | \(0.212651\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.28630e15 | − | 7.57878e13i | 0.471900 | − | 0.0156429i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.04561e14 | 0.0415748 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.61419e15 | −1.52384 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.14402e15 | + | 1.19093e15i | 0.422545 | + | 0.234710i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.33514e14 | + | 1.61689e15i | −0.181181 | + | 0.313814i | −0.942283 | − | 0.334818i | \(-0.891325\pi\) |
0.761102 | + | 0.648632i | \(0.224659\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.98315e14 | − | 3.59679e14i | 0.152592 | − | 0.0687498i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.09840e14 | + | 6.62891e15i | 0.0206775 | + | 1.24791i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.00510e15 | + | 1.73500e15i | −0.557186 | + | 0.321691i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.47515e15i | 0.634649i | 0.948317 | + | 0.317325i | \(0.102784\pi\) | ||||
−0.948317 | + | 0.317325i | \(0.897216\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.53162e15 | − | 5.51714e14i | 0.995063 | − | 0.0992460i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.31839e15 | − | 4.01557e15i | −0.410810 | − | 0.711544i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.25145e15 | − | 3.60928e15i | −1.09121 | − | 0.630011i | −0.157313 | − | 0.987549i | \(-0.550283\pi\) |
−0.933899 | + | 0.357537i | \(0.883616\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.76490e15 | + | 2.06330e15i | −0.303488 | + | 0.354799i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.92201e15 | − | 3.99643e15i | −1.17263 | − | 0.677019i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.60280e15 | − | 7.97229e15i | −0.768206 | − | 1.33057i | −0.938535 | − | 0.345185i | \(-0.887816\pi\) |
0.170328 | − | 0.985387i | \(-0.445517\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.05465e13 | − | 5.09399e13i | −0.00502297 | − | 0.00837642i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.13612e16i | − | 1.84072i | −0.391074 | − | 0.920359i | \(-0.627896\pi\) | ||
0.391074 | − | 0.920359i | \(-0.372104\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.20907e15 | − | 1.27541e15i | 0.352655 | − | 0.203605i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.79154e15 | + | 6.09170e15i | 0.596421 | + | 0.958242i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.88830e15 | + | 2.65296e15i | −0.912725 | + | 0.411227i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.44479e15 | + | 7.69860e15i | −0.678940 | + | 1.17596i | 0.296360 | + | 0.955076i | \(0.404227\pi\) |
−0.975300 | + | 0.220883i | \(0.929106\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.29225e15 | − | 9.52758e15i | 0.796651 | − | 1.43420i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.81742e15 | −0.269617 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.93247e15 | −0.282543 | −0.141272 | − | 0.989971i | \(-0.545119\pi\) | ||||
−0.141272 | + | 0.989971i | \(0.545119\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.01756e14 | − | 9.03305e14i | 0.0723040 | − | 0.130168i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.80383e15 | − | 3.12432e15i | 0.256200 | − | 0.443751i | −0.709021 | − | 0.705188i | \(-0.750863\pi\) |
0.965221 | + | 0.261436i | \(0.0841961\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.46910e15 | + | 2.48457e14i | 0.345664 | + | 0.0347830i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.22991e15 | − | 5.18935e15i | −0.445710 | − | 0.716103i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.81810e16 | − | 1.04968e16i | 2.47311 | − | 1.42785i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.94760e15i | 0.261159i | 0.991438 | + | 0.130579i | \(0.0416838\pi\) | ||||
−0.991438 | + | 0.130579i | \(0.958316\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.18219e15 | + | 3.63906e15i | 0.288465 | + | 0.481050i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.28222e15 | + | 2.22087e15i | 0.167100 | + | 0.289425i | 0.937399 | − | 0.348257i | \(-0.113226\pi\) |
−0.770299 | + | 0.637683i | \(0.779893\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.41768e15 | − | 1.39585e15i | −0.310627 | − | 0.179341i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.20513e15 | − | 6.88550e14i | −1.03937 | − | 0.0872208i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.80251e13 | + | 2.19538e13i | 0.00474913 | + | 0.00274191i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.65085e15 | − | 4.59141e15i | −0.326441 | − | 0.565413i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.36639e14 | − | 6.76719e15i | −0.0408766 | − | 0.821710i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.16214e15i | 0.258881i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.52454e15 | + | 8.80192e14i | −0.180002 | + | 0.103924i | −0.587294 | − | 0.809374i | \(-0.699807\pi\) |
0.407292 | + | 0.913298i | \(0.366473\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.57337e14 | − | 9.49542e15i | −0.0183192 | − | 1.10558i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.01579e15 | − | 7.31160e14i | −0.116636 | − | 0.0839541i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.02796e16 | + | 1.78047e16i | −1.16405 | + | 2.01620i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.44445e15 | − | 2.46874e15i | −0.496363 | − | 0.275713i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.15235e16 | 1.26930 | 0.634648 | − | 0.772801i | \(-0.281145\pi\) | ||||
0.634648 | + | 0.772801i | \(0.281145\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.76954e16 | −1.92245 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.82378e15 | − | 2.59348e14i | 0.838374 | − | 0.0277910i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.30495e16 | + | 2.26024e16i | −1.37930 | + | 2.38902i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.06400e13 | + | 4.03869e14i | −0.00423717 | + | 0.0421078i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.86925e15 | + | 3.09731e13i | −0.192249 | + | 0.00318552i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.67377e15 | − | 4.43045e15i | 0.778560 | − | 0.449502i | −0.0573597 | − | 0.998354i | \(-0.518268\pi\) |
0.835920 | + | 0.548852i | \(0.184935\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 4.08074e15i | − | 0.408436i | −0.978925 | − | 0.204218i | \(-0.934535\pi\) | ||
0.978925 | − | 0.204218i | \(-0.0654652\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.97087e15 | + | 4.77979e15i | −0.787060 | + | 0.471966i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.84453e13 | + | 1.70512e14i | 0.00959021 | + | 0.0166107i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.01448e13 | + | 1.16306e13i | 0.00193616 | + | 0.00111784i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.40592e15 | − | 2.09047e16i | 0.133321 | − | 1.98236i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.27365e16 | − | 7.35343e15i | −1.19169 | − | 0.688023i | −0.233001 | − | 0.972477i | \(-0.574854\pi\) |
−0.958690 | + | 0.284454i | \(0.908188\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.84910e14 | + | 8.39889e14i | 0.0447674 | + | 0.0775395i | 0.887541 | − | 0.460729i | \(-0.152412\pi\) |
−0.842773 | + | 0.538268i | \(0.819079\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.20940e16 | + | 7.25225e15i | −1.10173 | + | 0.660657i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.82412e15i | 0.433648i | 0.976211 | + | 0.216824i | \(0.0695699\pi\) | ||||
−0.976211 | + | 0.216824i | \(0.930430\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.28967e15 | + | 3.05399e15i | −0.469223 | + | 0.270906i | −0.715914 | − | 0.698188i | \(-0.753990\pi\) |
0.246692 | + | 0.969094i | \(0.420657\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.20340e16 | − | 1.99401e14i | 1.05343 | − | 0.0174551i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.38550e16 | − | 1.56645e16i | 1.19690 | − | 1.35322i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.84069e14 | + | 1.01164e15i | −0.0497954 | + | 0.0862481i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.57955e15 | − | 2.95674e15i | 0.385330 | − | 0.248784i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.68190e16 | −1.39672 | −0.698360 | − | 0.715747i | \(-0.746087\pi\) | ||||
−0.698360 | + | 0.715747i | \(0.746087\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.94225e15 | 0.323122 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.10211e15 | + | 2.83405e15i | 0.412761 | + | 0.229275i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.61695e15 | + | 1.49250e16i | −0.688084 | + | 1.19180i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.85197e15 | − | 1.96471e16i | −0.697720 | − | 1.54860i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.82418e13 | + | 3.51494e15i | 0.00453151 | + | 0.273480i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.06604e15 | + | 6.15477e14i | −0.0818766 | + | 0.0472715i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1.38889e16i | − | 1.05305i | −0.850159 | − | 0.526526i | \(-0.823494\pi\) | ||
0.850159 | − | 0.526526i | \(-0.176506\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.70492e13 | + | 1.44438e13i | 0.00202461 | + | 0.00108110i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.57068e15 | − | 6.18459e15i | −0.263849 | − | 0.457000i | 0.703412 | − | 0.710782i | \(-0.251659\pi\) |
−0.967262 | + | 0.253782i | \(0.918326\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.23330e15 | + | 3.59880e15i | 0.454732 | + | 0.262540i | 0.709827 | − | 0.704376i | \(-0.248773\pi\) |
−0.255094 | + | 0.966916i | \(0.582107\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.59532e15 | + | 1.40138e16i | 0.475027 | + | 1.00934i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.29698e16 | + | 7.48810e15i | 0.922302 | + | 0.532491i | 0.884369 | − | 0.466789i | \(-0.154589\pi\) |
0.0379333 | + | 0.999280i | \(0.487923\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.92320e15 | − | 6.79518e15i | −0.275456 | − | 0.477103i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.67934e16 | + | 2.80050e16i | 1.16421 | + | 1.94147i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.13308e16i | − | 0.775625i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.09826e16 | + | 1.21143e16i | −1.41827 | + | 0.818841i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.96055e13 | + | 3.70991e13i | −0.00397839 | + | 0.00247620i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.37443e15 | − | 1.02452e16i | 0.486053 | − | 0.675267i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.71763e15 | − | 8.17118e15i | 0.307062 | − | 0.531847i | −0.670656 | − | 0.741768i | \(-0.733987\pi\) |
0.977718 | + | 0.209921i | \(0.0673207\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.66474e14 | + | 2.99700e14i | −0.0107006 | + | 0.0192641i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.15600e15 | 0.581217 | 0.290608 | − | 0.956842i | \(-0.406142\pi\) | ||||
0.290608 | + | 0.956842i | \(0.406142\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.66081e15 | 0.354891 | 0.177445 | − | 0.984131i | \(-0.443217\pi\) | ||||
0.177445 | + | 0.984131i | \(0.443217\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.26282e15 | + | 9.47459e15i | −0.325859 | + | 0.586641i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.33808e15 | − | 1.09779e16i | 0.387595 | − | 0.671334i | −0.604531 | − | 0.796582i | \(-0.706639\pi\) |
0.992125 | + | 0.125248i | \(0.0399726\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.08289e16 | + | 1.50444e16i | −0.654068 | + | 0.908687i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.82352e15 | − | 2.74749e16i | −0.108788 | − | 1.63911i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.68790e13 | − | 4.43861e13i | 0.00453027 | − | 0.00261555i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 4.97780e15i | − | 0.289742i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.61085e15 | − | 2.68629e15i | −0.0926183 | − | 0.154452i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.32199e15 | − | 5.75386e15i | −0.188678 | − | 0.326799i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.39121e16 | + | 1.95792e16i | 1.90269 | + | 1.09852i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.49405e15 | + | 7.42417e15i | 0.193663 | + | 0.411496i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.20774e15 | − | 3.58404e15i | −0.339912 | − | 0.196248i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.59053e15 | − | 1.48792e16i | −0.464708 | − | 0.804897i | 0.534481 | − | 0.845181i | \(-0.320507\pi\) |
−0.999188 | + | 0.0402836i | \(0.987174\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.07285e16 | − | 2.00915e16i | 0.573374 | − | 1.07377i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.11490e16i | 0.588685i | 0.955700 | + | 0.294343i | \(0.0951007\pi\) | ||||
−0.955700 | + | 0.294343i | \(0.904899\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.07793e16 | − | 1.77704e16i | 1.60572 | − | 0.927062i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.75844e14 | − | 1.06124e16i | −0.00906385 | − | 0.547010i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.35289e16 | + | 3.00276e16i | 0.689018 | + | 1.52929i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.00179e14 | − | 5.19925e14i | 0.0151058 | − | 0.0261641i | −0.858374 | − | 0.513025i | \(-0.828525\pi\) |
0.873480 | + | 0.486861i | \(0.161858\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.02599e16 | − | 1.12537e16i | −1.00742 | − | 0.559587i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.60710e16 | −0.789648 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.67991e16 | 0.815657 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.15566e14 | − | 3.48628e15i | −0.00554485 | − | 0.167272i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.11234e14 | + | 5.39074e14i | −0.0147571 | + | 0.0255601i | −0.873310 | − | 0.487166i | \(-0.838031\pi\) |
0.858553 | + | 0.512726i | \(0.171364\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.09021e13 | + | 1.02808e14i | −0.000979417 | + | 0.00481731i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.08939e15 | + | 1.00900e14i | −0.281984 | + | 0.00467242i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.62200e16 | + | 1.51381e16i | −1.19997 | + | 0.692801i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.09590e16i | 0.495681i | 0.968801 | + | 0.247841i | \(0.0797209\pi\) | ||||
−0.968801 | + | 0.247841i | \(0.920279\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.75730e15 | + | 5.85103e15i | −0.436183 | + | 0.261560i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.25535e16 | + | 2.17433e16i | 0.554653 | + | 0.960687i | 0.997930 | + | 0.0643028i | \(0.0204824\pi\) |
−0.443277 | + | 0.896385i | \(0.646184\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.00523e15 | + | 1.15772e15i | 0.0875688 | + | 0.0505579i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.92773e15 | + | 9.62891e15i | 0.212702 | + | 0.415626i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.72938e16 | + | 9.98456e15i | 0.737844 | + | 0.425994i | 0.821285 | − | 0.570518i | \(-0.193258\pi\) |
−0.0834409 | + | 0.996513i | \(0.526591\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.95569e16 | + | 6.85146e16i | 1.66824 | + | 2.88947i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.38826e16 | + | 1.43214e16i | −0.995608 | + | 0.597023i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 3.48840e15i | − | 0.143752i | −0.997414 | − | 0.0718762i | \(-0.977101\pi\) | ||
0.997414 | − | 0.0718762i | \(-0.0228987\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.45926e16 | − | 8.42502e15i | 0.594447 | − | 0.343204i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.35563e16 | + | 5.56021e14i | −1.35132 | + | 0.0223911i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.83974e15 | + | 1.82828e16i | −0.0732409 | + | 0.727847i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.00316e16 | + | 1.73753e16i | −0.394813 | + | 0.683837i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.52401e14 | + | 2.57145e16i | 0.0331665 | + | 1.00054i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.63452e15 | −0.0628768 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.99693e16 | 1.90045 | 0.950227 | − | 0.311559i | \(-0.100851\pi\) | ||||
0.950227 | + | 0.311559i | \(0.100851\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.06465e14 | − | 1.14685e14i | −0.00776365 | − | 0.00431245i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.78361e16 | − | 3.08930e16i | 0.663121 | − | 1.14856i | −0.316670 | − | 0.948536i | \(-0.602565\pi\) |
0.979791 | − | 0.200024i | \(-0.0641020\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.30401e16 | + | 2.37821e16i | 1.21456 | + | 0.874237i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.08205e14 | + | 4.27407e16i | 0.0257415 | + | 1.55352i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.83993e16 | + | 1.06229e16i | −0.661274 | + | 0.381787i | −0.792762 | − | 0.609531i | \(-0.791358\pi\) |
0.131488 | + | 0.991318i | \(0.458025\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 3.87743e16i | − | 1.37797i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.65664e15 | − | 8.72060e15i | 0.163641 | − | 0.306455i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.16801e15 | − | 1.58795e16i | −0.318589 | − | 0.551812i | 0.661605 | − | 0.749853i | \(-0.269876\pi\) |
−0.980194 | + | 0.198040i | \(0.936542\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.60543e16 | − | 9.26896e15i | −0.551686 | − | 0.318516i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.12043e16 | + | 2.61857e15i | 1.06040 | + | 0.0889856i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.06232e15 | + | 6.13332e14i | 0.0357007 | + | 0.0206118i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.26417e15 | − | 1.25819e16i | −0.241424 | − | 0.418159i | 0.719696 | − | 0.694289i | \(-0.244281\pi\) |
−0.961120 | + | 0.276130i | \(0.910948\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.46692e15 | + | 2.44626e15i | 0.0482153 | + | 0.0804049i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.73626e16i | 0.564402i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.81880e16 | − | 1.05009e16i | 0.584739 | − | 0.337599i | −0.178275 | − | 0.983981i | \(-0.557052\pi\) |
0.763015 | + | 0.646381i | \(0.223718\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.49695e16 | + | 2.91874e16i | −0.475988 | + | 0.928079i |
(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.5.20 | ✓ | 56 | |
3.2 | odd | 2 | inner | 84.12.k.b.5.28 | yes | 56 | |
7.3 | odd | 6 | inner | 84.12.k.b.17.28 | yes | 56 | |
21.17 | even | 6 | inner | 84.12.k.b.17.20 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.12.k.b.5.20 | ✓ | 56 | 1.1 | even | 1 | trivial | |
84.12.k.b.5.28 | yes | 56 | 3.2 | odd | 2 | inner | |
84.12.k.b.17.20 | yes | 56 | 21.17 | even | 6 | inner | |
84.12.k.b.17.28 | yes | 56 | 7.3 | odd | 6 | inner |