Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,7,Mod(19,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.19");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.l (of order \(4\), 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: | \(11.0425960138\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.8 | ||
Character | \(\chi\) | \(=\) | 48.43 |
Dual form | 48.7.l.a.19.8 |
$q$-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 \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(31\) | \(37\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.75499 | + | 7.06400i | −0.469374 | + | 0.883000i | ||||
\(3\) | −11.0227 | − | 11.0227i | −0.408248 | − | 0.408248i | ||||
\(4\) | −35.8001 | − | 53.0505i | −0.559376 | − | 0.828914i | ||||
\(5\) | 107.837 | + | 107.837i | 0.862693 | + | 0.862693i | 0.991650 | − | 0.128957i | \(-0.0411629\pi\) |
−0.128957 | + | 0.991650i | \(0.541163\pi\) | |||||||
\(6\) | 119.254 | − | 36.4742i | 0.552104 | − | 0.168862i | ||||
\(7\) | 5.36994 | 0.0156558 | 0.00782790 | − | 0.999969i | \(-0.497508\pi\) | ||||
0.00782790 | + | 0.999969i | \(0.497508\pi\) | |||||||
\(8\) | 509.177 | − | 53.6875i | 0.994487 | − | 0.104858i | ||||
\(9\) | 243.000i | 0.333333i | ||||||||
\(10\) | −1166.68 | + | 356.832i | −1.16668 | + | 0.356832i | ||||
\(11\) | −48.9517 | + | 48.9517i | −0.0367781 | + | 0.0367781i | −0.725257 | − | 0.688479i | \(-0.758279\pi\) |
0.688479 | + | 0.725257i | \(0.258279\pi\) | |||||||
\(12\) | −190.146 | + | 979.373i | −0.110038 | + | 0.566767i | ||||
\(13\) | −2118.46 | + | 2118.46i | −0.964252 | + | 0.964252i | −0.999383 | − | 0.0351311i | \(-0.988815\pi\) |
0.0351311 | + | 0.999383i | \(0.488815\pi\) | |||||||
\(14\) | −20.1641 | + | 37.9332i | −0.00734843 | + | 0.0138241i | ||||
\(15\) | − | 2377.30i | − | 0.704386i | ||||||
\(16\) | −1532.71 | + | 3798.42i | −0.374196 | + | 0.927349i | ||||
\(17\) | −3884.97 | −0.790753 | −0.395377 | − | 0.918519i | \(-0.629386\pi\) | ||||
−0.395377 | + | 0.918519i | \(0.629386\pi\) | |||||||
\(18\) | −1716.55 | − | 912.463i | −0.294333 | − | 0.156458i | ||||
\(19\) | −5877.62 | − | 5877.62i | −0.856921 | − | 0.856921i | 0.134053 | − | 0.990974i | \(-0.457201\pi\) |
−0.990974 | + | 0.134053i | \(0.957201\pi\) | |||||||
\(20\) | 1860.23 | − | 9581.35i | 0.232528 | − | 1.19767i | ||||
\(21\) | −59.1913 | − | 59.1913i | −0.00639146 | − | 0.00639146i | ||||
\(22\) | −161.981 | − | 529.608i | −0.0152124 | − | 0.0497377i | ||||
\(23\) | −3237.03 | −0.266050 | −0.133025 | − | 0.991113i | \(-0.542469\pi\) | ||||
−0.133025 | + | 0.991113i | \(0.542469\pi\) | |||||||
\(24\) | −6204.29 | − | 5020.73i | −0.448806 | − | 0.363189i | ||||
\(25\) | 7632.48i | 0.488479i | ||||||||
\(26\) | −7010.00 | − | 22919.6i | −0.398839 | − | 1.30403i | ||||
\(27\) | 2678.52 | − | 2678.52i | 0.136083 | − | 0.136083i | ||||
\(28\) | −192.244 | − | 284.878i | −0.00875749 | − | 0.0129773i | ||||
\(29\) | −30583.8 | + | 30583.8i | −1.25400 | + | 1.25400i | −0.300087 | + | 0.953912i | \(0.597016\pi\) |
−0.953912 | + | 0.300087i | \(0.902984\pi\) | |||||||
\(30\) | 16793.3 | + | 8926.75i | 0.621973 | + | 0.330620i | ||||
\(31\) | 54018.7i | 1.81326i | 0.421932 | + | 0.906628i | \(0.361352\pi\) | ||||
−0.421932 | + | 0.906628i | \(0.638648\pi\) | |||||||
\(32\) | −21076.7 | − | 25090.1i | −0.643211 | − | 0.765689i | ||||
\(33\) | 1079.16 | 0.0300292 | ||||||||
\(34\) | 14588.0 | − | 27443.4i | 0.371159 | − | 0.698235i | ||||
\(35\) | 579.076 | + | 579.076i | 0.0135062 | + | 0.0135062i | ||||
\(36\) | 12891.3 | − | 8699.42i | 0.276305 | − | 0.186459i | ||||
\(37\) | 33650.8 | + | 33650.8i | 0.664339 | + | 0.664339i | 0.956400 | − | 0.292060i | \(-0.0943408\pi\) |
−0.292060 | + | 0.956400i | \(0.594341\pi\) | |||||||
\(38\) | 63589.9 | − | 19449.1i | 1.15888 | − | 0.354444i | ||||
\(39\) | 46702.3 | 0.787308 | ||||||||
\(40\) | 60697.5 | + | 49118.5i | 0.948398 | + | 0.767477i | ||||
\(41\) | − | 29052.0i | − | 0.421526i | −0.977537 | − | 0.210763i | \(-0.932405\pi\) | ||
0.977537 | − | 0.210763i | \(-0.0675949\pi\) | |||||||
\(42\) | 640.390 | − | 195.864i | 0.00864363 | − | 0.00264367i | ||||
\(43\) | −24548.9 | + | 24548.9i | −0.308764 | + | 0.308764i | −0.844430 | − | 0.535666i | \(-0.820061\pi\) |
0.535666 | + | 0.844430i | \(0.320061\pi\) | |||||||
\(44\) | 4349.38 | + | 844.436i | 0.0510587 | + | 0.00991309i | ||||
\(45\) | −26204.3 | + | 26204.3i | −0.287564 | + | 0.287564i | ||||
\(46\) | 12155.0 | − | 22866.4i | 0.124877 | − | 0.234922i | ||||
\(47\) | − | 58193.1i | − | 0.560503i | −0.959927 | − | 0.280251i | \(-0.909582\pi\) | ||
0.959927 | − | 0.280251i | \(-0.0904178\pi\) | |||||||
\(48\) | 58763.5 | − | 24974.3i | 0.531354 | − | 0.225824i | ||||
\(49\) | −117620. | −0.999755 | ||||||||
\(50\) | −53915.8 | − | 28659.9i | −0.431327 | − | 0.229279i | ||||
\(51\) | 42822.9 | + | 42822.9i | 0.322824 | + | 0.322824i | ||||
\(52\) | 188226. | + | 36544.3i | 1.33866 | + | 0.259902i | ||||
\(53\) | 27071.8 | + | 27071.8i | 0.181840 | + | 0.181840i | 0.792157 | − | 0.610317i | \(-0.208958\pi\) |
−0.610317 | + | 0.792157i | \(0.708958\pi\) | |||||||
\(54\) | 8863.23 | + | 28978.8i | 0.0562873 | + | 0.184035i | ||||
\(55\) | −10557.6 | −0.0634565 | ||||||||
\(56\) | 2734.25 | − | 288.299i | 0.0155695 | − | 0.00164164i | ||||
\(57\) | 129575.i | 0.699673i | ||||||||
\(58\) | −101202. | − | 330885.i | −0.518686 | − | 1.69587i | ||||
\(59\) | 225328. | − | 225328.i | 1.09713 | − | 1.09713i | 0.102387 | − | 0.994745i | \(-0.467352\pi\) |
0.994745 | − | 0.102387i | \(-0.0326481\pi\) | |||||||
\(60\) | −126117. | + | 85107.6i | −0.583875 | + | 0.394017i | ||||
\(61\) | −1789.71 | + | 1789.71i | −0.00788485 | + | 0.00788485i | −0.711038 | − | 0.703153i | \(-0.751775\pi\) |
0.703153 | + | 0.711038i | \(0.251775\pi\) | |||||||
\(62\) | −381588. | − | 202840.i | −1.60110 | − | 0.851095i | ||||
\(63\) | 1304.90i | 0.00521860i | ||||||||
\(64\) | 256379. | − | 54672.9i | 0.978009 | − | 0.208561i | ||||
\(65\) | −456895. | −1.66371 | ||||||||
\(66\) | −4052.24 | + | 7623.18i | −0.0140949 | + | 0.0265158i | ||||
\(67\) | 122582. | + | 122582.i | 0.407571 | + | 0.407571i | 0.880891 | − | 0.473320i | \(-0.156944\pi\) |
−0.473320 | + | 0.880891i | \(0.656944\pi\) | |||||||
\(68\) | 139082. | + | 206100.i | 0.442329 | + | 0.655466i | ||||
\(69\) | 35680.9 | + | 35680.9i | 0.108615 | + | 0.108615i | ||||
\(70\) | −6265.02 | + | 1916.17i | −0.0182654 | + | 0.00558649i | ||||
\(71\) | −213921. | −0.597692 | −0.298846 | − | 0.954301i | \(-0.596602\pi\) | ||||
−0.298846 | + | 0.954301i | \(0.596602\pi\) | |||||||
\(72\) | 13046.1 | + | 123730.i | 0.0349528 | + | 0.331496i | ||||
\(73\) | 337380.i | 0.867263i | 0.901090 | + | 0.433631i | \(0.142768\pi\) | ||||
−0.901090 | + | 0.433631i | \(0.857232\pi\) | |||||||
\(74\) | −364067. | + | 111351.i | −0.898435 | + | 0.274788i | ||||
\(75\) | 84130.6 | − | 84130.6i | 0.199421 | − | 0.199421i | ||||
\(76\) | −101391. | + | 522230.i | −0.230972 | + | 1.18965i | ||||
\(77\) | −262.868 | + | 262.868i | −0.000575791 | + | 0.000575791i | ||||
\(78\) | −175367. | + | 329905.i | −0.369542 | + | 0.695193i | ||||
\(79\) | − | 715537.i | − | 1.45128i | −0.688075 | − | 0.725639i | \(-0.741544\pi\) | ||
0.688075 | − | 0.725639i | \(-0.258456\pi\) | |||||||
\(80\) | −574891. | + | 244327.i | −1.12283 | + | 0.477201i | ||||
\(81\) | −59049.0 | −0.111111 | ||||||||
\(82\) | 205223. | + | 109090.i | 0.372207 | + | 0.197853i | ||||
\(83\) | 338143. | + | 338143.i | 0.591380 | + | 0.591380i | 0.938004 | − | 0.346624i | \(-0.112672\pi\) |
−0.346624 | + | 0.938004i | \(0.612672\pi\) | |||||||
\(84\) | −1021.07 | + | 5259.18i | −0.00172274 | + | 0.00887319i | ||||
\(85\) | −418942. | − | 418942.i | −0.682177 | − | 0.682177i | ||||
\(86\) | −81232.4 | − | 265594.i | −0.127713 | − | 0.417564i | ||||
\(87\) | 674232. | 1.02389 | ||||||||
\(88\) | −22297.0 | + | 27553.2i | −0.0327189 | + | 0.0404319i | ||||
\(89\) | − | 527375.i | − | 0.748083i | −0.927412 | − | 0.374041i | \(-0.877972\pi\) | ||
0.927412 | − | 0.374041i | \(-0.122028\pi\) | |||||||
\(90\) | −86710.2 | − | 283504.i | −0.118944 | − | 0.388894i | ||||
\(91\) | −11376.0 | + | 11376.0i | −0.0150961 | + | 0.0150961i | ||||
\(92\) | 115886. | + | 171726.i | 0.148822 | + | 0.220533i | ||||
\(93\) | 595432. | − | 595432.i | 0.740258 | − | 0.740258i | ||||
\(94\) | 411076. | + | 218515.i | 0.494924 | + | 0.263085i | ||||
\(95\) | − | 1.26765e6i | − | 1.47852i | ||||||
\(96\) | −44238.0 | + | 508883.i | −0.0500013 | + | 0.575181i | ||||
\(97\) | −1.55143e6 | −1.69987 | −0.849937 | − | 0.526884i | \(-0.823360\pi\) | ||||
−0.849937 | + | 0.526884i | \(0.823360\pi\) | |||||||
\(98\) | 441663. | − | 830868.i | 0.469259 | − | 0.882783i | ||||
\(99\) | −11895.3 | − | 11895.3i | −0.0122594 | − | 0.0122594i | ||||
\(100\) | 404907. | − | 273244.i | 0.404907 | − | 0.273244i | ||||
\(101\) | 1.16299e6 | + | 1.16299e6i | 1.12879 | + | 1.12879i | 0.990375 | + | 0.138413i | \(0.0442002\pi\) |
0.138413 | + | 0.990375i | \(0.455800\pi\) | |||||||
\(102\) | −463300. | + | 141701.i | −0.436578 | + | 0.133528i | ||||
\(103\) | 1.22358e6 | 1.11975 | 0.559873 | − | 0.828578i | \(-0.310850\pi\) | ||||
0.559873 | + | 0.828578i | \(0.310850\pi\) | |||||||
\(104\) | −964938. | + | 1.19241e6i | −0.857826 | + | 1.06005i | ||||
\(105\) | − | 12766.0i | − | 0.0110277i | ||||||
\(106\) | −292889. | + | 89580.7i | −0.245916 | + | 0.0752137i | ||||
\(107\) | 421967. | − | 421967.i | 0.344450 | − | 0.344450i | −0.513587 | − | 0.858038i | \(-0.671684\pi\) |
0.858038 | + | 0.513587i | \(0.171684\pi\) | |||||||
\(108\) | −237988. | − | 46205.5i | −0.188922 | − | 0.0366794i | ||||
\(109\) | −966244. | + | 966244.i | −0.746118 | + | 0.746118i | −0.973748 | − | 0.227630i | \(-0.926902\pi\) |
0.227630 | + | 0.973748i | \(0.426902\pi\) | |||||||
\(110\) | 39643.6 | − | 74578.6i | 0.0297848 | − | 0.0560320i | ||||
\(111\) | − | 741845.i | − | 0.542431i | ||||||
\(112\) | −8230.55 | + | 20397.3i | −0.00585835 | + | 0.0145184i | ||||
\(113\) | 1.34165e6 | 0.929833 | 0.464916 | − | 0.885355i | \(-0.346084\pi\) | ||||
0.464916 | + | 0.885355i | \(0.346084\pi\) | |||||||
\(114\) | −915314. | − | 486551.i | −0.617811 | − | 0.328408i | ||||
\(115\) | −349071. | − | 349071.i | −0.229520 | − | 0.229520i | ||||
\(116\) | 2.71739e6 | + | 527583.i | 1.74091 | + | 0.338000i | ||||
\(117\) | −514786. | − | 514786.i | −0.321417 | − | 0.321417i | ||||
\(118\) | 745611. | + | 2.43782e6i | 0.453802 | + | 1.48373i | ||||
\(119\) | −20862.1 | −0.0123799 | ||||||||
\(120\) | −127631. | − | 1.21047e6i | −0.0738608 | − | 0.700503i | ||||
\(121\) | 1.76677e6i | 0.997295i | ||||||||
\(122\) | −5922.16 | − | 19362.9i | −0.00326138 | − | 0.0106633i | ||||
\(123\) | −320232. | + | 320232.i | −0.172087 | + | 0.172087i | ||||
\(124\) | 2.86572e6 | − | 1.93387e6i | 1.50303 | − | 1.01429i | ||||
\(125\) | 861886. | − | 861886.i | 0.441286 | − | 0.441286i | ||||
\(126\) | −9217.78 | − | 4899.87i | −0.00460802 | − | 0.00244948i | ||||
\(127\) | − | 512988.i | − | 0.250435i | −0.992129 | − | 0.125218i | \(-0.960037\pi\) | ||
0.992129 | − | 0.125218i | \(-0.0399629\pi\) | |||||||
\(128\) | −576493. | + | 2.01636e6i | −0.274893 | + | 0.961475i | ||||
\(129\) | 541191. | 0.252105 | ||||||||
\(130\) | 1.71564e6 | − | 3.22751e6i | 0.780900 | − | 1.46905i | ||||
\(131\) | 1.55668e6 | + | 1.55668e6i | 0.692444 | + | 0.692444i | 0.962769 | − | 0.270325i | \(-0.0871312\pi\) |
−0.270325 | + | 0.962769i | \(0.587131\pi\) | |||||||
\(132\) | −38634.0 | − | 57249.9i | −0.0167976 | − | 0.0248916i | ||||
\(133\) | −31562.5 | − | 31562.5i | −0.0134158 | − | 0.0134158i | ||||
\(134\) | −1.32622e6 | + | 405626.i | −0.551188 | + | 0.168582i | ||||
\(135\) | 577685. | 0.234795 | ||||||||
\(136\) | −1.97814e6 | + | 208574.i | −0.786394 | + | 0.0829171i | ||||
\(137\) | − | 24036.2i | − | 0.00934768i | −0.999989 | − | 0.00467384i | \(-0.998512\pi\) | ||
0.999989 | − | 0.00467384i | \(-0.00148773\pi\) | |||||||
\(138\) | −386031. | + | 118068.i | −0.146887 | + | 0.0449258i | ||||
\(139\) | −3.76939e6 | + | 3.76939e6i | −1.40355 | + | 1.40355i | −0.615086 | + | 0.788460i | \(0.710879\pi\) |
−0.788460 | + | 0.615086i | \(0.789121\pi\) | |||||||
\(140\) | 9989.30 | − | 51451.3i | 0.00364042 | − | 0.0187505i | ||||
\(141\) | −641445. | + | 641445.i | −0.228824 | + | 0.228824i | ||||
\(142\) | 803270. | − | 1.51113e6i | 0.280541 | − | 0.527762i | ||||
\(143\) | − | 207404.i | − | 0.0709267i | ||||||
\(144\) | −923017. | − | 372448.i | −0.309116 | − | 0.124732i | ||||
\(145\) | −6.59610e6 | −2.16363 | ||||||||
\(146\) | −2.38325e6 | − | 1.26686e6i | −0.765793 | − | 0.407071i | ||||
\(147\) | 1.29649e6 | + | 1.29649e6i | 0.408148 | + | 0.408148i | ||||
\(148\) | 580490. | − | 2.98989e6i | 0.179064 | − | 0.922296i | ||||
\(149\) | 2.54711e6 | + | 2.54711e6i | 0.769998 | + | 0.769998i | 0.978106 | − | 0.208108i | \(-0.0667306\pi\) |
−0.208108 | + | 0.978106i | \(0.566731\pi\) | |||||||
\(150\) | 278389. | + | 910208.i | 0.0824855 | + | 0.269691i | ||||
\(151\) | −4.85437e6 | −1.40995 | −0.704973 | − | 0.709235i | \(-0.749041\pi\) | ||||
−0.704973 | + | 0.709235i | \(0.749041\pi\) | |||||||
\(152\) | −3.30831e6 | − | 2.67720e6i | −0.942052 | − | 0.762341i | ||||
\(153\) | − | 944048.i | − | 0.263584i | ||||||
\(154\) | −869.830 | − | 2843.96i | −0.000238162 | − | 0.000778684i | ||||
\(155\) | −5.82519e6 | + | 5.82519e6i | −1.56428 | + | 1.56428i | ||||
\(156\) | −1.67195e6 | − | 2.47758e6i | −0.440401 | − | 0.652611i | ||||
\(157\) | 4.73206e6 | − | 4.73206e6i | 1.22279 | − | 1.22279i | 0.256151 | − | 0.966637i | \(-0.417546\pi\) |
0.966637 | − | 0.256151i | \(-0.0824544\pi\) | |||||||
\(158\) | 5.05455e6 | + | 2.68683e6i | 1.28148 | + | 0.681192i | ||||
\(159\) | − | 596809.i | − | 0.148472i | ||||||
\(160\) | 432786. | − | 4.97848e6i | 0.105661 | − | 1.21545i | ||||
\(161\) | −17382.7 | −0.00416523 | ||||||||
\(162\) | 221728. | − | 417122.i | 0.0521527 | − | 0.0981111i | ||||
\(163\) | 2.25527e6 | + | 2.25527e6i | 0.520758 | + | 0.520758i | 0.917800 | − | 0.397042i | \(-0.129963\pi\) |
−0.397042 | + | 0.917800i | \(0.629963\pi\) | |||||||
\(164\) | −1.54122e6 | + | 1.04006e6i | −0.349409 | + | 0.235792i | ||||
\(165\) | 116373. | + | 116373.i | 0.0259060 | + | 0.0259060i | ||||
\(166\) | −3.65837e6 | + | 1.11892e6i | −0.799767 | + | 0.244610i | ||||
\(167\) | −5.96746e6 | −1.28127 | −0.640634 | − | 0.767846i | \(-0.721329\pi\) | ||||
−0.640634 | + | 0.767846i | \(0.721329\pi\) | |||||||
\(168\) | −33316.7 | − | 26961.0i | −0.00702642 | − | 0.00568602i | ||||
\(169\) | − | 4.14894e6i | − | 0.859562i | ||||||
\(170\) | 4.53253e6 | − | 1.38628e6i | 0.922559 | − | 0.282166i | ||||
\(171\) | 1.42826e6 | − | 1.42826e6i | 0.285640 | − | 0.285640i | ||||
\(172\) | 2.18118e6 | + | 423479.i | 0.428654 | + | 0.0832235i | ||||
\(173\) | 6.11242e6 | − | 6.11242e6i | 1.18052 | − | 1.18052i | 0.200916 | − | 0.979609i | \(-0.435608\pi\) |
0.979609 | − | 0.200916i | \(-0.0643917\pi\) | |||||||
\(174\) | −2.53173e6 | + | 4.76277e6i | −0.480585 | + | 0.904091i | ||||
\(175\) | 40986.0i | 0.00764753i | ||||||||
\(176\) | −110911. | − | 260968.i | −0.0203439 | − | 0.0478684i | ||||
\(177\) | −4.96744e6 | −0.895804 | ||||||||
\(178\) | 3.72538e6 | + | 1.98029e6i | 0.660557 | + | 0.351130i | ||||
\(179\) | −328581. | − | 328581.i | −0.0572906 | − | 0.0572906i | 0.677881 | − | 0.735172i | \(-0.262898\pi\) |
−0.735172 | + | 0.677881i | \(0.762898\pi\) | |||||||
\(180\) | 2.32827e6 | + | 452035.i | 0.399223 | + | 0.0775094i | ||||
\(181\) | 1.85271e6 | + | 1.85271e6i | 0.312444 | + | 0.312444i | 0.845856 | − | 0.533412i | \(-0.179090\pi\) |
−0.533412 | + | 0.845856i | \(0.679090\pi\) | |||||||
\(182\) | −37643.3 | − | 123077.i | −0.00624415 | − | 0.0204156i | ||||
\(183\) | 39454.9 | 0.00643795 | ||||||||
\(184\) | −1.64822e6 | + | 173788.i | −0.264584 | + | 0.0278976i | ||||
\(185\) | 7.25758e6i | 1.14624i | ||||||||
\(186\) | 1.97029e6 | + | 6.44197e6i | 0.306190 | + | 1.00111i | ||||
\(187\) | 190176. | − | 190176.i | 0.0290824 | − | 0.0290824i | ||||
\(188\) | −3.08717e6 | + | 2.08332e6i | −0.464609 | + | 0.313532i | ||||
\(189\) | 14383.5 | − | 14383.5i | 0.00213049 | − | 0.00213049i | ||||
\(190\) | 8.95464e6 | + | 4.76000e6i | 1.30553 | + | 0.693979i | ||||
\(191\) | − | 8.50584e6i | − | 1.22072i | −0.792123 | − | 0.610361i | \(-0.791024\pi\) | ||
0.792123 | − | 0.610361i | \(-0.208976\pi\) | |||||||
\(192\) | −3.42864e6 | − | 2.22335e6i | −0.484415 | − | 0.314126i | ||||
\(193\) | 4.58702e6 | 0.638056 | 0.319028 | − | 0.947745i | \(-0.396644\pi\) | ||||
0.319028 | + | 0.947745i | \(0.396644\pi\) | |||||||
\(194\) | 5.82561e6 | − | 1.09593e7i | 0.797877 | − | 1.50099i | ||||
\(195\) | 5.03622e6 | + | 5.03622e6i | 0.679205 | + | 0.679205i | ||||
\(196\) | 4.21081e6 | + | 6.23981e6i | 0.559239 | + | 0.828711i | ||||
\(197\) | 5.84236e6 | + | 5.84236e6i | 0.764169 | + | 0.764169i | 0.977073 | − | 0.212904i | \(-0.0682922\pi\) |
−0.212904 | + | 0.977073i | \(0.568292\pi\) | |||||||
\(198\) | 128695. | − | 39361.5i | 0.0165792 | − | 0.00507079i | ||||
\(199\) | 2.72449e6 | 0.345721 | 0.172861 | − | 0.984946i | \(-0.444699\pi\) | ||||
0.172861 | + | 0.984946i | \(0.444699\pi\) | |||||||
\(200\) | 409769. | + | 3.88629e6i | 0.0512211 | + | 0.485786i | ||||
\(201\) | − | 2.70238e6i | − | 0.332780i | ||||||
\(202\) | −1.25824e7 | + | 3.84834e6i | −1.52654 | + | 0.466896i | ||||
\(203\) | −164233. | + | 164233.i | −0.0196324 | + | 0.0196324i | ||||
\(204\) | 738712. | − | 3.80484e6i | 0.0870131 | − | 0.448173i | ||||
\(205\) | 3.13287e6 | − | 3.13287e6i | 0.363648 | − | 0.363648i | ||||
\(206\) | −4.59452e6 | + | 8.64334e6i | −0.525580 | + | 0.988735i | ||||
\(207\) | − | 786599.i | − | 0.0886834i | ||||||
\(208\) | −4.79983e6 | − | 1.12938e7i | −0.533379 | − | 1.25502i | ||||
\(209\) | 575439. | 0.0630319 | ||||||||
\(210\) | 90178.8 | + | 47936.1i | 0.00973748 | + | 0.00517613i | ||||
\(211\) | 4.15605e6 | + | 4.15605e6i | 0.442419 | + | 0.442419i | 0.892824 | − | 0.450405i | \(-0.148720\pi\) |
−0.450405 | + | 0.892824i | \(0.648720\pi\) | |||||||
\(212\) | 466999. | − | 2.40534e6i | 0.0490127 | − | 0.252447i | ||||
\(213\) | 2.35798e6 | + | 2.35798e6i | 0.244007 | + | 0.244007i | ||||
\(214\) | 1.39629e6 | + | 4.56525e6i | 0.142474 | + | 0.465826i | ||||
\(215\) | −5.29454e6 | −0.532737 | ||||||||
\(216\) | 1.22004e6 | − | 1.50764e6i | 0.121063 | − | 0.149602i | ||||
\(217\) | 290077.i | 0.0283880i | ||||||||
\(218\) | −3.19731e6 | − | 1.04538e7i | −0.308613 | − | 1.00903i | ||||
\(219\) | 3.71884e6 | − | 3.71884e6i | 0.354059 | − | 0.354059i | ||||
\(220\) | 377962. | + | 560084.i | 0.0354960 | + | 0.0525999i | ||||
\(221\) | 8.23016e6 | − | 8.23016e6i | 0.762485 | − | 0.762485i | ||||
\(222\) | 5.24039e6 | + | 2.78562e6i | 0.478966 | + | 0.254603i | ||||
\(223\) | − | 2.24265e6i | − | 0.202230i | −0.994875 | − | 0.101115i | \(-0.967759\pi\) | ||
0.994875 | − | 0.101115i | \(-0.0322411\pi\) | |||||||
\(224\) | −113181. | − | 134732.i | −0.0100700 | − | 0.0119875i | ||||
\(225\) | −1.85469e6 | −0.162826 | ||||||||
\(226\) | −5.03789e6 | + | 9.47743e6i | −0.436439 | + | 0.821042i | ||||
\(227\) | −1.51072e7 | − | 1.51072e7i | −1.29154 | − | 1.29154i | −0.933837 | − | 0.357700i | \(-0.883561\pi\) |
−0.357700 | − | 0.933837i | \(-0.616439\pi\) | |||||||
\(228\) | 6.87399e6 | − | 4.63878e6i | 0.579969 | − | 0.391380i | ||||
\(229\) | 4.67653e6 | + | 4.67653e6i | 0.389419 | + | 0.389419i | 0.874480 | − | 0.485061i | \(-0.161203\pi\) |
−0.485061 | + | 0.874480i | \(0.661203\pi\) | |||||||
\(230\) | 3.77659e6 | − | 1.15508e6i | 0.310396 | − | 0.0949352i | ||||
\(231\) | 5795.02 | 0.000470131 | ||||||||
\(232\) | −1.39306e7 | + | 1.72145e7i | −1.11559 | + | 1.37858i | ||||
\(233\) | − | 1.98032e7i | − | 1.56555i | −0.622304 | − | 0.782776i | \(-0.713803\pi\) | ||
0.622304 | − | 0.782776i | \(-0.286197\pi\) | |||||||
\(234\) | 5.56946e6 | − | 1.70343e6i | 0.434676 | − | 0.132946i | ||||
\(235\) | 6.27535e6 | − | 6.27535e6i | 0.483542 | − | 0.483542i | ||||
\(236\) | −2.00205e7 | − | 3.88700e6i | −1.52314 | − | 0.295718i | ||||
\(237\) | −7.88715e6 | + | 7.88715e6i | −0.592482 | + | 0.592482i | ||||
\(238\) | 78336.9 | − | 147370.i | 0.00581079 | − | 0.0109314i | ||||
\(239\) | − | 3.78826e6i | − | 0.277489i | −0.990328 | − | 0.138745i | \(-0.955693\pi\) | ||
0.990328 | − | 0.138745i | \(-0.0443067\pi\) | |||||||
\(240\) | 9.03000e6 | + | 3.64371e6i | 0.653212 | + | 0.263579i | ||||
\(241\) | −1.52426e7 | −1.08895 | −0.544475 | − | 0.838777i | \(-0.683271\pi\) | ||||
−0.544475 | + | 0.838777i | \(0.683271\pi\) | |||||||
\(242\) | −1.24804e7 | − | 6.63420e6i | −0.880611 | − | 0.468104i | ||||
\(243\) | 650880. | + | 650880.i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 159017. | + | 30873.2i | 0.0109465 | + | 0.00212526i | ||||
\(245\) | −1.26838e7 | − | 1.26838e7i | −0.862482 | − | 0.862482i | ||||
\(246\) | −1.05965e6 | − | 3.46458e6i | −0.0711797 | − | 0.232726i | ||||
\(247\) | 2.49030e7 | 1.65257 | ||||||||
\(248\) | 2.90013e6 | + | 2.75051e7i | 0.190135 | + | 1.80326i | ||||
\(249\) | − | 7.45451e6i | − | 0.482860i | ||||||
\(250\) | 2.85199e6 | + | 9.32474e6i | 0.182527 | + | 0.596783i | ||||
\(251\) | −1.55084e7 | + | 1.55084e7i | −0.980720 | + | 0.980720i | −0.999818 | − | 0.0190975i | \(-0.993921\pi\) |
0.0190975 | + | 0.999818i | \(0.493921\pi\) | |||||||
\(252\) | 69225.4 | − | 46715.4i | 0.00432577 | − | 0.00291916i | ||||
\(253\) | 158458. | − | 158458.i | 0.00978483 | − | 0.00978483i | ||||
\(254\) | 3.62374e6 | + | 1.92626e6i | 0.221134 | + | 0.117548i | ||||
\(255\) | 9.23575e6i | 0.556996i | ||||||||
\(256\) | −1.20788e7 | − | 1.16438e7i | −0.719954 | − | 0.694022i | ||||
\(257\) | 2.30378e7 | 1.35720 | 0.678598 | − | 0.734510i | \(-0.262588\pi\) | ||||
0.678598 | + | 0.734510i | \(0.262588\pi\) | |||||||
\(258\) | −2.03217e6 | + | 3.82297e6i | −0.118331 | + | 0.222608i | ||||
\(259\) | 180703. | + | 180703.i | 0.0104008 | + | 0.0104008i | ||||
\(260\) | 1.63569e7 | + | 2.42385e7i | 0.930638 | + | 1.37907i | ||||
\(261\) | −7.43186e6 | − | 7.43186e6i | −0.418000 | − | 0.418000i | ||||
\(262\) | −1.68417e7 | + | 5.15105e6i | −0.936443 | + | 0.286413i | ||||
\(263\) | −1.14678e7 | −0.630395 | −0.315198 | − | 0.949026i | \(-0.602071\pi\) | ||||
−0.315198 | + | 0.949026i | \(0.602071\pi\) | |||||||
\(264\) | 549484. | − | 57937.4i | 0.0298637 | − | 0.00314882i | ||||
\(265\) | 5.83866e6i | 0.313744i | ||||||||
\(266\) | 341474. | − | 104440.i | 0.0181432 | − | 0.00554911i | ||||
\(267\) | −5.81310e6 | + | 5.81310e6i | −0.305403 | + | 0.305403i | ||||
\(268\) | 2.11460e6 | − | 1.08915e7i | 0.109856 | − | 0.565827i | ||||
\(269\) | −1.81452e7 | + | 1.81452e7i | −0.932191 | + | 0.932191i | −0.997843 | − | 0.0656520i | \(-0.979087\pi\) |
0.0656520 | + | 0.997843i | \(0.479087\pi\) | |||||||
\(270\) | −2.16920e6 | + | 4.08076e6i | −0.110207 | + | 0.207324i | ||||
\(271\) | 1.68065e7i | 0.844441i | 0.906493 | + | 0.422221i | \(0.138749\pi\) | ||||
−0.906493 | + | 0.422221i | \(0.861251\pi\) | |||||||
\(272\) | 5.95453e6 | − | 1.47568e7i | 0.295897 | − | 0.733305i | ||||
\(273\) | 250789. | 0.0123259 | ||||||||
\(274\) | 169791. | + | 90255.6i | 0.00825399 | + | 0.00438756i | ||||
\(275\) | −373623. | − | 373623.i | −0.0179653 | − | 0.0179653i | ||||
\(276\) | 615509. | − | 3.17026e6i | 0.0292757 | − | 0.150789i | ||||
\(277\) | −1.32183e7 | − | 1.32183e7i | −0.621922 | − | 0.621922i | 0.324101 | − | 0.946022i | \(-0.394938\pi\) |
−0.946022 | + | 0.324101i | \(0.894938\pi\) | |||||||
\(278\) | −1.24729e7 | − | 4.07810e7i | −0.580543 | − | 1.89812i | ||||
\(279\) | −1.31265e7 | −0.604418 | ||||||||
\(280\) | 325942. | + | 263763.i | 0.0148479 | + | 0.0120155i | ||||
\(281\) | 3.78604e7i | 1.70634i | 0.521632 | + | 0.853170i | \(0.325323\pi\) | ||||
−0.521632 | + | 0.853170i | \(0.674677\pi\) | |||||||
\(282\) | −2.12255e6 | − | 6.93979e6i | −0.0946476 | − | 0.309456i | ||||
\(283\) | 2.50461e7 | − | 2.50461e7i | 1.10505 | − | 1.10505i | 0.111254 | − | 0.993792i | \(-0.464513\pi\) |
0.993792 | − | 0.111254i | \(-0.0354866\pi\) | |||||||
\(284\) | 7.65838e6 | + | 1.13486e7i | 0.334335 | + | 0.495436i | ||||
\(285\) | −1.39729e7 | + | 1.39729e7i | −0.603603 | + | 0.603603i | ||||
\(286\) | 1.46510e6 | + | 778802.i | 0.0626283 | + | 0.0332912i | ||||
\(287\) | − | 156008.i | − | 0.00659933i | ||||||
\(288\) | 6.09689e6 | − | 5.12165e6i | 0.255230 | − | 0.214404i | ||||
\(289\) | −9.04457e6 | −0.374709 | ||||||||
\(290\) | 2.47683e7 | − | 4.65948e7i | 1.01555 | − | 1.91049i | ||||
\(291\) | 1.71010e7 | + | 1.71010e7i | 0.693971 | + | 0.693971i | ||||
\(292\) | 1.78982e7 | − | 1.20782e7i | 0.718886 | − | 0.485126i | ||||
\(293\) | 2.24773e7 | + | 2.24773e7i | 0.893596 | + | 0.893596i | 0.994860 | − | 0.101263i | \(-0.0322885\pi\) |
−0.101263 | + | 0.994860i | \(0.532289\pi\) | |||||||
\(294\) | −1.40267e7 | + | 4.29010e6i | −0.551969 | + | 0.168821i | ||||
\(295\) | 4.85972e7 | 1.89298 | ||||||||
\(296\) | 1.89408e7 | + | 1.53276e7i | 0.730339 | + | 0.591015i | ||||
\(297\) | 262236.i | 0.0100097i | ||||||||
\(298\) | −2.75572e7 | + | 8.42841e6i | −1.04132 | + | 0.318491i | ||||
\(299\) | 6.85753e6 | − | 6.85753e6i | 0.256539 | − | 0.256539i | ||||
\(300\) | −7.47505e6 | − | 1.45129e6i | −0.276854 | − | 0.0537514i | ||||
\(301\) | −131826. | + | 131826.i | −0.00483395 | + | 0.00483395i | ||||
\(302\) | 1.82281e7 | − | 3.42913e7i | 0.661791 | − | 1.24498i | ||||
\(303\) | − | 2.56386e7i | − | 0.921651i | ||||||
\(304\) | 3.13344e7 | − | 1.33170e7i | 1.11532 | − | 0.474008i | ||||
\(305\) | −385993. | −0.0136044 | ||||||||
\(306\) | 6.66875e6 | + | 3.54489e6i | 0.232745 | + | 0.123720i | ||||
\(307\) | −2.44973e7 | − | 2.44973e7i | −0.846650 | − | 0.846650i | 0.143063 | − | 0.989714i | \(-0.454305\pi\) |
−0.989714 | + | 0.143063i | \(0.954305\pi\) | |||||||
\(308\) | 23355.9 | + | 4534.57i | 0.000799365 | + | 0.000155197i | ||||
\(309\) | −1.34871e7 | − | 1.34871e7i | −0.457134 | − | 0.457134i | ||||
\(310\) | −1.92756e7 | − | 6.30227e7i | −0.647027 | − | 2.11549i | ||||
\(311\) | −2.12390e7 | −0.706078 | −0.353039 | − | 0.935609i | \(-0.614852\pi\) | ||||
−0.353039 | + | 0.935609i | \(0.614852\pi\) | |||||||
\(312\) | 2.37798e7 | − | 2.50733e6i | 0.782968 | − | 0.0825559i | ||||
\(313\) | 3.85664e7i | 1.25770i | 0.777527 | + | 0.628849i | \(0.216474\pi\) | ||||
−0.777527 | + | 0.628849i | \(0.783526\pi\) | |||||||
\(314\) | 1.56584e7 | + | 5.11961e7i | 0.505776 | + | 1.65367i | ||||
\(315\) | −140716. | + | 140716.i | −0.00450205 | + | 0.00450205i | ||||
\(316\) | −3.79596e7 | + | 2.56163e7i | −1.20298 | + | 0.811811i | ||||
\(317\) | −2.55878e7 | + | 2.55878e7i | −0.803257 | + | 0.803257i | −0.983603 | − | 0.180346i | \(-0.942278\pi\) |
0.180346 | + | 0.983603i | \(0.442278\pi\) | |||||||
\(318\) | 4.21585e6 | + | 2.24101e6i | 0.131100 | + | 0.0696888i | ||||
\(319\) | − | 2.99425e6i | − | 0.0922394i | ||||||
\(320\) | 3.35428e7 | + | 2.17513e7i | 1.02365 | + | 0.663798i | ||||
\(321\) | −9.30243e6 | −0.281243 | ||||||||
\(322\) | 65271.8 | − | 122791.i | 0.00195505 | − | 0.00367790i | ||||
\(323\) | 2.28344e7 | + | 2.28344e7i | 0.677613 | + | 0.677613i | ||||
\(324\) | 2.11396e6 | + | 3.13258e6i | 0.0621529 | + | 0.0921015i | ||||
\(325\) | −1.61691e7 | − | 1.61691e7i | −0.471017 | − | 0.471017i | ||||
\(326\) | −2.43998e7 | + | 7.46270e6i | −0.704259 | + | 0.215399i | ||||
\(327\) | 2.13012e7 | 0.609203 | ||||||||
\(328\) | −1.55973e6 | − | 1.47926e7i | −0.0442006 | − | 0.419202i | ||||
\(329\) | − | 312493.i | − | 0.00877512i | ||||||
\(330\) | −1.25904e6 | + | 385079.i | −0.0350346 | + | 0.0107154i | ||||
\(331\) | 4.02071e6 | − | 4.02071e6i | 0.110871 | − | 0.110871i | −0.649495 | − | 0.760366i | \(-0.725020\pi\) |
0.760366 | + | 0.649495i | \(0.225020\pi\) | |||||||
\(332\) | 5.83311e6 | − | 3.00442e7i | 0.159399 | − | 0.821007i | ||||
\(333\) | −8.17714e6 | + | 8.17714e6i | −0.221446 | + | 0.221446i | ||||
\(334\) | 2.24078e7 | − | 4.21541e7i | 0.601394 | − | 1.13136i | ||||
\(335\) | 2.64377e7i | 0.703218i | ||||||||
\(336\) | 315556. | − | 134111.i | 0.00831877 | − | 0.00353545i | ||||
\(337\) | 1.58536e7 | 0.414226 | 0.207113 | − | 0.978317i | \(-0.433593\pi\) | ||||
0.207113 | + | 0.978317i | \(0.433593\pi\) | |||||||
\(338\) | 2.93081e7 | + | 1.55792e7i | 0.758993 | + | 0.403456i | ||||
\(339\) | −1.47886e7 | − | 1.47886e7i | −0.379603 | − | 0.379603i | ||||
\(340\) | −7.22692e6 | + | 3.72233e7i | −0.183872 | + | 0.947060i | ||||
\(341\) | −2.64431e6 | − | 2.64431e6i | −0.0666881 | − | 0.0666881i | ||||
\(342\) | 4.72612e6 | + | 1.54523e7i | 0.118148 | + | 0.386292i | ||||
\(343\) | −1.26338e6 | −0.0313078 | ||||||||
\(344\) | −1.11818e7 | + | 1.38177e7i | −0.274685 | + | 0.339438i | ||||
\(345\) | 7.69541e6i | 0.187402i | ||||||||
\(346\) | 2.02260e7 | + | 6.61302e7i | 0.488295 | + | 1.59651i | ||||
\(347\) | 3.19130e7 | − | 3.19130e7i | 0.763798 | − | 0.763798i | −0.213208 | − | 0.977007i | \(-0.568391\pi\) |
0.977007 | + | 0.213208i | \(0.0683913\pi\) | |||||||
\(348\) | −2.41376e7 | − | 3.57683e7i | −0.572737 | − | 0.848713i | ||||
\(349\) | 2.14408e7 | − | 2.14408e7i | 0.504388 | − | 0.504388i | −0.408411 | − | 0.912798i | \(-0.633917\pi\) |
0.912798 | + | 0.408411i | \(0.133917\pi\) | |||||||
\(350\) | −289525. | − | 153902.i | −0.00675277 | − | 0.00358955i | ||||
\(351\) | 1.13487e7i | 0.262436i | ||||||||
\(352\) | 2.25994e6 | + | 196460.i | 0.0518167 | + | 0.00450450i | ||||
\(353\) | 4.67083e7 | 1.06187 | 0.530933 | − | 0.847414i | \(-0.321841\pi\) | ||||
0.530933 | + | 0.847414i | \(0.321841\pi\) | |||||||
\(354\) | 1.86527e7 | − | 3.50900e7i | 0.420467 | − | 0.790995i | ||||
\(355\) | −2.30685e7 | − | 2.30685e7i | −0.515625 | − | 0.515625i | ||||
\(356\) | −2.79775e7 | + | 1.88801e7i | −0.620096 | + | 0.418460i | ||||
\(357\) | 229956. | + | 229956.i | 0.00505406 | + | 0.00505406i | ||||
\(358\) | 3.55491e6 | − | 1.08728e6i | 0.0774783 | − | 0.0236969i | ||||
\(359\) | −2.17927e7 | −0.471006 | −0.235503 | − | 0.971874i | \(-0.575674\pi\) | ||||
−0.235503 | + | 0.971874i | \(0.575674\pi\) | |||||||
\(360\) | −1.19358e7 | + | 1.47495e7i | −0.255826 | + | 0.316133i | ||||
\(361\) | 2.20470e7i | 0.468627i | ||||||||
\(362\) | −2.00445e7 | + | 6.13063e6i | −0.422541 | + | 0.129235i | ||||
\(363\) | 1.94746e7 | − | 1.94746e7i | 0.407144 | − | 0.407144i | ||||
\(364\) | 1.01076e6 | + | 196241.i | 0.0209578 | + | 0.00406898i | ||||
\(365\) | −3.63819e7 | + | 3.63819e7i | −0.748182 | + | 0.748182i | ||||
\(366\) | −148153. | + | 278709.i | −0.00302181 | + | 0.00568471i | ||||
\(367\) | 8.36110e7i | 1.69147i | 0.533600 | + | 0.845737i | \(0.320839\pi\) | ||||
−0.533600 | + | 0.845737i | \(0.679161\pi\) | |||||||
\(368\) | 4.96143e6 | − | 1.22956e7i | 0.0995551 | − | 0.246722i | ||||
\(369\) | 7.05964e6 | 0.140509 | ||||||||
\(370\) | −5.12675e7 | − | 2.72521e7i | −1.01213 | − | 0.538016i | ||||
\(371\) | 145374. | + | 145374.i | 0.00284685 | + | 0.00284685i | ||||
\(372\) | −5.29045e7 | − | 1.02714e7i | −1.02769 | − | 0.199527i | ||||
\(373\) | −3.88117e7 | − | 3.88117e7i | −0.747887 | − | 0.747887i | 0.226195 | − | 0.974082i | \(-0.427371\pi\) |
−0.974082 | + | 0.226195i | \(0.927371\pi\) | |||||||
\(374\) | 629293. | + | 2.05751e6i | 0.0120292 | + | 0.0393303i | ||||
\(375\) | −1.90006e7 | −0.360308 | ||||||||
\(376\) | −3.12424e6 | − | 2.96306e7i | −0.0587734 | − | 0.557413i | ||||
\(377\) | − | 1.29581e8i | − | 2.41834i | ||||||
\(378\) | 47595.0 | + | 155615.i | 0.000881223 | + | 0.00288121i | ||||
\(379\) | −5.20448e7 | + | 5.20448e7i | −0.956004 | + | 0.956004i | −0.999072 | − | 0.0430678i | \(-0.986287\pi\) |
0.0430678 | + | 0.999072i | \(0.486287\pi\) | |||||||
\(380\) | −6.72492e7 | + | 4.53818e7i | −1.22557 | + | 0.827049i | ||||
\(381\) | −5.65451e6 | + | 5.65451e6i | −0.102240 | + | 0.102240i | ||||
\(382\) | 6.00852e7 | + | 3.19393e7i | 1.07790 | + | 0.572975i | ||||
\(383\) | − | 1.32415e7i | − | 0.235691i | −0.993032 | − | 0.117845i | \(-0.962401\pi\) | ||
0.993032 | − | 0.117845i | \(-0.0375987\pi\) | |||||||
\(384\) | 2.85802e7 | − | 1.58712e7i | 0.504745 | − | 0.280296i | ||||
\(385\) | −56693.5 | −0.000993462 | ||||||||
\(386\) | −1.72242e7 | + | 3.24027e7i | −0.299487 | + | 0.563403i | ||||
\(387\) | −5.96538e6 | − | 5.96538e6i | −0.102921 | − | 0.102921i | ||||
\(388\) | 5.55413e7 | + | 8.23041e7i | 0.950870 | + | 1.40905i | ||||
\(389\) | −2.91185e6 | − | 2.91185e6i | −0.0494675 | − | 0.0494675i | 0.681940 | − | 0.731408i | \(-0.261136\pi\) |
−0.731408 | + | 0.681940i | \(0.761136\pi\) | |||||||
\(390\) | −5.44868e7 | + | 1.66649e7i | −0.918539 | + | 0.280937i | ||||
\(391\) | 1.25758e7 | 0.210380 | ||||||||
\(392\) | −5.98895e7 | + | 6.31473e6i | −0.994243 | + | 0.104833i | ||||
\(393\) | − | 3.43176e7i | − | 0.565378i | ||||||
\(394\) | −6.32084e7 | + | 1.93324e7i | −1.03344 | + | 0.316080i | ||||
\(395\) | 7.71611e7 | − | 7.71611e7i | 1.25201 | − | 1.25201i | ||||
\(396\) | −205198. | + | 1.05690e6i | −0.00330436 | + | 0.0170196i | ||||
\(397\) | 1.15219e7 | − | 1.15219e7i | 0.184142 | − | 0.184142i | −0.609016 | − | 0.793158i | \(-0.708435\pi\) |
0.793158 | + | 0.609016i | \(0.208435\pi\) | |||||||
\(398\) | −1.02304e7 | + | 1.92458e7i | −0.162273 | + | 0.305272i | ||||
\(399\) | 695808.i | 0.0109539i | ||||||||
\(400\) | −2.89914e7 | − | 1.16984e7i | −0.452991 | − | 0.182787i | ||||
\(401\) | 7.10441e7 | 1.10178 | 0.550890 | − | 0.834578i | \(-0.314288\pi\) | ||||
0.550890 | + | 0.834578i | \(0.314288\pi\) | |||||||
\(402\) | 1.90896e7 | + | 1.01474e7i | 0.293845 | + | 0.156198i | ||||
\(403\) | −1.14436e8 | − | 1.14436e8i | −1.74843 | − | 1.74843i | ||||
\(404\) | 2.00621e7 | − | 1.03332e8i | 0.304251 | − | 1.56708i | ||||
\(405\) | −6.36765e6 | − | 6.36765e6i | −0.0958548 | − | 0.0958548i | ||||
\(406\) | −543448. | − | 1.77684e6i | −0.00812045 | − | 0.0265503i | ||||
\(407\) | −3.29452e6 | −0.0488663 | ||||||||
\(408\) | 2.41035e7 | + | 1.95054e7i | 0.354895 | + | 0.287193i | ||||
\(409\) | − | 1.89990e7i | − | 0.277691i | −0.990314 | − | 0.138845i | \(-0.955661\pi\) | ||
0.990314 | − | 0.138845i | \(-0.0443391\pi\) | |||||||
\(410\) | 1.03667e7 | + | 3.38945e7i | 0.150414 | + | 0.491788i | ||||
\(411\) | −264944. | + | 264944.i | −0.00381617 | + | 0.00381617i | ||||
\(412\) | −4.38042e7 | − | 6.49113e7i | −0.626359 | − | 0.928173i | ||||
\(413\) | 1.21000e6 | − | 1.21000e6i | 0.0171765 | − | 0.0171765i | ||||
\(414\) | 5.55653e6 | + | 2.95367e6i | 0.0783074 | + | 0.0416257i | ||||
\(415\) | 7.29285e7i | 1.02036i | ||||||||
\(416\) | 9.78026e7 | + | 8.50213e6i | 1.35853 | + | 0.118099i | ||||
\(417\) | 8.30977e7 | 1.14599 | ||||||||
\(418\) | −2.16077e6 | + | 4.06490e6i | −0.0295855 | + | 0.0556571i | ||||
\(419\) | −3.56420e7 | − | 3.56420e7i | −0.484529 | − | 0.484529i | 0.422045 | − | 0.906575i | \(-0.361312\pi\) |
−0.906575 | + | 0.422045i | \(0.861312\pi\) | |||||||
\(420\) | −677241. | + | 457023.i | −0.00914104 | + | 0.00616865i | ||||
\(421\) | 4.15849e7 | + | 4.15849e7i | 0.557301 | + | 0.557301i | 0.928538 | − | 0.371237i | \(-0.121066\pi\) |
−0.371237 | + | 0.928538i | \(0.621066\pi\) | |||||||
\(422\) | −4.49643e7 | + | 1.37524e7i | −0.598316 | + | 0.182996i | ||||
\(423\) | 1.41409e7 | 0.186834 | ||||||||
\(424\) | 1.52378e7 | + | 1.23309e7i | 0.199905 | + | 0.161770i | ||||
\(425\) | − | 2.96520e7i | − | 0.386266i | ||||||
\(426\) | −2.55110e7 | + | 7.80258e6i | −0.329988 | + | 0.100927i | ||||
\(427\) | −9610.64 | + | 9610.64i | −0.000123444 | + | 0.000123444i | ||||
\(428\) | −3.74920e7 | − | 7.27910e6i | −0.478197 | − | 0.0928424i | ||||
\(429\) | −2.28616e6 | + | 2.28616e6i | −0.0289557 | + | 0.0289557i | ||||
\(430\) | 1.98810e7 | − | 3.74006e7i | 0.250053 | − | 0.470407i | ||||
\(431\) | 6.32371e7i | 0.789842i | 0.918715 | + | 0.394921i | \(0.129228\pi\) | ||||
−0.918715 | + | 0.394921i | \(0.870772\pi\) | |||||||
\(432\) | 6.06876e6 | + | 1.42795e7i | 0.0752746 | + | 0.177118i | ||||
\(433\) | 4.88658e6 | 0.0601924 | 0.0300962 | − | 0.999547i | \(-0.490419\pi\) | ||||
0.0300962 | + | 0.999547i | \(0.490419\pi\) | |||||||
\(434\) | −2.04910e6 | − | 1.08924e6i | −0.0250666 | − | 0.0133246i | ||||
\(435\) | 7.27069e7 | + | 7.27069e7i | 0.883299 | + | 0.883299i | ||||
\(436\) | 8.58513e7 | + | 1.66681e7i | 1.03583 | + | 0.201107i | ||||
\(437\) | 1.90261e7 | + | 1.90261e7i | 0.227984 | + | 0.227984i | ||||
\(438\) | 1.23057e7 | + | 4.02341e7i | 0.146448 | + | 0.478819i | ||||
\(439\) | 1.89631e7 | 0.224138 | 0.112069 | − | 0.993700i | \(-0.464252\pi\) | ||||
0.112069 | + | 0.993700i | \(0.464252\pi\) | |||||||
\(440\) | −5.37568e6 | + | 566810.i | −0.0631066 | + | 0.00665394i | ||||
\(441\) | − | 2.85817e7i | − | 0.333252i | ||||||
\(442\) | 2.72336e7 | + | 8.90420e7i | 0.315383 | + | 1.03116i | ||||
\(443\) | −7.56690e7 | + | 7.56690e7i | −0.870376 | + | 0.870376i | −0.992513 | − | 0.122137i | \(-0.961025\pi\) |
0.122137 | + | 0.992513i | \(0.461025\pi\) | |||||||
\(444\) | −3.93553e7 | + | 2.65581e7i | −0.449628 | + | 0.303423i | ||||
\(445\) | 5.68704e7 | − | 5.68704e7i | 0.645366 | − | 0.645366i | ||||
\(446\) | 1.58420e7 | + | 8.42112e6i | 0.178569 | + | 0.0949216i | ||||
\(447\) | − | 5.61522e7i | − | 0.628701i | ||||||
\(448\) | 1.37674e6 | − | 293590.i | 0.0153115 | − | 0.00326519i | ||||
\(449\) | −3.34359e7 | −0.369381 | −0.184690 | − | 0.982797i | \(-0.559128\pi\) | ||||
−0.184690 | + | 0.982797i | \(0.559128\pi\) | |||||||
\(450\) | 6.96436e6 | − | 1.31015e7i | 0.0764264 | − | 0.143776i | ||||
\(451\) | 1.42214e6 | + | 1.42214e6i | 0.0155029 | + | 0.0155029i | ||||
\(452\) | −4.80313e7 | − | 7.11753e7i | −0.520126 | − | 0.770751i | ||||
\(453\) | 5.35083e7 | + | 5.35083e7i | 0.575608 | + | 0.575608i | ||||
\(454\) | 1.63445e8 | − | 4.99898e7i | 1.74664 | − | 0.534213i | ||||
\(455\) | −2.45350e6 | −0.0260467 | ||||||||
\(456\) | 6.95653e6 | + | 6.59764e7i | 0.0733666 | + | 0.695816i | ||||
\(457\) | 5.54209e7i | 0.580664i | 0.956926 | + | 0.290332i | \(0.0937657\pi\) | ||||
−0.956926 | + | 0.290332i | \(0.906234\pi\) | |||||||
\(458\) | −5.05953e7 | + | 1.54746e7i | −0.526640 | + | 0.161074i | ||||
\(459\) | −1.04060e7 | + | 1.04060e7i | −0.107608 | + | 0.107608i | ||||
\(460\) | −6.02161e6 | + | 3.10151e7i | −0.0618642 | + | 0.318640i | ||||
\(461\) | 2.76199e7 | − | 2.76199e7i | 0.281916 | − | 0.281916i | −0.551957 | − | 0.833873i | \(-0.686119\pi\) |
0.833873 | + | 0.551957i | \(0.186119\pi\) | |||||||
\(462\) | −21760.3 | + | 40936.0i | −0.000220667 | + | 0.000415126i | ||||
\(463\) | 6.48037e7i | 0.652915i | 0.945212 | + | 0.326457i | \(0.105855\pi\) | ||||
−0.945212 | + | 0.326457i | \(0.894145\pi\) | |||||||
\(464\) | −6.92941e7 | − | 1.63046e8i | −0.693653 | − | 1.63214i | ||||
\(465\) | 1.28419e8 | 1.27723 | ||||||||
\(466\) | 1.39890e8 | + | 7.43608e7i | 1.38238 | + | 0.734829i | ||||
\(467\) | 1.01369e8 | + | 1.01369e8i | 0.995297 | + | 0.995297i | 0.999989 | − | 0.00469233i | \(-0.00149362\pi\) |
−0.00469233 | + | 0.999989i | \(0.501494\pi\) | |||||||
\(468\) | −8.88027e6 | + | 4.57390e7i | −0.0866340 | + | 0.446220i | ||||
\(469\) | 658260. | + | 658260.i | 0.00638085 | + | 0.00638085i | ||||
\(470\) | 2.07652e7 | + | 6.78929e7i | 0.200005 | + | 0.653929i | ||||
\(471\) | −1.04320e8 | −0.998402 | ||||||||
\(472\) | 1.02635e8 | − | 1.26829e8i | 0.976040 | − | 1.20613i | ||||
\(473\) | − | 2.40342e6i | − | 0.0227115i | ||||||
\(474\) | −2.60986e7 | − | 8.53310e7i | −0.245066 | − | 0.801257i | ||||
\(475\) | 4.48608e7 | − | 4.48608e7i | 0.418588 | − | 0.418588i | ||||
\(476\) | 746864. | + | 1.10674e6i | 0.00692501 | + | 0.0102619i | ||||
\(477\) | −6.57845e6 | + | 6.57845e6i | −0.0606133 | + | 0.0606133i | ||||
\(478\) | 2.67603e7 | + | 1.42249e7i | 0.245023 | + | 0.130246i | ||||
\(479\) | − | 5.97214e7i | − | 0.543404i | −0.962381 | − | 0.271702i | \(-0.912413\pi\) | ||
0.962381 | − | 0.271702i | \(-0.0875866\pi\) | |||||||
\(480\) | −5.96467e7 | + | 5.01058e7i | −0.539341 | + | 0.453069i | ||||
\(481\) | −1.42576e8 | −1.28118 | ||||||||
\(482\) | 5.72358e7 | − | 1.07674e8i | 0.511124 | − | 0.961542i | ||||
\(483\) | 191604. | + | 191604.i | 0.00170045 | + | 0.00170045i | ||||
\(484\) | 9.37279e7 | − | 6.32505e7i | 0.826671 | − | 0.557863i | ||||
\(485\) | −1.67301e8 | − | 1.67301e8i | −1.46647 | − | 1.46647i | ||||
\(486\) | −7.04186e6 | + | 2.15376e6i | −0.0613449 | + | 0.0187624i | ||||
\(487\) | −8.93709e7 | −0.773765 | −0.386882 | − | 0.922129i | \(-0.626448\pi\) | ||||
−0.386882 | + | 0.922129i | \(0.626448\pi\) | |||||||
\(488\) | −815195. | + | 1.00737e6i | −0.00701459 | + | 0.00866818i | ||||
\(489\) | − | 4.97184e7i | − | 0.425197i | ||||||
\(490\) | 1.37225e8 | − | 4.19706e7i | 1.16640 | − | 0.356745i | ||||
\(491\) | −5.33343e7 | + | 5.33343e7i | −0.450570 | + | 0.450570i | −0.895544 | − | 0.444974i | \(-0.853213\pi\) |
0.444974 | + | 0.895544i | \(0.353213\pi\) | |||||||
\(492\) | 2.84528e7 | + | 5.52413e6i | 0.238907 | + | 0.0463840i | ||||
\(493\) | 1.18817e8 | − | 1.18817e8i | 0.991604 | − | 0.991604i | ||||
\(494\) | −9.35106e7 | + | 1.75915e8i | −0.775675 | + | 1.45922i | ||||
\(495\) | − | 2.56549e6i | − | 0.0211522i | ||||||
\(496\) | −2.05186e8 | − | 8.27949e7i | −1.68152 | − | 0.678514i | ||||
\(497\) | −1.14874e6 | −0.00935736 | ||||||||
\(498\) | 5.26586e7 | + | 2.79916e7i | 0.426365 | + | 0.226642i | ||||
\(499\) | −1.13240e8 | − | 1.13240e8i | −0.911379 | − | 0.911379i | 0.0850014 | − | 0.996381i | \(-0.472911\pi\) |
−0.996381 | + | 0.0850014i | \(0.972911\pi\) | |||||||
\(500\) | −7.65791e7 | − | 1.48679e7i | −0.612633 | − | 0.118943i | ||||
\(501\) | 6.57776e7 | + | 6.57776e7i | 0.523076 | + | 0.523076i | ||||
\(502\) | −5.13173e7 | − | 1.67785e8i | −0.405651 | − | 1.32630i | ||||
\(503\) | −4.14356e7 | −0.325589 | −0.162794 | − | 0.986660i | \(-0.552051\pi\) | ||||
−0.162794 | + | 0.986660i | \(0.552051\pi\) | |||||||
\(504\) | 70056.6 | + | 664423.i | 0.000547214 | + | 0.00518983i | ||||
\(505\) | 2.50826e8i | 1.94760i | ||||||||
\(506\) | 524339. | + | 1.71436e6i | 0.00404726 | + | 0.0132327i | ||||
\(507\) | −4.57326e7 | + | 4.57326e7i | −0.350915 | + | 0.350915i | ||||
\(508\) | −2.72142e7 | + | 1.83650e7i | −0.207589 | + | 0.140088i | ||||
\(509\) | −7.15789e7 | + | 7.15789e7i | −0.542790 | + | 0.542790i | −0.924346 | − | 0.381556i | \(-0.875388\pi\) |
0.381556 | + | 0.924346i | \(0.375388\pi\) | |||||||
\(510\) | −6.52413e7 | − | 3.46802e7i | −0.491827 | − | 0.261439i | ||||
\(511\) | 1.81171e6i | 0.0135777i | ||||||||
\(512\) | 1.27607e8 | − | 4.16026e7i | 0.950748 | − | 0.309963i | ||||
\(513\) | −3.14866e7 | −0.233224 | ||||||||
\(514\) | −8.65069e7 | + | 1.62739e8i | −0.637032 | + | 1.19840i | ||||
\(515\) | 1.31946e8 | + | 1.31946e8i | 0.965997 | + | 0.965997i | ||||
\(516\) | −1.93747e7 | − | 2.87104e7i | −0.141021 | − | 0.208973i | ||||
\(517\) | 2.84865e6 | + | 2.84865e6i | 0.0206142 | + | 0.0206142i | ||||
\(518\) | −1.95502e6 | + | 597946.i | −0.0140657 | + | 0.00430202i | ||||
\(519\) | −1.34751e8 | −0.963894 | ||||||||
\(520\) | −2.32641e8 | + | 2.45296e7i | −1.65453 | + | 0.174454i | ||||
\(521\) | 7.24342e7i | 0.512189i | 0.966652 | + | 0.256095i | \(0.0824358\pi\) | ||||
−0.966652 | + | 0.256095i | \(0.917564\pi\) | |||||||
\(522\) | 8.04052e7 | − | 2.45921e7i | 0.565292 | − | 0.172895i | ||||
\(523\) | −1.89689e8 | + | 1.89689e8i | −1.32598 | + | 1.32598i | −0.417135 | + | 0.908845i | \(0.636966\pi\) |
−0.908845 | + | 0.417135i | \(0.863034\pi\) | |||||||
\(524\) | 2.68533e7 | − | 1.38312e8i | 0.186640 | − | 0.961313i | ||||
\(525\) | 451776. | − | 451776.i | 0.00312209 | − | 0.00312209i | ||||
\(526\) | 4.30615e7 | − | 8.10085e7i | 0.295891 | − | 0.556639i | ||||
\(527\) | − | 2.09861e8i | − | 1.43384i | ||||||
\(528\) | −1.65404e6 | + | 4.09911e6i | −0.0112368 | + | 0.0278476i | ||||
\(529\) | −1.37558e8 | −0.929217 | ||||||||
\(530\) | −4.12443e7 | − | 2.19241e7i | −0.277036 | − | 0.147263i | ||||
\(531\) | 5.47547e7 | + | 5.47547e7i | 0.365711 | + | 0.365711i | ||||
\(532\) | −544466. | + | 2.80434e6i | −0.00361606 | + | 0.0186250i | ||||
\(533\) | 6.15455e7 | + | 6.15455e7i | 0.406457 | + | 0.406457i | ||||
\(534\) | −1.92356e7 | − | 6.28918e7i | −0.126323 | − | 0.413019i | ||||
\(535\) | 9.10069e7 | 0.594310 | ||||||||
\(536\) | 6.89973e7 | + | 5.58350e7i | 0.448062 | + | 0.362587i | ||||
\(537\) | 7.24370e6i | 0.0467776i | ||||||||
\(538\) | −6.00425e7 | − | 1.96313e8i | −0.385578 | − | 1.26067i | ||||
\(539\) | 5.75770e6 | − | 5.75770e6i | 0.0367691 | − | 0.0367691i | ||||
\(540\) | −2.06812e7 | − | 3.06464e7i | −0.131339 | − | 0.194625i | ||||
\(541\) | −1.36734e8 | + | 1.36734e8i | −0.863545 | + | 0.863545i | −0.991748 | − | 0.128203i | \(-0.959079\pi\) |
0.128203 | + | 0.991748i | \(0.459079\pi\) | |||||||
\(542\) | −1.18721e8 | − | 6.31083e7i | −0.745641 | − | 0.396359i | ||||
\(543\) | − | 4.08438e7i | − | 0.255110i | ||||||
\(544\) | 8.18825e7 | + | 9.74743e7i | 0.508621 | + | 0.605471i | ||||
\(545\) | −2.08393e8 | −1.28734 | ||||||||
\(546\) | −941710. | + | 1.77157e6i | −0.00578548 | + | 0.0108838i | ||||
\(547\) | 5.12718e7 | + | 5.12718e7i | 0.313269 | + | 0.313269i | 0.846175 | − | 0.532906i | \(-0.178900\pi\) |
−0.532906 | + | 0.846175i | \(0.678900\pi\) | |||||||
\(548\) | −1.27513e6 | + | 860497.i | −0.00774842 | + | 0.00522887i | ||||
\(549\) | −434900. | − | 434900.i | −0.00262828 | − | 0.00262828i | ||||
\(550\) | 4.04222e6 | − | 1.23632e6i | 0.0242958 | − | 0.00743092i | ||||
\(551\) | 3.59520e8 | 2.14916 | ||||||||
\(552\) | 2.00835e7 | + | 1.62523e7i | 0.119405 | + | 0.0966266i | ||||
\(553\) | − | 3.84239e6i | − | 0.0227209i | ||||||
\(554\) | 1.43008e8 | − | 4.37393e7i | 0.841070 | − | 0.257243i | ||||
\(555\) | 7.99981e7 | − | 7.99981e7i | 0.467951 | − | 0.467951i | ||||
\(556\) | 3.34912e8 | + | 6.50235e7i | 1.94853 | + | 0.378308i | ||||
\(557\) | 5.82264e7 | − | 5.82264e7i | 0.336941 | − | 0.336941i | −0.518274 | − | 0.855215i | \(-0.673425\pi\) |
0.855215 | + | 0.518274i | \(0.173425\pi\) | |||||||
\(558\) | 4.92901e7 | − | 9.27258e7i | 0.283698 | − | 0.533701i | ||||
\(559\) | − | 1.04012e8i | − | 0.595452i | ||||||
\(560\) | −3.08713e6 | + | 1.31202e6i | −0.0175789 | + | 0.00747097i | ||||
\(561\) | −4.19250e6 | −0.0237457 | ||||||||
\(562\) | −2.67445e8 | − | 1.42165e8i | −1.50670 | − | 0.800912i | ||||
\(563\) | 8.25505e6 | + | 8.25505e6i | 0.0462588 | + | 0.0462588i | 0.729858 | − | 0.683599i | \(-0.239586\pi\) |
−0.683599 | + | 0.729858i | \(0.739586\pi\) | |||||||
\(564\) | 5.69928e7 | + | 1.10652e7i | 0.317675 | + | 0.0616768i | ||||
\(565\) | 1.44679e8 | + | 1.44679e8i | 0.802160 | + | 0.802160i | ||||
\(566\) | 8.28776e7 | + | 2.70973e8i | 0.457075 | + | 1.49443i | ||||
\(567\) | −317090. | −0.00173953 | ||||||||
\(568\) | −1.08924e8 | + | 1.14849e7i | −0.594397 | + | 0.0626731i | ||||
\(569\) | 8.93722e7i | 0.485138i | 0.970134 | + | 0.242569i | \(0.0779902\pi\) | ||||
−0.970134 | + | 0.242569i | \(0.922010\pi\) | |||||||
\(570\) | −4.62363e7 | − | 1.51172e8i | −0.249666 | − | 0.816297i | ||||
\(571\) | −3.04844e7 | + | 3.04844e7i | −0.163746 | + | 0.163746i | −0.784224 | − | 0.620478i | \(-0.786939\pi\) |
0.620478 | + | 0.784224i | \(0.286939\pi\) | |||||||
\(572\) | −1.10029e7 | + | 7.42509e6i | −0.0587921 | + | 0.0396747i | ||||
\(573\) | −9.37573e7 | + | 9.37573e7i | −0.498358 | + | 0.498358i | ||||
\(574\) | 1.10204e6 | + | 585807.i | 0.00582721 | + | 0.00309755i | ||||
\(575\) | − | 2.47066e7i | − | 0.129960i | ||||||
\(576\) | 1.32855e7 | + | 6.23002e7i | 0.0695202 | + | 0.326003i | ||||
\(577\) | −5.99952e7 | −0.312312 | −0.156156 | − | 0.987732i | \(-0.549910\pi\) | ||||
−0.156156 | + | 0.987732i | \(0.549910\pi\) | |||||||
\(578\) | 3.39623e7 | − | 6.38908e7i | 0.175879 | − | 0.330868i | ||||
\(579\) | −5.05613e7 | − | 5.05613e7i | −0.260485 | − | 0.260485i | ||||
\(580\) | 2.36141e8 | + | 3.49927e8i | 1.21028 | + | 1.79346i | ||||
\(581\) | 1.81581e6 | + | 1.81581e6i | 0.00925853 | + | 0.00925853i | ||||
\(582\) | −1.85015e8 | + | 5.65871e7i | −0.938508 | + | 0.287044i | ||||
\(583\) | −2.65042e6 | −0.0133755 | ||||||||
\(584\) | 1.81131e7 | + | 1.71786e8i | 0.0909398 | + | 0.862482i | ||||
\(585\) | − | 1.11026e8i | − | 0.554569i | ||||||
\(586\) | −2.43182e8 | + | 7.43775e7i | −1.20848 | + | 0.369614i | ||||
\(587\) | 9.99854e7 | − | 9.99854e7i | 0.494336 | − | 0.494336i | −0.415333 | − | 0.909669i | \(-0.636335\pi\) |
0.909669 | + | 0.415333i | \(0.136335\pi\) | |||||||
\(588\) | 2.23650e7 | − | 1.15194e8i | 0.110011 | − | 0.566628i | ||||
\(589\) | 3.17501e8 | − | 3.17501e8i | 1.55382 | − | 1.55382i | ||||
\(590\) | −1.82482e8 | + | 3.43290e8i | −0.888514 | + | 1.67150i | ||||
\(591\) | − | 1.28797e8i | − | 0.623941i | ||||||
\(592\) | −1.79397e8 | + | 7.62431e7i | −0.864668 | + | 0.367481i | ||||
\(593\) | −1.00872e8 | −0.483734 | −0.241867 | − | 0.970309i | \(-0.577760\pi\) | ||||
−0.241867 | + | 0.970309i | \(0.577760\pi\) | |||||||
\(594\) | −1.85243e6 | − | 984693.i | −0.00883859 | − | 0.00469831i | ||||
\(595\) | −2.24970e6 | − | 2.24970e6i | −0.0106800 | − | 0.0106800i | ||||
\(596\) | 4.39387e7 | − | 2.26312e8i | 0.207543 | − | 1.06898i | ||||
\(597\) | −3.00313e7 | − | 3.00313e7i | −0.141140 | − | 0.141140i | ||||
\(598\) | 2.26916e7 | + | 7.41915e7i | 0.106111 | + | 0.346937i | ||||
\(599\) | 3.34581e7 | 0.155676 | 0.0778379 | − | 0.996966i | \(-0.475198\pi\) | ||||
0.0778379 | + | 0.996966i | \(0.475198\pi\) | |||||||
\(600\) | 3.83206e7 | − | 4.73542e7i | 0.177410 | − | 0.219232i | ||||
\(601\) | − | 1.30304e8i | − | 0.600251i | −0.953900 | − | 0.300126i | \(-0.902971\pi\) | ||
0.953900 | − | 0.300126i | \(-0.0970286\pi\) | |||||||
\(602\) | −436213. | − | 1.42623e6i | −0.00199945 | − | 0.00653730i | ||||
\(603\) | −2.97875e7 | + | 2.97875e7i | −0.135857 | + | 0.135857i | ||||
\(604\) | 1.73787e8 | + | 2.57527e8i | 0.788690 | + | 1.16872i | ||||
\(605\) | −1.90522e8 | + | 1.90522e8i | −0.860359 | + | 0.860359i | ||||
\(606\) | 1.81111e8 | + | 9.62728e7i | 0.813818 | + | 0.432599i | ||||
\(607\) | − | 3.04854e8i | − | 1.36309i | −0.731775 | − | 0.681546i | \(-0.761308\pi\) | ||
0.731775 | − | 0.681546i | \(-0.238692\pi\) | |||||||
\(608\) | −2.35890e7 | + | 2.71351e8i | −0.104954 | + | 1.20732i | ||||
\(609\) | 3.62058e6 | 0.0160298 | ||||||||
\(610\) | 1.44940e6 | − | 2.72665e6i | 0.00638556 | − | 0.0120127i | ||||
\(611\) | 1.23280e8 | + | 1.23280e8i | 0.540466 | + | 0.540466i | ||||
\(612\) | −5.00822e7 | + | 3.37970e7i | −0.218489 | + | 0.147443i | ||||
\(613\) | −6.47373e7 | − | 6.47373e7i | −0.281043 | − | 0.281043i | 0.552482 | − | 0.833525i | \(-0.313681\pi\) |
−0.833525 | + | 0.552482i | \(0.813681\pi\) | |||||||
\(614\) | 2.65037e8 | − | 8.10618e7i | 1.14499 | − | 0.350196i | ||||
\(615\) | −6.90654e7 | −0.296917 | ||||||||
\(616\) | −119734. | + | 147959.i | −0.000512240 | + | 0.000632993i | ||||
\(617\) | − | 1.34382e8i | − | 0.572117i | −0.958212 | − | 0.286059i | \(-0.907655\pi\) | ||
0.958212 | − | 0.286059i | \(-0.0923452\pi\) | |||||||
\(618\) | 1.45917e8 | − | 4.46290e7i | 0.618216 | − | 0.189083i | ||||
\(619\) | 1.65022e8 | − | 1.65022e8i | 0.695776 | − | 0.695776i | −0.267720 | − | 0.963497i | \(-0.586270\pi\) |
0.963497 | + | 0.267720i | \(0.0862703\pi\) | |||||||
\(620\) | 5.17572e8 | + | 1.00487e8i | 2.17168 | + | 0.421633i | ||||
\(621\) | −8.67045e6 | + | 8.67045e6i | −0.0362049 | + | 0.0362049i | ||||
\(622\) | 7.97523e7 | − | 1.50032e8i | 0.331415 | − | 0.623467i | ||||
\(623\) | − | 2.83197e6i | − | 0.0117118i | ||||||
\(624\) | −7.15811e7 | + | 1.77395e8i | −0.294608 | + | 0.730110i | ||||
\(625\) | 3.05143e8 | 1.24987 | ||||||||
\(626\) | −2.72433e8 | − | 1.44817e8i | −1.11055 | − | 0.590331i | ||||
\(627\) | −6.34289e6 | − | 6.34289e6i | −0.0257327 | − | 0.0257327i | ||||
\(628\) | −4.20446e8 | − | 8.16299e7i | −1.69758 | − | 0.329587i | ||||
\(629\) | −1.30732e8 | − | 1.30732e8i | −0.525329 | − | 0.525329i | ||||
\(630\) | −465628. | − | 1.52240e6i | −0.00186216 | − | 0.00608846i | ||||
\(631\) | 3.33511e8 | 1.32746 | 0.663731 | − | 0.747971i | \(-0.268972\pi\) | ||||
0.663731 | + | 0.747971i | \(0.268972\pi\) | |||||||
\(632\) | −3.84154e7 | − | 3.64335e8i | −0.152179 | − | 1.44328i | ||||
\(633\) | − | 9.16219e7i | − | 0.361234i | ||||||
\(634\) | −8.46700e7 | − | 2.76834e8i | −0.332248 | − | 1.08630i | ||||
\(635\) | 5.53189e7 | − | 5.53189e7i | 0.216049 | − | 0.216049i | ||||
\(636\) | −3.16610e7 | + | 2.13658e7i | −0.123070 | + | 0.0830516i | ||||
\(637\) | 2.49174e8 | − | 2.49174e8i | 0.964015 | − | 0.964015i | ||||
\(638\) | 2.11514e7 | + | 1.12434e7i | 0.0814474 | + | 0.0432948i | ||||
\(639\) | − | 5.19827e7i | − | 0.199231i | ||||||
\(640\) | −2.79604e8 | + | 1.55270e8i | −1.06661 | + | 0.592309i | ||||
\(641\) | −2.80056e8 | −1.06334 | −0.531669 | − | 0.846952i | \(-0.678435\pi\) | ||||
−0.531669 | + | 0.846952i | \(0.678435\pi\) | |||||||
\(642\) | 3.49305e7 | − | 6.57123e7i | 0.132008 | − | 0.248337i | ||||
\(643\) | −3.76599e7 | − | 3.76599e7i | −0.141660 | − | 0.141660i | 0.632721 | − | 0.774380i | \(-0.281938\pi\) |
−0.774380 | + | 0.632721i | \(0.781938\pi\) | |||||||
\(644\) | 622301. | + | 922160.i | 0.00232993 | + | 0.00345262i | ||||
\(645\) | 5.83602e7 | + | 5.83602e7i | 0.217489 | + | 0.217489i | ||||
\(646\) | −2.47045e8 | + | 7.55591e7i | −0.916386 | + | 0.280278i | ||||
\(647\) | 2.17484e8 | 0.802999 | 0.401500 | − | 0.915859i | \(-0.368489\pi\) | ||||
0.401500 | + | 0.915859i | \(0.368489\pi\) | |||||||
\(648\) | −3.00664e7 | + | 3.17019e6i | −0.110499 | + | 0.0116509i | ||||
\(649\) | 2.20604e7i | 0.0807009i | ||||||||
\(650\) | 1.74933e8 | − | 5.35037e7i | 0.636990 | − | 0.194825i | ||||
\(651\) | 3.19743e6 | − | 3.19743e6i | 0.0115893 | − | 0.0115893i | ||||
\(652\) | 3.89043e7 | − | 2.00382e8i | 0.140364 | − | 0.722963i | ||||
\(653\) | −1.83718e7 | + | 1.83718e7i | −0.0659800 | + | 0.0659800i | −0.739327 | − | 0.673347i | \(-0.764856\pi\) |
0.673347 | + | 0.739327i | \(0.264856\pi\) | |||||||
\(654\) | −7.99860e7 | + | 1.50472e8i | −0.285944 | + | 0.537926i | ||||
\(655\) | 3.35734e8i | 1.19473i | ||||||||
\(656\) | 1.10352e8 | + | 4.45283e7i | 0.390902 | + | 0.157734i | ||||
\(657\) | −8.19833e7 | −0.289088 | ||||||||
\(658\) | 2.20745e6 | + | 1.17341e6i | 0.00774843 | + | 0.00411881i | ||||
\(659\) | 2.77669e8 | + | 2.77669e8i | 0.970221 | + | 0.970221i | 0.999569 | − | 0.0293478i | \(-0.00934305\pi\) |
−0.0293478 | + | 0.999569i | \(0.509343\pi\) | |||||||
\(660\) | 2.00748e6 | − | 1.03398e7i | 0.00698264 | − | 0.0359650i | ||||
\(661\) | 9.11648e7 | + | 9.11648e7i | 0.315662 | + | 0.315662i | 0.847098 | − | 0.531436i | \(-0.178347\pi\) |
−0.531436 | + | 0.847098i | \(0.678347\pi\) | |||||||
\(662\) | 1.33046e7 | + | 4.35000e7i | 0.0458592 | + | 0.149939i | ||||
\(663\) | −1.81437e8 | −0.622567 | ||||||||
\(664\) | 1.90329e8 | + | 1.54021e8i | 0.650131 | + | 0.526109i | ||||
\(665\) | − | 6.80718e6i | − | 0.0231474i | ||||||
\(666\) | −2.70582e7 | − | 8.84684e7i | −0.0915959 | − | 0.299478i | ||||
\(667\) | 9.90007e7 | − | 9.90007e7i | 0.333627 | − | 0.333627i | ||||
\(668\) | 2.13636e8 | + | 3.16577e8i | 0.716711 | + | 1.06206i | ||||
\(669\) | −2.47200e7 | + | 2.47200e7i | −0.0825602 | + | 0.0825602i | ||||
\(670\) | −1.86756e8 | − | 9.92735e7i | −0.620941 | − | 0.330072i | ||||
\(671\) | − | 175219.i | − | 0.000579980i | ||||||
\(672\) | −237555. | + | 2.73267e6i | −0.000782811 | + | 0.00900492i | ||||
\(673\) | −5.24674e8 | −1.72125 | −0.860626 | − | 0.509238i | \(-0.829927\pi\) | ||||
−0.860626 | + | 0.509238i | \(0.829927\pi\) | |||||||
\(674\) | −5.95300e7 | + | 1.11990e8i | −0.194427 | + | 0.365761i | ||||
\(675\) | 2.04437e7 | + | 2.04437e7i | 0.0664736 | + | 0.0664736i | ||||
\(676\) | −2.20103e8 | + | 1.48533e8i | −0.712503 | + | 0.480819i | ||||
\(677\) | 4.13584e8 | + | 4.13584e8i | 1.33290 | + | 1.33290i | 0.902764 | + | 0.430136i | \(0.141534\pi\) |
0.430136 | + | 0.902764i | \(0.358466\pi\) | |||||||
\(678\) | 1.59998e8 | − | 4.89357e7i | 0.513364 | − | 0.157013i | ||||
\(679\) | −8.33109e6 | −0.0266129 | ||||||||
\(680\) | −2.35808e8 | − | 1.90824e8i | −0.749949 | − | 0.606885i | ||||
\(681\) | 3.33045e8i | 1.05454i | ||||||||
\(682\) | 2.86087e7 | − | 8.75002e6i | 0.0901872 | − | 0.0275839i | ||||
\(683\) | −1.09574e8 | + | 1.09574e8i | −0.343911 | + | 0.343911i | −0.857836 | − | 0.513924i | \(-0.828191\pi\) |
0.513924 | + | 0.857836i | \(0.328191\pi\) | |||||||
\(684\) | −1.26902e8 | − | 2.46381e7i | −0.396552 | − | 0.0769908i | ||||
\(685\) | 2.59198e6 | − | 2.59198e6i | 0.00806418 | − | 0.00806418i | ||||
\(686\) | 4.74399e6 | − | 8.92452e6i | 0.0146951 | − | 0.0276447i | ||||
\(687\) | − | 1.03096e8i | − | 0.317959i | ||||||
\(688\) | −5.56208e7 | − | 1.30873e8i | −0.170794 | − | 0.401871i | ||||
\(689\) | −1.14701e8 | −0.350679 | ||||||||
\(690\) | −5.43603e7 | − | 2.88962e7i | −0.165476 | − | 0.0879616i | ||||
\(691\) | −2.60873e8 | − | 2.60873e8i | −0.790669 | − | 0.790669i | 0.190934 | − | 0.981603i | \(-0.438848\pi\) |
−0.981603 | + | 0.190934i | \(0.938848\pi\) | |||||||
\(692\) | −5.43092e8 | − | 1.05442e8i | −1.63891 | − | 0.318196i | ||||
\(693\) | −63876.8 | − | 63876.8i | −0.000191930 | − | 0.000191930i | ||||
\(694\) | 1.05600e8 | + | 3.45266e8i | 0.315927 | + | 1.03294i | ||||
\(695\) | −8.12957e8 | −2.42166 | ||||||||
\(696\) | 3.43304e8 | − | 3.61978e7i | 1.01824 | − | 0.107363i | ||||
\(697\) | 1.12866e8i | 0.333323i | ||||||||
\(698\) | 7.09477e7 | + | 2.31968e8i | 0.208628 | + | 0.682120i | ||||
\(699\) | −2.18285e8 | + | 2.18285e8i | −0.639134 | + | 0.639134i | ||||
\(700\) | 2.17433e6 | − | 1.46730e6i | 0.00633914 | − | 0.00427785i | ||||
\(701\) | −5.66448e7 | + | 5.66448e7i | −0.164439 | + | 0.164439i | −0.784530 | − | 0.620091i | \(-0.787096\pi\) |
0.620091 | + | 0.784530i | \(0.287096\pi\) | |||||||
\(702\) | −8.01669e7 | − | 4.26141e7i | −0.231731 | − | 0.123181i | ||||
\(703\) | − | 3.95573e8i | − | 1.13857i | ||||||
\(704\) | −9.87386e6 | + | 1.52265e7i | −0.0282989 | + | 0.0436398i | ||||
\(705\) | −1.38343e8 | −0.394810 | ||||||||
\(706\) | −1.75389e8 | + | 3.29947e8i | −0.498412 | + | 0.937628i | ||||
\(707\) | 6.24519e6 | + | 6.24519e6i | 0.0176721 | + | 0.0176721i | ||||
\(708\) | 1.77835e8 | + | 2.63525e8i | 0.501092 | + | 0.742545i | ||||
\(709\) | 2.04815e8 | + | 2.04815e8i | 0.574676 | + | 0.574676i | 0.933432 | − | 0.358755i | \(-0.116799\pi\) |
−0.358755 | + | 0.933432i | \(0.616799\pi\) | |||||||
\(710\) | 2.49578e8 | − | 7.63337e7i | 0.697318 | − | 0.213276i | ||||
\(711\) | 1.73875e8 | 0.483760 | ||||||||
\(712\) | −2.83135e7 | − | 2.68527e8i | −0.0784428 | − | 0.743959i | ||||
\(713\) | − | 1.74860e8i | − | 0.482417i | ||||||
\(714\) | −2.48790e6 | + | 760927.i | −0.00683498 | + | 0.00209049i | ||||
\(715\) | 2.23658e7 | − | 2.23658e7i | 0.0611880 | − | 0.0611880i | ||||
\(716\) | −5.66816e6 | + | 2.91946e7i | −0.0154420 | + | 0.0795360i | ||||
\(717\) | −4.17569e7 | + | 4.17569e7i | −0.113285 | + | 0.113285i | ||||
\(718\) | 8.18312e7 | − | 1.53943e8i | 0.221078 | − | 0.415898i | ||||
\(719\) | − | 6.77714e8i | − | 1.82331i | −0.410959 | − | 0.911654i | \(-0.634806\pi\) | ||
0.410959 | − | 0.911654i | \(-0.365194\pi\) | |||||||
\(720\) | −5.93715e7 | − | 1.39699e8i | −0.159067 | − | 0.374278i | ||||
\(721\) | 6.57054e6 | 0.0175305 | ||||||||
\(722\) | −1.55740e8 | − | 8.27861e7i | −0.413797 | − | 0.219961i | ||||
\(723\) | 1.68015e8 | + | 1.68015e8i | 0.444562 | + | 0.444562i | ||||
\(724\) | 3.19600e7 | − | 1.64615e8i | 0.0842154 | − | 0.433763i | ||||
\(725\) | −2.33430e8 | − | 2.33430e8i | −0.612552 | − | 0.612552i | ||||
\(726\) | 6.44414e7 | + | 2.10695e8i | 0.168405 | + | 0.550611i | ||||
\(727\) | 3.48046e8 | 0.905802 | 0.452901 | − | 0.891561i | \(-0.350389\pi\) | ||||
0.452901 | + | 0.891561i | \(0.350389\pi\) | |||||||
\(728\) | −5.18166e6 | + | 6.40316e6i | −0.0134300 | + | 0.0165959i | ||||
\(729\) | − | 1.43489e7i | − | 0.0370370i | ||||||
\(730\) | −1.20388e8 | − | 3.93616e8i | −0.309467 | − | 1.01182i | ||||
\(731\) | 9.53718e7 | − | 9.53718e7i | 0.244156 | − | 0.244156i | ||||
\(732\) | −1.41249e6 | − | 2.09310e6i | −0.00360124 | − | 0.00533651i | ||||
\(733\) | 1.36324e7 | − | 1.36324e7i | 0.0346146 | − | 0.0346146i | −0.689588 | − | 0.724202i | \(-0.742208\pi\) |
0.724202 | + | 0.689588i | \(0.242208\pi\) | |||||||
\(734\) | −5.90628e8 | − | 3.13959e8i | −1.49357 | − | 0.793934i | ||||
\(735\) | 2.79619e8i | 0.704213i | ||||||||
\(736\) | 6.82261e7 | + | 8.12175e7i | 0.171126 | + | 0.203712i | ||||
\(737\) | −1.20012e7 | −0.0299794 | ||||||||
\(738\) | −2.65089e7 | + | 4.98692e7i | −0.0659511 | + | 0.124069i | ||||
\(739\) | 2.89963e8 | + | 2.89963e8i | 0.718470 | + | 0.718470i | 0.968292 | − | 0.249821i | \(-0.0803719\pi\) |
−0.249821 | + | 0.968292i | \(0.580372\pi\) | |||||||
\(740\) | 3.85018e8 | − | 2.59822e8i | 0.950136 | − | 0.641181i | ||||
\(741\) | −2.74499e8 | − | 2.74499e8i | −0.674661 | − | 0.674661i | ||||
\(742\) | −1.57280e6 | + | 481043.i | −0.00385001 | + | 0.00117753i | ||||
\(743\) | −5.94522e8 | −1.44944 | −0.724722 | − | 0.689041i | \(-0.758032\pi\) | ||||
−0.724722 | + | 0.689041i | \(0.758032\pi\) | |||||||
\(744\) | 2.71213e8 | − | 3.35148e8i | 0.658555 | − | 0.813800i | ||||
\(745\) | 5.49344e8i | 1.32854i | ||||||||
\(746\) | 4.19903e8 | − | 1.28428e8i | 1.01142 | − | 0.309345i | ||||
\(747\) | −8.21689e7 | + | 8.21689e7i | −0.197127 | + | 0.197127i | ||||
\(748\) | −1.68972e7 | − | 3.28061e6i | −0.0403748 | − | 0.00783881i | ||||
\(749\) | 2.26594e6 | − | 2.26594e6i | 0.00539265 | − | 0.00539265i | ||||
\(750\) | 7.13472e7 | − | 1.34220e8i | 0.169119 | − | 0.318152i | ||||
\(751\) | 5.29349e8i | 1.24975i | 0.780726 | + | 0.624874i | \(0.214850\pi\) | ||||
−0.780726 | + | 0.624874i | \(0.785150\pi\) | |||||||
\(752\) | 2.21042e8 | + | 8.91930e7i | 0.519782 | + | 0.209738i | ||||
\(753\) | 3.41888e8 | 0.800755 | ||||||||
\(754\) | 9.15360e8 | + | 4.86576e8i | 2.13539 | + | 1.13511i | ||||
\(755\) | −5.23479e8 | − | 5.23479e8i | −1.21635 | − | 1.21635i | ||||
\(756\) | −1.27798e6 | − | 248121.i | −0.00295773 | − | 0.000574246i | ||||
\(757\) | −2.90978e8 | − | 2.90978e8i | −0.670768 | − | 0.670768i | 0.287125 | − | 0.957893i | \(-0.407300\pi\) |
−0.957893 | + | 0.287125i | \(0.907300\pi\) | |||||||
\(758\) | −1.72217e8 | − | 5.63072e8i | −0.395428 | − | 1.29287i | ||||
\(759\) | −3.49328e6 | −0.00798928 | ||||||||
\(760\) | −6.80567e7 | − | 6.45457e8i | −0.155035 | − | 1.47037i | ||||
\(761\) | − | 1.25159e8i | − | 0.283994i | −0.989867 | − | 0.141997i | \(-0.954648\pi\) | ||
0.989867 | − | 0.141997i | \(-0.0453524\pi\) | |||||||
\(762\) | −1.87108e7 | − | 6.11761e7i | −0.0422890 | − | 0.138266i | ||||
\(763\) | −5.18867e6 | + | 5.18867e6i | −0.0116811 | + | 0.0116811i | ||||
\(764\) | −4.51239e8 | + | 3.04510e8i | −1.01187 | + | 0.682843i | ||||
\(765\) | 1.01803e8 | − | 1.01803e8i | 0.227392 | − | 0.227392i | ||||
\(766\) | 9.35382e7 | + | 4.97219e7i | 0.208115 | + | 0.110627i | ||||
\(767\) | 9.54696e8i | 2.11582i | ||||||||
\(768\) | 4.79569e6 | + | 2.61487e8i | 0.0105869 | + | 0.577253i | ||||
\(769\) | 2.33480e8 | 0.513418 | 0.256709 | − | 0.966489i | \(-0.417362\pi\) | ||||
0.256709 | + | 0.966489i | \(0.417362\pi\) | |||||||
\(770\) | 212884. | − | 400483.i | 0.000466305 | − | 0.000877226i | ||||
\(771\) | −2.53939e8 | − | 2.53939e8i | −0.554073 | − | 0.554073i | ||||
\(772\) | −1.64216e8 | − | 2.43344e8i | −0.356913 | − | 0.528893i | ||||
\(773\) | 1.82416e8 | + | 1.82416e8i | 0.394934 | + | 0.394934i | 0.876442 | − | 0.481507i | \(-0.159911\pi\) |
−0.481507 | + | 0.876442i | \(0.659911\pi\) | |||||||
\(774\) | 6.45394e7 | − | 1.97395e7i | 0.139188 | − | 0.0425709i | ||||
\(775\) | −4.12297e8 | −0.885737 | ||||||||
\(776\) | −7.89953e8 | + | 8.32924e7i | −1.69050 | + | 0.178246i | ||||
\(777\) | − | 3.98367e6i | − | 0.00849219i | ||||||
\(778\) | 3.15033e7 | − | 9.63532e6i | 0.0668986 | − | 0.0204610i | ||||
\(779\) | −1.70757e8 | + | 1.70757e8i | −0.361215 | + | 0.361215i | ||||
\(780\) | 8.68769e7 | − | 4.47471e8i | 0.183071 | − | 0.942934i | ||||
\(781\) | 1.04718e7 | − | 1.04718e7i | 0.0219820 | − | 0.0219820i | ||||
\(782\) | −4.72220e7 | + | 8.88353e7i | −0.0987469 | + | 0.185766i | ||||
\(783\) | 1.63838e8i | 0.341295i | ||||||||
\(784\) | 1.80277e8 | − | 4.46771e8i | 0.374105 | − | 0.927122i | ||||
\(785\) | 1.02058e9 | 2.10978 | ||||||||
\(786\) | 2.42419e8 | + | 1.28862e8i | 0.499229 | + | 0.265374i | ||||
\(787\) | 5.04645e8 | + | 5.04645e8i | 1.03529 | + | 1.03529i | 0.999354 | + | 0.0359348i | \(0.0114409\pi\) |
0.0359348 | + | 0.999354i | \(0.488559\pi\) | |||||||
\(788\) | 1.00783e8 | − | 5.19097e8i | 0.205972 | − | 1.06089i | ||||
\(789\) | 1.26406e8 | + | 1.26406e8i | 0.257358 | + | 0.257358i | ||||
\(790\) | 2.55326e8 | + | 8.34805e8i | 0.517863 | + | 1.69318i | ||||
\(791\) | 7.20460e6 | 0.0145573 | ||||||||
\(792\) | −6.69542e6 | − | 5.41817e6i | −0.0134773 | − | 0.0109063i | ||||
\(793\) | − | 7.58287e6i | − | 0.0152060i | ||||||
\(794\) | 3.81261e7 | + | 1.24656e8i | 0.0761660 | + | 0.249029i | ||||
\(795\) | 6.43578e7 | − | 6.43578e7i | 0.128086 | − | 0.128086i | ||||
\(796\) | −9.75370e7 | − | 1.44536e8i | −0.193388 | − | 0.286573i | ||||
\(797\) | 1.49530e8 | − | 1.49530e8i | 0.295362 | − | 0.295362i | −0.543832 | − | 0.839194i | \(-0.683027\pi\) |
0.839194 | + | 0.543832i | \(0.183027\pi\) | |||||||
\(798\) | −4.91518e6 | − | 2.61275e6i | −0.00967233 | − | 0.00514150i | ||||
\(799\) | 2.26078e8i | 0.443219i | ||||||||
\(800\) | 1.91500e8 | − | 1.60868e8i | 0.374023 | − | 0.314195i | ||||
\(801\) | 1.28152e8 | 0.249361 | ||||||||
\(802\) | −2.66770e8 | + | 5.01855e8i | −0.517147 | + | 0.972872i | ||||
\(803\) | −1.65153e7 | − | 1.65153e7i | −0.0318963 | − | 0.0318963i | ||||
\(804\) | −1.43362e8 | + | 9.67453e7i | −0.275846 | + | 0.186150i | ||||
\(805\) | −1.87449e6 | − | 1.87449e6i | −0.00359332 | − | 0.00359332i | ||||
\(806\) | 1.23809e9 | − | 3.78671e8i | 2.36454 | − | 0.723197i | ||||
\(807\) | 4.00018e8 | 0.761130 | ||||||||
\(808\) | 6.54607e8 | + | 5.29731e8i | 1.24093 | + | 1.00420i | ||||
\(809\) | − | 6.79235e8i | − | 1.28285i | −0.767187 | − | 0.641423i | \(-0.778344\pi\) | ||
0.767187 | − | 0.641423i | \(-0.221656\pi\) | |||||||
\(810\) | 6.88915e7 | − | 2.10706e7i | 0.129631 | − | 0.0396480i | ||||
\(811\) | −6.71312e8 | + | 6.71312e8i | −1.25852 | + | 1.25852i | −0.306727 | + | 0.951798i | \(0.599234\pi\) |
−0.951798 | + | 0.306727i | \(0.900766\pi\) | |||||||
\(812\) | 1.45922e7 | + | 2.83309e6i | 0.0272554 | + | 0.00529166i | ||||
\(813\) | 1.85253e8 | − | 1.85253e8i | 0.344742 | − | 0.344742i | ||||
\(814\) | 1.23709e7 | − | 2.32725e7i | 0.0229366 | − | 0.0431489i | ||||
\(815\) | 4.86402e8i | 0.898509i | ||||||||
\(816\) | −2.28294e8 | + | 9.70245e7i | −0.420170 | + | 0.178571i | ||||
\(817\) | 2.88578e8 | 0.529173 | ||||||||
\(818\) | 1.34209e8 | + | 7.13412e7i | 0.245201 | + | 0.130341i | ||||
\(819\) | −2.76437e6 | − | 2.76437e6i | −0.00503204 | − | 0.00503204i | ||||
\(820\) | −2.78357e8 | − | 5.40433e7i | −0.504849 | − | 0.0980167i | ||||
\(821\) | −1.13933e8 | − | 1.13933e8i | −0.205882 | − | 0.205882i | 0.596632 | − | 0.802515i | \(-0.296505\pi\) |
−0.802515 | + | 0.596632i | \(0.796505\pi\) | |||||||
\(822\) | −876700. | − | 2.86642e6i | −0.00157847 | − | 0.00516089i | ||||
\(823\) | 3.09924e8 | 0.555975 | 0.277987 | − | 0.960585i | \(-0.410333\pi\) | ||||
0.277987 | + | 0.960585i | \(0.410333\pi\) | |||||||
\(824\) | 6.23018e8 | − | 6.56908e7i | 1.11357 | − | 0.117415i | ||||
\(825\) | 8.23667e6i | 0.0146686i | ||||||||
\(826\) | 4.00389e6 | + | 1.30909e7i | 0.00710463 | + | 0.0232290i | ||||
\(827\) | −2.49487e8 | + | 2.49487e8i | −0.441095 | + | 0.441095i | −0.892380 | − | 0.451285i | \(-0.850966\pi\) |
0.451285 | + | 0.892380i | \(0.350966\pi\) | |||||||
\(828\) | −4.17295e7 | + | 2.81603e7i | −0.0735109 | + | 0.0496074i | ||||
\(829\) | −6.63974e8 | + | 6.63974e8i | −1.16543 | + | 1.16543i | −0.182165 | + | 0.983268i | \(0.558310\pi\) |
−0.983268 | + | 0.182165i | \(0.941690\pi\) | |||||||
\(830\) | −5.15167e8 | − | 2.73846e8i | −0.900977 | − | 0.478930i | ||||
\(831\) | 2.91402e8i | 0.507797i | ||||||||
\(832\) | −4.27307e8 | + | 6.58952e8i | −0.741942 | + | 1.14415i | ||||
\(833\) | 4.56951e8 | 0.790560 | ||||||||
\(834\) | −3.12031e8 | + | 5.87002e8i | −0.537898 | + | 1.01191i | ||||
\(835\) | −6.43511e8 | − | 6.43511e8i | −1.10534 | − | 1.10534i | ||||
\(836\) | −2.06008e7 | − | 3.05273e7i | −0.0352585 | − | 0.0522480i | ||||
\(837\) | 1.44690e8 | + | 1.44690e8i | 0.246753 | + | 0.246753i | ||||
\(838\) | 3.85610e8 | − | 1.17940e8i | 0.655265 | − | 0.200414i | ||||
\(839\) | 4.18417e7 | 0.0708473 | 0.0354237 | − | 0.999372i | \(-0.488722\pi\) | ||||
0.0354237 | + | 0.999372i | \(0.488722\pi\) | |||||||
\(840\) | −685373. | − | 6.50015e6i | −0.00115635 | − | 0.0109669i | ||||
\(841\) | − | 1.27591e9i | − | 2.14503i | ||||||
\(842\) | −4.49907e8 | + | 1.37605e8i | −0.753679 | + | 0.230514i | ||||
\(843\) | 4.17324e8 | − | 4.17324e8i | 0.696611 | − | 0.696611i | ||||
\(844\) | 7.16936e7 | − | 3.69268e8i | 0.119249 | − | 0.614206i | ||||
\(845\) | 4.47408e8 | − | 4.47408e8i | 0.741539 | − | 0.741539i | ||||
\(846\) | −5.30990e7 | + | 9.98914e7i | −0.0876951 | + | 0.164975i | ||||
\(847\) | 9.48744e6i | 0.0156135i | ||||||||
\(848\) | −1.44323e8 | + | 6.13370e7i | −0.236673 | + | 0.100585i | ||||
\(849\) | −5.52151e8 | −0.902266 | ||||||||
\(850\) | 2.09461e8 | + | 1.11343e8i | 0.341073 | + | 0.181303i | ||||
\(851\) | −1.08929e8 | − | 1.08929e8i | −0.176748 | − | 0.176748i | ||||
\(852\) | 4.06762e7 | − | 2.09508e8i | 0.0657690 | − | 0.338752i | ||||
\(853\) | −6.18731e8 | − | 6.18731e8i | −0.996908 | − | 0.996908i | 0.00308725 | − | 0.999995i | \(-0.499017\pi\) |
−0.999995 | + | 0.00308725i | \(0.999017\pi\) | |||||||
\(854\) | −31801.7 | − | 103977.i | −5.10595e−5 | − | 0.000166942i | ||||
\(855\) | 3.08038e8 | 0.492840 | ||||||||
\(856\) | 1.92202e8 | − | 2.37510e8i | 0.306433 | − | 0.378670i | ||||
\(857\) | 9.35284e8i | 1.48594i | 0.669325 | + | 0.742970i | \(0.266583\pi\) | ||||
−0.669325 | + | 0.742970i | \(0.733417\pi\) | |||||||
\(858\) | −7.56491e6 | − | 2.47339e7i | −0.0119768 | − | 0.0391589i | ||||
\(859\) | 3.05653e8 | − | 3.05653e8i | 0.482225 | − | 0.482225i | −0.423617 | − | 0.905841i | \(-0.639240\pi\) |
0.905841 | + | 0.423617i | \(0.139240\pi\) | |||||||
\(860\) | 1.89545e8 | + | 2.80878e8i | 0.298001 | + | 0.441593i | ||||
\(861\) | −1.71963e6 | + | 1.71963e6i | −0.00269417 | + | 0.00269417i | ||||
\(862\) | −4.46707e8 | − | 2.37455e8i | −0.697430 | − | 0.370731i | ||||
\(863\) | − | 1.52011e8i | − | 0.236506i | −0.992984 | − | 0.118253i | \(-0.962271\pi\) | ||
0.992984 | − | 0.118253i | \(-0.0377293\pi\) | |||||||
\(864\) | −1.23659e8 | − | 1.07498e7i | −0.191727 | − | 0.0166671i | ||||
\(865\) | 1.31829e9 | 2.03686 | ||||||||
\(866\) | −1.83491e7 | + | 3.45188e7i | −0.0282527 | + | 0.0531498i | ||||
\(867\) | 9.96956e7 | + | 9.96956e7i | 0.152974 | + | 0.152974i | ||||
\(868\) | 1.53887e7 | − | 1.03848e7i | 0.0235312 | − | 0.0158796i | ||||
\(869\) | 3.50267e7 | + | 3.50267e7i | 0.0533753 | + | 0.0533753i | ||||
\(870\) | −7.86615e8 | + | 2.40587e8i | −1.19455 | + | 0.365355i | ||||
\(871\) | −5.19372e8 | −0.786002 | ||||||||
\(872\) | −4.40114e8 | + | 5.43865e8i | −0.663768 | + | 0.820241i | ||||
\(873\) | − | 3.76997e8i | − | 0.566625i | ||||||
\(874\) | −2.05843e8 | + | 6.29573e7i | −0.308320 | + | 0.0943000i | ||||
\(875\) | 4.62828e6 | − | 4.62828e6i | 0.00690868 | − | 0.00690868i | ||||
\(876\) | −3.30421e8 | − | 6.41515e7i | −0.491536 | − | 0.0954321i | ||||
\(877\) | −6.76555e8 | + | 6.76555e8i | −1.00301 | + | 1.00301i | −0.00301200 | + | 0.999995i | \(0.500959\pi\) |
−0.999995 | + | 0.00301200i | \(0.999041\pi\) | |||||||
\(878\) | −7.12062e7 | + | 1.33955e8i | −0.105204 | + | 0.197914i | ||||
\(879\) | − | 4.95521e8i | − | 0.729618i | ||||||
\(880\) | 1.61817e7 | − | 4.01021e7i | 0.0237452 | − | 0.0588463i | ||||
\(881\) | 5.67082e8 | 0.829313 | 0.414656 | − | 0.909978i | \(-0.363902\pi\) | ||||
0.414656 | + | 0.909978i | \(0.363902\pi\) | |||||||
\(882\) | 2.01901e8 | + | 1.07324e8i | 0.294261 | + | 0.156420i | ||||
\(883\) | −2.70776e8 | − | 2.70776e8i | −0.393303 | − | 0.393303i | 0.482560 | − | 0.875863i | \(-0.339707\pi\) |
−0.875863 | + | 0.482560i | \(0.839707\pi\) | |||||||
\(884\) | −7.31254e8 | − | 1.41974e8i | −1.05855 | − | 0.205518i | ||||
\(885\) | −5.35673e8 | − | 5.35673e8i | −0.772804 | − | 0.772804i | ||||
\(886\) | −2.50389e8 | − | 8.18662e8i | −0.360010 | − | 1.17707i | ||||
\(887\) | 8.61154e8 | 1.23399 | 0.616993 | − | 0.786969i | \(-0.288351\pi\) | ||||
0.616993 | + | 0.786969i | \(0.288351\pi\) | |||||||
\(888\) | −3.98278e7 | − | 3.77731e8i | −0.0568784 | − | 0.539441i | ||||
\(889\) | − | 2.75471e6i | − | 0.00392077i | ||||||
\(890\) | 1.88184e8 | + | 6.15280e8i | 0.266940 | + | 0.872775i | ||||
\(891\) | 2.89055e6 | − | 2.89055e6i | 0.00408646 | − | 0.00408646i | ||||
\(892\) | −1.18974e8 | + | 8.02869e7i | −0.167632 | + | 0.113123i | ||||
\(893\) | −3.42037e8 | + | 3.42037e8i | −0.480307 | + | 0.480307i | ||||
\(894\) | 3.96659e8 | + | 2.10851e8i | 0.555142 | + | 0.295096i | ||||
\(895\) | − | 7.08661e7i | − | 0.0988484i | ||||||
\(896\) | −3.09573e6 | + | 1.08277e7i | −0.00430367 | + | 0.0150527i | ||||
\(897\) | −1.51177e8 | −0.209464 | ||||||||
\(898\) | 1.25552e8 | − | 2.36191e8i | 0.173378 | − | 0.326163i | ||||
\(899\) | −1.65210e9 | − | 1.65210e9i | −2.27382 | − | 2.27382i | ||||
\(900\) | 6.63982e7 | + | 9.83924e7i | 0.0910812 | + | 0.134969i | ||||
\(901\) | −1.05173e8 | − | 1.05173e8i | −0.143791 | − | 0.143791i | ||||
\(902\) | −1.53862e7 | + | 4.70588e6i | −0.0209658 | + | 0.00641241i | ||||
\(903\) | 2.90616e6 | 0.00394690 | ||||||||
\(904\) | 6.83139e8 | − | 7.20300e7i | 0.924707 | − | 0.0975008i | ||||
\(905\) | 3.99581e8i | 0.539087i | ||||||||
\(906\) | −5.78906e8 | + | 1.77059e8i | −0.778437 | + | 0.238086i | ||||
\(907\) | 4.01148e8 | − | 4.01148e8i | 0.537629 | − | 0.537629i | −0.385203 | − | 0.922832i | \(-0.625868\pi\) |
0.922832 | + | 0.385203i | \(0.125868\pi\) | |||||||
\(908\) | −2.60606e8 | + | 1.34228e9i | −0.348118 | + | 1.79303i | ||||
\(909\) | −2.82607e8 | + | 2.82607e8i | −0.376263 | + | 0.376263i | ||||
\(910\) | 9.21288e6 | − | 1.73315e7i | 0.0122256 | − | 0.0229992i | ||||
\(911\) | 9.73411e7i | 0.128748i | 0.997926 | + | 0.0643741i | \(0.0205051\pi\) | ||||
−0.997926 | + | 0.0643741i | \(0.979495\pi\) | |||||||
\(912\) | −4.92179e8 | − | 1.98600e8i | −0.648841 | − | 0.261815i | ||||
\(913\) | −3.31054e7 | −0.0434997 | ||||||||
\(914\) | −3.91493e8 | − | 2.08105e8i | −0.512726 | − | 0.272549i | ||||
\(915\) | 4.25469e6 | + | 4.25469e6i | 0.00555398 | + | 0.00555398i | ||||
\(916\) | 8.06720e7 | − | 4.15512e8i | 0.104963 | − | 0.540626i | ||||
\(917\) | 8.35927e6 | + | 8.35927e6i | 0.0108408 | + | 0.0108408i | ||||
\(918\) | −3.44334e7 | − | 1.12582e8i | −0.0445094 | − | 0.145526i | ||||
\(919\) | −7.96503e8 | −1.02622 | −0.513110 | − | 0.858323i | \(-0.671507\pi\) | ||||
−0.513110 | + | 0.858323i | \(0.671507\pi\) | |||||||
\(920\) | −1.96480e8 | − | 1.58998e8i | −0.252322 | − | 0.204187i | ||||
\(921\) | 5.40054e8i | 0.691287i | ||||||||
\(922\) | 9.13944e7 | + | 2.98819e8i | 0.116608 | + | 0.381256i | ||||
\(923\) | 4.53183e8 | − | 4.53183e8i | 0.576326 | − | 0.576326i | ||||
\(924\) | −207462. | − | 307429.i | −0.000262980 | − | 0.000389698i | ||||
\(925\) | −2.56839e8 | + | 2.56839e8i | −0.324516 | + | 0.324516i | ||||
\(926\) | −4.57773e8 | − | 2.43337e8i | −0.576524 | − | 0.306461i | ||||
\(927\) | 2.97329e8i | 0.373249i | ||||||||
\(928\) | 1.41196e9 | + | 1.22743e8i | 1.76676 | + | 0.153587i | ||||
\(929\) | 7.73176e7 | 0.0964342 | 0.0482171 | − | 0.998837i | \(-0.484646\pi\) | ||||
0.0482171 | + | 0.998837i | \(0.484646\pi\) | |||||||
\(930\) | −4.82211e8 | + | 9.07150e8i | −0.599499 | + | 1.12779i | ||||
\(931\) | 6.91327e8 | + | 6.91327e8i | 0.856711 | + | 0.856711i | ||||
\(932\) | −1.05057e9 | + | 7.08956e8i | −1.29771 | + | 0.875733i | ||||
\(933\) | 2.34111e8 | + | 2.34111e8i | 0.288255 | + | 0.288255i | ||||
\(934\) | −1.09670e9 | + | 3.35429e8i | −1.34601 | + | 0.411680i | ||||
\(935\) | 4.10159e7 | 0.0501784 | ||||||||
\(936\) | −2.89755e8 | − | 2.34480e8i | −0.353349 | − | 0.285942i | ||||
\(937\) | − | 1.24173e9i | − | 1.50941i | −0.656063 | − | 0.754706i | \(-0.727780\pi\) | ||
0.656063 | − | 0.754706i | \(-0.272220\pi\) | |||||||
\(938\) | −7.12171e6 | + | 2.17819e6i | −0.00862930 | + | 0.00263928i | ||||
\(939\) | 4.25106e8 | − | 4.25106e8i | 0.513453 | − | 0.513453i | ||||
\(940\) | −5.57568e8 | − | 1.08252e8i | −0.671297 | − | 0.130333i | ||||
\(941\) | 6.89816e8 | − | 6.89816e8i | 0.827874 | − | 0.827874i | −0.159349 | − | 0.987222i | \(-0.550939\pi\) |
0.987222 | + | 0.159349i | \(0.0509394\pi\) | |||||||
\(942\) | 3.91721e8 | − | 7.36917e8i | 0.468624 | − | 0.881588i | ||||
\(943\) | 9.40423e7i | 0.112147i | ||||||||
\(944\) | 5.10529e8 | + | 1.20125e9i | 0.606882 | + | 1.42797i | ||||
\(945\) | 3.10213e6 | 0.00367591 | ||||||||
\(946\) | 1.69777e7 | + | 9.02482e6i | 0.0200543 | + | 0.0106602i | ||||
\(947\) | 5.78686e8 | + | 5.78686e8i | 0.681386 | + | 0.681386i | 0.960313 | − | 0.278926i | \(-0.0899785\pi\) |
−0.278926 | + | 0.960313i | \(0.589979\pi\) | |||||||
\(948\) | 7.00778e8 | + | 1.36057e8i | 0.822537 | + | 0.159696i | ||||
\(949\) | −7.14726e8 | − | 7.14726e8i | −0.836260 | − | 0.836260i | ||||
\(950\) | 1.48445e8 | + | 4.85349e8i | 0.173139 | + | 0.566087i | ||||
\(951\) | 5.64093e8 | 0.655857 | ||||||||
\(952\) | −1.06225e7 | + | 1.12003e6i | −0.0123116 | + | 0.00129813i | ||||
\(953\) | 1.10265e9i | 1.27397i | 0.770875 | + | 0.636986i | \(0.219819\pi\) | ||||
−0.770875 | + | 0.636986i | \(0.780181\pi\) | |||||||
\(954\) | −2.17681e7 | − | 7.11721e7i | −0.0250712 | − | 0.0819719i | ||||
\(955\) | 9.17241e8 | − | 9.17241e8i | 1.05311 | − | 1.05311i | ||||
\(956\) | −2.00969e8 | + | 1.35620e8i | −0.230015 | + | 0.155221i | ||||
\(957\) | −3.30048e7 | + | 3.30048e7i | −0.0376566 | + | 0.0376566i | ||||
\(958\) | 4.21871e8 | + | 2.24253e8i | 0.479826 | + | 0.255060i | ||||
\(959\) | − | 129073.i | − | 0.000146345i | ||||||
\(960\) | −1.29974e8 | − | 6.09491e8i | −0.146907 | − | 0.688896i | ||||
\(961\) | −2.03052e9 | −2.28790 | ||||||||
\(962\) | 5.35371e8 | − | 1.00715e9i | 0.601353 | − | 1.13128i | ||||
\(963\) | 1.02538e8 | + | 1.02538e8i | 0.114817 | + | 0.114817i | ||||
\(964\) | 5.45686e8 | + | 8.08627e8i | 0.609132 | + | 0.902645i | ||||
\(965\) | 4.94649e8 | + | 4.94649e8i | 0.550446 | + | 0.550446i | ||||
\(966\) | −2.07296e6 | + | 634019.i | −0.00229964 | + | 0.000703349i | ||||
\(967\) | −7.32629e8 | −0.810223 | −0.405111 | − | 0.914267i | \(-0.632767\pi\) | ||||
−0.405111 | + | 0.914267i | \(0.632767\pi\) | |||||||
\(968\) | 9.48534e7 | + | 8.99599e8i | 0.104575 | + | 0.991797i | ||||
\(969\) | − | 5.03393e8i | − | 0.553269i | ||||||
\(970\) | 1.81003e9 | − | 5.53600e8i | 1.98322 | − | 0.606570i | ||||
\(971\) | 6.01418e8 | − | 6.01418e8i | 0.656930 | − | 0.656930i | −0.297723 | − | 0.954652i | \(-0.596227\pi\) |
0.954652 | + | 0.297723i | \(0.0962270\pi\) | |||||||
\(972\) | 1.12279e7 | − | 5.78310e7i | 0.0122265 | − | 0.0629741i | ||||
\(973\) | −2.02414e7 | + | 2.02414e7i | −0.0219736 | + | 0.0219736i | ||||
\(974\) | 3.35587e8 | − | 6.31315e8i | 0.363185 | − | 0.683234i | ||||
\(975\) | 3.56455e8i | 0.384583i | ||||||||
\(976\) | −4.05498e6 | − | 9.54119e6i | −0.00436153 | − | 0.0102625i | ||||
\(977\) | 6.27375e8 | 0.672734 | 0.336367 | − | 0.941731i | \(-0.390802\pi\) | ||||
0.336367 | + | 0.941731i | \(0.390802\pi\) | |||||||
\(978\) | 3.51210e8 | + | 1.86692e8i | 0.375449 | + | 0.199576i | ||||
\(979\) | 2.58159e7 | + | 2.58159e7i | 0.0275131 | + | 0.0275131i | ||||
\(980\) | −2.18800e8 | + | 1.12696e9i | −0.232471 | + | 1.19737i | ||||
\(981\) | −2.34797e8 | − | 2.34797e8i | −0.248706 | − | 0.248706i | ||||
\(982\) | −1.76484e8 | − | 5.77023e8i | −0.186367 | − | 0.609339i | ||||
\(983\) | 7.60602e8 | 0.800750 | 0.400375 | − | 0.916351i | \(-0.368880\pi\) | ||||
0.400375 | + | 0.916351i | \(0.368880\pi\) | |||||||
\(984\) | −1.45862e8 | + | 1.80247e8i | −0.153094 | + | 0.189183i | ||||
\(985\) | 1.26004e9i | 1.31849i | ||||||||
\(986\) | 3.93166e8 | + | 1.28548e9i | 0.410153 | + | 1.34102i | ||||
\(987\) | −3.44452e6 | + | 3.44452e6i | −0.00358243 | + | 0.00358243i | ||||
\(988\) | −8.91530e8 | − | 1.32112e9i | −0.924411 | − | 1.36984i | ||||
\(989\) | 7.94656e7 | − | 7.94656e7i | 0.0821468 | − | 0.0821468i | ||||
\(990\) | 1.81226e7 | + | 9.63339e6i | 0.0186773 | + | 0.00992827i | ||||
\(991\) | − | 1.26374e8i | − | 0.129848i | −0.997890 | − | 0.0649240i | \(-0.979319\pi\) | ||
0.997890 | − | 0.0649240i | \(-0.0206805\pi\) | |||||||
\(992\) | 1.35533e9 | − | 1.13854e9i | 1.38839 | − | 1.16631i | ||||
\(993\) | −8.86382e7 | −0.0905260 | ||||||||
\(994\) | 4.31351e6 | − | 8.11471e6i | 0.00439210 | − | 0.00826254i | ||||
\(995\) | 2.93800e8 | + | 2.93800e8i | 0.298251 | + | 0.298251i | ||||
\(996\) | −3.95465e8 | + | 2.66872e8i | −0.400249 | + | 0.270100i | ||||
\(997\) | 1.36158e9 | + | 1.36158e9i | 1.37391 | + | 1.37391i | 0.854563 | + | 0.519348i | \(0.173825\pi\) |
0.519348 | + | 0.854563i | \(0.326175\pi\) | |||||||
\(998\) | 1.22514e9 | − | 3.74713e8i | 1.23253 | − | 0.376970i | ||||
\(999\) | 1.80268e8 | 0.180810 |
(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 | 48.7.l.a.43.8 | yes | 48 | |
4.3 | odd | 2 | 192.7.l.a.79.23 | 48 | |||
8.3 | odd | 2 | 384.7.l.a.31.2 | 48 | |||
8.5 | even | 2 | 384.7.l.b.31.23 | 48 | |||
16.3 | odd | 4 | inner | 48.7.l.a.19.8 | ✓ | 48 | |
16.5 | even | 4 | 384.7.l.a.223.2 | 48 | |||
16.11 | odd | 4 | 384.7.l.b.223.23 | 48 | |||
16.13 | even | 4 | 192.7.l.a.175.23 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.7.l.a.19.8 | ✓ | 48 | 16.3 | odd | 4 | inner | |
48.7.l.a.43.8 | yes | 48 | 1.1 | even | 1 | trivial | |
192.7.l.a.79.23 | 48 | 4.3 | odd | 2 | |||
192.7.l.a.175.23 | 48 | 16.13 | even | 4 | |||
384.7.l.a.31.2 | 48 | 8.3 | odd | 2 | |||
384.7.l.a.223.2 | 48 | 16.5 | even | 4 | |||
384.7.l.b.31.23 | 48 | 8.5 | even | 2 | |||
384.7.l.b.223.23 | 48 | 16.11 | odd | 4 |