Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,8,Mod(37,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.37");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.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: | \(22.4917218349\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 206x^{10} + 24336x^{8} - 1510912x^{6} + 398721024x^{4} - 55297703936x^{2} + 4398046511104 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{30}\cdot 3^{6}\cdot 5^{2}\cdot 13^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 37.2 | ||
Root | \(10.6405 + 3.84452i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 72.37 |
Dual form | 72.8.d.c.37.1 |
$q$-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 \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(55\) | \(65\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.6405 | + | 3.84452i | −0.940494 | + | 0.339811i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 98.4393 | − | 81.8151i | 0.769057 | − | 0.639180i | ||||
\(5\) | − | 209.469i | − | 0.749420i | −0.927142 | − | 0.374710i | \(-0.877742\pi\) | ||
0.927142 | − | 0.374710i | \(-0.122258\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1301.46 | −1.43413 | −0.717064 | − | 0.697008i | \(-0.754514\pi\) | ||||
−0.717064 | + | 0.697008i | \(0.754514\pi\) | |||||||
\(8\) | −732.900 | + | 1249.00i | −0.506093 | + | 0.862479i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 805.310 | + | 2228.85i | 0.254661 | + | 0.704825i | ||||
\(11\) | 7074.87i | 1.60267i | 0.598216 | + | 0.801335i | \(0.295877\pi\) | ||||
−0.598216 | + | 0.801335i | \(0.704123\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 14331.3i | − | 1.80919i | −0.426273 | − | 0.904594i | \(-0.640174\pi\) | ||
0.426273 | − | 0.904594i | \(-0.359826\pi\) | |||||||
\(14\) | 13848.1 | − | 5003.49i | 1.34879 | − | 0.487332i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2996.58 | − | 16107.6i | 0.182897 | − | 0.983132i | ||||
\(17\) | −19199.4 | −0.947800 | −0.473900 | − | 0.880579i | \(-0.657154\pi\) | ||||
−0.473900 | + | 0.880579i | \(0.657154\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 9617.13i | 0.321668i | 0.986981 | + | 0.160834i | \(0.0514184\pi\) | ||||
−0.986981 | + | 0.160834i | \(0.948582\pi\) | |||||||
\(20\) | −17137.8 | − | 20620.0i | −0.479015 | − | 0.576347i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −27199.5 | − | 75280.0i | −0.544605 | − | 1.50730i | ||||
\(23\) | 86666.4 | 1.48526 | 0.742632 | − | 0.669700i | \(-0.233577\pi\) | ||||
0.742632 | + | 0.669700i | \(0.233577\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 34247.6 | 0.438369 | ||||||||
\(26\) | 55097.0 | + | 152492.i | 0.614782 | + | 1.70153i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −128115. | + | 106479.i | −1.10293 | + | 0.916666i | ||||
\(29\) | 101787.i | 0.774997i | 0.921870 | + | 0.387498i | \(0.126661\pi\) | ||||
−0.921870 | + | 0.387498i | \(0.873339\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 28412.3 | 0.171293 | 0.0856466 | − | 0.996326i | \(-0.472704\pi\) | ||||
0.0856466 | + | 0.996326i | \(0.472704\pi\) | |||||||
\(32\) | 30041.1 | + | 182913.i | 0.162066 | + | 0.986780i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 204291. | − | 73812.6i | 0.891400 | − | 0.322073i | ||||
\(35\) | 272616.i | 1.07476i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 76289.0i | 0.247603i | 0.992307 | + | 0.123801i | \(0.0395086\pi\) | ||||
−0.992307 | + | 0.123801i | \(0.960491\pi\) | |||||||
\(38\) | −36973.3 | − | 102331.i | −0.109306 | − | 0.302527i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 261628. | + | 153520.i | 0.646359 | + | 0.379276i | ||||
\(41\) | 510168. | 1.15603 | 0.578016 | − | 0.816026i | \(-0.303827\pi\) | ||||
0.578016 | + | 0.816026i | \(0.303827\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 784099.i | 1.50394i | 0.659196 | + | 0.751971i | \(0.270897\pi\) | ||||
−0.659196 | + | 0.751971i | \(0.729103\pi\) | |||||||
\(44\) | 578831. | + | 696445.i | 1.02440 | + | 1.23254i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −922172. | + | 333191.i | −1.39688 | + | 0.504709i | ||||
\(47\) | −180049. | −0.252957 | −0.126479 | − | 0.991969i | \(-0.540368\pi\) | ||||
−0.126479 | + | 0.991969i | \(0.540368\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 870255. | 1.05672 | ||||||||
\(50\) | −364410. | + | 131666.i | −0.412283 | + | 0.148963i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.17252e6 | − | 1.41076e6i | −1.15640 | − | 1.39137i | ||||
\(53\) | 880974.i | 0.812826i | 0.913689 | + | 0.406413i | \(0.133221\pi\) | ||||
−0.913689 | + | 0.406413i | \(0.866779\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.48197e6 | 1.20107 | ||||||||
\(56\) | 953840. | − | 1.62553e6i | 0.725801 | − | 1.23690i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −391323. | − | 1.08306e6i | −0.263352 | − | 0.728880i | ||||
\(59\) | − | 92535.3i | − | 0.0586577i | −0.999570 | − | 0.0293289i | \(-0.990663\pi\) | ||
0.999570 | − | 0.0293289i | \(-0.00933701\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.40486e6i | 1.35655i | 0.734809 | + | 0.678274i | \(0.237272\pi\) | ||||
−0.734809 | + | 0.678274i | \(0.762728\pi\) | |||||||
\(62\) | −302320. | + | 109232.i | −0.161100 | + | 0.0582073i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.02287e6 | − | 1.83079e6i | −0.487741 | − | 0.872989i | ||||
\(65\) | −3.00197e6 | −1.35584 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.99319e6i | − | 0.809630i | −0.914399 | − | 0.404815i | \(-0.867336\pi\) | ||
0.914399 | − | 0.404815i | \(-0.132664\pi\) | |||||||
\(68\) | −1.88998e6 | + | 1.57080e6i | −0.728912 | + | 0.605815i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.04808e6 | − | 2.90076e6i | −0.365217 | − | 1.01081i | ||||
\(71\) | 3.60291e6 | 1.19467 | 0.597337 | − | 0.801990i | \(-0.296225\pi\) | ||||
0.597337 | + | 0.801990i | \(0.296225\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.68585e6 | 0.507211 | 0.253605 | − | 0.967308i | \(-0.418384\pi\) | ||||
0.253605 | + | 0.967308i | \(0.418384\pi\) | |||||||
\(74\) | −293295. | − | 811751.i | −0.0841382 | − | 0.232869i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 786826. | + | 946703.i | 0.205604 | + | 0.247381i | ||||
\(77\) | − | 9.20766e6i | − | 2.29843i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.81609e6 | 1.09901 | 0.549503 | − | 0.835492i | \(-0.314817\pi\) | ||||
0.549503 | + | 0.835492i | \(0.314817\pi\) | |||||||
\(80\) | −3.37406e6 | − | 627693.i | −0.736779 | − | 0.137067i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.42843e6 | + | 1.96135e6i | −1.08724 | + | 0.392832i | ||||
\(83\) | − | 1.23628e6i | − | 0.237325i | −0.992935 | − | 0.118662i | \(-0.962139\pi\) | ||
0.992935 | − | 0.118662i | \(-0.0378606\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.02169e6i | 0.710301i | ||||||||
\(86\) | −3.01449e6 | − | 8.34318e6i | −0.511056 | − | 1.41445i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.83654e6 | − | 5.18518e6i | −1.38227 | − | 0.811100i | ||||
\(89\) | −9.48855e6 | −1.42671 | −0.713353 | − | 0.700805i | \(-0.752824\pi\) | ||||
−0.713353 | + | 0.700805i | \(0.752824\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.86516e7i | 2.59461i | ||||||||
\(92\) | 8.53138e6 | − | 7.09062e6i | 1.14225 | − | 0.949351i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.91580e6 | − | 692201.i | 0.237905 | − | 0.0859577i | ||||
\(95\) | 2.01449e6 | 0.241065 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.45734e7 | 1.62129 | 0.810645 | − | 0.585538i | \(-0.199117\pi\) | ||||
0.810645 | + | 0.585538i | \(0.199117\pi\) | |||||||
\(98\) | −9.25992e6 | + | 3.34571e6i | −0.993839 | + | 0.359085i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.37131e6 | − | 2.80197e6i | 0.337131 | − | 0.280197i | ||||
\(101\) | 1.12238e7i | 1.08396i | 0.840390 | + | 0.541982i | \(0.182326\pi\) | ||||
−0.840390 | + | 0.541982i | \(0.817674\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.39417e6 | 0.125715 | 0.0628574 | − | 0.998023i | \(-0.479979\pi\) | ||||
0.0628574 | + | 0.998023i | \(0.479979\pi\) | |||||||
\(104\) | 1.78998e7 | + | 1.05034e7i | 1.56039 | + | 0.915617i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.38693e6 | − | 9.37398e6i | −0.276207 | − | 0.764458i | ||||
\(107\) | 3.22163e6i | 0.254233i | 0.991888 | + | 0.127117i | \(0.0405723\pi\) | ||||
−0.991888 | + | 0.127117i | \(0.959428\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 4.22797e6i | − | 0.312708i | −0.987701 | − | 0.156354i | \(-0.950026\pi\) | ||
0.987701 | − | 0.156354i | \(-0.0499741\pi\) | |||||||
\(110\) | −1.57688e7 | + | 5.69746e6i | −1.12960 | + | 0.408138i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.89993e6 | + | 2.09634e7i | −0.262297 | + | 1.40994i | ||||
\(113\) | −2.63919e6 | −0.172066 | −0.0860332 | − | 0.996292i | \(-0.527419\pi\) | ||||
−0.0860332 | + | 0.996292i | \(0.527419\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1.81540e7i | − | 1.11309i | ||||||
\(116\) | 8.32772e6 | + | 1.00199e7i | 0.495363 | + | 0.596017i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 355754. | + | 984619.i | 0.0199325 | + | 0.0551672i | ||||
\(119\) | 2.49873e7 | 1.35927 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.05666e7 | −1.56855 | ||||||||
\(122\) | −9.24553e6 | − | 2.55888e7i | −0.460970 | − | 1.27582i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.79688e6 | − | 2.32455e6i | 0.131734 | − | 0.109487i | ||||
\(125\) | − | 2.35386e7i | − | 1.07794i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.02119e7 | −0.442376 | −0.221188 | − | 0.975231i | \(-0.570993\pi\) | ||||
−0.221188 | + | 0.975231i | \(0.570993\pi\) | |||||||
\(128\) | 1.79223e7 | + | 1.55480e7i | 0.755368 | + | 0.655301i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.19424e7 | − | 1.15411e7i | 1.27516 | − | 0.460730i | ||||
\(131\) | 4.73463e7i | 1.84008i | 0.391825 | + | 0.920040i | \(0.371844\pi\) | ||||
−0.391825 | + | 0.920040i | \(0.628156\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 1.25163e7i | − | 0.461313i | ||||||
\(134\) | 7.66286e6 | + | 2.12085e7i | 0.275121 | + | 0.761452i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.40713e7 | − | 2.39801e7i | 0.479675 | − | 0.817458i | ||||
\(137\) | −5.06415e7 | −1.68261 | −0.841307 | − | 0.540557i | \(-0.818213\pi\) | ||||
−0.841307 | + | 0.540557i | \(0.818213\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2.58884e7i | − | 0.817623i | −0.912619 | − | 0.408812i | \(-0.865943\pi\) | ||
0.912619 | − | 0.408812i | \(-0.134057\pi\) | |||||||
\(140\) | 2.23041e7 | + | 2.68361e7i | 0.686968 | + | 0.826555i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.83367e7 | + | 1.38515e7i | −1.12358 | + | 0.405964i | ||||
\(143\) | 1.01392e8 | 2.89953 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.13213e7 | 0.580798 | ||||||||
\(146\) | −1.79382e7 | + | 6.48128e6i | −0.477029 | + | 0.172356i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.24159e6 | + | 7.50983e6i | 0.158263 | + | 0.190421i | ||||
\(149\) | 1.48513e7i | 0.367802i | 0.982945 | + | 0.183901i | \(0.0588726\pi\) | ||||
−0.982945 | + | 0.183901i | \(0.941127\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.63661e7 | −0.623200 | −0.311600 | − | 0.950213i | \(-0.600865\pi\) | ||||
−0.311600 | + | 0.950213i | \(0.600865\pi\) | |||||||
\(152\) | −1.20118e7 | − | 7.04840e6i | −0.277432 | − | 0.162794i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.53991e7 | + | 9.79739e7i | 0.781033 | + | 2.16166i | ||||
\(155\) | − | 5.95150e6i | − | 0.128371i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 8.47599e6i | − | 0.174800i | −0.996173 | − | 0.0874001i | \(-0.972144\pi\) | ||
0.996173 | − | 0.0874001i | \(-0.0278558\pi\) | |||||||
\(158\) | −5.12455e7 | + | 1.85156e7i | −1.03361 | + | 0.373454i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.83147e7 | − | 6.29269e6i | 0.739513 | − | 0.121455i | ||||
\(161\) | −1.12793e8 | −2.13006 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.54067e6i | 0.172553i | 0.996271 | + | 0.0862764i | \(0.0274968\pi\) | ||||
−0.996271 | + | 0.0862764i | \(0.972503\pi\) | |||||||
\(164\) | 5.02205e7 | − | 4.17394e7i | 0.889054 | − | 0.738912i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.75290e6 | + | 1.31546e7i | 0.0806456 | + | 0.223202i | ||||
\(167\) | 1.44929e7 | 0.240796 | 0.120398 | − | 0.992726i | \(-0.461583\pi\) | ||||
0.120398 | + | 0.992726i | \(0.461583\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.42638e8 | −2.27316 | ||||||||
\(170\) | −1.54615e7 | − | 4.27927e7i | −0.241368 | − | 0.668034i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.41511e7 | + | 7.71862e7i | 0.961291 | + | 1.15662i | ||||
\(173\) | − | 6.08908e7i | − | 0.894109i | −0.894507 | − | 0.447054i | \(-0.852473\pi\) | ||
0.894507 | − | 0.447054i | \(-0.147527\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.45719e7 | −0.628677 | ||||||||
\(176\) | 1.13959e8 | + | 2.12004e7i | 1.57564 | + | 0.293124i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.00963e8 | − | 3.64789e7i | 1.34181 | − | 0.484811i | ||||
\(179\) | 2.27852e7i | 0.296939i | 0.988917 | + | 0.148469i | \(0.0474347\pi\) | ||||
−0.988917 | + | 0.148469i | \(0.952565\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 8.06800e6i | − | 0.101132i | −0.998721 | − | 0.0505662i | \(-0.983897\pi\) | ||
0.998721 | − | 0.0505662i | \(-0.0161026\pi\) | |||||||
\(182\) | −7.17066e7 | − | 1.98462e8i | −0.881676 | − | 2.44021i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.35179e7 | + | 1.08247e8i | −0.751681 | + | 1.28101i | ||||
\(185\) | 1.59802e7 | 0.185559 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1.35833e8i | − | 1.51901i | ||||||
\(188\) | −1.77239e7 | + | 1.47307e7i | −0.194539 | + | 0.161685i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.14352e7 | + | 7.74477e6i | −0.226720 | + | 0.0819164i | ||||
\(191\) | −4.57539e7 | −0.475129 | −0.237564 | − | 0.971372i | \(-0.576349\pi\) | ||||
−0.237564 | + | 0.971372i | \(0.576349\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.21552e8 | 1.21706 | 0.608529 | − | 0.793532i | \(-0.291760\pi\) | ||||
0.608529 | + | 0.793532i | \(0.291760\pi\) | |||||||
\(194\) | −1.55068e8 | + | 5.60279e7i | −1.52481 | + | 0.550932i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.56672e7 | − | 7.12000e7i | 0.812678 | − | 0.675435i | ||||
\(197\) | − | 1.71007e8i | − | 1.59361i | −0.604238 | − | 0.796804i | \(-0.706522\pi\) | ||
0.604238 | − | 0.796804i | \(-0.293478\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.51211e7 | −0.136018 | −0.0680091 | − | 0.997685i | \(-0.521665\pi\) | ||||
−0.0680091 | + | 0.997685i | \(0.521665\pi\) | |||||||
\(200\) | −2.51001e7 | + | 4.27753e7i | −0.221855 | + | 0.378084i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.31501e7 | − | 1.19426e8i | −0.368343 | − | 1.01946i | ||||
\(203\) | − | 1.32472e8i | − | 1.11144i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 1.06865e8i | − | 0.866353i | ||||||
\(206\) | −1.48347e7 | + | 5.35993e6i | −0.118234 | + | 0.0427193i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.30843e8 | − | 4.29449e7i | −1.77867 | − | 0.330895i | ||||
\(209\) | −6.80399e7 | −0.515528 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.28562e8i | 1.67500i | 0.546437 | + | 0.837500i | \(0.315984\pi\) | ||||
−0.546437 | + | 0.837500i | \(0.684016\pi\) | |||||||
\(212\) | 7.20770e7 | + | 8.67225e7i | 0.519543 | + | 0.625110i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.23856e7 | − | 3.42797e7i | −0.0863913 | − | 0.239105i | ||||
\(215\) | 1.64245e8 | 1.12709 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.69774e7 | −0.245656 | ||||||||
\(218\) | 1.62545e7 | + | 4.49876e7i | 0.106262 | + | 0.294100i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.45884e8 | − | 1.21247e8i | 0.923694 | − | 0.767703i | ||||
\(221\) | 2.75153e8i | 1.71475i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.65483e7 | 0.341470 | 0.170735 | − | 0.985317i | \(-0.445386\pi\) | ||||
0.170735 | + | 0.985317i | \(0.445386\pi\) | |||||||
\(224\) | −3.90973e7 | − | 2.38054e8i | −0.232423 | − | 1.41517i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.80822e7 | − | 1.01464e7i | 0.161827 | − | 0.0584700i | ||||
\(227\) | 1.78749e8i | 1.01427i | 0.861867 | + | 0.507135i | \(0.169296\pi\) | ||||
−0.861867 | + | 0.507135i | \(0.830704\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 5.90997e7i | − | 0.325208i | −0.986691 | − | 0.162604i | \(-0.948011\pi\) | ||
0.986691 | − | 0.162604i | \(-0.0519893\pi\) | |||||||
\(230\) | 6.97934e7 | + | 1.93167e8i | 0.378239 | + | 1.04685i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.27132e8 | − | 7.45998e7i | −0.668419 | − | 0.392220i | ||||
\(233\) | −1.82022e8 | −0.942709 | −0.471355 | − | 0.881944i | \(-0.656235\pi\) | ||||
−0.471355 | + | 0.881944i | \(0.656235\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.77147e7i | 0.189571i | ||||||||
\(236\) | −7.57078e6 | − | 9.10910e6i | −0.0374929 | − | 0.0451111i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.65876e8 | + | 9.60642e7i | −1.27838 | + | 0.461894i | ||||
\(239\) | 6.73710e7 | 0.319213 | 0.159606 | − | 0.987181i | \(-0.448977\pi\) | ||||
0.159606 | + | 0.987181i | \(0.448977\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.70435e8 | 0.784333 | 0.392166 | − | 0.919894i | \(-0.371726\pi\) | ||||
0.392166 | + | 0.919894i | \(0.371726\pi\) | |||||||
\(242\) | 3.25243e8 | − | 1.17514e8i | 1.47521 | − | 0.533011i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.96754e8 | + | 2.36732e8i | 0.867078 | + | 1.04326i | ||||
\(245\) | − | 1.82292e8i | − | 0.791928i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.37826e8 | 0.581958 | ||||||||
\(248\) | −2.08234e7 | + | 3.54870e7i | −0.0866902 | + | 0.147737i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.04948e7 | + | 2.50462e8i | 0.366297 | + | 1.01380i | ||||
\(251\) | 9.22637e7i | 0.368275i | 0.982900 | + | 0.184138i | \(0.0589492\pi\) | ||||
−0.982900 | + | 0.184138i | \(0.941051\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.13154e8i | 2.38039i | ||||||||
\(254\) | 1.08659e8 | − | 3.92597e7i | 0.416052 | − | 0.150324i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.50476e8 | − | 9.65358e7i | −0.933097 | − | 0.359624i | ||||
\(257\) | 4.30168e8 | 1.58078 | 0.790391 | − | 0.612603i | \(-0.209877\pi\) | ||||
0.790391 | + | 0.612603i | \(0.209877\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 9.92870e7i | − | 0.355094i | ||||||
\(260\) | −2.95512e8 | + | 2.45606e8i | −1.04272 | + | 0.866628i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.82024e8 | − | 5.03787e8i | −0.625279 | − | 1.73058i | ||||
\(263\) | −1.87195e8 | −0.634526 | −0.317263 | − | 0.948338i | \(-0.602764\pi\) | ||||
−0.317263 | + | 0.948338i | \(0.602764\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.84537e8 | 0.609149 | ||||||||
\(266\) | 4.81192e7 | + | 1.33179e8i | 0.156759 | + | 0.433862i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.63073e8 | − | 1.96208e8i | −0.517500 | − | 0.622652i | ||||
\(269\) | 3.68317e8i | 1.15369i | 0.816854 | + | 0.576845i | \(0.195716\pi\) | ||||
−0.816854 | + | 0.576845i | \(0.804284\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.53681e8 | 1.38471 | 0.692354 | − | 0.721558i | \(-0.256574\pi\) | ||||
0.692354 | + | 0.721558i | \(0.256574\pi\) | |||||||
\(272\) | −5.75327e7 | + | 3.09257e8i | −0.173350 | + | 0.931813i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.38850e8 | − | 1.94692e8i | 1.58249 | − | 0.571771i | ||||
\(275\) | 2.42297e8i | 0.702561i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.63451e8i | 1.31016i | 0.755559 | + | 0.655081i | \(0.227365\pi\) | ||||
−0.755559 | + | 0.655081i | \(0.772635\pi\) | |||||||
\(278\) | 9.95285e7 | + | 2.75465e8i | 0.277837 | + | 0.768969i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.40498e8 | − | 1.99800e8i | −0.926962 | − | 0.543930i | ||||
\(281\) | 5.49202e8 | 1.47659 | 0.738295 | − | 0.674478i | \(-0.235631\pi\) | ||||
0.738295 | + | 0.674478i | \(0.235631\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.01427e8i | 1.05282i | 0.850231 | + | 0.526410i | \(0.176462\pi\) | ||||
−0.850231 | + | 0.526410i | \(0.823538\pi\) | |||||||
\(284\) | 3.54668e8 | − | 2.94773e8i | 0.918772 | − | 0.763612i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.07886e9 | + | 3.89804e8i | −2.72699 | + | 0.985293i | ||||
\(287\) | −6.63963e8 | −1.65790 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.17209e7 | −0.101674 | ||||||||
\(290\) | −2.26869e8 | + | 8.19702e7i | −0.546237 | + | 0.197362i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.65954e8 | − | 1.37928e8i | 0.390074 | − | 0.324199i | ||||
\(293\) | 4.20278e8i | 0.976112i | 0.872812 | + | 0.488056i | \(0.162294\pi\) | ||||
−0.872812 | + | 0.488056i | \(0.837706\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.93833e7 | −0.0439593 | ||||||||
\(296\) | −9.52852e7 | − | 5.59122e7i | −0.213552 | − | 0.125310i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.70964e7 | − | 1.58025e8i | −0.124983 | − | 0.345915i | ||||
\(299\) | − | 1.24204e9i | − | 2.68712i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 1.02047e9i | − | 2.15685i | ||||||
\(302\) | 2.80548e8 | − | 1.01365e8i | 0.586115 | − | 0.211770i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.54909e8 | + | 2.88185e7i | 0.316242 | + | 0.0588321i | ||||
\(305\) | 5.03744e8 | 1.01662 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4.12131e8i | − | 0.812925i | −0.913667 | − | 0.406463i | \(-0.866762\pi\) | ||
0.913667 | − | 0.406463i | \(-0.133238\pi\) | |||||||
\(308\) | −7.53326e8 | − | 9.06396e8i | −1.46911 | − | 1.76763i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.28807e7 | + | 6.33268e7i | 0.0436218 | + | 0.120732i | ||||
\(311\) | −6.54901e8 | −1.23457 | −0.617283 | − | 0.786741i | \(-0.711767\pi\) | ||||
−0.617283 | + | 0.786741i | \(0.711767\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.92213e8 | 0.722963 | 0.361482 | − | 0.932379i | \(-0.382271\pi\) | ||||
0.361482 | + | 0.932379i | \(0.382271\pi\) | |||||||
\(314\) | 3.25861e7 | + | 9.01886e7i | 0.0593990 | + | 0.164398i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.74092e8 | − | 3.94029e8i | 0.845197 | − | 0.702462i | ||||
\(317\) | − | 6.67005e8i | − | 1.17604i | −0.808847 | − | 0.588019i | \(-0.799908\pi\) | ||
0.808847 | − | 0.588019i | \(-0.200092\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.20131e8 | −1.24206 | ||||||||
\(320\) | −3.83494e8 | + | 2.14259e8i | −0.654236 | + | 0.365523i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.20017e9 | − | 4.33635e8i | 2.00331 | − | 0.723817i | ||||
\(323\) | − | 1.84643e8i | − | 0.304877i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 4.90812e8i | − | 0.793092i | ||||||
\(326\) | −3.66793e7 | − | 1.01517e8i | −0.0586354 | − | 0.162285i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.73902e8 | + | 6.37201e8i | −0.585059 | + | 0.997053i | ||||
\(329\) | 2.34326e8 | 0.362773 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.23035e8i | 0.792744i | 0.918090 | + | 0.396372i | \(0.129731\pi\) | ||||
−0.918090 | + | 0.396372i | \(0.870269\pi\) | |||||||
\(332\) | −1.01146e8 | − | 1.21698e8i | −0.151693 | − | 0.182516i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.54212e8 | + | 5.57184e7i | −0.226467 | + | 0.0818250i | ||||
\(335\) | −4.17512e8 | −0.606754 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.13571e9 | −1.61645 | −0.808224 | − | 0.588875i | \(-0.799571\pi\) | ||||
−0.808224 | + | 0.588875i | \(0.799571\pi\) | |||||||
\(338\) | 1.51773e9 | − | 5.48374e8i | 2.13790 | − | 0.772446i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.29035e8 | + | 3.95892e8i | 0.454010 | + | 0.546262i | ||||
\(341\) | 2.01013e8i | 0.274527i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.07934e7 | −0.0813443 | ||||||||
\(344\) | −9.79342e8 | − | 5.74667e8i | −1.29712 | − | 0.761134i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.34096e8 | + | 6.47907e8i | 0.303828 | + | 0.840904i | ||||
\(347\) | 9.94124e8i | 1.27728i | 0.769504 | + | 0.638642i | \(0.220503\pi\) | ||||
−0.769504 | + | 0.638642i | \(0.779497\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.70786e8i | 1.09653i | 0.836303 | + | 0.548267i | \(0.184712\pi\) | ||||
−0.836303 | + | 0.548267i | \(0.815288\pi\) | |||||||
\(350\) | 4.74266e8 | − | 1.71358e8i | 0.591267 | − | 0.213631i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.29409e9 | + | 2.12537e8i | −1.58148 | + | 0.259738i | ||||
\(353\) | −7.47327e8 | −0.904273 | −0.452136 | − | 0.891949i | \(-0.649338\pi\) | ||||
−0.452136 | + | 0.891949i | \(0.649338\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 7.54700e8i | − | 0.895313i | ||||||
\(356\) | −9.34046e8 | + | 7.76306e8i | −1.09722 | + | 0.911923i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.75982e7 | − | 2.42445e8i | −0.100903 | − | 0.279269i | ||||
\(359\) | −8.39765e8 | −0.957915 | −0.478958 | − | 0.877838i | \(-0.658985\pi\) | ||||
−0.478958 | + | 0.877838i | \(0.658985\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.01383e8 | 0.896530 | ||||||||
\(362\) | 3.10176e7 | + | 8.58473e7i | 0.0343659 | + | 0.0951145i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.52598e9 | + | 1.83605e9i | 1.65842 | + | 1.99540i | ||||
\(365\) | − | 3.53134e8i | − | 0.380114i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.85579e8 | 0.301575 | 0.150788 | − | 0.988566i | \(-0.451819\pi\) | ||||
0.150788 | + | 0.988566i | \(0.451819\pi\) | |||||||
\(368\) | 2.59703e8 | − | 1.39599e9i | 0.271650 | − | 1.46021i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.70037e8 | + | 6.14363e7i | −0.174517 | + | 0.0630549i | ||||
\(371\) | − | 1.14655e9i | − | 1.16570i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 2.13291e8i | − | 0.212810i | −0.994323 | − | 0.106405i | \(-0.966066\pi\) | ||
0.994323 | − | 0.106405i | \(-0.0339340\pi\) | |||||||
\(374\) | 5.22215e8 | + | 1.44533e9i | 0.516177 | + | 1.42862i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.31958e8 | − | 2.24881e8i | 0.128020 | − | 0.218170i | ||||
\(377\) | 1.45874e9 | 1.40212 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.77655e8i | − | 0.167625i | −0.996482 | − | 0.0838127i | \(-0.973290\pi\) | ||
0.996482 | − | 0.0838127i | \(-0.0267098\pi\) | |||||||
\(380\) | 1.98305e8 | − | 1.64816e8i | 0.185392 | − | 0.154084i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.86843e8 | − | 1.75902e8i | 0.446856 | − | 0.161454i | ||||
\(383\) | 1.03999e9 | 0.945876 | 0.472938 | − | 0.881096i | \(-0.343193\pi\) | ||||
0.472938 | + | 0.881096i | \(0.343193\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.92872e9 | −1.72249 | ||||||||
\(386\) | −1.29337e9 | + | 4.67309e8i | −1.14464 | + | 0.413570i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.43460e9 | − | 1.19233e9i | 1.24686 | − | 1.03630i | ||||
\(389\) | 1.52613e9i | 1.31452i | 0.753663 | + | 0.657261i | \(0.228285\pi\) | ||||
−0.753663 | + | 0.657261i | \(0.771715\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.66395e9 | −1.40773 | ||||||||
\(392\) | −6.37810e8 | + | 1.08695e9i | −0.534798 | + | 0.911399i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.57439e8 | + | 1.81959e9i | 0.541525 | + | 1.49878i | ||||
\(395\) | − | 1.00882e9i | − | 0.823617i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 1.40941e9i | − | 1.13050i | −0.824919 | − | 0.565250i | \(-0.808780\pi\) | ||
0.824919 | − | 0.565250i | \(-0.191220\pi\) | |||||||
\(398\) | 1.60895e8 | − | 5.81334e7i | 0.127924 | − | 0.0462205i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.02626e8 | − | 5.51648e8i | 0.0801764 | − | 0.430975i | ||||
\(401\) | 1.43905e9 | 1.11448 | 0.557238 | − | 0.830353i | \(-0.311861\pi\) | ||||
0.557238 | + | 0.830353i | \(0.311861\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 4.07185e8i | − | 0.309902i | ||||||
\(404\) | 9.18276e8 | + | 1.10486e9i | 0.692849 | + | 0.833630i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.09291e8 | + | 1.40956e9i | 0.377681 | + | 1.04531i | ||||
\(407\) | −5.39735e8 | −0.396826 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.10100e8 | −0.151843 | −0.0759214 | − | 0.997114i | \(-0.524190\pi\) | ||||
−0.0759214 | + | 0.997114i | \(0.524190\pi\) | |||||||
\(410\) | 4.10843e8 | + | 1.13709e9i | 0.294396 | + | 0.814800i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.37241e8 | − | 1.14064e8i | 0.0966818 | − | 0.0803544i | ||||
\(413\) | 1.20431e8i | 0.0841226i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.58962e8 | −0.177856 | ||||||||
\(416\) | 2.62139e9 | − | 4.30528e8i | 1.78527 | − | 0.293207i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.23977e8 | − | 2.61581e8i | 0.484850 | − | 0.175182i | ||||
\(419\) | 2.02032e9i | 1.34175i | 0.741572 | + | 0.670873i | \(0.234080\pi\) | ||||
−0.741572 | + | 0.670873i | \(0.765920\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 8.78781e8i | − | 0.573975i | −0.957934 | − | 0.286988i | \(-0.907346\pi\) | ||
0.957934 | − | 0.286988i | \(-0.0926539\pi\) | |||||||
\(422\) | −8.78711e8 | − | 2.43200e9i | −0.569184 | − | 1.57533i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.10034e9 | − | 6.45666e8i | −0.701046 | − | 0.411365i | ||||
\(425\) | −6.57534e8 | −0.415486 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 3.12983e9i | − | 1.94546i | ||||||
\(428\) | 2.63578e8 | + | 3.17135e8i | 0.162501 | + | 0.195520i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.74764e9 | + | 6.31443e8i | −1.06002 | + | 0.382996i | ||||
\(431\) | −1.53441e9 | −0.923150 | −0.461575 | − | 0.887101i | \(-0.652715\pi\) | ||||
−0.461575 | + | 0.887101i | \(0.652715\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.25446e8 | 0.251847 | 0.125924 | − | 0.992040i | \(-0.459811\pi\) | ||||
0.125924 | + | 0.992040i | \(0.459811\pi\) | |||||||
\(434\) | 3.93457e8 | − | 1.42161e8i | 0.231038 | − | 0.0834767i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.45912e8 | − | 4.16198e8i | −0.199877 | − | 0.240490i | ||||
\(437\) | 8.33482e8i | 0.477762i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.51493e8 | 0.198285 | 0.0991427 | − | 0.995073i | \(-0.468390\pi\) | ||||
0.0991427 | + | 0.995073i | \(0.468390\pi\) | |||||||
\(440\) | −1.08614e9 | + | 1.85098e9i | −0.607855 | + | 1.03590i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.05783e9 | − | 2.92775e9i | −0.582691 | − | 1.61271i | ||||
\(443\) | 3.38530e9i | 1.85005i | 0.379904 | + | 0.925026i | \(0.375957\pi\) | ||||
−0.379904 | + | 0.925026i | \(0.624043\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.98756e9i | 1.06920i | ||||||||
\(446\) | −6.01700e8 | + | 2.17401e8i | −0.321150 | + | 0.116035i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.33122e9 | + | 2.38270e9i | 0.699482 | + | 1.25198i | ||||
\(449\) | 3.28992e7 | 0.0171523 | 0.00857617 | − | 0.999963i | \(-0.497270\pi\) | ||||
0.00857617 | + | 0.999963i | \(0.497270\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.60937e9i | 1.85274i | ||||||||
\(452\) | −2.59800e8 | + | 2.15925e8i | −0.132329 | + | 0.109981i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.87206e8 | − | 1.90198e9i | −0.344660 | − | 0.953915i | ||||
\(455\) | 3.90694e9 | 1.94445 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.54142e8 | 0.369612 | 0.184806 | − | 0.982775i | \(-0.440834\pi\) | ||||
0.184806 | + | 0.982775i | \(0.440834\pi\) | |||||||
\(458\) | 2.27210e8 | + | 6.28849e8i | 0.110509 | + | 0.305856i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.48527e9 | − | 1.78706e9i | −0.711463 | − | 0.856027i | ||||
\(461\) | − | 1.59847e9i | − | 0.759893i | −0.925008 | − | 0.379946i | \(-0.875942\pi\) | ||
0.925008 | − | 0.379946i | \(-0.124058\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.90911e9 | 1.36216 | 0.681079 | − | 0.732210i | \(-0.261511\pi\) | ||||
0.681079 | + | 0.732210i | \(0.261511\pi\) | |||||||
\(464\) | 1.63955e9 | + | 3.05014e8i | 0.761924 | + | 0.141745i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.93680e9 | − | 6.99787e8i | 0.886612 | − | 0.320343i | ||||
\(467\) | − | 2.61345e9i | − | 1.18742i | −0.804679 | − | 0.593711i | \(-0.797662\pi\) | ||
0.804679 | − | 0.593711i | \(-0.202338\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.59406e9i | 1.16111i | ||||||||
\(470\) | −1.44995e8 | − | 4.01302e8i | −0.0644185 | − | 0.178291i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.15577e8 | + | 6.78191e7i | 0.0505911 | + | 0.0296862i | ||||
\(473\) | −5.54740e9 | −2.41032 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.29363e8i | 0.141009i | ||||||||
\(476\) | 2.45973e9 | − | 2.04434e9i | 1.04535 | − | 0.868816i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.16859e8 | + | 2.59009e8i | −0.300218 | + | 0.108472i | ||||
\(479\) | 3.07163e9 | 1.27701 | 0.638506 | − | 0.769617i | \(-0.279553\pi\) | ||||
0.638506 | + | 0.769617i | \(0.279553\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.09332e9 | 0.447960 | ||||||||
\(482\) | −1.81351e9 | + | 6.55243e8i | −0.737660 | + | 0.266525i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.00896e9 | + | 2.50081e9i | −1.20631 | + | 1.00259i | ||||
\(485\) | − | 3.05269e9i | − | 1.21503i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.06292e8 | 0.198632 | 0.0993161 | − | 0.995056i | \(-0.468334\pi\) | ||||
0.0993161 | + | 0.995056i | \(0.468334\pi\) | |||||||
\(488\) | −3.00367e9 | − | 1.76252e9i | −1.16999 | − | 0.686538i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7.00825e8 | + | 1.93967e9i | 0.269106 | + | 0.744803i | ||||
\(491\) | − | 1.83863e9i | − | 0.700985i | −0.936566 | − | 0.350492i | \(-0.886014\pi\) | ||
0.936566 | − | 0.350492i | \(-0.113986\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1.95425e9i | − | 0.734542i | ||||||
\(494\) | −1.46653e9 | + | 5.29875e8i | −0.547328 | + | 0.197756i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.51398e7 | − | 4.57655e8i | 0.0313290 | − | 0.168404i | ||||
\(497\) | −4.68905e9 | −1.71331 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.44032e9i | 1.23950i | 0.784799 | + | 0.619750i | \(0.212766\pi\) | ||||
−0.784799 | + | 0.619750i | \(0.787234\pi\) | |||||||
\(500\) | −1.92581e9 | − | 2.31712e9i | −0.689000 | − | 0.829000i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.54710e8 | − | 9.81729e8i | −0.125144 | − | 0.346361i | ||||
\(503\) | 2.78650e9 | 0.976271 | 0.488136 | − | 0.872768i | \(-0.337677\pi\) | ||||
0.488136 | + | 0.872768i | \(0.337677\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.35104e9 | 0.812345 | ||||||||
\(506\) | −2.35728e9 | − | 6.52425e9i | −0.808882 | − | 2.23874i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.00525e9 | + | 8.35484e8i | −0.340212 | + | 0.282758i | ||||
\(509\) | 7.16492e8i | 0.240824i | 0.992724 | + | 0.120412i | \(0.0384215\pi\) | ||||
−0.992724 | + | 0.120412i | \(0.961579\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.19406e9 | −0.727405 | ||||||||
\(512\) | 3.03632e9 | + | 6.42236e7i | 0.999776 | + | 0.0211471i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.57719e9 | + | 1.65379e9i | −1.48672 | + | 0.537167i | ||||
\(515\) | − | 2.92036e8i | − | 0.0942132i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.27382e9i | − | 0.405407i | ||||||
\(518\) | 3.81711e8 | + | 1.05646e9i | 0.120665 | + | 0.333964i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.20014e9 | − | 3.74947e9i | 0.686182 | − | 1.16939i | ||||
\(521\) | 1.71400e8 | 0.0530980 | 0.0265490 | − | 0.999648i | \(-0.491548\pi\) | ||||
0.0265490 | + | 0.999648i | \(0.491548\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.14809e9i | 1.26792i | 0.773365 | + | 0.633961i | \(0.218572\pi\) | ||||
−0.773365 | + | 0.633961i | \(0.781428\pi\) | |||||||
\(524\) | 3.87364e9 | + | 4.66074e9i | 1.17614 | + | 1.41513i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.99184e9 | − | 7.19676e8i | 0.596767 | − | 0.215619i | ||||
\(527\) | −5.45499e8 | −0.162352 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.10625e9 | 1.20601 | ||||||||
\(530\) | −1.96356e9 | + | 7.09457e8i | −0.572900 | + | 0.206995i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.02402e9 | − | 1.23210e9i | −0.294862 | − | 0.354776i | ||||
\(533\) | − | 7.31137e9i | − | 2.09148i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.74833e8 | 0.190528 | ||||||||
\(536\) | 2.48950e9 | + | 1.46081e9i | 0.698289 | + | 0.409748i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.41600e9 | − | 3.91907e9i | −0.392036 | − | 1.08504i | ||||
\(539\) | 6.15694e9i | 1.69357i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.07583e9i | 1.10669i | 0.832953 | + | 0.553344i | \(0.186649\pi\) | ||||
−0.832953 | + | 0.553344i | \(0.813351\pi\) | |||||||
\(542\) | −4.82738e9 | + | 1.74419e9i | −1.30231 | + | 0.470539i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.76772e8 | − | 3.51183e9i | −0.153606 | − | 0.935271i | ||||
\(545\) | −8.85630e8 | −0.234350 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 3.64381e9i | − | 0.951919i | −0.879467 | − | 0.475960i | \(-0.842101\pi\) | ||
0.879467 | − | 0.475960i | \(-0.157899\pi\) | |||||||
\(548\) | −4.98511e9 | + | 4.14324e9i | −1.29403 | + | 1.07549i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −9.31517e8 | − | 2.57816e9i | −0.238738 | − | 0.660754i | ||||
\(551\) | −9.78900e8 | −0.249292 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.26795e9 | −1.57611 | ||||||||
\(554\) | −1.78175e9 | − | 4.93134e9i | −0.445207 | − | 1.23220i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.11806e9 | − | 2.54843e9i | −0.522609 | − | 0.628799i | ||||
\(557\) | 4.47720e9i | 1.09777i | 0.835896 | + | 0.548887i | \(0.184948\pi\) | ||||
−0.835896 | + | 0.548887i | \(0.815052\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.12372e10 | 2.72092 | ||||||||
\(560\) | 4.39120e9 | + | 8.16917e8i | 1.05664 | + | 0.196571i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.84376e9 | + | 2.11142e9i | −1.38872 | + | 0.501761i | ||||
\(563\) | − | 3.55388e9i | − | 0.839311i | −0.907683 | − | 0.419656i | \(-0.862151\pi\) | ||
0.907683 | − | 0.419656i | \(-0.137849\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.52829e8i | 0.128950i | ||||||||
\(566\) | −1.54329e9 | − | 4.27137e9i | −0.357760 | − | 0.990170i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.64058e9 | + | 4.50005e9i | −0.604616 | + | 1.03038i | ||||
\(569\) | 7.15092e8 | 0.162731 | 0.0813653 | − | 0.996684i | \(-0.474072\pi\) | ||||
0.0813653 | + | 0.996684i | \(0.474072\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 5.46695e9i | − | 1.22891i | −0.788954 | − | 0.614453i | \(-0.789377\pi\) | ||
0.788954 | − | 0.614453i | \(-0.210623\pi\) | |||||||
\(572\) | 9.98097e9 | − | 8.29540e9i | 2.22991 | − | 1.85332i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.06488e9 | − | 2.55262e9i | 1.55924 | − | 0.563371i | ||||
\(575\) | 2.96812e9 | 0.651094 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.63907e9 | 1.22206 | 0.611030 | − | 0.791608i | \(-0.290756\pi\) | ||||
0.611030 | + | 0.791608i | \(0.290756\pi\) | |||||||
\(578\) | 4.43930e8 | − | 1.60397e8i | 0.0956240 | − | 0.0345500i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.09885e9 | − | 1.74440e9i | 0.446667 | − | 0.371235i | ||||
\(581\) | 1.60897e9i | 0.340354i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.23278e9 | −1.30269 | ||||||||
\(584\) | −1.23556e9 | + | 2.10563e9i | −0.256696 | + | 0.437459i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.61577e9 | − | 4.47195e9i | −0.331694 | − | 0.918027i | ||||
\(587\) | 1.70729e9i | 0.348396i | 0.984711 | + | 0.174198i | \(0.0557332\pi\) | ||||
−0.984711 | + | 0.174198i | \(0.944267\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.73245e8i | 0.0550995i | ||||||||
\(590\) | 2.06247e8 | − | 7.45196e7i | 0.0413434 | − | 0.0149379i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.22884e9 | + | 2.28606e8i | 0.243426 | + | 0.0452858i | ||||
\(593\) | −4.95214e9 | −0.975218 | −0.487609 | − | 0.873062i | \(-0.662131\pi\) | ||||
−0.487609 | + | 0.873062i | \(0.662131\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 5.23407e9i | − | 1.01866i | ||||||
\(596\) | 1.21506e9 | + | 1.46196e9i | 0.235092 | + | 0.282861i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.77506e9 | + | 1.32159e10i | 0.913114 | + | 2.52722i | ||||
\(599\) | 3.14394e8 | 0.0597697 | 0.0298848 | − | 0.999553i | \(-0.490486\pi\) | ||||
0.0298848 | + | 0.999553i | \(0.490486\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.52006e9 | −1.41306 | −0.706530 | − | 0.707683i | \(-0.749741\pi\) | ||||
−0.706530 | + | 0.707683i | \(0.749741\pi\) | |||||||
\(602\) | 3.92323e9 | + | 1.08583e10i | 0.732920 | + | 2.02850i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.59546e9 | + | 2.15715e9i | −0.479276 | + | 0.398337i | ||||
\(605\) | 6.40277e9i | 1.17550i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.76620e9 | −1.77241 | −0.886207 | − | 0.463290i | \(-0.846669\pi\) | ||||
−0.886207 | + | 0.463290i | \(0.846669\pi\) | |||||||
\(608\) | −1.75910e9 | + | 2.88909e8i | −0.317415 | + | 0.0521313i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.36007e9 | + | 1.93666e9i | −0.956129 | + | 0.345460i | ||||
\(611\) | 2.58033e9i | 0.457648i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.97523e9i | 0.872371i | 0.899857 | + | 0.436185i | \(0.143671\pi\) | ||||
−0.899857 | + | 0.436185i | \(0.856329\pi\) | |||||||
\(614\) | 1.58445e9 | + | 4.38526e9i | 0.276241 | + | 0.764551i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.15004e10 | + | 6.74830e9i | 1.98235 | + | 1.16322i | ||||
\(617\) | 2.86237e9 | 0.490600 | 0.245300 | − | 0.969447i | \(-0.421113\pi\) | ||||
0.245300 | + | 0.969447i | \(0.421113\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.71027e9i | 1.47609i | 0.674749 | + | 0.738047i | \(0.264252\pi\) | ||||
−0.674749 | + | 0.738047i | \(0.735748\pi\) | |||||||
\(620\) | −4.86923e8 | − | 5.85862e8i | −0.0820520 | − | 0.0987243i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.96846e9 | − | 2.51778e9i | 1.16110 | − | 0.419519i | ||||
\(623\) | 1.23490e10 | 2.04608 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.25503e9 | −0.369464 | ||||||||
\(626\) | −4.17333e9 | + | 1.50787e9i | −0.679942 | + | 0.245671i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.93464e8 | − | 8.34371e8i | −0.111729 | − | 0.134431i | ||||
\(629\) | − | 1.46470e9i | − | 0.234678i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.83120e8 | −0.0290157 | −0.0145078 | − | 0.999895i | \(-0.504618\pi\) | ||||
−0.0145078 | + | 0.999895i | \(0.504618\pi\) | |||||||
\(632\) | −3.52971e9 | + | 6.01531e9i | −0.556198 | + | 0.947869i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.56432e9 | + | 7.09724e9i | 0.399631 | + | 1.10606i | ||||
\(635\) | 2.13907e9i | 0.331526i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.24719e10i | − | 1.91181i | ||||||
\(638\) | 7.66253e9 | − | 2.76856e9i | 1.16815 | − | 0.422067i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.25684e9 | − | 3.75417e9i | 0.491096 | − | 0.566088i | ||||
\(641\) | 2.45117e9 | 0.367596 | 0.183798 | − | 0.982964i | \(-0.441161\pi\) | ||||
0.183798 | + | 0.982964i | \(0.441161\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 3.25861e9i | − | 0.483387i | −0.970353 | − | 0.241693i | \(-0.922297\pi\) | ||
0.970353 | − | 0.241693i | \(-0.0777028\pi\) | |||||||
\(644\) | −1.11033e10 | + | 9.22816e9i | −1.63813 | + | 1.36149i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.09865e8 | + | 1.96469e9i | 0.103601 | + | 0.286735i | ||||
\(647\) | −6.42294e8 | −0.0932328 | −0.0466164 | − | 0.998913i | \(-0.514844\pi\) | ||||
−0.0466164 | + | 0.998913i | \(0.514844\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.54675e8 | 0.0940090 | ||||||||
\(650\) | 1.88694e9 | + | 5.22248e9i | 0.269502 | + | 0.745898i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.80571e8 | + | 9.39177e8i | 0.110292 | + | 0.132703i | ||||
\(653\) | − | 1.32066e10i | − | 1.85607i | −0.372491 | − | 0.928036i | \(-0.621496\pi\) | ||
0.372491 | − | 0.928036i | \(-0.378504\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.91760e9 | 1.37899 | ||||||||
\(656\) | 1.52876e9 | − | 8.21760e9i | 0.211435 | − | 1.13653i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.49334e9 | + | 9.00872e8i | −0.341186 | + | 0.123274i | ||||
\(659\) | 6.38485e9i | 0.869064i | 0.900656 | + | 0.434532i | \(0.143086\pi\) | ||||
−0.900656 | + | 0.434532i | \(0.856914\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1.12927e10i | − | 1.52087i | −0.649416 | − | 0.760433i | \(-0.724987\pi\) | ||
0.649416 | − | 0.760433i | \(-0.275013\pi\) | |||||||
\(662\) | −2.01082e9 | − | 5.56534e9i | −0.269383 | − | 0.745571i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.54412e9 | + | 9.06069e8i | 0.204688 | + | 0.120108i | ||||
\(665\) | −2.62178e9 | −0.345717 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.82153e9i | 1.15107i | ||||||||
\(668\) | 1.42667e9 | − | 1.18574e9i | 0.185186 | − | 0.153912i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.44253e9 | − | 1.60514e9i | 0.570648 | − | 0.206182i | ||||
\(671\) | −1.70141e10 | −2.17410 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.21934e9 | 0.154195 | 0.0770977 | − | 0.997024i | \(-0.475435\pi\) | ||||
0.0770977 | + | 0.997024i | \(0.475435\pi\) | |||||||
\(674\) | 1.20845e10 | − | 4.36625e9i | 1.52026 | − | 0.549287i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.40412e10 | + | 1.16699e10i | −1.74819 | + | 1.45296i | ||||
\(677\) | 1.32664e10i | 1.64321i | 0.570054 | + | 0.821607i | \(0.306922\pi\) | ||||
−0.570054 | + | 0.821607i | \(0.693078\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.89667e10 | −2.32514 | ||||||||
\(680\) | −5.02310e9 | − | 2.94750e9i | −0.612620 | − | 0.359478i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.72800e8 | − | 2.13888e9i | −0.0932872 | − | 0.258190i | ||||
\(683\) | − | 8.29925e9i | − | 0.996704i | −0.866975 | − | 0.498352i | \(-0.833939\pi\) | ||
0.866975 | − | 0.498352i | \(-0.166061\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.06078e10i | 1.26099i | ||||||||
\(686\) | 6.46871e8 | − | 2.33722e8i | 0.0765038 | − | 0.0276417i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.26300e10 | + | 2.34962e9i | 1.47857 | + | 0.275067i | ||||
\(689\) | 1.26255e10 | 1.47056 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1.05496e10i | − | 1.21636i | −0.793798 | − | 0.608182i | \(-0.791899\pi\) | ||
0.793798 | − | 0.608182i | \(-0.208101\pi\) | |||||||
\(692\) | −4.98179e9 | − | 5.99405e9i | −0.571497 | − | 0.687620i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.82193e9 | − | 1.05779e10i | −0.434035 | − | 1.20128i | ||||
\(695\) | −5.42282e9 | −0.612743 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.79493e9 | −1.09569 | ||||||||
\(698\) | −3.34776e9 | − | 9.26557e9i | −0.372615 | − | 1.03128i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.38762e9 | + | 3.64665e9i | −0.483488 | + | 0.401838i | ||||
\(701\) | 3.64147e8i | 0.0399267i | 0.999801 | + | 0.0199633i | \(0.00635495\pi\) | ||||
−0.999801 | + | 0.0199633i | \(0.993645\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.33681e8 | −0.0796459 | ||||||||
\(704\) | 1.29526e10 | − | 7.23665e9i | 1.39911 | − | 0.781687i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.95192e9 | − | 2.87312e9i | 0.850463 | − | 0.307282i | ||||
\(707\) | − | 1.46073e10i | − | 1.55454i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 3.73743e9i | − | 0.393832i | −0.980420 | − | 0.196916i | \(-0.936907\pi\) | ||
0.980420 | − | 0.196916i | \(-0.0630927\pi\) | |||||||
\(710\) | 2.90146e9 | + | 8.03036e9i | 0.304237 | + | 0.842037i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.95416e9 | − | 1.18512e10i | 0.722046 | − | 1.23050i | ||||
\(713\) | 2.46239e9 | 0.254416 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 2.12385e10i | − | 2.17297i | ||||||
\(716\) | 1.86417e9 | + | 2.24296e9i | 0.189798 | + | 0.228363i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.93549e9 | − | 3.22849e9i | 0.900913 | − | 0.325510i | ||||
\(719\) | −1.38910e10 | −1.39374 | −0.696870 | − | 0.717197i | \(-0.745425\pi\) | ||||
−0.696870 | + | 0.717197i | \(0.745425\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.81446e9 | −0.180291 | ||||||||
\(722\) | −8.52709e9 | + | 3.08093e9i | −0.843181 | + | 0.304651i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.60084e8 | − | 7.94208e8i | −0.0646419 | − | 0.0777766i | ||||
\(725\) | 3.48596e9i | 0.339735i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.81417e9 | −0.464677 | −0.232338 | − | 0.972635i | \(-0.574638\pi\) | ||||
−0.232338 | + | 0.972635i | \(0.574638\pi\) | |||||||
\(728\) | −2.32959e10 | − | 1.36698e10i | −2.23779 | − | 1.31311i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.35763e9 | + | 3.75751e9i | 0.129167 | + | 0.357495i | ||||
\(731\) | − | 1.50542e10i | − | 1.42544i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1.05175e10i | − | 0.986390i | −0.869919 | − | 0.493195i | \(-0.835829\pi\) | ||
0.869919 | − | 0.493195i | \(-0.164171\pi\) | |||||||
\(734\) | −3.03870e9 | + | 1.09792e9i | −0.283630 | + | 0.102479i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.60356e9 | + | 1.58524e10i | 0.240710 | + | 1.46563i | ||||
\(737\) | 1.41016e10 | 1.29757 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.01835e10i | 0.928203i | 0.885782 | + | 0.464102i | \(0.153623\pi\) | ||||
−0.885782 | + | 0.464102i | \(0.846377\pi\) | |||||||
\(740\) | 1.57308e9 | − | 1.30742e9i | 0.142705 | − | 0.118605i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.40795e9 | + | 1.21999e10i | 0.396116 | + | 1.09633i | ||||
\(743\) | −1.88665e10 | −1.68744 | −0.843722 | − | 0.536780i | \(-0.819640\pi\) | ||||
−0.843722 | + | 0.536780i | \(0.819640\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.11090e9 | 0.275638 | ||||||||
\(746\) | 8.20003e8 | + | 2.26952e9i | 0.0723152 | + | 0.200146i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.11132e10 | − | 1.33713e10i | −0.970922 | − | 1.16821i | ||||
\(749\) | − | 4.19282e9i | − | 0.364603i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.93566e10 | 1.66759 | 0.833795 | − | 0.552074i | \(-0.186164\pi\) | ||||
0.833795 | + | 0.552074i | \(0.186164\pi\) | |||||||
\(752\) | −5.39531e8 | + | 2.90016e9i | −0.0462651 | + | 0.248691i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.55217e10 | + | 5.60817e9i | −1.31868 | + | 0.476454i | ||||
\(755\) | 5.52290e9i | 0.467039i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.46403e8i | 0.0625371i | 0.999511 | + | 0.0312686i | \(0.00995472\pi\) | ||||
−0.999511 | + | 0.0312686i | \(0.990045\pi\) | |||||||
\(758\) | 6.82998e8 | + | 1.89033e9i | 0.0569610 | + | 0.157651i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.47642e9 | + | 2.51611e9i | −0.122001 | + | 0.207913i | ||||
\(761\) | 7.94454e9 | 0.653465 | 0.326733 | − | 0.945117i | \(-0.394052\pi\) | ||||
0.326733 | + | 0.945117i | \(0.394052\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.50253e9i | 0.448463i | ||||||||
\(764\) | −4.50398e9 | + | 3.74336e9i | −0.365401 | + | 0.303693i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.10660e10 | + | 3.99827e9i | −0.889591 | + | 0.321419i | ||||
\(767\) | −1.32615e9 | −0.106123 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.43124e9 | −0.430682 | −0.215341 | − | 0.976539i | \(-0.569086\pi\) | ||||
−0.215341 | + | 0.976539i | \(0.569086\pi\) | |||||||
\(770\) | 2.05225e10 | − | 7.41502e9i | 1.61999 | − | 0.585322i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.19655e10 | − | 9.94478e9i | 0.935987 | − | 0.777920i | ||||
\(773\) | 6.10644e9i | 0.475510i | 0.971325 | + | 0.237755i | \(0.0764116\pi\) | ||||
−0.971325 | + | 0.237755i | \(0.923588\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.73052e8 | 0.0750896 | ||||||||
\(776\) | −1.06809e10 | + | 1.82023e10i | −0.820523 | + | 1.39833i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.86724e9 | − | 1.62387e10i | −0.446689 | − | 1.23630i | ||||
\(779\) | 4.90635e9i | 0.371858i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.54901e10i | 1.91467i | ||||||||
\(782\) | 1.77052e10 | − | 6.39708e9i | 1.32396 | − | 0.478363i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.60779e9 | − | 1.40177e10i | 0.193271 | − | 1.03890i | ||||
\(785\) | −1.77546e9 | −0.130999 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.55127e10i | 1.86571i | 0.360249 | + | 0.932856i | \(0.382692\pi\) | ||||
−0.360249 | + | 0.932856i | \(0.617308\pi\) | |||||||
\(788\) | −1.39909e10 | − | 1.68338e10i | −1.01860 | − | 1.22557i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.87844e9 | + | 1.07344e10i | 0.279874 | + | 0.774606i | ||||
\(791\) | 3.43480e9 | 0.246765 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.44647e10 | 2.45425 | ||||||||
\(794\) | 5.41851e9 | + | 1.49968e10i | 0.384157 | + | 1.06323i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.48851e9 | + | 1.23713e9i | −0.104606 | + | 0.0869402i | ||||
\(797\) | − | 1.11066e10i | − | 0.777102i | −0.921427 | − | 0.388551i | \(-0.872976\pi\) | ||
0.921427 | − | 0.388551i | \(-0.127024\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.45683e9 | 0.239753 | ||||||||
\(800\) | 1.02884e9 | + | 6.26434e9i | 0.0710446 | + | 0.432574i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.53122e10 | + | 5.53246e9i | −1.04816 | + | 0.378711i | ||||
\(803\) | 1.19272e10i | 0.812892i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.36267e10i | 1.59631i | ||||||||
\(806\) | 1.56543e9 | + | 4.33264e9i | 0.105308 | + | 0.291461i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.40186e10 | − | 8.22592e9i | −0.934897 | − | 0.548586i | ||||
\(809\) | 1.80950e10 | 1.20154 | 0.600769 | − | 0.799422i | \(-0.294861\pi\) | ||||
0.600769 | + | 0.799422i | \(0.294861\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 3.12449e9i | − | 0.205686i | −0.994698 | − | 0.102843i | \(-0.967206\pi\) | ||
0.994698 | − | 0.102843i | \(-0.0327940\pi\) | |||||||
\(812\) | −1.08382e10 | − | 1.30404e10i | −0.710413 | − | 0.854764i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.74303e9 | − | 2.07502e9i | 0.373212 | − | 0.134846i | ||||
\(815\) | 1.99848e9 | 0.129315 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.54078e9 | −0.483770 | ||||||||
\(818\) | 2.23556e9 | − | 8.07734e8i | 0.142807 | − | 0.0515979i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.74313e9 | − | 1.05197e10i | −0.553756 | − | 0.666275i | ||||
\(821\) | − | 1.65303e9i | − | 0.104251i | −0.998641 | − | 0.0521256i | \(-0.983400\pi\) | ||
0.998641 | − | 0.0521256i | \(-0.0165996\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.07490e9 | −0.0672153 | −0.0336077 | − | 0.999435i | \(-0.510700\pi\) | ||||
−0.0336077 | + | 0.999435i | \(0.510700\pi\) | |||||||
\(824\) | −1.02179e9 | + | 1.74133e9i | −0.0636233 | + | 0.108426i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.63000e8 | − | 1.28144e9i | −0.0285858 | − | 0.0791168i | ||||
\(827\) | − | 1.76287e10i | − | 1.08380i | −0.840442 | − | 0.541902i | \(-0.817704\pi\) | ||
0.840442 | − | 0.541902i | \(-0.182296\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1.43986e10i | − | 0.877767i | −0.898544 | − | 0.438884i | \(-0.855374\pi\) | ||
0.898544 | − | 0.438884i | \(-0.144626\pi\) | |||||||
\(830\) | 2.75548e9 | − | 9.95587e8i | 0.167272 | − | 0.0604374i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.62376e10 | + | 1.46590e10i | −1.57940 | + | 0.882415i | ||||
\(833\) | −1.67084e10 | −1.00156 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 3.03583e9i | − | 0.180457i | ||||||
\(836\) | −6.69780e9 | + | 5.56669e9i | −0.396470 | + | 0.329515i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7.76715e9 | − | 2.14971e10i | −0.455940 | − | 1.26190i | ||||
\(839\) | 2.19576e10 | 1.28357 | 0.641783 | − | 0.766886i | \(-0.278195\pi\) | ||||
0.641783 | + | 0.766886i | \(0.278195\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.88926e9 | 0.399380 | ||||||||
\(842\) | 3.37849e9 | + | 9.35064e9i | 0.195043 | + | 0.539820i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.86998e10 | + | 2.24995e10i | 1.07063 | + | 1.28817i | ||||
\(845\) | 2.98782e10i | 1.70356i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.97812e10 | 2.24950 | ||||||||
\(848\) | 1.41904e10 | + | 2.63991e9i | 0.799116 | + | 0.148663i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.99647e9 | − | 2.52790e9i | 0.390762 | − | 0.141187i | ||||
\(851\) | 6.61169e9i | 0.367756i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.54683e9i | 0.306001i | 0.988226 | + | 0.153001i | \(0.0488936\pi\) | ||||
−0.988226 | + | 0.153001i | \(0.951106\pi\) | |||||||
\(854\) | 1.20327e10 | + | 3.33028e10i | 0.661089 | + | 1.82969i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.02383e9 | − | 2.36114e9i | −0.219271 | − | 0.128666i | ||||
\(857\) | 4.05471e8 | 0.0220053 | 0.0110027 | − | 0.999939i | \(-0.496498\pi\) | ||||
0.0110027 | + | 0.999939i | \(0.496498\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 2.10697e10i | − | 1.13418i | −0.823655 | − | 0.567091i | \(-0.808069\pi\) | ||
0.823655 | − | 0.567091i | \(-0.191931\pi\) | |||||||
\(860\) | 1.61681e10 | − | 1.34377e10i | 0.866793 | − | 0.720411i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.63269e10 | − | 5.89909e9i | 0.868217 | − | 0.313697i | ||||
\(863\) | −2.45154e10 | −1.29838 | −0.649190 | − | 0.760626i | \(-0.724892\pi\) | ||||
−0.649190 | + | 0.760626i | \(0.724892\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.27548e10 | −0.670063 | ||||||||
\(866\) | −4.52695e9 | + | 1.63564e9i | −0.236861 | + | 0.0855804i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.64003e9 | + | 3.02531e9i | −0.188924 | + | 0.157019i | ||||
\(869\) | 3.40732e10i | 1.76134i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.85650e10 | −1.46477 | ||||||||
\(872\) | 5.28075e9 | + | 3.09868e9i | 0.269704 | + | 0.158259i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.20434e9 | − | 8.86864e9i | −0.162349 | − | 0.449332i | ||||
\(875\) | 3.06346e10i | 1.54591i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 8.74791e9i | − | 0.437931i | −0.975733 | − | 0.218965i | \(-0.929732\pi\) | ||
0.975733 | − | 0.218965i | \(-0.0702682\pi\) | |||||||
\(878\) | −3.74005e9 | + | 1.35132e9i | −0.186486 | + | 0.0673795i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.44084e9 | − | 2.38710e10i | 0.219673 | − | 1.18081i | ||||
\(881\) | 2.32920e10 | 1.14760 | 0.573801 | − | 0.818995i | \(-0.305468\pi\) | ||||
0.573801 | + | 0.818995i | \(0.305468\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.88930e10i | 0.923502i | 0.887010 | + | 0.461751i | \(0.152779\pi\) | ||||
−0.887010 | + | 0.461751i | \(0.847221\pi\) | |||||||
\(884\) | 2.25116e10 | + | 2.70858e10i | 1.09603 | + | 1.31874i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.30149e10 | − | 3.60212e10i | −0.628668 | − | 1.73996i | ||||
\(887\) | −6.20541e9 | −0.298564 | −0.149282 | − | 0.988795i | \(-0.547696\pi\) | ||||
−0.149282 | + | 0.988795i | \(0.547696\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.32903e10 | 0.634424 | ||||||||
\(890\) | −7.64122e9 | − | 2.11486e10i | −0.363327 | − | 1.00558i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.56657e9 | − | 4.62650e9i | 0.262610 | − | 0.218261i | ||||
\(893\) | − | 1.73155e9i | − | 0.0813683i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.77280e9 | 0.222532 | ||||||||
\(896\) | −2.33251e10 | − | 2.02351e10i | −1.08329 | − | 0.939784i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.50063e8 | + | 1.26482e8i | −0.0161317 | + | 0.00582855i | ||||
\(899\) | 2.89200e9i | 0.132752i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.69142e10i | − | 0.770397i | ||||||
\(902\) | −1.38763e10 | − | 3.84054e10i | −0.629580 | − | 1.74249i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.93426e9 | − | 3.29636e9i | 0.0870815 | − | 0.148404i | ||||
\(905\) | −1.69000e9 | −0.0757908 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.35965e10i | 1.05008i | 0.851078 | + | 0.525040i | \(0.175950\pi\) | ||||
−0.851078 | + | 0.525040i | \(0.824050\pi\) | |||||||
\(908\) | 1.46244e10 | + | 1.75959e10i | 0.648302 | + | 0.780032i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.15717e10 | + | 1.50203e10i | −1.82874 | + | 0.660746i | ||||
\(911\) | 1.75129e10 | 0.767437 | 0.383718 | − | 0.923450i | \(-0.374643\pi\) | ||||
0.383718 | + | 0.923450i | \(0.374643\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.74651e9 | 0.380353 | ||||||||
\(914\) | −8.02442e9 | + | 2.89932e9i | −0.347618 | + | 0.125598i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.83525e9 | − | 5.81773e9i | −0.207867 | − | 0.250103i | ||||
\(917\) | − | 6.16193e10i | − | 2.63891i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.35772e10 | −1.00205 | −0.501024 | − | 0.865434i | \(-0.667043\pi\) | ||||
−0.501024 | + | 0.865434i | \(0.667043\pi\) | |||||||
\(920\) | 2.26744e10 | + | 1.33050e10i | 0.960014 | + | 0.563325i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.14537e9 | + | 1.70085e10i | 0.258220 | + | 0.714675i | ||||
\(923\) | − | 5.16344e10i | − | 2.16139i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.61271e9i | 0.108541i | ||||||||
\(926\) | −3.09544e10 | + | 1.11842e10i | −1.28110 | + | 0.462876i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.86182e10 | + | 3.05780e9i | −0.764751 | + | 0.125600i | ||||
\(929\) | −2.00974e10 | −0.822404 | −0.411202 | − | 0.911544i | \(-0.634891\pi\) | ||||
−0.411202 | + | 0.911544i | \(0.634891\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.36935e9i | 0.339913i | ||||||||
\(932\) | −1.79181e10 | + | 1.48921e10i | −0.724997 | + | 0.602561i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.00475e10 | + | 2.78083e10i | 0.403499 | + | 1.11676i | ||||
\(935\) | −2.84529e10 | −1.13838 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.82209e10 | 0.723572 | 0.361786 | − | 0.932261i | \(-0.382167\pi\) | ||||
0.361786 | + | 0.932261i | \(0.382167\pi\) | |||||||
\(938\) | −9.97291e9 | − | 2.76020e10i | −0.394559 | − | 1.09202i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.08563e9 | + | 3.71261e9i | 0.121170 | + | 0.145791i | ||||
\(941\) | − | 2.27533e10i | − | 0.890186i | −0.895484 | − | 0.445093i | \(-0.853171\pi\) | ||
0.895484 | − | 0.445093i | \(-0.146829\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.42144e10 | 1.71701 | ||||||||
\(944\) | −1.49052e9 | − | 2.77290e8i | −0.0576683 | − | 0.0107283i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.90270e10 | − | 2.13271e10i | 2.26690 | − | 0.819055i | ||||
\(947\) | 2.13355e10i | 0.816355i | 0.912903 | + | 0.408177i | \(0.133836\pi\) | ||||
−0.912903 | + | 0.408177i | \(0.866164\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 2.41604e10i | − | 0.917640i | ||||||
\(950\) | −1.26625e9 | − | 3.50458e9i | −0.0479165 | − | 0.132618i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.83132e10 | + | 3.12092e10i | −0.687915 | + | 1.17234i | ||||
\(953\) | 6.44765e9 | 0.241310 | 0.120655 | − | 0.992694i | \(-0.461500\pi\) | ||||
0.120655 | + | 0.992694i | \(0.461500\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.58404e9i | 0.356071i | ||||||||
\(956\) | 6.63195e9 | − | 5.51196e9i | 0.245493 | − | 0.204035i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.26836e10 | + | 1.18090e10i | −1.20102 | + | 0.433943i | ||||
\(959\) | 6.59079e10 | 2.41308 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.67054e10 | −0.970659 | ||||||||
\(962\) | −1.16334e10 | + | 4.20330e9i | −0.421304 | + | 0.152222i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.67775e10 | − | 1.39442e10i | 0.603196 | − | 0.501330i | ||||
\(965\) | − | 2.54614e10i | − | 0.912088i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.49318e10 | −1.95358 | −0.976789 | − | 0.214202i | \(-0.931285\pi\) | ||||
−0.976789 | + | 0.214202i | \(0.931285\pi\) | |||||||
\(968\) | 2.24023e10 | − | 3.81778e10i | 0.793832 | − | 1.35284i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.17361e10 | + | 3.24820e10i | 0.412880 | + | 1.14273i | ||||
\(971\) | 5.77679e8i | 0.0202497i | 0.999949 | + | 0.0101249i | \(0.00322290\pi\) | ||||
−0.999949 | + | 0.0101249i | \(0.996777\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.36927e10i | 1.17258i | ||||||||
\(974\) | −5.38719e9 | + | 1.94645e9i | −0.186812 | + | 0.0674975i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.87366e10 | + | 7.20636e9i | 1.33367 | + | 0.248108i | ||||
\(977\) | −4.47160e10 | −1.53402 | −0.767011 | − | 0.641634i | \(-0.778257\pi\) | ||||
−0.767011 | + | 0.641634i | \(0.778257\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 6.71302e10i | − | 2.28654i | ||||||
\(980\) | −1.49142e10 | − | 1.79447e10i | −0.506185 | − | 0.609038i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.06865e9 | + | 1.95639e10i | 0.238202 | + | 0.659272i | ||||
\(983\) | 2.34992e10 | 0.789071 | 0.394536 | − | 0.918881i | \(-0.370906\pi\) | ||||
0.394536 | + | 0.918881i | \(0.370906\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.58207e10 | −1.19428 | ||||||||
\(986\) | 7.51318e9 | + | 2.07942e10i | 0.249606 | + | 0.690832i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.35675e10 | − | 1.12762e10i | 0.447559 | − | 0.371976i | ||||
\(989\) | 6.79551e10i | 2.23375i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.91884e9 | 0.291106 | 0.145553 | − | 0.989350i | \(-0.453504\pi\) | ||||
0.145553 | + | 0.989350i | \(0.453504\pi\) | |||||||
\(992\) | 8.53537e8 | + | 5.19698e9i | 0.0277608 | + | 0.169029i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.98937e10 | − | 1.80271e10i | 1.61136 | − | 0.582203i | ||||
\(995\) | 3.16740e9i | 0.101935i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.98963e10i | 0.635828i | 0.948120 | + | 0.317914i | \(0.102982\pi\) | ||||
−0.948120 | + | 0.317914i | \(0.897018\pi\) | |||||||
\(998\) | −1.32264e10 | − | 3.66066e10i | −0.421196 | − | 1.16574i | ||||
\(999\) | 0 | 0 |
(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 | 72.8.d.c.37.2 | yes | 12 | |
3.2 | odd | 2 | inner | 72.8.d.c.37.11 | yes | 12 | |
4.3 | odd | 2 | 288.8.d.c.145.3 | 12 | |||
8.3 | odd | 2 | 288.8.d.c.145.10 | 12 | |||
8.5 | even | 2 | inner | 72.8.d.c.37.1 | ✓ | 12 | |
12.11 | even | 2 | 288.8.d.c.145.9 | 12 | |||
24.5 | odd | 2 | inner | 72.8.d.c.37.12 | yes | 12 | |
24.11 | even | 2 | 288.8.d.c.145.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.8.d.c.37.1 | ✓ | 12 | 8.5 | even | 2 | inner | |
72.8.d.c.37.2 | yes | 12 | 1.1 | even | 1 | trivial | |
72.8.d.c.37.11 | yes | 12 | 3.2 | odd | 2 | inner | |
72.8.d.c.37.12 | yes | 12 | 24.5 | odd | 2 | inner | |
288.8.d.c.145.3 | 12 | 4.3 | odd | 2 | |||
288.8.d.c.145.4 | 12 | 24.11 | even | 2 | |||
288.8.d.c.145.9 | 12 | 12.11 | even | 2 | |||
288.8.d.c.145.10 | 12 | 8.3 | odd | 2 |