Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,8,Mod(75,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.75");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(23.7412619368\) |
Analytic rank: | \(0\) |
Dimension: | \(68\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 75.14 | ||
Character | \(\chi\) | \(=\) | 76.75 |
Dual form | 76.8.d.a.75.13 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −9.59747 | + | 5.99070i | −0.848305 | + | 0.529508i | ||||
\(3\) | −1.36022 | −0.0290860 | −0.0145430 | − | 0.999894i | \(-0.504629\pi\) | ||||
−0.0145430 | + | 0.999894i | \(0.504629\pi\) | |||||||
\(4\) | 56.2230 | − | 114.991i | 0.439242 | − | 0.898369i | ||||
\(5\) | 59.9018 | 0.214311 | 0.107156 | − | 0.994242i | \(-0.465826\pi\) | ||||
0.107156 | + | 0.994242i | \(0.465826\pi\) | |||||||
\(6\) | 13.0547 | − | 8.14867i | 0.0246738 | − | 0.0154013i | ||||
\(7\) | 254.899i | 0.280883i | 0.990089 | + | 0.140441i | \(0.0448521\pi\) | ||||
−0.990089 | + | 0.140441i | \(0.955148\pi\) | |||||||
\(8\) | 149.279 | + | 1440.44i | 0.103082 | + | 0.994673i | ||||
\(9\) | −2185.15 | −0.999154 | ||||||||
\(10\) | −574.906 | + | 358.854i | −0.181801 | + | 0.113480i | ||||
\(11\) | − | 5031.67i | − | 1.13982i | −0.821706 | − | 0.569912i | \(-0.806977\pi\) | ||
0.821706 | − | 0.569912i | \(-0.193023\pi\) | |||||||
\(12\) | −76.4756 | + | 156.413i | −0.0127758 | + | 0.0261300i | ||||
\(13\) | 5860.07i | 0.739777i | 0.929076 | + | 0.369889i | \(0.120604\pi\) | ||||
−0.929076 | + | 0.369889i | \(0.879396\pi\) | |||||||
\(14\) | −1527.02 | − | 2446.39i | −0.148730 | − | 0.238274i | ||||
\(15\) | −81.4796 | −0.00623346 | ||||||||
\(16\) | −10061.9 | − | 12930.3i | −0.614133 | − | 0.789203i | ||||
\(17\) | 23510.7 | 1.16063 | 0.580315 | − | 0.814392i | \(-0.302929\pi\) | ||||
0.580315 | + | 0.814392i | \(0.302929\pi\) | |||||||
\(18\) | 20971.9 | − | 13090.6i | 0.847587 | − | 0.529060i | ||||
\(19\) | 26650.7 | − | 13550.3i | 0.891397 | − | 0.453223i | ||||
\(20\) | 3367.86 | − | 6888.18i | 0.0941345 | − | 0.192530i | ||||
\(21\) | − | 346.719i | − | 0.00816976i | ||||||
\(22\) | 30143.2 | + | 48291.3i | 0.603546 | + | 0.966917i | ||||
\(23\) | 18898.7i | 0.323880i | 0.986801 | + | 0.161940i | \(0.0517752\pi\) | ||||
−0.986801 | + | 0.161940i | \(0.948225\pi\) | |||||||
\(24\) | −203.052 | − | 1959.31i | −0.00299826 | − | 0.0289311i | ||||
\(25\) | −74536.8 | −0.954071 | ||||||||
\(26\) | −35105.9 | − | 56241.8i | −0.391718 | − | 0.627557i | ||||
\(27\) | 5947.08 | 0.0581475 | ||||||||
\(28\) | 29311.1 | + | 14331.2i | 0.252336 | + | 0.123376i | ||||
\(29\) | 116601.i | 0.887788i | 0.896079 | + | 0.443894i | \(0.146403\pi\) | ||||
−0.896079 | + | 0.443894i | \(0.853597\pi\) | |||||||
\(30\) | 781.998 | − | 488.120i | 0.00528788 | − | 0.00330067i | ||||
\(31\) | 28852.9 | 0.173949 | 0.0869747 | − | 0.996211i | \(-0.472280\pi\) | ||||
0.0869747 | + | 0.996211i | \(0.472280\pi\) | |||||||
\(32\) | 174031. | + | 63820.1i | 0.938861 | + | 0.344296i | ||||
\(33\) | 6844.17i | 0.0331529i | ||||||||
\(34\) | −225643. | + | 140845.i | −0.984568 | + | 0.614563i | ||||
\(35\) | 15268.9i | 0.0601963i | ||||||||
\(36\) | −122856. | + | 251273.i | −0.438871 | + | 0.897609i | ||||
\(37\) | 412015.i | 1.33723i | 0.743608 | + | 0.668616i | \(0.233113\pi\) | ||||
−0.743608 | + | 0.668616i | \(0.766887\pi\) | |||||||
\(38\) | −174603. | + | 289705.i | −0.516191 | + | 0.856474i | ||||
\(39\) | − | 7970.98i | − | 0.0215172i | ||||||
\(40\) | 8942.09 | + | 86284.9i | 0.0220917 | + | 0.213170i | ||||
\(41\) | 42123.5i | 0.0954511i | 0.998860 | + | 0.0477255i | \(0.0151973\pi\) | ||||
−0.998860 | + | 0.0477255i | \(0.984803\pi\) | |||||||
\(42\) | 2077.09 | + | 3327.62i | 0.00432596 | + | 0.00693045i | ||||
\(43\) | 377606.i | 0.724267i | 0.932126 | + | 0.362134i | \(0.117952\pi\) | ||||
−0.932126 | + | 0.362134i | \(0.882048\pi\) | |||||||
\(44\) | −578597. | − | 282895.i | −1.02398 | − | 0.500658i | ||||
\(45\) | −130894. | −0.214130 | ||||||||
\(46\) | −113217. | − | 181380.i | −0.171497 | − | 0.274749i | ||||
\(47\) | 1.20215e6i | 1.68895i | 0.535595 | + | 0.844475i | \(0.320087\pi\) | ||||
−0.535595 | + | 0.844475i | \(0.679913\pi\) | |||||||
\(48\) | 13686.5 | + | 17588.0i | 0.0178627 | + | 0.0229548i | ||||
\(49\) | 758570. | 0.921105 | ||||||||
\(50\) | 715365. | − | 446528.i | 0.809343 | − | 0.505188i | ||||
\(51\) | −31979.7 | −0.0337581 | ||||||||
\(52\) | 673856. | + | 329471.i | 0.664593 | + | 0.324941i | ||||
\(53\) | 1.22067e6i | 1.12624i | 0.826375 | + | 0.563120i | \(0.190399\pi\) | ||||
−0.826375 | + | 0.563120i | \(0.809601\pi\) | |||||||
\(54\) | −57077.0 | + | 35627.2i | −0.0493268 | + | 0.0307896i | ||||
\(55\) | − | 301406.i | − | 0.244277i | ||||||
\(56\) | −367167. | + | 38051.1i | −0.279386 | + | 0.0289540i | ||||
\(57\) | −36250.8 | + | 18431.4i | −0.0259272 | + | 0.0131825i | ||||
\(58\) | −698522. | − | 1.11907e6i | −0.470091 | − | 0.753115i | ||||
\(59\) | −618478. | −0.392051 | −0.196025 | − | 0.980599i | \(-0.562803\pi\) | ||||
−0.196025 | + | 0.980599i | \(0.562803\pi\) | |||||||
\(60\) | −4581.03 | + | 9369.43i | −0.00273800 | + | 0.00559995i | ||||
\(61\) | 1.20389e6 | 0.679098 | 0.339549 | − | 0.940588i | \(-0.389726\pi\) | ||||
0.339549 | + | 0.940588i | \(0.389726\pi\) | |||||||
\(62\) | −276914. | + | 172849.i | −0.147562 | + | 0.0921076i | ||||
\(63\) | − | 556992.i | − | 0.280645i | ||||||
\(64\) | −2.05258e6 | + | 430055.i | −0.978748 | + | 0.205066i | ||||
\(65\) | 351029.i | 0.158543i | ||||||||
\(66\) | −41001.4 | − | 65686.7i | −0.0175548 | − | 0.0281238i | ||||
\(67\) | 3.49955e6 | 1.42151 | 0.710756 | − | 0.703438i | \(-0.248353\pi\) | ||||
0.710756 | + | 0.703438i | \(0.248353\pi\) | |||||||
\(68\) | 1.32184e6 | − | 2.70352e6i | 0.509798 | − | 1.04267i | ||||
\(69\) | − | 25706.4i | − | 0.00942040i | ||||||
\(70\) | −91471.5 | − | 146543.i | −0.0318744 | − | 0.0510648i | ||||
\(71\) | −5.00869e6 | −1.66081 | −0.830405 | − | 0.557161i | \(-0.811891\pi\) | ||||
−0.830405 | + | 0.557161i | \(0.811891\pi\) | |||||||
\(72\) | −326197. | − | 3.14758e6i | −0.102995 | − | 0.993831i | ||||
\(73\) | 4.87137e6 | 1.46562 | 0.732809 | − | 0.680434i | \(-0.238209\pi\) | ||||
0.732809 | + | 0.680434i | \(0.238209\pi\) | |||||||
\(74\) | −2.46826e6 | − | 3.95430e6i | −0.708075 | − | 1.13438i | ||||
\(75\) | 101386. | 0.0277501 | ||||||||
\(76\) | −59785.9 | − | 3.82644e6i | −0.0156225 | − | 0.999878i | ||||
\(77\) | 1.28257e6 | 0.320157 | ||||||||
\(78\) | 47751.7 | + | 76501.3i | 0.0113935 | + | 0.0182531i | ||||
\(79\) | −2.80653e6 | −0.640435 | −0.320218 | − | 0.947344i | \(-0.603756\pi\) | ||||
−0.320218 | + | 0.947344i | \(0.603756\pi\) | |||||||
\(80\) | −602729. | − | 774548.i | −0.131615 | − | 0.169135i | ||||
\(81\) | 4.77083e6 | 0.997463 | ||||||||
\(82\) | −252349. | − | 404279.i | −0.0505421 | − | 0.0809716i | ||||
\(83\) | 5.18427e6i | 0.995209i | 0.867404 | + | 0.497604i | \(0.165787\pi\) | ||||
−0.867404 | + | 0.497604i | \(0.834213\pi\) | |||||||
\(84\) | −39869.6 | − | 19493.6i | −0.00733946 | − | 0.00358851i | ||||
\(85\) | 1.40833e6 | 0.248736 | ||||||||
\(86\) | −2.26212e6 | − | 3.62406e6i | −0.383506 | − | 0.614400i | ||||
\(87\) | − | 158603.i | − | 0.0258222i | ||||||
\(88\) | 7.24781e6 | − | 751123.i | 1.13375 | − | 0.117496i | ||||
\(89\) | − | 2.38832e6i | − | 0.359109i | −0.983748 | − | 0.179555i | \(-0.942534\pi\) | ||
0.983748 | − | 0.179555i | \(-0.0574657\pi\) | |||||||
\(90\) | 1.25626e6 | − | 784149.i | 0.181647 | − | 0.113384i | ||||
\(91\) | −1.49373e6 | −0.207791 | ||||||||
\(92\) | 2.17318e6 | + | 1.06254e6i | 0.290964 | + | 0.142262i | ||||
\(93\) | −39246.2 | −0.00505950 | ||||||||
\(94\) | −7.20173e6 | − | 1.15376e7i | −0.894313 | − | 1.43274i | ||||
\(95\) | 1.59643e6 | − | 811689.i | 0.191036 | − | 0.0971308i | ||||
\(96\) | −236720. | − | 86809.3i | −0.0273077 | − | 0.0100142i | ||||
\(97\) | − | 7.55047e6i | − | 0.839987i | −0.907527 | − | 0.419994i | \(-0.862032\pi\) | ||
0.907527 | − | 0.419994i | \(-0.137968\pi\) | |||||||
\(98\) | −7.28035e6 | + | 4.54436e6i | −0.781378 | + | 0.487733i | ||||
\(99\) | 1.09949e7i | 1.13886i | ||||||||
\(100\) | −4.19068e6 | + | 8.57107e6i | −0.419068 | + | 0.857107i | ||||
\(101\) | 1.19892e7 | 1.15789 | 0.578943 | − | 0.815368i | \(-0.303465\pi\) | ||||
0.578943 | + | 0.815368i | \(0.303465\pi\) | |||||||
\(102\) | 306924. | − | 191581.i | 0.0286372 | − | 0.0178752i | ||||
\(103\) | −9.61064e6 | −0.866607 | −0.433303 | − | 0.901248i | \(-0.642652\pi\) | ||||
−0.433303 | + | 0.901248i | \(0.642652\pi\) | |||||||
\(104\) | −8.44108e6 | + | 874786.i | −0.735836 | + | 0.0762579i | ||||
\(105\) | − | 20769.1i | − | 0.00175087i | ||||||
\(106\) | −7.31264e6 | − | 1.17153e7i | −0.596354 | − | 0.955395i | ||||
\(107\) | −6.47522e6 | −0.510989 | −0.255494 | − | 0.966811i | \(-0.582238\pi\) | ||||
−0.255494 | + | 0.966811i | \(0.582238\pi\) | |||||||
\(108\) | 334363. | − | 683862.i | 0.0255408 | − | 0.0522379i | ||||
\(109\) | 1.06715e7i | 0.789280i | 0.918836 | + | 0.394640i | \(0.129131\pi\) | ||||
−0.918836 | + | 0.394640i | \(0.870869\pi\) | |||||||
\(110\) | 1.80563e6 | + | 2.89273e6i | 0.129347 | + | 0.207221i | ||||
\(111\) | − | 560431.i | − | 0.0388948i | ||||||
\(112\) | 3.29592e6 | − | 2.56478e6i | 0.221673 | − | 0.172499i | ||||
\(113\) | 2.42665e7i | 1.58210i | 0.611753 | + | 0.791049i | \(0.290465\pi\) | ||||
−0.611753 | + | 0.791049i | \(0.709535\pi\) | |||||||
\(114\) | 237499. | − | 394063.i | 0.0150139 | − | 0.0249114i | ||||
\(115\) | 1.13207e6i | 0.0694112i | ||||||||
\(116\) | 1.34081e7 | + | 6.55566e6i | 0.797561 | + | 0.389954i | ||||
\(117\) | − | 1.28051e7i | − | 0.739151i | ||||||
\(118\) | 5.93583e6 | − | 3.70512e6i | 0.332578 | − | 0.207594i | ||||
\(119\) | 5.99285e6i | 0.326001i | ||||||||
\(120\) | −12163.2 | − | 117366.i | −0.000642560 | − | 0.00620026i | ||||
\(121\) | −5.83050e6 | −0.299197 | ||||||||
\(122\) | −1.15543e7 | + | 7.21214e6i | −0.576082 | + | 0.359588i | ||||
\(123\) | − | 57297.2i | − | 0.00277629i | ||||||
\(124\) | 1.62219e6 | − | 3.31782e6i | 0.0764059 | − | 0.156271i | ||||
\(125\) | −9.14471e6 | −0.418779 | ||||||||
\(126\) | 3.33678e6 | + | 5.34572e6i | 0.148604 | + | 0.238073i | ||||
\(127\) | 3.61018e7 | 1.56392 | 0.781962 | − | 0.623327i | \(-0.214219\pi\) | ||||
0.781962 | + | 0.623327i | \(0.214219\pi\) | |||||||
\(128\) | 1.71233e7 | − | 1.64239e7i | 0.721692 | − | 0.692214i | ||||
\(129\) | − | 513627.i | − | 0.0210661i | ||||||
\(130\) | −2.10291e6 | − | 3.36899e6i | −0.0839496 | − | 0.134492i | ||||
\(131\) | − | 8.16284e6i | − | 0.317243i | −0.987339 | − | 0.158621i | \(-0.949295\pi\) | ||
0.987339 | − | 0.158621i | \(-0.0507049\pi\) | |||||||
\(132\) | 787019. | + | 384800.i | 0.0297836 | + | 0.0145622i | ||||
\(133\) | 3.45397e6 | + | 6.79324e6i | 0.127303 | + | 0.250378i | ||||
\(134\) | −3.35869e7 | + | 2.09648e7i | −1.20588 | + | 0.752702i | ||||
\(135\) | 356241. | 0.0124617 | ||||||||
\(136\) | 3.50965e6 | + | 3.38657e7i | 0.119640 | + | 1.15445i | ||||
\(137\) | −1.46485e7 | −0.486710 | −0.243355 | − | 0.969937i | \(-0.578248\pi\) | ||||
−0.243355 | + | 0.969937i | \(0.578248\pi\) | |||||||
\(138\) | 153999. | + | 246716.i | 0.00498818 | + | 0.00799137i | ||||
\(139\) | − | 4.99434e7i | − | 1.57734i | −0.614815 | − | 0.788671i | \(-0.710769\pi\) | ||
0.614815 | − | 0.788671i | \(-0.289231\pi\) | |||||||
\(140\) | 1.75579e6 | + | 858464.i | 0.0540785 | + | 0.0264408i | ||||
\(141\) | − | 1.63519e6i | − | 0.0491249i | ||||||
\(142\) | 4.80708e7 | − | 3.00056e7i | 1.40887 | − | 0.879412i | ||||
\(143\) | 2.94859e7 | 0.843215 | ||||||||
\(144\) | 2.19869e7 | + | 2.82546e7i | 0.613613 | + | 0.788535i | ||||
\(145\) | 6.98461e6i | 0.190263i | ||||||||
\(146\) | −4.67528e7 | + | 2.91829e7i | −1.24329 | + | 0.776057i | ||||
\(147\) | −1.03182e6 | −0.0267913 | ||||||||
\(148\) | 4.73781e7 | + | 2.31647e7i | 1.20133 | + | 0.587369i | ||||
\(149\) | −1.04112e7 | −0.257839 | −0.128919 | − | 0.991655i | \(-0.541151\pi\) | ||||
−0.128919 | + | 0.991655i | \(0.541151\pi\) | |||||||
\(150\) | −973053. | + | 607375.i | −0.0235406 | + | 0.0146939i | ||||
\(151\) | 1.45002e7 | 0.342732 | 0.171366 | − | 0.985207i | \(-0.445182\pi\) | ||||
0.171366 | + | 0.985207i | \(0.445182\pi\) | |||||||
\(152\) | 2.34968e7 | + | 3.63660e7i | 0.542696 | + | 0.839929i | ||||
\(153\) | −5.13743e7 | −1.15965 | ||||||||
\(154\) | −1.23094e7 | + | 7.68347e6i | −0.271590 | + | 0.169526i | ||||
\(155\) | 1.72834e6 | 0.0372793 | ||||||||
\(156\) | −916592. | − | 448152.i | −0.0193304 | − | 0.00945126i | ||||
\(157\) | −6.31804e7 | −1.30297 | −0.651483 | − | 0.758663i | \(-0.725853\pi\) | ||||
−0.651483 | + | 0.758663i | \(0.725853\pi\) | |||||||
\(158\) | 2.69356e7 | − | 1.68131e7i | 0.543284 | − | 0.339116i | ||||
\(159\) | − | 1.66037e6i | − | 0.0327579i | ||||||
\(160\) | 1.04248e7 | + | 3.82294e6i | 0.201208 | + | 0.0737866i | ||||
\(161\) | −4.81726e6 | −0.0909724 | ||||||||
\(162\) | −4.57879e7 | + | 2.85806e7i | −0.846152 | + | 0.528165i | ||||
\(163\) | 2.10168e7i | 0.380110i | 0.981773 | + | 0.190055i | \(0.0608667\pi\) | ||||
−0.981773 | + | 0.190055i | \(0.939133\pi\) | |||||||
\(164\) | 4.84383e6 | + | 2.36831e6i | 0.0857503 | + | 0.0419261i | ||||
\(165\) | 409978.i | 0.00710505i | ||||||||
\(166\) | −3.10574e7 | − | 4.97559e7i | −0.526971 | − | 0.844240i | ||||
\(167\) | −7.39391e7 | −1.22848 | −0.614238 | − | 0.789121i | \(-0.710536\pi\) | ||||
−0.614238 | + | 0.789121i | \(0.710536\pi\) | |||||||
\(168\) | 499427. | − | 51757.8i | 0.00812624 | − | 0.000842158i | ||||
\(169\) | 2.84081e7 | 0.452730 | ||||||||
\(170\) | −1.35164e7 | + | 8.43689e6i | −0.211004 | + | 0.131708i | ||||
\(171\) | −5.82358e7 | + | 2.96095e7i | −0.890643 | + | 0.452840i | ||||
\(172\) | 4.34213e7 | + | 2.12301e7i | 0.650659 | + | 0.318129i | ||||
\(173\) | − | 5.29824e7i | − | 0.777983i | −0.921241 | − | 0.388992i | \(-0.872824\pi\) | ||
0.921241 | − | 0.388992i | \(-0.127176\pi\) | |||||||
\(174\) | 950143. | + | 1.52219e6i | 0.0136731 | + | 0.0219051i | ||||
\(175\) | − | 1.89993e7i | − | 0.267982i | ||||||
\(176\) | −6.50610e7 | + | 5.06284e7i | −0.899552 | + | 0.700003i | ||||
\(177\) | 841266. | 0.0114032 | ||||||||
\(178\) | 1.43077e7 | + | 2.29218e7i | 0.190151 | + | 0.304634i | ||||
\(179\) | 1.29684e8 | 1.69005 | 0.845027 | − | 0.534724i | \(-0.179584\pi\) | ||||
0.845027 | + | 0.534724i | \(0.179584\pi\) | |||||||
\(180\) | −7.35928e6 | + | 1.50517e7i | −0.0940549 | + | 0.192368i | ||||
\(181\) | − | 4.90787e7i | − | 0.615202i | −0.951515 | − | 0.307601i | \(-0.900474\pi\) | ||
0.951515 | − | 0.307601i | \(-0.0995262\pi\) | |||||||
\(182\) | 1.43360e7 | − | 8.94846e6i | 0.176270 | − | 0.110027i | ||||
\(183\) | −1.63755e6 | −0.0197523 | ||||||||
\(184\) | −2.72225e7 | + | 2.82118e6i | −0.322155 | + | 0.0333863i | ||||
\(185\) | 2.46804e7i | 0.286584i | ||||||||
\(186\) | 376664. | − | 235112.i | 0.00429200 | − | 0.00267905i | ||||
\(187\) | − | 1.18298e8i | − | 1.32291i | ||||||
\(188\) | 1.38237e8 | + | 6.75886e7i | 1.51730 | + | 0.741858i | ||||
\(189\) | 1.51591e6i | 0.0163326i | ||||||||
\(190\) | −1.04591e7 | + | 1.73539e7i | −0.110625 | + | 0.183552i | ||||
\(191\) | 8.28854e7i | 0.860718i | 0.902658 | + | 0.430359i | \(0.141613\pi\) | ||||
−0.902658 | + | 0.430359i | \(0.858387\pi\) | |||||||
\(192\) | 2.79196e6 | − | 584969.i | 0.0284679 | − | 0.00596457i | ||||
\(193\) | − | 1.64768e8i | − | 1.64977i | −0.565302 | − | 0.824884i | \(-0.691240\pi\) | ||
0.565302 | − | 0.824884i | \(-0.308760\pi\) | |||||||
\(194\) | 4.52326e7 | + | 7.24654e7i | 0.444780 | + | 0.712565i | ||||
\(195\) | − | 477476.i | − | 0.00461137i | ||||||
\(196\) | 4.26491e7 | − | 8.72288e7i | 0.404588 | − | 0.827492i | ||||
\(197\) | −4.79190e7 | −0.446556 | −0.223278 | − | 0.974755i | \(-0.571676\pi\) | ||||
−0.223278 | + | 0.974755i | \(0.571676\pi\) | |||||||
\(198\) | −6.58674e7 | − | 1.05524e8i | −0.603035 | − | 0.966099i | ||||
\(199\) | − | 1.30874e8i | − | 1.17725i | −0.808407 | − | 0.588624i | \(-0.799670\pi\) | ||
0.808407 | − | 0.588624i | \(-0.200330\pi\) | |||||||
\(200\) | −1.11268e7 | − | 1.07366e8i | −0.0983478 | − | 0.948988i | ||||
\(201\) | −4.76016e6 | −0.0413462 | ||||||||
\(202\) | −1.15066e8 | + | 7.18238e7i | −0.982241 | + | 0.613111i | ||||
\(203\) | −2.97215e7 | −0.249364 | ||||||||
\(204\) | −1.79799e6 | + | 3.67738e6i | −0.0148280 | + | 0.0303273i | ||||
\(205\) | 2.52327e6i | 0.0204562i | ||||||||
\(206\) | 9.22379e7 | − | 5.75745e7i | 0.735147 | − | 0.458875i | ||||
\(207\) | − | 4.12965e7i | − | 0.323606i | ||||||
\(208\) | 7.57724e7 | − | 5.89637e7i | 0.583834 | − | 0.454321i | ||||
\(209\) | −6.81807e7 | − | 1.34097e8i | −0.516594 | − | 1.01603i | ||||
\(210\) | 124421. | + | 199331.i | 0.000927101 | + | 0.00148527i | ||||
\(211\) | −8.86686e7 | −0.649802 | −0.324901 | − | 0.945748i | \(-0.605331\pi\) | ||||
−0.324901 | + | 0.945748i | \(0.605331\pi\) | |||||||
\(212\) | 1.40366e8 | + | 6.86295e7i | 1.01178 | + | 0.494692i | ||||
\(213\) | 6.81292e6 | 0.0483064 | ||||||||
\(214\) | 6.21458e7 | − | 3.87911e7i | 0.433474 | − | 0.270573i | ||||
\(215\) | 2.26193e7i | 0.155219i | ||||||||
\(216\) | 887775. | + | 8.56642e6i | 0.00599397 | + | 0.0578377i | ||||
\(217\) | 7.35456e6i | 0.0488594i | ||||||||
\(218\) | −6.39295e7 | − | 1.02419e8i | −0.417930 | − | 0.669550i | ||||
\(219\) | −6.62613e6 | −0.0426291 | ||||||||
\(220\) | −3.46590e7 | − | 1.69459e7i | −0.219451 | − | 0.107297i | ||||
\(221\) | 1.37774e8i | 0.858608i | ||||||||
\(222\) | 3.35737e6 | + | 5.37872e6i | 0.0205951 | + | 0.0329946i | ||||
\(223\) | 6.78902e7 | 0.409959 | 0.204979 | − | 0.978766i | \(-0.434287\pi\) | ||||
0.204979 | + | 0.978766i | \(0.434287\pi\) | |||||||
\(224\) | −1.62677e7 | + | 4.43603e7i | −0.0967069 | + | 0.263710i | ||||
\(225\) | 1.62874e8 | 0.953264 | ||||||||
\(226\) | −1.45374e8 | − | 2.32897e8i | −0.837734 | − | 1.34210i | ||||
\(227\) | 1.99723e7 | 0.113328 | 0.0566641 | − | 0.998393i | \(-0.481954\pi\) | ||||
0.0566641 | + | 0.998393i | \(0.481954\pi\) | |||||||
\(228\) | 81322.0 | + | 5.20479e6i | 0.000454398 | + | 0.0290825i | ||||
\(229\) | 8.04097e7 | 0.442470 | 0.221235 | − | 0.975220i | \(-0.428991\pi\) | ||||
0.221235 | + | 0.975220i | \(0.428991\pi\) | |||||||
\(230\) | −6.78187e6 | − | 1.08650e7i | −0.0367538 | − | 0.0588819i | ||||
\(231\) | −1.74457e6 | −0.00931209 | ||||||||
\(232\) | −1.67957e8 | + | 1.74061e7i | −0.883059 | + | 0.0915152i | ||||
\(233\) | −9.38810e6 | −0.0486219 | −0.0243110 | − | 0.999704i | \(-0.507739\pi\) | ||||
−0.0243110 | + | 0.999704i | \(0.507739\pi\) | |||||||
\(234\) | 7.67117e7 | + | 1.22897e8i | 0.391387 | + | 0.627026i | ||||
\(235\) | 7.20110e7i | 0.361961i | ||||||||
\(236\) | −3.47727e7 | + | 7.11195e7i | −0.172205 | + | 0.352206i | ||||
\(237\) | 3.81750e6 | 0.0186277 | ||||||||
\(238\) | −3.59014e7 | − | 5.75162e7i | −0.172620 | − | 0.276548i | ||||
\(239\) | − | 1.71095e8i | − | 0.810672i | −0.914168 | − | 0.405336i | \(-0.867155\pi\) | ||
0.914168 | − | 0.405336i | \(-0.132845\pi\) | |||||||
\(240\) | 819843. | + | 1.05356e6i | 0.00382817 | + | 0.00491947i | ||||
\(241\) | 3.36062e8i | 1.54654i | 0.634080 | + | 0.773268i | \(0.281379\pi\) | ||||
−0.634080 | + | 0.773268i | \(0.718621\pi\) | |||||||
\(242\) | 5.59580e7 | − | 3.49288e7i | 0.253810 | − | 0.158427i | ||||
\(243\) | −1.94957e7 | −0.0871597 | ||||||||
\(244\) | 6.76863e7 | − | 1.38437e8i | 0.298288 | − | 0.610080i | ||||
\(245\) | 4.54397e7 | 0.197403 | ||||||||
\(246\) | 343250. | + | 549908.i | 0.00147007 | + | 0.00235514i | ||||
\(247\) | 7.94059e7 | + | 1.56175e8i | 0.335284 | + | 0.659435i | ||||
\(248\) | 4.30713e6 | + | 4.15608e7i | 0.0179311 | + | 0.173023i | ||||
\(249\) | − | 7.05174e6i | − | 0.0289467i | ||||||
\(250\) | 8.77662e7 | − | 5.47832e7i | 0.355252 | − | 0.221747i | ||||
\(251\) | 1.13733e8i | 0.453972i | 0.973898 | + | 0.226986i | \(0.0728871\pi\) | ||||
−0.973898 | + | 0.226986i | \(0.927113\pi\) | |||||||
\(252\) | −6.40492e7 | − | 3.13158e7i | −0.252123 | − | 0.123271i | ||||
\(253\) | 9.50920e7 | 0.369166 | ||||||||
\(254\) | −3.46486e8 | + | 2.16275e8i | −1.32668 | + | 0.828110i | ||||
\(255\) | −1.91564e6 | −0.00723475 | ||||||||
\(256\) | −6.59498e7 | + | 2.60208e8i | −0.245682 | + | 0.969350i | ||||
\(257\) | − | 3.84283e7i | − | 0.141217i | −0.997504 | − | 0.0706083i | \(-0.977506\pi\) | ||
0.997504 | − | 0.0706083i | \(-0.0224940\pi\) | |||||||
\(258\) | 3.07698e6 | + | 4.92952e6i | 0.0111547 | + | 0.0178704i | ||||
\(259\) | −1.05022e8 | −0.375605 | ||||||||
\(260\) | 4.03652e7 | + | 1.97359e7i | 0.142430 | + | 0.0696386i | ||||
\(261\) | − | 2.54791e8i | − | 0.887037i | ||||||
\(262\) | 4.89011e7 | + | 7.83426e7i | 0.167983 | + | 0.269118i | ||||
\(263\) | 2.54125e8i | 0.861396i | 0.902496 | + | 0.430698i | \(0.141733\pi\) | ||||
−0.902496 | + | 0.430698i | \(0.858267\pi\) | |||||||
\(264\) | −9.85862e6 | + | 1.02169e6i | −0.0329763 | + | 0.00341748i | ||||
\(265\) | 7.31201e7i | 0.241366i | ||||||||
\(266\) | −7.38456e7 | − | 4.45063e7i | −0.240569 | − | 0.144989i | ||||
\(267\) | 3.24863e6i | 0.0104451i | ||||||||
\(268\) | 1.96755e8 | − | 4.02418e8i | 0.624388 | − | 1.27704i | ||||
\(269\) | 5.05355e8i | 1.58294i | 0.611209 | + | 0.791469i | \(0.290683\pi\) | ||||
−0.611209 | + | 0.791469i | \(0.709317\pi\) | |||||||
\(270\) | −3.41901e6 | + | 2.13413e6i | −0.0105713 | + | 0.00659855i | ||||
\(271\) | 3.71301e8i | 1.13327i | 0.823969 | + | 0.566635i | \(0.191755\pi\) | ||||
−0.823969 | + | 0.566635i | \(0.808245\pi\) | |||||||
\(272\) | −2.36563e8 | − | 3.04000e8i | −0.712781 | − | 0.915973i | ||||
\(273\) | 2.03179e6 | 0.00604381 | ||||||||
\(274\) | 1.40588e8 | − | 8.77546e7i | 0.412878 | − | 0.257717i | ||||
\(275\) | 3.75044e8i | 1.08747i | ||||||||
\(276\) | −2.95601e6 | − | 1.44529e6i | −0.00846299 | − | 0.00413784i | ||||
\(277\) | 2.33010e8 | 0.658711 | 0.329356 | − | 0.944206i | \(-0.393169\pi\) | ||||
0.329356 | + | 0.944206i | \(0.393169\pi\) | |||||||
\(278\) | 2.99196e8 | + | 4.79330e8i | 0.835216 | + | 1.33807i | ||||
\(279\) | −6.30478e7 | −0.173802 | ||||||||
\(280\) | −2.19939e7 | + | 2.27933e6i | −0.0598756 | + | 0.00620517i | ||||
\(281\) | 5.89101e8i | 1.58386i | 0.610609 | + | 0.791932i | \(0.290925\pi\) | ||||
−0.610609 | + | 0.791932i | \(0.709075\pi\) | |||||||
\(282\) | 9.79593e6 | + | 1.56937e7i | 0.0260120 | + | 0.0416729i | ||||
\(283\) | − | 1.56644e8i | − | 0.410828i | −0.978675 | − | 0.205414i | \(-0.934146\pi\) | ||
0.978675 | − | 0.205414i | \(-0.0658541\pi\) | |||||||
\(284\) | −2.81603e8 | + | 5.75955e8i | −0.729498 | + | 1.49202i | ||||
\(285\) | −2.17149e6 | + | 1.10408e6i | −0.00555649 | + | 0.00282515i | ||||
\(286\) | −2.82990e8 | + | 1.76641e8i | −0.715303 | + | 0.446489i | ||||
\(287\) | −1.07372e7 | −0.0268106 | ||||||||
\(288\) | −3.80283e8 | − | 1.39456e8i | −0.938067 | − | 0.344005i | ||||
\(289\) | 1.42413e8 | 0.347063 | ||||||||
\(290\) | −4.18427e7 | − | 6.70346e7i | −0.100746 | − | 0.161401i | ||||
\(291\) | 1.02703e7i | 0.0244319i | ||||||||
\(292\) | 2.73883e8 | − | 5.60165e8i | 0.643762 | − | 1.31667i | ||||
\(293\) | − | 1.29551e8i | − | 0.300888i | −0.988619 | − | 0.150444i | \(-0.951930\pi\) | ||
0.988619 | − | 0.150444i | \(-0.0480704\pi\) | |||||||
\(294\) | 9.90287e6 | − | 6.18133e6i | 0.0227272 | − | 0.0141862i | ||||
\(295\) | −3.70479e7 | −0.0840208 | ||||||||
\(296\) | −5.93483e8 | + | 6.15052e7i | −1.33011 | + | 0.137845i | ||||
\(297\) | − | 2.99237e7i | − | 0.0662778i | ||||||
\(298\) | 9.99210e7 | − | 6.23703e7i | 0.218726 | − | 0.136528i | ||||
\(299\) | −1.10748e8 | −0.239599 | ||||||||
\(300\) | 5.70025e6 | − | 1.16585e7i | 0.0121890 | − | 0.0249299i | ||||
\(301\) | −9.62513e7 | −0.203434 | ||||||||
\(302\) | −1.39165e8 | + | 8.68664e7i | −0.290741 | + | 0.181480i | ||||
\(303\) | −1.63080e7 | −0.0336783 | ||||||||
\(304\) | −4.43368e8 | − | 2.08259e8i | −0.905121 | − | 0.425154i | ||||
\(305\) | 7.21152e7 | 0.145538 | ||||||||
\(306\) | 4.93064e8 | − | 3.07768e8i | 0.983735 | − | 0.614043i | ||||
\(307\) | −3.37575e8 | −0.665864 | −0.332932 | − | 0.942951i | \(-0.608038\pi\) | ||||
−0.332932 | + | 0.942951i | \(0.608038\pi\) | |||||||
\(308\) | 7.21097e7 | − | 1.47484e8i | 0.140626 | − | 0.287619i | ||||
\(309\) | 1.30726e7 | 0.0252062 | ||||||||
\(310\) | −1.65877e7 | + | 1.03540e7i | −0.0316242 | + | 0.0197397i | ||||
\(311\) | − | 3.39278e8i | − | 0.639580i | −0.947488 | − | 0.319790i | \(-0.896388\pi\) | ||
0.947488 | − | 0.319790i | \(-0.103612\pi\) | |||||||
\(312\) | 1.14817e7 | − | 1.18990e6i | 0.0214026 | − | 0.00221804i | ||||
\(313\) | 6.02290e8 | 1.11020 | 0.555099 | − | 0.831784i | \(-0.312680\pi\) | ||||
0.555099 | + | 0.831784i | \(0.312680\pi\) | |||||||
\(314\) | 6.06372e8 | − | 3.78495e8i | 1.10531 | − | 0.689931i | ||||
\(315\) | − | 3.33648e7i | − | 0.0601454i | ||||||
\(316\) | −1.57792e8 | + | 3.22727e8i | −0.281306 | + | 0.575347i | ||||
\(317\) | 6.39970e8i | 1.12837i | 0.825648 | + | 0.564186i | \(0.190810\pi\) | ||||
−0.825648 | + | 0.564186i | \(0.809190\pi\) | |||||||
\(318\) | 9.94680e6 | + | 1.59354e7i | 0.0173456 | + | 0.0277887i | ||||
\(319\) | 5.86697e8 | 1.01192 | ||||||||
\(320\) | −1.22953e8 | + | 2.57611e7i | −0.209757 | + | 0.0439480i | ||||
\(321\) | 8.80772e6 | 0.0148626 | ||||||||
\(322\) | 4.62335e7 | − | 2.88588e7i | 0.0771723 | − | 0.0481706i | ||||
\(323\) | 6.26576e8 | − | 3.18577e8i | 1.03458 | − | 0.526025i | ||||
\(324\) | 2.68231e8 | − | 5.48604e8i | 0.438128 | − | 0.896089i | ||||
\(325\) | − | 4.36791e8i | − | 0.705800i | ||||||
\(326\) | −1.25905e8 | − | 2.01708e8i | −0.201271 | − | 0.322449i | ||||
\(327\) | − | 1.45155e7i | − | 0.0229570i | ||||||
\(328\) | −6.06764e7 | + | 6.28816e6i | −0.0949426 | + | 0.00983931i | ||||
\(329\) | −3.06427e8 | −0.474397 | ||||||||
\(330\) | −2.45606e6 | − | 3.93475e6i | −0.00376218 | − | 0.00602724i | ||||
\(331\) | −8.36585e8 | −1.26798 | −0.633989 | − | 0.773342i | \(-0.718584\pi\) | ||||
−0.633989 | + | 0.773342i | \(0.718584\pi\) | |||||||
\(332\) | 5.96145e8 | + | 2.91475e8i | 0.894064 | + | 0.437138i | ||||
\(333\) | − | 9.00314e8i | − | 1.33610i | ||||||
\(334\) | 7.09628e8 | − | 4.42947e8i | 1.04212 | − | 0.650488i | ||||
\(335\) | 2.09629e8 | 0.304646 | ||||||||
\(336\) | −4.48317e6 | + | 3.48866e6i | −0.00644760 | + | 0.00501732i | ||||
\(337\) | − | 7.49773e8i | − | 1.06715i | −0.845753 | − | 0.533574i | \(-0.820848\pi\) | ||
0.845753 | − | 0.533574i | \(-0.179152\pi\) | |||||||
\(338\) | −2.72646e8 | + | 1.70185e8i | −0.384053 | + | 0.239724i | ||||
\(339\) | − | 3.30078e7i | − | 0.0460170i | ||||||
\(340\) | 7.91806e7 | − | 1.61946e8i | 0.109255 | − | 0.223457i | ||||
\(341\) | − | 1.45178e8i | − | 0.198271i | ||||||
\(342\) | 3.81535e8 | − | 6.33050e8i | 0.515754 | − | 0.855749i | ||||
\(343\) | 4.03279e8i | 0.539605i | ||||||||
\(344\) | −5.43918e8 | + | 5.63686e7i | −0.720409 | + | 0.0746591i | ||||
\(345\) | − | 1.53986e6i | − | 0.00201890i | ||||||
\(346\) | 3.17402e8 | + | 5.08497e8i | 0.411948 | + | 0.659967i | ||||
\(347\) | − | 1.13846e9i | − | 1.46273i | −0.681987 | − | 0.731364i | \(-0.738884\pi\) | ||
0.681987 | − | 0.731364i | \(-0.261116\pi\) | |||||||
\(348\) | −1.82379e7 | − | 8.91713e6i | −0.0231979 | − | 0.0113422i | ||||
\(349\) | 3.28510e8 | 0.413675 | 0.206838 | − | 0.978375i | \(-0.433683\pi\) | ||||
0.206838 | + | 0.978375i | \(0.433683\pi\) | |||||||
\(350\) | 1.13819e8 | + | 1.82346e8i | 0.141899 | + | 0.227330i | ||||
\(351\) | 3.48503e7i | 0.0430162i | ||||||||
\(352\) | 3.21121e8 | − | 8.75665e8i | 0.392437 | − | 1.07014i | ||||
\(353\) | −8.16440e8 | −0.987900 | −0.493950 | − | 0.869490i | \(-0.664447\pi\) | ||||
−0.493950 | + | 0.869490i | \(0.664447\pi\) | |||||||
\(354\) | −8.07403e6 | + | 5.03977e6i | −0.00967339 | + | 0.00603809i | ||||
\(355\) | −3.00029e8 | −0.355930 | ||||||||
\(356\) | −2.74635e8 | − | 1.34278e8i | −0.322613 | − | 0.157736i | ||||
\(357\) | − | 8.15159e6i | − | 0.00948208i | ||||||
\(358\) | −1.24464e9 | + | 7.76897e8i | −1.43368 | + | 0.894897i | ||||
\(359\) | 2.50076e8i | 0.285260i | 0.989776 | + | 0.142630i | \(0.0455560\pi\) | ||||
−0.989776 | + | 0.142630i | \(0.954444\pi\) | |||||||
\(360\) | −1.95398e7 | − | 1.88546e8i | −0.0220730 | − | 0.212989i | ||||
\(361\) | 5.26649e8 | − | 7.22252e8i | 0.589177 | − | 0.808004i | ||||
\(362\) | 2.94016e8 | + | 4.71031e8i | 0.325754 | + | 0.521879i | ||||
\(363\) | 7.93075e6 | 0.00870245 | ||||||||
\(364\) | −8.39817e7 | + | 1.71765e8i | −0.0912704 | + | 0.186673i | ||||
\(365\) | 2.91804e8 | 0.314099 | ||||||||
\(366\) | 1.57164e7 | − | 9.81010e6i | 0.0167559 | − | 0.0104590i | ||||
\(367\) | 2.85531e8i | 0.301524i | 0.988570 | + | 0.150762i | \(0.0481727\pi\) | ||||
−0.988570 | + | 0.150762i | \(0.951827\pi\) | |||||||
\(368\) | 2.44366e8 | − | 1.90158e8i | 0.255607 | − | 0.198906i | ||||
\(369\) | − | 9.20461e7i | − | 0.0953703i | ||||||
\(370\) | −1.47853e8 | − | 2.36870e8i | −0.151748 | − | 0.243110i | ||||
\(371\) | −3.11146e8 | −0.316341 | ||||||||
\(372\) | −2.20654e6 | + | 4.51297e6i | −0.00222234 | + | 0.00454529i | ||||
\(373\) | 9.83051e8i | 0.980833i | 0.871488 | + | 0.490416i | \(0.163155\pi\) | ||||
−0.871488 | + | 0.490416i | \(0.836845\pi\) | |||||||
\(374\) | 7.08687e8 | + | 1.13536e9i | 0.700493 | + | 1.12223i | ||||
\(375\) | 1.24388e7 | 0.0121806 | ||||||||
\(376\) | −1.73163e9 | + | 1.79456e8i | −1.67995 | + | 0.174101i | ||||
\(377\) | −6.83290e8 | −0.656765 | ||||||||
\(378\) | −9.08134e6 | − | 1.45489e7i | −0.00864825 | − | 0.0138550i | ||||
\(379\) | −1.01345e9 | −0.956237 | −0.478118 | − | 0.878295i | \(-0.658681\pi\) | ||||
−0.478118 | + | 0.878295i | \(0.658681\pi\) | |||||||
\(380\) | −3.58128e6 | − | 2.29210e8i | −0.00334808 | − | 0.214285i | ||||
\(381\) | −4.91063e7 | −0.0454883 | ||||||||
\(382\) | −4.96541e8 | − | 7.95490e8i | −0.455757 | − | 0.730151i | ||||
\(383\) | 7.20156e8 | 0.654985 | 0.327492 | − | 0.944854i | \(-0.393796\pi\) | ||||
0.327492 | + | 0.944854i | \(0.393796\pi\) | |||||||
\(384\) | −2.32914e7 | + | 2.23401e7i | −0.0209912 | + | 0.0201338i | ||||
\(385\) | 7.68280e7 | 0.0686131 | ||||||||
\(386\) | 9.87077e8 | + | 1.58136e9i | 0.873566 | + | 1.39951i | ||||
\(387\) | − | 8.25125e8i | − | 0.723655i | ||||||
\(388\) | −8.68237e8 | − | 4.24510e8i | −0.754618 | − | 0.368958i | ||||
\(389\) | −1.55137e9 | −1.33627 | −0.668133 | − | 0.744042i | \(-0.732906\pi\) | ||||
−0.668133 | + | 0.744042i | \(0.732906\pi\) | |||||||
\(390\) | 2.86042e6 | + | 4.58256e6i | 0.00244176 | + | 0.00391185i | ||||
\(391\) | 4.44321e8i | 0.375905i | ||||||||
\(392\) | 1.13239e8 | + | 1.09267e9i | 0.0949496 | + | 0.916198i | ||||
\(393\) | 1.11032e7i | 0.00922733i | ||||||||
\(394\) | 4.59901e8 | − | 2.87068e8i | 0.378816 | − | 0.236455i | ||||
\(395\) | −1.68116e8 | −0.137252 | ||||||||
\(396\) | 1.26432e9 | + | 6.18169e8i | 1.02312 | + | 0.500235i | ||||
\(397\) | −1.62177e9 | −1.30083 | −0.650416 | − | 0.759578i | \(-0.725405\pi\) | ||||
−0.650416 | + | 0.759578i | \(0.725405\pi\) | |||||||
\(398\) | 7.84028e8 | + | 1.25606e9i | 0.623363 | + | 0.998665i | ||||
\(399\) | −4.69815e6 | − | 9.24030e6i | −0.00370273 | − | 0.00728250i | ||||
\(400\) | 7.49985e8 | + | 9.63783e8i | 0.585926 | + | 0.752955i | ||||
\(401\) | − | 6.46218e8i | − | 0.500465i | −0.968186 | − | 0.250233i | \(-0.919493\pi\) | ||
0.968186 | − | 0.250233i | \(-0.0805071\pi\) | |||||||
\(402\) | 4.56855e7 | − | 2.85167e7i | 0.0350742 | − | 0.0218931i | ||||
\(403\) | 1.69080e8i | 0.128684i | ||||||||
\(404\) | 6.74070e8 | − | 1.37865e9i | 0.508593 | − | 1.04021i | ||||
\(405\) | 2.85781e8 | 0.213767 | ||||||||
\(406\) | 2.85251e8 | − | 1.78052e8i | 0.211537 | − | 0.132040i | ||||
\(407\) | 2.07312e9 | 1.52421 | ||||||||
\(408\) | −4.77390e6 | − | 4.60648e7i | −0.00347987 | − | 0.0335783i | ||||
\(409\) | − | 1.95371e9i | − | 1.41198i | −0.708223 | − | 0.705989i | \(-0.750503\pi\) | ||
0.708223 | − | 0.705989i | \(-0.249497\pi\) | |||||||
\(410\) | −1.51162e7 | − | 2.42170e7i | −0.0108317 | − | 0.0173531i | ||||
\(411\) | 1.99251e7 | 0.0141565 | ||||||||
\(412\) | −5.40339e8 | + | 1.10514e9i | −0.380650 | + | 0.778532i | ||||
\(413\) | − | 1.57649e8i | − | 0.110120i | ||||||
\(414\) | 2.47395e8 | + | 3.96342e8i | 0.171352 | + | 0.274517i | ||||
\(415\) | 3.10547e8i | 0.213284i | ||||||||
\(416\) | −3.73990e8 | + | 1.01983e9i | −0.254703 | + | 0.694548i | ||||
\(417\) | 6.79339e7i | 0.0458786i | ||||||||
\(418\) | 1.45770e9 | + | 8.78547e8i | 0.976228 | + | 0.588366i | ||||
\(419\) | − | 1.86031e8i | − | 0.123548i | −0.998090 | − | 0.0617742i | \(-0.980324\pi\) | ||
0.998090 | − | 0.0617742i | \(-0.0196759\pi\) | |||||||
\(420\) | −2.38826e6 | − | 1.16770e6i | −0.00157293 | − | 0.000769057i | ||||
\(421\) | − | 2.21882e8i | − | 0.144922i | −0.997371 | − | 0.0724609i | \(-0.976915\pi\) | ||
0.997371 | − | 0.0724609i | \(-0.0230853\pi\) | |||||||
\(422\) | 8.50994e8 | − | 5.31187e8i | 0.551230 | − | 0.344076i | ||||
\(423\) | − | 2.62688e9i | − | 1.68752i | ||||||
\(424\) | −1.75830e9 | + | 1.82220e8i | −1.12024 | + | 0.116095i | ||||
\(425\) | −1.75241e9 | −1.10732 | ||||||||
\(426\) | −6.53868e7 | + | 4.08141e7i | −0.0409785 | + | 0.0255786i | ||||
\(427\) | 3.06870e8i | 0.190747i | ||||||||
\(428\) | −3.64056e8 | + | 7.44593e8i | −0.224448 | + | 0.459056i | ||||
\(429\) | −4.01073e7 | −0.0245258 | ||||||||
\(430\) | −1.35505e8 | − | 2.17088e8i | −0.0821895 | − | 0.131673i | ||||
\(431\) | 2.25776e8 | 0.135833 | 0.0679167 | − | 0.997691i | \(-0.478365\pi\) | ||||
0.0679167 | + | 0.997691i | \(0.478365\pi\) | |||||||
\(432\) | −5.98392e7 | − | 7.68976e7i | −0.0357103 | − | 0.0458902i | ||||
\(433\) | 2.32222e9i | 1.37466i | 0.726344 | + | 0.687331i | \(0.241218\pi\) | ||||
−0.726344 | + | 0.687331i | \(0.758782\pi\) | |||||||
\(434\) | −4.40590e7 | − | 7.05852e7i | −0.0258714 | − | 0.0414476i | ||||
\(435\) | − | 9.50060e6i | − | 0.00553399i | ||||||
\(436\) | 1.22712e9 | + | 5.99981e8i | 0.709064 | + | 0.346685i | ||||
\(437\) | 2.56084e8 | + | 5.03664e8i | 0.146790 | + | 0.288706i | ||||
\(438\) | 6.35941e7 | − | 3.96952e7i | 0.0361624 | − | 0.0225724i | ||||
\(439\) | 1.95077e9 | 1.10047 | 0.550237 | − | 0.835008i | \(-0.314537\pi\) | ||||
0.550237 | + | 0.835008i | \(0.314537\pi\) | |||||||
\(440\) | 4.34157e8 | − | 4.49936e7i | 0.242976 | − | 0.0251806i | ||||
\(441\) | −1.65759e9 | −0.920326 | ||||||||
\(442\) | −8.25364e8 | − | 1.32228e9i | −0.454640 | − | 0.728361i | ||||
\(443\) | 1.02331e6i | 0.000559236i | 1.00000 | 0.000279618i | \(8.90051e-5\pi\) | |||||
−1.00000 | 0.000279618i | \(0.999911\pi\) | ||||||||
\(444\) | −6.44446e7 | − | 3.15091e7i | −0.0349419 | − | 0.0170842i | ||||
\(445\) | − | 1.43064e8i | − | 0.0769611i | ||||||
\(446\) | −6.51574e8 | + | 4.06710e8i | −0.347770 | + | 0.217076i | ||||
\(447\) | 1.41615e7 | 0.00749950 | ||||||||
\(448\) | −1.09621e8 | − | 5.23201e8i | −0.0575996 | − | 0.274913i | ||||
\(449\) | 3.36338e9i | 1.75353i | 0.480918 | + | 0.876765i | \(0.340303\pi\) | ||||
−0.480918 | + | 0.876765i | \(0.659697\pi\) | |||||||
\(450\) | −1.56318e9 | + | 9.75730e8i | −0.808658 | + | 0.504761i | ||||
\(451\) | 2.11951e8 | 0.108797 | ||||||||
\(452\) | 2.79044e9 | + | 1.36434e9i | 1.42131 | + | 0.694924i | ||||
\(453\) | −1.97235e7 | −0.00996872 | ||||||||
\(454\) | −1.91684e8 | + | 1.19648e8i | −0.0961368 | + | 0.0600082i | ||||
\(455\) | −8.94768e7 | −0.0445318 | ||||||||
\(456\) | −3.19609e7 | − | 4.94657e7i | −0.0157849 | − | 0.0244302i | ||||
\(457\) | 2.71435e9 | 1.33033 | 0.665164 | − | 0.746697i | \(-0.268362\pi\) | ||||
0.665164 | + | 0.746697i | \(0.268362\pi\) | |||||||
\(458\) | −7.71730e8 | + | 4.81710e8i | −0.375350 | + | 0.234292i | ||||
\(459\) | 1.39820e8 | 0.0674877 | ||||||||
\(460\) | 1.30178e8 | + | 6.36482e7i | 0.0623568 | + | 0.0304883i | ||||
\(461\) | −3.25986e8 | −0.154969 | −0.0774847 | − | 0.996994i | \(-0.524689\pi\) | ||||
−0.0774847 | + | 0.996994i | \(0.524689\pi\) | |||||||
\(462\) | 1.67435e7 | − | 1.04512e7i | 0.00789949 | − | 0.00493083i | ||||
\(463\) | − | 6.99885e8i | − | 0.327713i | −0.986484 | − | 0.163856i | \(-0.947607\pi\) | ||
0.986484 | − | 0.163856i | \(-0.0523934\pi\) | |||||||
\(464\) | 1.50769e9 | − | 1.17323e9i | 0.700645 | − | 0.545220i | ||||
\(465\) | −2.35092e6 | −0.00108431 | ||||||||
\(466\) | 9.01021e7 | − | 5.62413e7i | 0.0412462 | − | 0.0257457i | ||||
\(467\) | − | 2.25108e9i | − | 1.02278i | −0.859349 | − | 0.511390i | \(-0.829131\pi\) | ||
0.859349 | − | 0.511390i | \(-0.170869\pi\) | |||||||
\(468\) | −1.47248e9 | − | 7.19943e8i | −0.664030 | − | 0.324666i | ||||
\(469\) | 8.92032e8i | 0.399278i | ||||||||
\(470\) | −4.31397e8 | − | 6.91124e8i | −0.191661 | − | 0.307053i | ||||
\(471\) | 8.59391e7 | 0.0378981 | ||||||||
\(472\) | −9.23258e7 | − | 8.90880e8i | −0.0404135 | − | 0.389962i | ||||
\(473\) | 1.89999e9 | 0.825537 | ||||||||
\(474\) | −3.66384e7 | + | 2.28695e7i | −0.0158020 | + | 0.00986353i | ||||
\(475\) | −1.98646e9 | + | 1.01000e9i | −0.850456 | + | 0.432407i | ||||
\(476\) | 6.89125e8 | + | 3.36936e8i | 0.292869 | + | 0.143193i | ||||
\(477\) | − | 2.66734e9i | − | 1.12529i | ||||||
\(478\) | 1.02498e9 | + | 1.64208e9i | 0.429257 | + | 0.687697i | ||||
\(479\) | 2.78889e9i | 1.15947i | 0.814807 | + | 0.579733i | \(0.196843\pi\) | ||||
−0.814807 | + | 0.579733i | \(0.803157\pi\) | |||||||
\(480\) | −1.41800e7 | − | 5.20003e6i | −0.00585236 | − | 0.00214616i | ||||
\(481\) | −2.41443e9 | −0.989254 | ||||||||
\(482\) | −2.01325e9 | − | 3.22535e9i | −0.818903 | − | 1.31193i | ||||
\(483\) | 6.55253e6 | 0.00264603 | ||||||||
\(484\) | −3.27808e8 | + | 6.70456e8i | −0.131420 | + | 0.268789i | ||||
\(485\) | − | 4.52286e8i | − | 0.180019i | ||||||
\(486\) | 1.87109e8 | − | 1.16793e8i | 0.0739380 | − | 0.0461518i | ||||
\(487\) | −1.24636e9 | −0.488983 | −0.244491 | − | 0.969651i | \(-0.578621\pi\) | ||||
−0.244491 | + | 0.969651i | \(0.578621\pi\) | |||||||
\(488\) | 1.79716e8 | + | 1.73413e9i | 0.0700030 | + | 0.675480i | ||||
\(489\) | − | 2.85874e7i | − | 0.0110559i | ||||||
\(490\) | −4.36106e8 | + | 2.72216e8i | −0.167458 | + | 0.104527i | ||||
\(491\) | 1.35954e9i | 0.518331i | 0.965833 | + | 0.259165i | \(0.0834474\pi\) | ||||
−0.965833 | + | 0.259165i | \(0.916553\pi\) | |||||||
\(492\) | −6.58867e6 | − | 3.22142e6i | −0.00249414 | − | 0.00121947i | ||||
\(493\) | 2.74137e9i | 1.03039i | ||||||||
\(494\) | −1.69769e9 | − | 1.02319e9i | −0.633600 | − | 0.381866i | ||||
\(495\) | 6.58617e8i | 0.244070i | ||||||||
\(496\) | −2.90316e8 | − | 3.73076e8i | −0.106828 | − | 0.137281i | ||||
\(497\) | − | 1.27671e9i | − | 0.466493i | ||||||
\(498\) | 4.22449e7 | + | 6.76789e7i | 0.0153275 | + | 0.0245556i | ||||
\(499\) | 6.40004e7i | 0.0230585i | 0.999934 | + | 0.0115292i | \(0.00366995\pi\) | ||||
−0.999934 | + | 0.0115292i | \(0.996330\pi\) | |||||||
\(500\) | −5.14143e8 | + | 1.05156e9i | −0.183945 | + | 0.376218i | ||||
\(501\) | 1.00573e8 | 0.0357315 | ||||||||
\(502\) | −6.81341e8 | − | 1.09155e9i | −0.240382 | − | 0.385106i | ||||
\(503\) | 2.53991e9i | 0.889878i | 0.895561 | + | 0.444939i | \(0.146775\pi\) | ||||
−0.895561 | + | 0.444939i | \(0.853225\pi\) | |||||||
\(504\) | 8.02314e8 | − | 8.31473e7i | 0.279150 | − | 0.0289295i | ||||
\(505\) | 7.18176e8 | 0.248148 | ||||||||
\(506\) | −9.12643e8 | + | 5.69668e8i | −0.313166 | + | 0.195477i | ||||
\(507\) | −3.86413e7 | −0.0131681 | ||||||||
\(508\) | 2.02975e9 | − | 4.15139e9i | 0.686941 | − | 1.40498i | ||||
\(509\) | − | 2.89291e9i | − | 0.972351i | −0.873861 | − | 0.486176i | \(-0.838392\pi\) | ||
0.873861 | − | 0.486176i | \(-0.161608\pi\) | |||||||
\(510\) | 1.83853e7 | − | 1.14760e7i | 0.00613727 | − | 0.00383086i | ||||
\(511\) | 1.24171e9i | 0.411667i | ||||||||
\(512\) | −9.25877e8 | − | 2.89243e9i | −0.304865 | − | 0.952395i | ||||
\(513\) | 1.58494e8 | − | 8.05849e7i | 0.0518325 | − | 0.0263538i | ||||
\(514\) | 2.30213e8 | + | 3.68815e8i | 0.0747753 | + | 0.119795i | ||||
\(515\) | −5.75695e8 | −0.185723 | ||||||||
\(516\) | −5.90625e7 | − | 2.88776e7i | −0.0189251 | − | 0.00925311i | ||||
\(517\) | 6.04883e9 | 1.92510 | ||||||||
\(518\) | 1.00795e9 | − | 6.29156e8i | 0.318628 | − | 0.198886i | ||||
\(519\) | 7.20677e7i | 0.0226284i | ||||||||
\(520\) | −5.05636e8 | + | 5.24012e7i | −0.157698 | + | 0.0163429i | ||||
\(521\) | 1.31837e8i | 0.0408419i | 0.999791 | + | 0.0204209i | \(0.00650064\pi\) | ||||
−0.999791 | + | 0.0204209i | \(0.993499\pi\) | |||||||
\(522\) | 1.52637e9 | + | 2.44535e9i | 0.469693 | + | 0.752478i | ||||
\(523\) | −2.71287e9 | −0.829226 | −0.414613 | − | 0.909998i | \(-0.636083\pi\) | ||||
−0.414613 | + | 0.909998i | \(0.636083\pi\) | |||||||
\(524\) | −9.38654e8 | − | 4.58939e8i | −0.285001 | − | 0.139346i | ||||
\(525\) | 2.58433e7i | 0.00779453i | ||||||||
\(526\) | −1.52239e9 | − | 2.43896e9i | −0.456116 | − | 0.730726i | ||||
\(527\) | 6.78350e8 | 0.201891 | ||||||||
\(528\) | 8.84972e7 | − | 6.88657e7i | 0.0261644 | − | 0.0203603i | ||||
\(529\) | 3.04766e9 | 0.895101 | ||||||||
\(530\) | −4.38040e8 | − | 7.01768e8i | −0.127805 | − | 0.204752i | ||||
\(531\) | 1.35147e9 | 0.391719 | ||||||||
\(532\) | 9.75355e8 | − | 1.52394e7i | 0.280848 | − | 0.00438810i | ||||
\(533\) | −2.46846e8 | −0.0706125 | ||||||||
\(534\) | −1.94616e7 | − | 3.11787e7i | −0.00553075 | − | 0.00886060i | ||||
\(535\) | −3.87877e8 | −0.109511 | ||||||||
\(536\) | 5.22410e8 | + | 5.04090e9i | 0.146533 | + | 1.41394i | ||||
\(537\) | −1.76399e8 | −0.0491570 | ||||||||
\(538\) | −3.02743e9 | − | 4.85014e9i | −0.838179 | − | 1.34281i | ||||
\(539\) | − | 3.81687e9i | − | 1.04990i | ||||||
\(540\) | 2.00289e7 | − | 4.09646e7i | 0.00547368 | − | 0.0111952i | ||||
\(541\) | 4.95285e9 | 1.34482 | 0.672411 | − | 0.740178i | \(-0.265259\pi\) | ||||
0.672411 | + | 0.740178i | \(0.265259\pi\) | |||||||
\(542\) | −2.22435e9 | − | 3.56355e9i | −0.600076 | − | 0.961358i | ||||
\(543\) | 6.67578e7i | 0.0178938i | ||||||||
\(544\) | 4.09158e9 | + | 1.50045e9i | 1.08967 | + | 0.399601i | ||||
\(545\) | 6.39239e8i | 0.169151i | ||||||||
\(546\) | −1.95001e7 | + | 1.21719e7i | −0.00512699 | + | 0.00320024i | ||||
\(547\) | −4.01383e9 | −1.04859 | −0.524293 | − | 0.851538i | \(-0.675670\pi\) | ||||
−0.524293 | + | 0.851538i | \(0.675670\pi\) | |||||||
\(548\) | −8.23581e8 | + | 1.68444e9i | −0.213784 | + | 0.437245i | ||||
\(549\) | −2.63068e9 | −0.678523 | ||||||||
\(550\) | −2.24678e9 | − | 3.59948e9i | −0.575825 | − | 0.922508i | ||||
\(551\) | 1.57998e9 | + | 3.10750e9i | 0.402366 | + | 0.791372i | ||||
\(552\) | 3.70285e7 | − | 3.83743e6i | 0.00937021 | − | 0.000971076i | ||||
\(553\) | − | 7.15382e8i | − | 0.179887i | ||||||
\(554\) | −2.23631e9 | + | 1.39589e9i | −0.558788 | + | 0.348793i | ||||
\(555\) | − | 3.35708e7i | − | 0.00833559i | ||||||
\(556\) | −5.74305e9 | − | 2.80797e9i | −1.41704 | − | 0.692835i | ||||
\(557\) | 2.94615e9 | 0.722373 | 0.361187 | − | 0.932494i | \(-0.382372\pi\) | ||||
0.361187 | + | 0.932494i | \(0.382372\pi\) | |||||||
\(558\) | 6.05100e8 | − | 3.77701e8i | 0.147437 | − | 0.0920297i | ||||
\(559\) | −2.21279e9 | −0.535796 | ||||||||
\(560\) | 1.97432e8 | − | 1.53635e8i | 0.0475071 | − | 0.0369685i | ||||
\(561\) | 1.60911e8i | 0.0384783i | ||||||||
\(562\) | −3.52913e9 | − | 5.65388e9i | −0.838669 | − | 1.34360i | ||||
\(563\) | −4.53737e9 | −1.07158 | −0.535790 | − | 0.844351i | \(-0.679986\pi\) | ||||
−0.535790 | + | 0.844351i | \(0.679986\pi\) | |||||||
\(564\) | −1.88032e8 | − | 9.19353e7i | −0.0441322 | − | 0.0215777i | ||||
\(565\) | 1.45361e9i | 0.339061i | ||||||||
\(566\) | 9.38405e8 | + | 1.50338e9i | 0.217537 | + | 0.348507i | ||||
\(567\) | 1.21608e9i | 0.280170i | ||||||||
\(568\) | −7.47692e8 | − | 7.21472e9i | −0.171200 | − | 1.65196i | ||||
\(569\) | 1.56073e9i | 0.355170i | 0.984106 | + | 0.177585i | \(0.0568284\pi\) | ||||
−0.984106 | + | 0.177585i | \(0.943172\pi\) | |||||||
\(570\) | 1.42266e7 | − | 2.36051e7i | 0.00321766 | − | 0.00533880i | ||||
\(571\) | 6.88077e9i | 1.54672i | 0.633970 | + | 0.773358i | \(0.281424\pi\) | ||||
−0.633970 | + | 0.773358i | \(0.718576\pi\) | |||||||
\(572\) | 1.65779e9 | − | 3.39062e9i | 0.370376 | − | 0.757518i | ||||
\(573\) | − | 1.12742e8i | − | 0.0250349i | ||||||
\(574\) | 1.03050e8 | − | 6.43236e7i | 0.0227435 | − | 0.0141964i | ||||
\(575\) | − | 1.40865e9i | − | 0.309005i | ||||||
\(576\) | 4.48520e9 | − | 9.39735e8i | 0.977920 | − | 0.204893i | ||||
\(577\) | 2.69810e9 | 0.584713 | 0.292357 | − | 0.956309i | \(-0.405561\pi\) | ||||
0.292357 | + | 0.956309i | \(0.405561\pi\) | |||||||
\(578\) | −1.36681e9 | + | 8.53155e8i | −0.294415 | + | 0.183772i | ||||
\(579\) | 2.24121e8i | 0.0479852i | ||||||||
\(580\) | 8.03168e8 | + | 3.92696e8i | 0.170926 | + | 0.0835715i | ||||
\(581\) | −1.32146e9 | −0.279537 | ||||||||
\(582\) | −6.15262e7 | − | 9.85688e7i | −0.0129369 | − | 0.0207257i | ||||
\(583\) | 6.14198e9 | 1.28372 | ||||||||
\(584\) | 7.27194e8 | + | 7.01692e9i | 0.151079 | + | 1.45781i | ||||
\(585\) | − | 7.67050e8i | − | 0.158408i | ||||||
\(586\) | 7.76104e8 | + | 1.24337e9i | 0.159323 | + | 0.255245i | ||||
\(587\) | − | 9.46703e9i | − | 1.93188i | −0.258762 | − | 0.965941i | \(-0.583315\pi\) | ||
0.258762 | − | 0.965941i | \(-0.416685\pi\) | |||||||
\(588\) | −5.80121e7 | + | 1.18650e8i | −0.0117679 | + | 0.0240685i | ||||
\(589\) | 7.68949e8 | − | 3.90966e8i | 0.155058 | − | 0.0788379i | ||||
\(590\) | 3.55567e8 | − | 2.21943e8i | 0.0712753 | − | 0.0444897i | ||||
\(591\) | 6.51803e7 | 0.0129885 | ||||||||
\(592\) | 5.32747e9 | − | 4.14567e9i | 1.05535 | − | 0.821238i | ||||
\(593\) | −1.17249e9 | −0.230896 | −0.115448 | − | 0.993314i | \(-0.536830\pi\) | ||||
−0.115448 | + | 0.993314i | \(0.536830\pi\) | |||||||
\(594\) | 1.79264e8 | + | 2.87192e8i | 0.0350947 | + | 0.0562238i | ||||
\(595\) | 3.58982e8i | 0.0698656i | ||||||||
\(596\) | −5.85348e8 | + | 1.19719e9i | −0.113254 | + | 0.231634i | ||||
\(597\) | 1.78018e8i | 0.0342415i | ||||||||
\(598\) | 1.06290e9 | − | 6.63456e8i | 0.203253 | − | 0.126870i | ||||
\(599\) | 7.02381e9 | 1.33530 | 0.667650 | − | 0.744475i | \(-0.267300\pi\) | ||||
0.667650 | + | 0.744475i | \(0.267300\pi\) | |||||||
\(600\) | 1.51349e7 | + | 1.46041e8i | 0.00286055 | + | 0.0276023i | ||||
\(601\) | − | 1.58778e9i | − | 0.298353i | −0.988811 | − | 0.149176i | \(-0.952338\pi\) | ||
0.988811 | − | 0.149176i | \(-0.0476622\pi\) | |||||||
\(602\) | 9.23769e8 | − | 5.76613e8i | 0.172574 | − | 0.107720i | ||||
\(603\) | −7.64705e9 | −1.42031 | ||||||||
\(604\) | 8.15245e8 | − | 1.66740e9i | 0.150542 | − | 0.307900i | ||||
\(605\) | −3.49257e8 | −0.0641212 | ||||||||
\(606\) | 1.56515e8 | − | 9.76962e7i | 0.0285695 | − | 0.0178330i | ||||
\(607\) | 8.31064e9 | 1.50825 | 0.754126 | − | 0.656730i | \(-0.228061\pi\) | ||||
0.754126 | + | 0.656730i | \(0.228061\pi\) | |||||||
\(608\) | 5.50283e9 | − | 6.57325e8i | 0.992941 | − | 0.118609i | ||||
\(609\) | 4.04277e7 | 0.00725302 | ||||||||
\(610\) | −6.92123e8 | + | 4.32020e8i | −0.123461 | + | 0.0770637i | ||||
\(611\) | −7.04469e9 | −1.24945 | ||||||||
\(612\) | −2.88842e9 | + | 5.90760e9i | −0.509366 | + | 1.04179i | ||||
\(613\) | −6.80459e9 | −1.19314 | −0.596569 | − | 0.802562i | \(-0.703470\pi\) | ||||
−0.596569 | + | 0.802562i | \(0.703470\pi\) | |||||||
\(614\) | 3.23986e9 | − | 2.02231e9i | 0.564855 | − | 0.352580i | ||||
\(615\) | − | 3.43220e6i | − | 0.000594991i | ||||||
\(616\) | 1.91460e8 | + | 1.84746e9i | 0.0330025 | + | 0.318451i | ||||
\(617\) | 7.23729e8 | 0.124045 | 0.0620223 | − | 0.998075i | \(-0.480245\pi\) | ||||
0.0620223 | + | 0.998075i | \(0.480245\pi\) | |||||||
\(618\) | −1.25464e8 | + | 7.83139e7i | −0.0213825 | + | 0.0133469i | ||||
\(619\) | − | 9.10263e9i | − | 1.54259i | −0.636480 | − | 0.771293i | \(-0.719610\pi\) | ||
0.636480 | − | 0.771293i | \(-0.280390\pi\) | |||||||
\(620\) | 9.71723e7 | − | 1.98744e8i | 0.0163746 | − | 0.0334905i | ||||
\(621\) | 1.12392e8i | 0.0188328i | ||||||||
\(622\) | 2.03252e9 | + | 3.25622e9i | 0.338663 | + | 0.542559i | ||||
\(623\) | 6.08779e8 | 0.100868 | ||||||||
\(624\) | −1.03067e8 | + | 8.02036e7i | −0.0169814 | + | 0.0132144i | ||||
\(625\) | 5.27540e9 | 0.864322 | ||||||||
\(626\) | −5.78047e9 | + | 3.60814e9i | −0.941787 | + | 0.587859i | ||||
\(627\) | 9.27408e7 | + | 1.82402e8i | 0.0150257 | + | 0.0295524i | ||||
\(628\) | −3.55219e9 | + | 7.26518e9i | −0.572318 | + | 1.17054i | ||||
\(629\) | 9.68675e9i | 1.55203i | ||||||||
\(630\) | 1.99879e8 | + | 3.20218e8i | 0.0318475 | + | 0.0510216i | ||||
\(631\) | 8.64278e9i | 1.36946i | 0.728795 | + | 0.684732i | \(0.240081\pi\) | ||||
−0.728795 | + | 0.684732i | \(0.759919\pi\) | |||||||
\(632\) | −4.18957e8 | − | 4.04264e9i | −0.0660175 | − | 0.637024i | ||||
\(633\) | 1.20609e8 | 0.0189002 | ||||||||
\(634\) | −3.83387e9 | − | 6.14209e9i | −0.597482 | − | 0.957203i | ||||
\(635\) | 2.16256e9 | 0.335166 | ||||||||
\(636\) | −1.90928e8 | − | 9.33512e7i | −0.0294287 | − | 0.0143886i | ||||
\(637\) | 4.44527e9i | 0.681412i | ||||||||
\(638\) | −5.63081e9 | + | 3.51473e9i | −0.858418 | + | 0.535821i | ||||
\(639\) | 1.09447e10 | 1.65940 | ||||||||
\(640\) | 1.02572e9 | − | 9.83819e8i | 0.154667 | − | 0.148349i | ||||
\(641\) | − | 7.51851e9i | − | 1.12753i | −0.825935 | − | 0.563766i | \(-0.809352\pi\) | ||
0.825935 | − | 0.563766i | \(-0.190648\pi\) | |||||||
\(642\) | −8.45319e7 | + | 5.27644e7i | −0.0126080 | + | 0.00786989i | ||||
\(643\) | 1.48432e9i | 0.220185i | 0.993921 | + | 0.110093i | \(0.0351148\pi\) | ||||
−0.993921 | + | 0.110093i | \(0.964885\pi\) | |||||||
\(644\) | −2.70841e8 | + | 5.53943e8i | −0.0399589 | + | 0.0817268i | ||||
\(645\) | − | 3.07672e7i | − | 0.00451469i | ||||||
\(646\) | −4.10505e9 | + | 6.81117e9i | −0.599107 | + | 0.994049i | ||||
\(647\) | 9.12649e9i | 1.32476i | 0.749166 | + | 0.662382i | \(0.230455\pi\) | ||||
−0.749166 | + | 0.662382i | \(0.769545\pi\) | |||||||
\(648\) | 7.12186e8 | + | 6.87210e9i | 0.102821 | + | 0.992149i | ||||
\(649\) | 3.11197e9i | 0.446868i | ||||||||
\(650\) | 2.61668e9 | + | 4.19209e9i | 0.373727 | + | 0.598733i | ||||
\(651\) | − | 1.00038e7i | − | 0.00142113i | ||||||
\(652\) | 2.41674e9 | + | 1.18163e9i | 0.341479 | + | 0.166960i | ||||
\(653\) | −1.01661e10 | −1.42876 | −0.714381 | − | 0.699757i | \(-0.753292\pi\) | ||||
−0.714381 | + | 0.699757i | \(0.753292\pi\) | |||||||
\(654\) | 8.69582e7 | + | 1.39312e8i | 0.0121559 | + | 0.0194746i | ||||
\(655\) | − | 4.88968e8i | − | 0.0679886i | ||||||
\(656\) | 5.44669e8 | − | 4.23844e8i | 0.0753303 | − | 0.0586196i | ||||
\(657\) | −1.06447e10 | −1.46438 | ||||||||
\(658\) | 2.94093e9 | − | 1.83571e9i | 0.402433 | − | 0.251197i | ||||
\(659\) | −8.99411e9 | −1.22422 | −0.612109 | − | 0.790773i | \(-0.709679\pi\) | ||||
−0.612109 | + | 0.790773i | \(0.709679\pi\) | |||||||
\(660\) | 4.71439e7 | + | 2.30502e7i | 0.00638295 | + | 0.00312084i | ||||
\(661\) | 2.45281e9i | 0.330339i | 0.986265 | + | 0.165169i | \(0.0528171\pi\) | ||||
−0.986265 | + | 0.165169i | \(0.947183\pi\) | |||||||
\(662\) | 8.02910e9 | − | 5.01173e9i | 1.07563 | − | 0.671405i | ||||
\(663\) | − | 1.87403e8i | − | 0.0249735i | ||||||
\(664\) | −7.46763e9 | + | 7.73903e8i | −0.989907 | + | 0.102588i | ||||
\(665\) | 2.06899e8 | + | 4.06927e8i | 0.0272824 | + | 0.0536588i | ||||
\(666\) | 5.39351e9 | + | 8.64074e9i | 0.707476 | + | 1.13342i | ||||
\(667\) | −2.20361e9 | −0.287537 | ||||||||
\(668\) | −4.15708e9 | + | 8.50234e9i | −0.539598 | + | 1.10362i | ||||
\(669\) | −9.23456e7 | −0.0119241 | ||||||||
\(670\) | −2.01191e9 | + | 1.25583e9i | −0.258433 | + | 0.161313i | ||||
\(671\) | − | 6.05757e9i | − | 0.774051i | ||||||
\(672\) | 2.21276e7 | − | 6.03397e7i | 0.00281282 | − | 0.00767027i | ||||
\(673\) | 5.45607e9i | 0.689965i | 0.938609 | + | 0.344982i | \(0.112115\pi\) | ||||
−0.938609 | + | 0.344982i | \(0.887885\pi\) | |||||||
\(674\) | 4.49166e9 | + | 7.19592e9i | 0.565064 | + | 0.905267i | ||||
\(675\) | −4.43276e8 | −0.0554768 | ||||||||
\(676\) | 1.59719e9 | − | 3.26668e9i | 0.198858 | − | 0.406718i | ||||
\(677\) | − | 1.39469e10i | − | 1.72750i | −0.503924 | − | 0.863748i | \(-0.668111\pi\) | ||
0.503924 | − | 0.863748i | \(-0.331889\pi\) | |||||||
\(678\) | 1.97740e8 | + | 3.16792e8i | 0.0243664 | + | 0.0390364i | ||||
\(679\) | 1.92461e9 | 0.235938 | ||||||||
\(680\) | 2.10234e8 | + | 2.02862e9i | 0.0256403 | + | 0.247411i | ||||
\(681\) | −2.71667e7 | −0.00329627 | ||||||||
\(682\) | 8.69718e8 | + | 1.39334e9i | 0.104986 | + | 0.168195i | ||||
\(683\) | −1.66071e9 | −0.199445 | −0.0997223 | − | 0.995015i | \(-0.531795\pi\) | ||||
−0.0997223 | + | 0.995015i | \(0.531795\pi\) | |||||||
\(684\) | 1.30641e8 | + | 8.36134e9i | 0.0156093 | + | 0.999032i | ||||
\(685\) | −8.77470e8 | −0.104307 | ||||||||
\(686\) | −2.41592e9 | − | 3.87046e9i | −0.285725 | − | 0.457750i | ||||
\(687\) | −1.09375e8 | −0.0128697 | ||||||||
\(688\) | 4.88255e9 | − | 3.79945e9i | 0.571594 | − | 0.444796i | ||||
\(689\) | −7.15318e9 | −0.833167 | ||||||||
\(690\) | 9.22483e6 | + | 1.47788e7i | 0.00106902 | + | 0.00171264i | ||||
\(691\) | − | 1.21758e10i | − | 1.40387i | −0.712243 | − | 0.701933i | \(-0.752321\pi\) | ||
0.712243 | − | 0.701933i | \(-0.247679\pi\) | |||||||
\(692\) | −6.09251e9 | − | 2.97883e9i | −0.698916 | − | 0.341723i | ||||
\(693\) | −2.80260e9 | −0.319886 | ||||||||
\(694\) | 6.82016e9 | + | 1.09263e10i | 0.774527 | + | 1.24084i | ||||
\(695\) | − | 2.99170e9i | − | 0.338042i | ||||||
\(696\) | 2.28458e8 | − | 2.36761e7i | 0.0256847 | − | 0.00266182i | ||||
\(697\) | 9.90352e8i | 0.110783i | ||||||||
\(698\) | −3.15286e9 | + | 1.96800e9i | −0.350923 | + | 0.219044i | ||||
\(699\) | 1.27699e7 | 0.00141422 | ||||||||
\(700\) | −2.18476e9 | − | 1.06820e9i | −0.240747 | − | 0.117709i | ||||
\(701\) | −9.34466e9 | −1.02459 | −0.512295 | − | 0.858809i | \(-0.671205\pi\) | ||||
−0.512295 | + | 0.858809i | \(0.671205\pi\) | |||||||
\(702\) | −2.08778e8 | − | 3.34475e8i | −0.0227774 | − | 0.0364908i | ||||
\(703\) | 5.58294e9 | + | 1.09805e10i | 0.606065 | + | 1.19200i | ||||
\(704\) | 2.16389e9 | + | 1.03279e10i | 0.233739 | + | 1.11560i | ||||
\(705\) | − | 9.79508e7i | − | 0.0105280i | ||||||
\(706\) | 7.83577e9 | − | 4.89105e9i | 0.838040 | − | 0.523101i | ||||
\(707\) | 3.05604e9i | 0.325230i | ||||||||
\(708\) | 4.72985e7 | − | 9.67381e7i | 0.00500877 | − | 0.0102443i | ||||
\(709\) | 2.60492e9 | 0.274494 | 0.137247 | − | 0.990537i | \(-0.456175\pi\) | ||||
0.137247 | + | 0.990537i | \(0.456175\pi\) | |||||||
\(710\) | 2.87952e9 | − | 1.79739e9i | 0.301937 | − | 0.188468i | ||||
\(711\) | 6.13269e9 | 0.639894 | ||||||||
\(712\) | 3.44023e9 | − | 3.56526e8i | 0.357196 | − | 0.0370178i | ||||
\(713\) | 5.45282e8i | 0.0563388i | ||||||||
\(714\) | 4.88337e7 | + | 7.82346e7i | 0.00502084 | + | 0.00804369i | ||||
\(715\) | 1.76626e9 | 0.180710 | ||||||||
\(716\) | 7.29122e9 | − | 1.49125e10i | 0.742343 | − | 1.51829i | ||||
\(717\) | 2.32727e8i | 0.0235792i | ||||||||
\(718\) | −1.49813e9 | − | 2.40010e9i | −0.151048 | − | 0.241988i | ||||
\(719\) | − | 9.98115e9i | − | 1.00145i | −0.865606 | − | 0.500725i | \(-0.833067\pi\) | ||
0.865606 | − | 0.500725i | \(-0.166933\pi\) | |||||||
\(720\) | 1.31705e9 | + | 1.69250e9i | 0.131504 | + | 0.168992i | ||||
\(721\) | − | 2.44974e9i | − | 0.243415i | ||||||
\(722\) | −7.27703e8 | + | 1.00868e10i | −0.0719571 | + | 0.997408i | ||||
\(723\) | − | 4.57118e8i | − | 0.0449826i | ||||||
\(724\) | −5.64361e9 | − | 2.75935e9i | −0.552678 | − | 0.270223i | ||||
\(725\) | − | 8.69106e9i | − | 0.847013i | ||||||
\(726\) | −7.61152e7 | + | 4.75108e7i | −0.00738233 | + | 0.00460802i | ||||
\(727\) | − | 1.61060e10i | − | 1.55459i | −0.629135 | − | 0.777296i | \(-0.716591\pi\) | ||
0.629135 | − | 0.777296i | \(-0.283409\pi\) | |||||||
\(728\) | −2.22982e8 | − | 2.15162e9i | −0.0214195 | − | 0.206684i | ||||
\(729\) | −1.04073e10 | −0.994928 | ||||||||
\(730\) | −2.80058e9 | + | 1.74811e9i | −0.266451 | + | 0.166318i | ||||
\(731\) | 8.87777e9i | 0.840607i | ||||||||
\(732\) | −9.20682e7 | + | 1.88304e8i | −0.00867603 | + | 0.0177448i | ||||
\(733\) | 1.68574e10 | 1.58098 | 0.790489 | − | 0.612476i | \(-0.209826\pi\) | ||||
0.790489 | + | 0.612476i | \(0.209826\pi\) | |||||||
\(734\) | −1.71053e9 | − | 2.74037e9i | −0.159659 | − | 0.255784i | ||||
\(735\) | −6.18079e7 | −0.00574167 | ||||||||
\(736\) | −1.20612e9 | + | 3.28896e9i | −0.111511 | + | 0.304079i | ||||
\(737\) | − | 1.76086e10i | − | 1.62027i | ||||||
\(738\) | 5.51421e8 | + | 8.83410e8i | 0.0504994 | + | 0.0809031i | ||||
\(739\) | − | 1.22933e9i | − | 0.112051i | −0.998429 | − | 0.0560253i | \(-0.982157\pi\) | ||
0.998429 | − | 0.0560253i | \(-0.0178427\pi\) | |||||||
\(740\) | 2.83803e9 | + | 1.38761e9i | 0.257458 | + | 0.125880i | ||||
\(741\) | −1.08009e8 | − | 2.12432e8i | −0.00975209 | − | 0.0191804i | ||||
\(742\) | 2.98622e9 | − | 1.86399e9i | 0.268354 | − | 0.167505i | ||||
\(743\) | 1.49196e10 | 1.33443 | 0.667216 | − | 0.744864i | \(-0.267486\pi\) | ||||
0.667216 | + | 0.744864i | \(0.267486\pi\) | |||||||
\(744\) | −5.85864e6 | − | 5.65318e7i | −0.000521545 | − | 0.00503254i | ||||
\(745\) | −6.23648e8 | −0.0552577 | ||||||||
\(746\) | −5.88916e9 | − | 9.43480e9i | −0.519359 | − | 0.832045i | ||||
\(747\) | − | 1.13284e10i | − | 0.994367i | ||||||
\(748\) | −1.36032e10 | − | 6.65106e9i | −1.18846 | − | 0.581079i | ||||
\(749\) | − | 1.65053e9i | − | 0.143528i | ||||||
\(750\) | −1.19381e8 | + | 7.45172e7i | −0.0103329 | + | 0.00644974i | ||||
\(751\) | −1.93559e10 | −1.66753 | −0.833766 | − | 0.552118i | \(-0.813820\pi\) | ||||
−0.833766 | + | 0.552118i | \(0.813820\pi\) | |||||||
\(752\) | 1.55442e10 | − | 1.20960e10i | 1.33292 | − | 1.03724i | ||||
\(753\) | − | 1.54702e8i | − | 0.0132042i | ||||||
\(754\) | 6.55786e9 | − | 4.09338e9i | 0.557137 | − | 0.347763i | ||||
\(755\) | 8.68589e8 | 0.0734514 | ||||||||
\(756\) | 1.74316e8 | + | 8.52288e7i | 0.0146727 | + | 0.00717397i | ||||
\(757\) | 7.36792e8 | 0.0617318 | 0.0308659 | − | 0.999524i | \(-0.490174\pi\) | ||||
0.0308659 | + | 0.999524i | \(0.490174\pi\) | |||||||
\(758\) | 9.72657e9 | − | 6.07128e9i | 0.811180 | − | 0.506335i | ||||
\(759\) | −1.29346e8 | −0.0107376 | ||||||||
\(760\) | 1.40750e9 | + | 2.17839e9i | 0.116306 | + | 0.180006i | ||||
\(761\) | 1.27424e10 | 1.04811 | 0.524055 | − | 0.851685i | \(-0.324419\pi\) | ||||
0.524055 | + | 0.851685i | \(0.324419\pi\) | |||||||
\(762\) | 4.71297e8 | − | 2.94181e8i | 0.0385880 | − | 0.0240864i | ||||
\(763\) | −2.72014e9 | −0.221695 | ||||||||
\(764\) | 9.53109e9 | + | 4.66006e9i | 0.773242 | + | 0.378064i | ||||
\(765\) | −3.07742e9 | −0.248526 | ||||||||
\(766\) | −6.91168e9 | + | 4.31424e9i | −0.555627 | + | 0.346820i | ||||
\(767\) | − | 3.62432e9i | − | 0.290030i | ||||||
\(768\) | 8.97063e7 | − | 3.53940e8i | 0.00714593 | − | 0.0281946i | ||||
\(769\) | 5.13236e9 | 0.406981 | 0.203491 | − | 0.979077i | \(-0.434771\pi\) | ||||
0.203491 | + | 0.979077i | \(0.434771\pi\) | |||||||
\(770\) | −7.37355e8 | + | 4.60254e8i | −0.0582048 | + | 0.0363312i | ||||
\(771\) | 5.22709e7i | 0.00410743i | ||||||||
\(772\) | −1.89469e10 | − | 9.26376e9i | −1.48210 | − | 0.724648i | ||||
\(773\) | − | 1.44754e10i | − | 1.12721i | −0.826045 | − | 0.563604i | \(-0.809415\pi\) | ||
0.826045 | − | 0.563604i | \(-0.190585\pi\) | |||||||
\(774\) | 4.94308e9 | + | 7.91912e9i | 0.383181 | + | 0.613880i | ||||
\(775\) | −2.15060e9 | −0.165960 | ||||||||
\(776\) | 1.08760e10 | − | 1.12713e9i | 0.835512 | − | 0.0865878i | ||||
\(777\) | 1.42853e8 | 0.0109249 | ||||||||
\(778\) | 1.48893e10 | − | 9.29382e9i | 1.13356 | − | 0.707564i | ||||
\(779\) | 5.70787e8 | + | 1.12262e9i | 0.0432607 | + | 0.0850848i | ||||
\(780\) | −5.49055e7 | − | 2.68451e7i | −0.00414271 | − | 0.00202551i | ||||
\(781\) | 2.52020e10i | 1.89303i | ||||||||
\(782\) | −2.66180e9 | − | 4.26436e9i | −0.199045 | − | 0.318882i | ||||
\(783\) | 6.93436e8i | 0.0516226i | ||||||||
\(784\) | −7.63269e9 | − | 9.80853e9i | −0.565681 | − | 0.726939i | ||||
\(785\) | −3.78462e9 | −0.279240 | ||||||||
\(786\) | −6.65162e7 | − | 1.06563e8i | −0.00488595 | − | 0.00782759i | ||||
\(787\) | −5.75058e9 | −0.420533 | −0.210267 | − | 0.977644i | \(-0.567433\pi\) | ||||
−0.210267 | + | 0.977644i | \(0.567433\pi\) | |||||||
\(788\) | −2.69415e9 | + | 5.51026e9i | −0.196146 | + | 0.401172i | ||||
\(789\) | − | 3.45666e8i | − | 0.0250546i | ||||||
\(790\) | 1.61349e9 | − | 1.00713e9i | 0.116432 | − | 0.0726763i | ||||
\(791\) | −6.18552e9 | −0.444384 | ||||||||
\(792\) | −1.58376e10 | + | 1.64132e9i | −1.13279 | + | 0.117396i | ||||
\(793\) | 7.05488e9i | 0.502381i | ||||||||
\(794\) | 1.55649e10 | − | 9.71551e9i | 1.10350 | − | 0.688801i | ||||
\(795\) | − | 9.94593e7i | − | 0.00702038i | ||||||
\(796\) | −1.50494e10 | − | 7.35814e9i | −1.05760 | − | 0.517097i | ||||
\(797\) | − | 2.32146e10i | − | 1.62427i | −0.583471 | − | 0.812134i | \(-0.698306\pi\) | ||
0.583471 | − | 0.812134i | \(-0.301694\pi\) | |||||||
\(798\) | 1.00446e8 | + | 6.05383e7i | 0.00699719 | + | 0.00421716i | ||||
\(799\) | 2.82634e10i | 1.96025i | ||||||||
\(800\) | −1.29717e10 | − | 4.75694e9i | −0.895740 | − | 0.328483i | ||||
\(801\) | 5.21883e9i | 0.358806i | ||||||||
\(802\) | 3.87130e9 | + | 6.20206e9i | 0.265000 | + | 0.424547i | ||||
\(803\) | − | 2.45111e10i | − | 1.67055i | ||||||
\(804\) | −2.67630e8 | + | 5.47376e8i | −0.0181610 | + | 0.0371441i | ||||
\(805\) | −2.88563e8 | −0.0194964 | ||||||||
\(806\) | −1.01291e9 | − | 1.62274e9i | −0.0681391 | − | 0.109163i | ||||
\(807\) | − | 6.87394e8i | − | 0.0460414i | ||||||
\(808\) | 1.78974e9 | + | 1.72698e10i | 0.119358 | + | 1.15172i | ||||
\(809\) | −1.95032e10 | −1.29505 | −0.647523 | − | 0.762046i | \(-0.724195\pi\) | ||||
−0.647523 | + | 0.762046i | \(0.724195\pi\) | |||||||
\(810\) | −2.74278e9 | + | 1.71203e9i | −0.181340 | + | 0.113192i | ||||
\(811\) | 9.57085e9 | 0.630054 | 0.315027 | − | 0.949083i | \(-0.397986\pi\) | ||||
0.315027 | + | 0.949083i | \(0.397986\pi\) | |||||||
\(812\) | −1.67103e9 | + | 3.41771e9i | −0.109531 | + | 0.224021i | ||||
\(813\) | − | 5.05051e8i | − | 0.0329623i | ||||||
\(814\) | −1.98967e10 | + | 1.24194e10i | −1.29299 | + | 0.807081i | ||||
\(815\) | 1.25894e9i | 0.0814619i | ||||||||
\(816\) | 3.21778e8 | + | 4.13507e8i | 0.0207320 | + | 0.0266420i | ||||
\(817\) | 5.11668e9 | + | 1.00635e10i | 0.328255 | + | 0.645610i | ||||
\(818\) | 1.17041e10 | + | 1.87506e10i | 0.747654 | + | 1.19779i | ||||
\(819\) | 3.26401e9 | 0.207615 | ||||||||
\(820\) | 2.90154e8 | + | 1.41866e8i | 0.0183772 | + | 0.00898524i | ||||
\(821\) | 1.53216e10 | 0.966283 | 0.483142 | − | 0.875542i | \(-0.339496\pi\) | ||||
0.483142 | + | 0.875542i | \(0.339496\pi\) | |||||||
\(822\) | −1.91231e8 | + | 1.19366e8i | −0.0120090 | + | 0.00749596i | ||||
\(823\) | 1.91024e10i | 1.19450i | 0.802054 | + | 0.597252i | \(0.203741\pi\) | ||||
−0.802054 | + | 0.597252i | \(0.796259\pi\) | |||||||
\(824\) | −1.43467e9 | − | 1.38436e10i | −0.0893318 | − | 0.861990i | ||||
\(825\) | − | 5.10142e8i | − | 0.0316302i | ||||||
\(826\) | 9.44430e8 | + | 1.51304e9i | 0.0583096 | + | 0.0934155i | ||||
\(827\) | −2.43449e10 | −1.49671 | −0.748356 | − | 0.663297i | \(-0.769157\pi\) | ||||
−0.748356 | + | 0.663297i | \(0.769157\pi\) | |||||||
\(828\) | −4.74873e9 | − | 2.32181e9i | −0.290718 | − | 0.142142i | ||||
\(829\) | − | 3.82880e9i | − | 0.233411i | −0.993167 | − | 0.116706i | \(-0.962767\pi\) | ||
0.993167 | − | 0.116706i | \(-0.0372334\pi\) | |||||||
\(830\) | −1.86039e9 | − | 2.98047e9i | −0.112936 | − | 0.180930i | ||||
\(831\) | −3.16944e8 | −0.0191593 | ||||||||
\(832\) | −2.52015e9 | − | 1.20283e10i | −0.151703 | − | 0.724055i | ||||
\(833\) | 1.78345e10 | 1.06906 | ||||||||
\(834\) | −4.06972e8 | − | 6.51994e8i | −0.0242931 | − | 0.0389191i | ||||
\(835\) | −4.42908e9 | −0.263276 | ||||||||
\(836\) | −1.92534e10 | + | 3.00823e8i | −1.13968 | + | 0.0178069i | ||||
\(837\) | 1.71590e8 | 0.0101147 | ||||||||
\(838\) | 1.11446e9 | + | 1.78543e9i | 0.0654198 | + | 0.104807i | ||||
\(839\) | 1.19767e10 | 0.700118 | 0.350059 | − | 0.936728i | \(-0.386162\pi\) | ||||
0.350059 | + | 0.936728i | \(0.386162\pi\) | |||||||
\(840\) | 2.99166e7 | − | 3.10039e6i | 0.00174154 | − | 0.000180484i | ||||
\(841\) | 3.65408e9 | 0.211833 | ||||||||
\(842\) | 1.32923e9 | + | 2.12950e9i | 0.0767373 | + | 0.122938i | ||||
\(843\) | − | 8.01307e8i | − | 0.0460683i | ||||||
\(844\) | −4.98521e9 | + | 1.01961e10i | −0.285421 | + | 0.583762i | ||||
\(845\) | 1.70170e9 | 0.0970250 | ||||||||
\(846\) | 1.57369e10 | + | 2.52114e10i | 0.893556 | + | 1.43153i | ||||
\(847\) | − | 1.48619e9i | − | 0.0840392i | ||||||
\(848\) | 1.57836e10 | − | 1.22823e10i | 0.888832 | − | 0.691661i | ||||
\(849\) | 2.13070e8i | 0.0119494i | ||||||||
\(850\) | 1.68187e10 | − | 1.04982e10i | 0.939348 | − | 0.586337i | ||||
\(851\) | −7.78655e9 | −0.433103 | ||||||||
\(852\) | 3.83043e8 | − | 7.83425e8i | 0.0212182 | − | 0.0433969i | ||||
\(853\) | 2.40197e9 | 0.132509 | 0.0662546 | − | 0.997803i | \(-0.478895\pi\) | ||||
0.0662546 | + | 0.997803i | \(0.478895\pi\) | |||||||
\(854\) | −1.83837e9 | − | 2.94518e9i | −0.101002 | − | 0.161811i | ||||
\(855\) | −3.48843e9 | + | 1.77366e9i | −0.190875 | + | 0.0970487i | ||||
\(856\) | −9.66615e8 | − | 9.32717e9i | −0.0526739 | − | 0.508267i | ||||
\(857\) | 1.19967e10i | 0.651073i | 0.945530 | + | 0.325536i | \(0.105545\pi\) | ||||
−0.945530 | + | 0.325536i | \(0.894455\pi\) | |||||||
\(858\) | 3.84929e8 | − | 2.40271e8i | 0.0208053 | − | 0.0129866i | ||||
\(859\) | 3.45337e10i | 1.85895i | 0.368888 | + | 0.929474i | \(0.379738\pi\) | ||||
−0.368888 | + | 0.929474i | \(0.620262\pi\) | |||||||
\(860\) | 2.60102e9 | + | 1.27172e9i | 0.139444 | + | 0.0681786i | ||||
\(861\) | 1.46050e7 | 0.000779813 | ||||||||
\(862\) | −2.16688e9 | + | 1.35255e9i | −0.115228 | + | 0.0719249i | ||||
\(863\) | 2.77540e10 | 1.46990 | 0.734951 | − | 0.678120i | \(-0.237205\pi\) | ||||
0.734951 | + | 0.678120i | \(0.237205\pi\) | |||||||
\(864\) | 1.03498e9 | + | 3.79543e8i | 0.0545924 | + | 0.0200200i | ||||
\(865\) | − | 3.17374e9i | − | 0.166730i | ||||||
\(866\) | −1.39117e10 | − | 2.22875e10i | −0.727895 | − | 1.16613i | ||||
\(867\) | −1.93713e8 | −0.0100947 | ||||||||
\(868\) | 8.45710e8 | + | 4.13496e8i | 0.0438937 | + | 0.0214611i | ||||
\(869\) | 1.41215e10i | 0.729983i | ||||||||
\(870\) | 5.69153e7 | + | 9.11818e7i | 0.00293029 | + | 0.00469451i | ||||
\(871\) | 2.05076e10i | 1.05160i | ||||||||
\(872\) | −1.53716e10 | + | 1.59303e9i | −0.785075 | + | 0.0813608i | ||||
\(873\) | 1.64989e10i | 0.839277i | ||||||||
\(874\) | −5.47506e9 | − | 3.29978e9i | −0.277395 | − | 0.167184i | ||||
\(875\) | − | 2.33098e9i | − | 0.117628i | ||||||
\(876\) | −3.72541e8 | + | 7.61947e8i | −0.0187245 | + | 0.0382966i | ||||
\(877\) | − | 5.71928e9i | − | 0.286314i | −0.989700 | − | 0.143157i | \(-0.954275\pi\) | ||
0.989700 | − | 0.143157i | \(-0.0457254\pi\) | |||||||
\(878\) | −1.87224e10 | + | 1.16865e10i | −0.933538 | + | 0.582710i | ||||
\(879\) | 1.76218e8i | 0.00875165i | ||||||||
\(880\) | −3.89727e9 | + | 3.03273e9i | −0.192784 | + | 0.150018i | ||||
\(881\) | 1.01339e10 | 0.499300 | 0.249650 | − | 0.968336i | \(-0.419684\pi\) | ||||
0.249650 | + | 0.968336i | \(0.419684\pi\) | |||||||
\(882\) | 1.59087e10 | − | 9.93011e9i | 0.780717 | − | 0.487320i | ||||
\(883\) | 3.62081e10i | 1.76988i | 0.465705 | + | 0.884940i | \(0.345801\pi\) | ||||
−0.465705 | + | 0.884940i | \(0.654199\pi\) | |||||||
\(884\) | 1.58428e10 | + | 7.74608e9i | 0.771346 | + | 0.377137i | ||||
\(885\) | 5.03933e7 | 0.00244383 | ||||||||
\(886\) | −6.13035e6 | − | 9.82120e6i | −0.000296120 | − | 0.000474402i | ||||
\(887\) | −1.39192e10 | −0.669704 | −0.334852 | − | 0.942271i | \(-0.608686\pi\) | ||||
−0.334852 | + | 0.942271i | \(0.608686\pi\) | |||||||
\(888\) | 8.07267e8 | − | 8.36606e7i | 0.0386876 | − | 0.00400936i | ||||
\(889\) | 9.20230e9i | 0.439279i | ||||||||
\(890\) | 8.57056e8 | + | 1.37306e9i | 0.0407516 | + | 0.0652865i | ||||
\(891\) | − | 2.40052e10i | − | 1.13693i | ||||||
\(892\) | 3.81699e9 | − | 7.80678e9i | 0.180071 | − | 0.368294i | ||||
\(893\) | 1.62896e10 | + | 3.20382e10i | 0.765472 | + | 1.50552i | ||||
\(894\) | −1.35915e8 | + | 8.48372e7i | −0.00636187 | + | 0.00397105i | ||||
\(895\) | 7.76830e9 | 0.362197 | ||||||||
\(896\) | 4.18642e9 | + | 4.36471e9i | 0.194431 | + | 0.202711i | ||||
\(897\) | 1.50641e8 | 0.00696900 | ||||||||
\(898\) | −2.01490e10 | − | 3.22799e10i | −0.928509 | − | 1.48753i | ||||
\(899\) | 3.36427e9i | 0.154430i | ||||||||
\(900\) | 9.15727e9 | − | 1.87291e10i | 0.418714 | − | 0.856382i | ||||
\(901\) | 2.86987e10i | 1.30715i | ||||||||
\(902\) | −2.03420e9 | + | 1.26974e9i | −0.0922933 | + | 0.0576091i | ||||
\(903\) | 1.30923e8 | 0.00591709 | ||||||||
\(904\) | −3.49545e10 | + | 3.62249e9i | −1.57367 | + | 0.163086i | ||||
\(905\) | − | 2.93990e9i | − | 0.131845i | ||||||
\(906\) | 1.89295e8 | − | 1.18157e8i | 0.00845652 | − | 0.00527852i | ||||
\(907\) | −3.42557e10 | −1.52443 | −0.762214 | − | 0.647325i | \(-0.775888\pi\) | ||||
−0.762214 | + | 0.647325i | \(0.775888\pi\) | |||||||
\(908\) | 1.12290e9 | − | 2.29664e9i | 0.0497785 | − | 0.101810i | ||||
\(909\) | −2.61982e10 | −1.15691 | ||||||||
\(910\) | 8.58751e8 | − | 5.36029e8i | 0.0377766 | − | 0.0235800i | ||||
\(911\) | 9.48213e9 | 0.415520 | 0.207760 | − | 0.978180i | \(-0.433383\pi\) | ||||
0.207760 | + | 0.978180i | \(0.433383\pi\) | |||||||
\(912\) | 6.03078e8 | + | 2.83278e8i | 0.0263264 | + | 0.0123660i | ||||
\(913\) | 2.60855e10 | 1.13436 | ||||||||
\(914\) | −2.60509e10 | + | 1.62608e10i | −1.12852 | + | 0.704419i | ||||
\(915\) | −9.80924e7 | −0.00423313 | ||||||||
\(916\) | 4.52087e9 | − | 9.24641e9i | 0.194352 | − | 0.397502i | ||||
\(917\) | 2.08070e9 | 0.0891080 | ||||||||
\(918\) | −1.34192e9 | + | 8.37620e8i | −0.0572502 | + | 0.0357353i | ||||
\(919\) | − | 3.80658e10i | − | 1.61782i | −0.587932 | − | 0.808910i | \(-0.700058\pi\) | ||
0.587932 | − | 0.808910i | \(-0.299942\pi\) | |||||||
\(920\) | −1.63067e9 | + | 1.68994e8i | −0.0690414 | + | 0.00715506i | ||||
\(921\) | 4.59175e8 | 0.0193673 | ||||||||
\(922\) | 3.12864e9 | − | 1.95288e9i | 0.131461 | − | 0.0820575i | ||||
\(923\) | − | 2.93513e10i | − | 1.22863i | ||||||
\(924\) | −9.80851e7 | + | 2.00610e8i | −0.00409026 | + | 0.00836569i | ||||
\(925\) | − | 3.07103e10i | − | 1.27581i | ||||||
\(926\) | 4.19280e9 | + | 6.71713e9i | 0.173527 | + | 0.278000i | ||||
\(927\) | 2.10007e10 | 0.865873 | ||||||||
\(928\) | −7.44149e9 | + | 2.02922e10i | −0.305662 | + | 0.833510i | ||||
\(929\) | −1.04108e10 | −0.426019 | −0.213010 | − | 0.977050i | \(-0.568327\pi\) | ||||
−0.213010 | + | 0.977050i | \(0.568327\pi\) | |||||||
\(930\) | 2.25629e7 | − | 1.40836e7i | 0.000919823 | − | 0.000574149i | ||||
\(931\) | 2.02164e10 | − | 1.02789e10i | 0.821070 | − | 0.417466i | ||||
\(932\) | −5.27827e8 | + | 1.07955e9i | −0.0213568 | + | 0.0436804i | ||||
\(933\) | 4.61493e8i | 0.0186028i | ||||||||
\(934\) | 1.34856e10 | + | 2.16047e10i | 0.541570 | + | 0.867629i | ||||
\(935\) | − | 7.08626e9i | − | 0.283515i | ||||||
\(936\) | 1.84450e10 | − | 1.91154e9i | 0.735214 | − | 0.0761934i | ||||
\(937\) | 1.58124e10 | 0.627926 | 0.313963 | − | 0.949435i | \(-0.398343\pi\) | ||||
0.313963 | + | 0.949435i | \(0.398343\pi\) | |||||||
\(938\) | −5.34390e9 | − | 8.56126e9i | −0.211421 | − | 0.338710i | ||||
\(939\) | −8.19247e8 | −0.0322913 | ||||||||
\(940\) | 8.28064e9 | + | 4.04868e9i | 0.325174 | + | 0.158988i | ||||
\(941\) | 2.44262e10i | 0.955635i | 0.878459 | + | 0.477817i | \(0.158572\pi\) | ||||
−0.878459 | + | 0.477817i | \(0.841428\pi\) | |||||||
\(942\) | −8.24799e8 | + | 5.14836e8i | −0.0321492 | + | 0.0200674i | ||||
\(943\) | −7.96079e8 | −0.0309147 | ||||||||
\(944\) | 6.22309e9 | + | 7.99710e9i | 0.240771 | + | 0.309407i | ||||
\(945\) | 9.08055e7i | 0.00350026i | ||||||||
\(946\) | −1.82351e10 | + | 1.13822e10i | −0.700307 | + | 0.437128i | ||||
\(947\) | 3.06234e10i | 1.17173i | 0.810407 | + | 0.585867i | \(0.199246\pi\) | ||||
−0.810407 | + | 0.585867i | \(0.800754\pi\) | |||||||
\(948\) | 2.14631e8 | − | 4.38979e8i | 0.00818208 | − | 0.0167346i | ||||
\(949\) | 2.85466e10i | 1.08423i | ||||||||
\(950\) | 1.30144e10 | − | 2.15937e10i | 0.492483 | − | 0.817136i | ||||
\(951\) | − | 8.70500e8i | − | 0.0328199i | ||||||
\(952\) | −8.63234e9 | + | 8.94607e8i | −0.324264 | + | 0.0336049i | ||||
\(953\) | − | 3.29377e10i | − | 1.23273i | −0.787461 | − | 0.616364i | \(-0.788605\pi\) | ||
0.787461 | − | 0.616364i | \(-0.211395\pi\) | |||||||
\(954\) | 1.59792e10 | + | 2.55997e10i | 0.595849 | + | 0.954587i | ||||
\(955\) | 4.96498e9i | 0.184462i | ||||||||
\(956\) | −1.96744e10 | − | 9.61948e9i | −0.728282 | − | 0.356081i | ||||
\(957\) | −7.98037e8 | −0.0294328 | ||||||||
\(958\) | −1.67074e10 | − | 2.67663e10i | −0.613946 | − | 0.983580i | ||||
\(959\) | − | 3.73388e9i | − | 0.136708i | ||||||
\(960\) | 1.67244e8 | − | 3.50407e7i | 0.00610099 | − | 0.00127827i | ||||
\(961\) | −2.66801e10 | −0.969742 | ||||||||
\(962\) | 2.31725e10 | − | 1.44642e10i | 0.839189 | − | 0.523818i | ||||
\(963\) | 1.41493e10 | 0.510556 | ||||||||
\(964\) | 3.86442e10 | + | 1.88944e10i | 1.38936 | + | 0.679303i | ||||
\(965\) | − | 9.86991e9i | − | 0.353564i | ||||||
\(966\) | −6.28878e7 | + | 3.92543e7i | −0.00224464 | + | 0.00140109i | ||||
\(967\) | 2.21774e10i | 0.788712i | 0.918958 | + | 0.394356i | \(0.129032\pi\) | ||||
−0.918958 | + | 0.394356i | \(0.870968\pi\) | |||||||
\(968\) | −8.70371e8 | − | 8.39848e9i | −0.0308419 | − | 0.297603i | ||||
\(969\) | −8.52281e8 | + | 4.33335e8i | −0.0300919 | + | 0.0153000i | ||||
\(970\) | 2.70951e9 | + | 4.34081e9i | 0.0953213 | + | 0.152711i | ||||
\(971\) | 3.11054e10 | 1.09036 | 0.545178 | − | 0.838320i | \(-0.316462\pi\) | ||||
0.545178 | + | 0.838320i | \(0.316462\pi\) | |||||||
\(972\) | −1.09610e9 | + | 2.24183e9i | −0.0382842 | + | 0.0783016i | ||||
\(973\) | 1.27305e10 | 0.443048 | ||||||||
\(974\) | 1.19619e10 | − | 7.46660e9i | 0.414806 | − | 0.258920i | ||||
\(975\) | 5.94131e8i | 0.0205289i | ||||||||
\(976\) | −1.21135e10 | − | 1.55667e10i | −0.417056 | − | 0.535946i | ||||
\(977\) | − | 1.32690e10i | − | 0.455206i | −0.973754 | − | 0.227603i | \(-0.926911\pi\) | ||
0.973754 | − | 0.227603i | \(-0.0730888\pi\) | |||||||
\(978\) | 1.71259e8 | + | 2.74367e8i | 0.00585419 | + | 0.00937878i | ||||
\(979\) | −1.20172e10 | −0.409321 | ||||||||
\(980\) | 2.55475e9 | − | 5.22516e9i | 0.0867078 | − | 0.177341i | ||||
\(981\) | − | 2.33187e10i | − | 0.788612i | ||||||
\(982\) | −8.14460e9 | − | 1.30482e10i | −0.274460 | − | 0.439702i | ||||
\(983\) | −4.58040e10 | −1.53803 | −0.769017 | − | 0.639228i | \(-0.779254\pi\) | ||||
−0.769017 | + | 0.639228i | \(0.779254\pi\) | |||||||
\(984\) | 8.25332e7 | − | 8.55327e6i | 0.00276150 | − | 0.000286187i | ||||
\(985\) | −2.87043e9 | −0.0957019 | ||||||||
\(986\) | −1.64227e10 | − | 2.63102e10i | −0.545602 | − | 0.874088i | ||||
\(987\) | 4.16808e8 | 0.0137983 | ||||||||
\(988\) | 2.24232e10 | − | 3.50350e8i | 0.739687 | − | 0.0115572i | ||||
\(989\) | −7.13626e9 | −0.234576 | ||||||||
\(990\) | −3.94558e9 | − | 6.32106e9i | −0.129237 | − | 0.207046i | ||||
\(991\) | −3.09073e10 | −1.00880 | −0.504399 | − | 0.863471i | \(-0.668286\pi\) | ||||
−0.504399 | + | 0.863471i | \(0.668286\pi\) | |||||||
\(992\) | 5.02129e9 | + | 1.84139e9i | 0.163314 | + | 0.0598901i | ||||
\(993\) | 1.13794e9 | 0.0368805 | ||||||||
\(994\) | 7.64839e9 | + | 1.22532e10i | 0.247012 | + | 0.395728i | ||||
\(995\) | − | 7.83960e9i | − | 0.252297i | ||||||
\(996\) | −8.10888e8 | − | 3.96470e8i | −0.0260048 | − | 0.0127146i | ||||
\(997\) | 3.82590e10 | 1.22265 | 0.611323 | − | 0.791381i | \(-0.290638\pi\) | ||||
0.611323 | + | 0.791381i | \(0.290638\pi\) | |||||||
\(998\) | −3.83407e8 | − | 6.14242e8i | −0.0122097 | − | 0.0195606i | ||||
\(999\) | 2.45029e9i | 0.0777567i |
(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 | 76.8.d.a.75.14 | yes | 68 | |
4.3 | odd | 2 | inner | 76.8.d.a.75.56 | yes | 68 | |
19.18 | odd | 2 | inner | 76.8.d.a.75.55 | yes | 68 | |
76.75 | even | 2 | inner | 76.8.d.a.75.13 | ✓ | 68 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.8.d.a.75.13 | ✓ | 68 | 76.75 | even | 2 | inner | |
76.8.d.a.75.14 | yes | 68 | 1.1 | even | 1 | trivial | |
76.8.d.a.75.55 | yes | 68 | 19.18 | odd | 2 | inner | |
76.8.d.a.75.56 | yes | 68 | 4.3 | odd | 2 | inner |