Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [83,13,Mod(82,83)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(83, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 13, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("83.82");
S:= CuspForms(chi, 13);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 83 \) |
Weight: | \( k \) | \(=\) | \( 13 \) |
Character orbit: | \([\chi]\) | \(=\) | 83.b (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: | \(75.8614868339\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 82.19 | ||
Character | \(\chi\) | \(=\) | 83.82 |
Dual form | 83.13.b.c.82.62 |
$q$-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 \(\left(\mathbb{Z}/83\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 82.5668i | − | 1.29011i | −0.764137 | − | 0.645053i | \(-0.776835\pi\) | ||
0.764137 | − | 0.645053i | \(-0.223165\pi\) | |||||||
\(3\) | −867.031 | −1.18934 | −0.594671 | − | 0.803969i | \(-0.702718\pi\) | ||||
−0.594671 | + | 0.803969i | \(0.702718\pi\) | |||||||
\(4\) | −2721.28 | −0.664376 | ||||||||
\(5\) | 8790.22i | 0.562574i | 0.959624 | + | 0.281287i | \(0.0907613\pi\) | ||||
−0.959624 | + | 0.281287i | \(0.909239\pi\) | |||||||
\(6\) | 71588.0i | 1.53438i | ||||||||
\(7\) | −11496.7 | −0.0977204 | −0.0488602 | − | 0.998806i | \(-0.515559\pi\) | ||||
−0.0488602 | + | 0.998806i | \(0.515559\pi\) | |||||||
\(8\) | − | 113506.i | − | 0.432991i | ||||||
\(9\) | 220301. | 0.414535 | ||||||||
\(10\) | 725781. | 0.725781 | ||||||||
\(11\) | 1.21224e6 | 0.684279 | 0.342139 | − | 0.939649i | \(-0.388848\pi\) | ||||
0.342139 | + | 0.939649i | \(0.388848\pi\) | |||||||
\(12\) | 2.35944e6 | 0.790171 | ||||||||
\(13\) | − | 5.08347e6i | − | 1.05318i | −0.850121 | − | 0.526588i | \(-0.823471\pi\) | ||
0.850121 | − | 0.526588i | \(-0.176529\pi\) | |||||||
\(14\) | 949247.i | 0.126070i | ||||||||
\(15\) | − | 7.62139e6i | − | 0.669094i | ||||||
\(16\) | −2.05182e7 | −1.22298 | ||||||||
\(17\) | −4.29631e7 | −1.77993 | −0.889963 | − | 0.456033i | \(-0.849270\pi\) | ||||
−0.889963 | + | 0.456033i | \(0.849270\pi\) | |||||||
\(18\) | − | 1.81896e7i | − | 0.534795i | ||||||
\(19\) | − | 1.94044e7i | − | 0.412458i | −0.978504 | − | 0.206229i | \(-0.933881\pi\) | ||
0.978504 | − | 0.206229i | \(-0.0661191\pi\) | |||||||
\(20\) | − | 2.39207e7i | − | 0.373761i | ||||||
\(21\) | 9.96800e6 | 0.116223 | ||||||||
\(22\) | − | 1.00091e8i | − | 0.882793i | ||||||
\(23\) | −7.29795e7 | −0.492985 | −0.246493 | − | 0.969145i | \(-0.579278\pi\) | ||||
−0.246493 | + | 0.969145i | \(0.579278\pi\) | |||||||
\(24\) | 9.84131e7i | 0.514974i | ||||||||
\(25\) | 1.66873e8 | 0.683510 | ||||||||
\(26\) | −4.19726e8 | −1.35871 | ||||||||
\(27\) | 2.69768e8 | 0.696318 | ||||||||
\(28\) | 3.12858e7 | 0.0649231 | ||||||||
\(29\) | −9.12773e8 | −1.53453 | −0.767264 | − | 0.641332i | \(-0.778382\pi\) | ||||
−0.767264 | + | 0.641332i | \(0.778382\pi\) | |||||||
\(30\) | −6.29274e8 | −0.863202 | ||||||||
\(31\) | 1.07602e8 | 0.121241 | 0.0606205 | − | 0.998161i | \(-0.480692\pi\) | ||||
0.0606205 | + | 0.998161i | \(0.480692\pi\) | |||||||
\(32\) | 1.22920e9i | 1.14478i | ||||||||
\(33\) | −1.05105e9 | −0.813842 | ||||||||
\(34\) | 3.54733e9i | 2.29629i | ||||||||
\(35\) | − | 1.01059e8i | − | 0.0549750i | ||||||
\(36\) | −5.99502e8 | −0.275407 | ||||||||
\(37\) | 1.17230e9 | 0.456906 | 0.228453 | − | 0.973555i | \(-0.426633\pi\) | ||||
0.228453 | + | 0.973555i | \(0.426633\pi\) | |||||||
\(38\) | −1.60216e9 | −0.532114 | ||||||||
\(39\) | 4.40753e9i | 1.25259i | ||||||||
\(40\) | 9.97743e8 | 0.243590 | ||||||||
\(41\) | −4.70768e9 | −0.991068 | −0.495534 | − | 0.868588i | \(-0.665028\pi\) | ||||
−0.495534 | + | 0.868588i | \(0.665028\pi\) | |||||||
\(42\) | − | 8.23026e8i | − | 0.149940i | ||||||
\(43\) | − | 5.03554e9i | − | 0.796590i | −0.917257 | − | 0.398295i | \(-0.869602\pi\) | ||
0.917257 | − | 0.398295i | \(-0.130398\pi\) | |||||||
\(44\) | −3.29885e9 | −0.454618 | ||||||||
\(45\) | 1.93650e9i | 0.233207i | ||||||||
\(46\) | 6.02569e9i | 0.636003i | ||||||||
\(47\) | 2.94237e9i | 0.272967i | 0.990642 | + | 0.136483i | \(0.0435800\pi\) | ||||
−0.990642 | + | 0.136483i | \(0.956420\pi\) | |||||||
\(48\) | 1.77899e10 | 1.45454 | ||||||||
\(49\) | −1.37091e10 | −0.990451 | ||||||||
\(50\) | − | 1.37781e10i | − | 0.881801i | ||||||
\(51\) | 3.72503e10 | 2.11694 | ||||||||
\(52\) | 1.38336e10i | 0.699704i | ||||||||
\(53\) | 2.41304e10i | 1.08870i | 0.838857 | + | 0.544352i | \(0.183224\pi\) | ||||
−0.838857 | + | 0.544352i | \(0.816776\pi\) | |||||||
\(54\) | − | 2.22739e10i | − | 0.898325i | ||||||
\(55\) | 1.06559e10i | 0.384958i | ||||||||
\(56\) | 1.30495e9i | 0.0423121i | ||||||||
\(57\) | 1.68242e10i | 0.490553i | ||||||||
\(58\) | 7.53648e10i | 1.97970i | ||||||||
\(59\) | 4.28123e9 | 0.101498 | 0.0507489 | − | 0.998711i | \(-0.483839\pi\) | ||||
0.0507489 | + | 0.998711i | \(0.483839\pi\) | |||||||
\(60\) | 2.07400e10i | 0.444530i | ||||||||
\(61\) | 3.04317e10 | 0.590673 | 0.295336 | − | 0.955393i | \(-0.404568\pi\) | ||||
0.295336 | + | 0.955393i | \(0.404568\pi\) | |||||||
\(62\) | − | 8.88434e9i | − | 0.156414i | ||||||
\(63\) | −2.53274e9 | −0.0405086 | ||||||||
\(64\) | 1.74489e10 | 0.253914 | ||||||||
\(65\) | 4.46849e10 | 0.592489 | ||||||||
\(66\) | 8.67819e10i | 1.04994i | ||||||||
\(67\) | − | 6.61861e9i | − | 0.0731675i | −0.999331 | − | 0.0365837i | \(-0.988352\pi\) | ||
0.999331 | − | 0.0365837i | \(-0.0116476\pi\) | |||||||
\(68\) | 1.16915e11 | 1.18254 | ||||||||
\(69\) | 6.32754e10 | 0.586328 | ||||||||
\(70\) | −8.34410e9 | −0.0709236 | ||||||||
\(71\) | 1.41623e11i | 1.10556i | 0.833327 | + | 0.552781i | \(0.186433\pi\) | ||||
−0.833327 | + | 0.552781i | \(0.813567\pi\) | |||||||
\(72\) | − | 2.50055e10i | − | 0.179490i | ||||||
\(73\) | − | 7.21726e10i | − | 0.476909i | −0.971154 | − | 0.238454i | \(-0.923359\pi\) | ||
0.971154 | − | 0.238454i | \(-0.0766408\pi\) | |||||||
\(74\) | − | 9.67927e10i | − | 0.589457i | ||||||
\(75\) | −1.44684e11 | −0.812928 | ||||||||
\(76\) | 5.28050e10i | 0.274027i | ||||||||
\(77\) | −1.39368e10 | −0.0668680 | ||||||||
\(78\) | 3.63916e11 | 1.61597 | ||||||||
\(79\) | − | 3.88746e11i | − | 1.59920i | −0.600532 | − | 0.799601i | \(-0.705045\pi\) | ||
0.600532 | − | 0.799601i | \(-0.294955\pi\) | |||||||
\(80\) | − | 1.80360e11i | − | 0.688017i | ||||||
\(81\) | −3.50974e11 | −1.24270 | ||||||||
\(82\) | 3.88698e11i | 1.27858i | ||||||||
\(83\) | 3.26193e11 | + | 2.20944e10i | 0.997714 | + | 0.0675793i | ||||
\(84\) | −2.71258e10 | −0.0772158 | ||||||||
\(85\) | − | 3.77655e11i | − | 1.00134i | ||||||
\(86\) | −4.15768e11 | −1.02769 | ||||||||
\(87\) | 7.91402e11 | 1.82508 | ||||||||
\(88\) | − | 1.37597e11i | − | 0.296286i | ||||||
\(89\) | − | 8.48384e11i | − | 1.70707i | −0.521032 | − | 0.853537i | \(-0.674453\pi\) | ||
0.521032 | − | 0.853537i | \(-0.325547\pi\) | |||||||
\(90\) | 1.59890e11 | 0.300862 | ||||||||
\(91\) | 5.84432e10i | 0.102917i | ||||||||
\(92\) | 1.98598e11 | 0.327527 | ||||||||
\(93\) | −9.32941e10 | −0.144197 | ||||||||
\(94\) | 2.42942e11 | 0.352156 | ||||||||
\(95\) | 1.70569e11 | 0.232038 | ||||||||
\(96\) | − | 1.06576e12i | − | 1.36154i | ||||||
\(97\) | 1.52273e12i | 1.82807i | 0.405632 | + | 0.914036i | \(0.367051\pi\) | ||||
−0.405632 | + | 0.914036i | \(0.632949\pi\) | |||||||
\(98\) | 1.13192e12i | 1.27779i | ||||||||
\(99\) | 2.67058e11 | 0.283658 | ||||||||
\(100\) | −4.54108e11 | −0.454108 | ||||||||
\(101\) | − | 2.81582e11i | − | 0.265263i | −0.991165 | − | 0.132631i | \(-0.957657\pi\) | ||
0.991165 | − | 0.132631i | \(-0.0423426\pi\) | |||||||
\(102\) | − | 3.07564e12i | − | 2.73108i | ||||||
\(103\) | − | 6.31888e11i | − | 0.529196i | −0.964359 | − | 0.264598i | \(-0.914761\pi\) | ||
0.964359 | − | 0.264598i | \(-0.0852393\pi\) | |||||||
\(104\) | −5.77005e11 | −0.456015 | ||||||||
\(105\) | 8.76210e10i | 0.0653841i | ||||||||
\(106\) | 1.99237e12 | 1.40454 | ||||||||
\(107\) | 9.99424e11i | 0.665959i | 0.942934 | + | 0.332979i | \(0.108054\pi\) | ||||
−0.942934 | + | 0.332979i | \(0.891946\pi\) | |||||||
\(108\) | −7.34115e11 | −0.462617 | ||||||||
\(109\) | 3.00150e12 | 1.78969 | 0.894847 | − | 0.446373i | \(-0.147285\pi\) | ||||
0.894847 | + | 0.446373i | \(0.147285\pi\) | |||||||
\(110\) | 8.79822e11 | 0.496637 | ||||||||
\(111\) | −1.01642e12 | −0.543417 | ||||||||
\(112\) | 2.35892e11 | 0.119510 | ||||||||
\(113\) | 1.11606e12 | 0.536064 | 0.268032 | − | 0.963410i | \(-0.413627\pi\) | ||||
0.268032 | + | 0.963410i | \(0.413627\pi\) | |||||||
\(114\) | 1.38912e12 | 0.632866 | ||||||||
\(115\) | − | 6.41506e11i | − | 0.277341i | ||||||
\(116\) | 2.48391e12 | 1.01950 | ||||||||
\(117\) | − | 1.11990e12i | − | 0.436578i | ||||||
\(118\) | − | 3.53488e11i | − | 0.130943i | ||||||
\(119\) | 4.93934e11 | 0.173935 | ||||||||
\(120\) | −8.65074e11 | −0.289711 | ||||||||
\(121\) | −1.66890e12 | −0.531763 | ||||||||
\(122\) | − | 2.51265e12i | − | 0.762031i | ||||||
\(123\) | 4.08170e12 | 1.17872 | ||||||||
\(124\) | −2.92815e11 | −0.0805496 | ||||||||
\(125\) | 3.61290e12i | 0.947100i | ||||||||
\(126\) | 2.09120e11i | 0.0522604i | ||||||||
\(127\) | −5.28863e10 | −0.0126044 | −0.00630219 | − | 0.999980i | \(-0.502006\pi\) | ||||
−0.00630219 | + | 0.999980i | \(0.502006\pi\) | |||||||
\(128\) | 3.59412e12i | 0.817208i | ||||||||
\(129\) | 4.36596e12i | 0.947418i | ||||||||
\(130\) | − | 3.68949e12i | − | 0.764375i | ||||||
\(131\) | 9.92149e12 | 1.96313 | 0.981565 | − | 0.191127i | \(-0.0612142\pi\) | ||||
0.981565 | + | 0.191127i | \(0.0612142\pi\) | |||||||
\(132\) | 2.86021e12 | 0.540697 | ||||||||
\(133\) | 2.23087e11i | 0.0403055i | ||||||||
\(134\) | −5.46478e11 | −0.0943939 | ||||||||
\(135\) | 2.37132e12i | 0.391731i | ||||||||
\(136\) | 4.87656e12i | 0.770691i | ||||||||
\(137\) | 9.50330e12i | 1.43731i | 0.695366 | + | 0.718656i | \(0.255242\pi\) | ||||
−0.695366 | + | 0.718656i | \(0.744758\pi\) | |||||||
\(138\) | − | 5.22445e12i | − | 0.756426i | ||||||
\(139\) | 1.24806e13i | 1.73040i | 0.501426 | + | 0.865200i | \(0.332809\pi\) | ||||
−0.501426 | + | 0.865200i | \(0.667191\pi\) | |||||||
\(140\) | 2.75009e11i | 0.0365241i | ||||||||
\(141\) | − | 2.55112e12i | − | 0.324651i | ||||||
\(142\) | 1.16933e13 | 1.42629 | ||||||||
\(143\) | − | 6.16240e12i | − | 0.720665i | ||||||
\(144\) | −4.52018e12 | −0.506969 | ||||||||
\(145\) | − | 8.02348e12i | − | 0.863286i | ||||||
\(146\) | −5.95907e12 | −0.615263 | ||||||||
\(147\) | 1.18862e13 | 1.17799 | ||||||||
\(148\) | −3.19015e12 | −0.303557 | ||||||||
\(149\) | 6.08559e12i | 0.556141i | 0.960561 | + | 0.278070i | \(0.0896949\pi\) | ||||
−0.960561 | + | 0.278070i | \(0.910305\pi\) | |||||||
\(150\) | 1.19461e13i | 1.04876i | ||||||||
\(151\) | −4.86349e12 | −0.410286 | −0.205143 | − | 0.978732i | \(-0.565766\pi\) | ||||
−0.205143 | + | 0.978732i | \(0.565766\pi\) | |||||||
\(152\) | −2.20252e12 | −0.178590 | ||||||||
\(153\) | −9.46481e12 | −0.737842 | ||||||||
\(154\) | 1.15072e12i | 0.0862669i | ||||||||
\(155\) | 9.45844e11i | 0.0682071i | ||||||||
\(156\) | − | 1.19941e13i | − | 0.832188i | ||||||
\(157\) | 6.07643e12i | 0.405743i | 0.979205 | + | 0.202871i | \(0.0650273\pi\) | ||||
−0.979205 | + | 0.202871i | \(0.934973\pi\) | |||||||
\(158\) | −3.20975e13 | −2.06314 | ||||||||
\(159\) | − | 2.09218e13i | − | 1.29484i | ||||||
\(160\) | −1.08050e13 | −0.644027 | ||||||||
\(161\) | 8.39024e11 | 0.0481747 | ||||||||
\(162\) | 2.89788e13i | 1.60321i | ||||||||
\(163\) | 2.37540e13i | 1.26652i | 0.773940 | + | 0.633259i | \(0.218283\pi\) | ||||
−0.773940 | + | 0.633259i | \(0.781717\pi\) | |||||||
\(164\) | 1.28109e13 | 0.658442 | ||||||||
\(165\) | − | 9.23897e12i | − | 0.457847i | ||||||
\(166\) | 1.82427e12 | − | 2.69327e13i | 0.0871846 | − | 1.28716i | ||||
\(167\) | −2.95286e12 | −0.136127 | −0.0680634 | − | 0.997681i | \(-0.521682\pi\) | ||||
−0.0680634 | + | 0.997681i | \(0.521682\pi\) | |||||||
\(168\) | − | 1.13143e12i | − | 0.0503235i | ||||||
\(169\) | −2.54363e12 | −0.109178 | ||||||||
\(170\) | −3.11818e13 | −1.29184 | ||||||||
\(171\) | − | 4.27482e12i | − | 0.170978i | ||||||
\(172\) | 1.37031e13i | 0.529235i | ||||||||
\(173\) | 3.60914e13 | 1.34625 | 0.673126 | − | 0.739528i | \(-0.264951\pi\) | ||||
0.673126 | + | 0.739528i | \(0.264951\pi\) | |||||||
\(174\) | − | 6.53436e13i | − | 2.35455i | ||||||
\(175\) | −1.91849e12 | −0.0667929 | ||||||||
\(176\) | −2.48730e13 | −0.836860 | ||||||||
\(177\) | −3.71196e12 | −0.120716 | ||||||||
\(178\) | −7.00484e13 | −2.20231 | ||||||||
\(179\) | − | 3.40909e13i | − | 1.03638i | −0.855265 | − | 0.518191i | \(-0.826606\pi\) | ||
0.855265 | − | 0.518191i | \(-0.173394\pi\) | |||||||
\(180\) | − | 5.26976e12i | − | 0.154937i | ||||||
\(181\) | 1.72907e13i | 0.491745i | 0.969302 | + | 0.245872i | \(0.0790744\pi\) | ||||
−0.969302 | + | 0.245872i | \(0.920926\pi\) | |||||||
\(182\) | 4.82547e12 | 0.132774 | ||||||||
\(183\) | −2.63852e13 | −0.702512 | ||||||||
\(184\) | 8.28361e12i | 0.213458i | ||||||||
\(185\) | 1.03047e13i | 0.257044i | ||||||||
\(186\) | 7.70300e12i | 0.186030i | ||||||||
\(187\) | −5.20816e13 | −1.21797 | ||||||||
\(188\) | − | 8.00702e12i | − | 0.181353i | ||||||
\(189\) | −3.10144e12 | −0.0680445 | ||||||||
\(190\) | − | 1.40834e13i | − | 0.299354i | ||||||
\(191\) | −6.13783e12 | −0.126420 | −0.0632098 | − | 0.998000i | \(-0.520134\pi\) | ||||
−0.0632098 | + | 0.998000i | \(0.520134\pi\) | |||||||
\(192\) | −1.51287e13 | −0.301991 | ||||||||
\(193\) | 4.47415e13 | 0.865699 | 0.432850 | − | 0.901466i | \(-0.357508\pi\) | ||||
0.432850 | + | 0.901466i | \(0.357508\pi\) | |||||||
\(194\) | 1.25727e14 | 2.35841 | ||||||||
\(195\) | −3.87432e13 | −0.704673 | ||||||||
\(196\) | 3.73064e13 | 0.658032 | ||||||||
\(197\) | 3.39180e13 | 0.580273 | 0.290137 | − | 0.956985i | \(-0.406299\pi\) | ||||
0.290137 | + | 0.956985i | \(0.406299\pi\) | |||||||
\(198\) | − | 2.20502e13i | − | 0.365949i | ||||||
\(199\) | −3.94240e13 | −0.634807 | −0.317404 | − | 0.948291i | \(-0.602811\pi\) | ||||
−0.317404 | + | 0.948291i | \(0.602811\pi\) | |||||||
\(200\) | − | 1.89410e13i | − | 0.295954i | ||||||
\(201\) | 5.73854e12i | 0.0870212i | ||||||||
\(202\) | −2.32493e13 | −0.342217 | ||||||||
\(203\) | 1.04939e13 | 0.149955 | ||||||||
\(204\) | −1.01369e14 | −1.40644 | ||||||||
\(205\) | − | 4.13815e13i | − | 0.557550i | ||||||
\(206\) | −5.21730e13 | −0.682720 | ||||||||
\(207\) | −1.60775e13 | −0.204360 | ||||||||
\(208\) | 1.04304e14i | 1.28801i | ||||||||
\(209\) | − | 2.35229e13i | − | 0.282236i | ||||||
\(210\) | 7.23459e12 | 0.0843525 | ||||||||
\(211\) | 8.21807e13i | 0.931269i | 0.884977 | + | 0.465635i | \(0.154174\pi\) | ||||
−0.884977 | + | 0.465635i | \(0.845826\pi\) | |||||||
\(212\) | − | 6.56657e13i | − | 0.723309i | ||||||
\(213\) | − | 1.22791e14i | − | 1.31489i | ||||||
\(214\) | 8.25193e13 | 0.859158 | ||||||||
\(215\) | 4.42635e13 | 0.448141 | ||||||||
\(216\) | − | 3.06202e13i | − | 0.301499i | ||||||
\(217\) | −1.23707e12 | −0.0118477 | ||||||||
\(218\) | − | 2.47824e14i | − | 2.30890i | ||||||
\(219\) | 6.25759e13i | 0.567208i | ||||||||
\(220\) | − | 2.89977e13i | − | 0.255757i | ||||||
\(221\) | 2.18402e14i | 1.87457i | ||||||||
\(222\) | 8.39223e13i | 0.701067i | ||||||||
\(223\) | 1.32645e14i | 1.07860i | 0.842114 | + | 0.539300i | \(0.181311\pi\) | ||||
−0.842114 | + | 0.539300i | \(0.818689\pi\) | |||||||
\(224\) | − | 1.41318e13i | − | 0.111869i | ||||||
\(225\) | 3.67622e13 | 0.283339 | ||||||||
\(226\) | − | 9.21495e13i | − | 0.691580i | ||||||
\(227\) | −9.70001e13 | −0.708953 | −0.354476 | − | 0.935065i | \(-0.615341\pi\) | ||||
−0.354476 | + | 0.935065i | \(0.615341\pi\) | |||||||
\(228\) | − | 4.57835e13i | − | 0.325912i | ||||||
\(229\) | −1.90648e14 | −1.32196 | −0.660981 | − | 0.750402i | \(-0.729860\pi\) | ||||
−0.660981 | + | 0.750402i | \(0.729860\pi\) | |||||||
\(230\) | −5.29671e13 | −0.357799 | ||||||||
\(231\) | 1.20836e13 | 0.0795290 | ||||||||
\(232\) | 1.03605e14i | 0.664436i | ||||||||
\(233\) | 1.31626e14i | 0.822634i | 0.911492 | + | 0.411317i | \(0.134931\pi\) | ||||
−0.911492 | + | 0.411317i | \(0.865069\pi\) | |||||||
\(234\) | −9.24662e13 | −0.563233 | ||||||||
\(235\) | −2.58641e13 | −0.153564 | ||||||||
\(236\) | −1.16504e13 | −0.0674327 | ||||||||
\(237\) | 3.37055e14i | 1.90200i | ||||||||
\(238\) | − | 4.07826e13i | − | 0.224395i | ||||||
\(239\) | 1.87659e14i | 1.00689i | 0.864028 | + | 0.503444i | \(0.167934\pi\) | ||||
−0.864028 | + | 0.503444i | \(0.832066\pi\) | |||||||
\(240\) | 1.56377e14i | 0.818288i | ||||||||
\(241\) | 5.69759e13 | 0.290796 | 0.145398 | − | 0.989373i | \(-0.453554\pi\) | ||||
0.145398 | + | 0.989373i | \(0.453554\pi\) | |||||||
\(242\) | 1.37796e14i | 0.686031i | ||||||||
\(243\) | 1.60940e14 | 0.781673 | ||||||||
\(244\) | −8.28132e13 | −0.392429 | ||||||||
\(245\) | − | 1.20506e14i | − | 0.557202i | ||||||
\(246\) | − | 3.37013e14i | − | 1.52067i | ||||||
\(247\) | −9.86419e13 | −0.434390 | ||||||||
\(248\) | − | 1.22134e13i | − | 0.0524962i | ||||||
\(249\) | −2.82819e14 | − | 1.91565e13i | −1.18662 | − | 0.0803750i | ||||
\(250\) | 2.98306e14 | 1.22186 | ||||||||
\(251\) | 2.68129e14i | 1.07226i | 0.844134 | + | 0.536131i | \(0.180115\pi\) | ||||
−0.844134 | + | 0.536131i | \(0.819885\pi\) | |||||||
\(252\) | 6.89230e12 | 0.0269129 | ||||||||
\(253\) | −8.84688e13 | −0.337339 | ||||||||
\(254\) | 4.36666e12i | 0.0162610i | ||||||||
\(255\) | 3.27439e14i | 1.19094i | ||||||||
\(256\) | 3.68226e14 | 1.30820 | ||||||||
\(257\) | 6.17317e13i | 0.214245i | 0.994246 | + | 0.107122i | \(0.0341636\pi\) | ||||
−0.994246 | + | 0.107122i | \(0.965836\pi\) | |||||||
\(258\) | 3.60484e14 | 1.22227 | ||||||||
\(259\) | −1.34775e13 | −0.0446490 | ||||||||
\(260\) | −1.21600e14 | −0.393636 | ||||||||
\(261\) | −2.01085e14 | −0.636116 | ||||||||
\(262\) | − | 8.19186e14i | − | 2.53265i | ||||||
\(263\) | − | 5.77976e13i | − | 0.174653i | −0.996180 | − | 0.0873264i | \(-0.972168\pi\) | ||
0.996180 | − | 0.0873264i | \(-0.0278323\pi\) | |||||||
\(264\) | 1.19300e14i | 0.352386i | ||||||||
\(265\) | −2.12112e14 | −0.612477 | ||||||||
\(266\) | 1.84196e13 | 0.0519985 | ||||||||
\(267\) | 7.35575e14i | 2.03030i | ||||||||
\(268\) | 1.80111e13i | 0.0486107i | ||||||||
\(269\) | − | 4.34618e14i | − | 1.14708i | −0.819177 | − | 0.573541i | \(-0.805569\pi\) | ||
0.819177 | − | 0.573541i | \(-0.194431\pi\) | |||||||
\(270\) | 1.95792e14 | 0.505374 | ||||||||
\(271\) | − | 3.23008e14i | − | 0.815451i | −0.913105 | − | 0.407725i | \(-0.866322\pi\) | ||
0.913105 | − | 0.407725i | \(-0.133678\pi\) | |||||||
\(272\) | 8.81525e14 | 2.17681 | ||||||||
\(273\) | − | 5.06721e13i | − | 0.122403i | ||||||
\(274\) | 7.84658e14 | 1.85429 | ||||||||
\(275\) | 2.02290e14 | 0.467711 | ||||||||
\(276\) | −1.72190e14 | −0.389542 | ||||||||
\(277\) | −2.30679e14 | −0.510657 | −0.255329 | − | 0.966854i | \(-0.582184\pi\) | ||||
−0.255329 | + | 0.966854i | \(0.582184\pi\) | |||||||
\(278\) | 1.03048e15 | 2.23240 | ||||||||
\(279\) | 2.37048e13 | 0.0502587 | ||||||||
\(280\) | −1.14708e13 | −0.0238037 | ||||||||
\(281\) | − | 6.76321e14i | − | 1.37377i | −0.726765 | − | 0.686886i | \(-0.758977\pi\) | ||
0.726765 | − | 0.686886i | \(-0.241023\pi\) | |||||||
\(282\) | −2.10638e14 | −0.418835 | ||||||||
\(283\) | − | 3.66389e14i | − | 0.713220i | −0.934253 | − | 0.356610i | \(-0.883933\pi\) | ||
0.934253 | − | 0.356610i | \(-0.116067\pi\) | |||||||
\(284\) | − | 3.85396e14i | − | 0.734509i | ||||||
\(285\) | −1.47889e14 | −0.275973 | ||||||||
\(286\) | −5.08810e14 | −0.929735 | ||||||||
\(287\) | 5.41228e13 | 0.0968476 | ||||||||
\(288\) | 2.70795e14i | 0.474554i | ||||||||
\(289\) | 1.26320e15 | 2.16813 | ||||||||
\(290\) | −6.62473e14 | −1.11373 | ||||||||
\(291\) | − | 1.32026e15i | − | 2.17420i | ||||||
\(292\) | 1.96402e14i | 0.316847i | ||||||||
\(293\) | 8.91901e14 | 1.40965 | 0.704824 | − | 0.709382i | \(-0.251026\pi\) | ||||
0.704824 | + | 0.709382i | \(0.251026\pi\) | |||||||
\(294\) | − | 9.81408e14i | − | 1.51973i | ||||||
\(295\) | 3.76330e13i | 0.0571000i | ||||||||
\(296\) | − | 1.33062e14i | − | 0.197836i | ||||||
\(297\) | 3.27024e14 | 0.476476 | ||||||||
\(298\) | 5.02468e14 | 0.717481 | ||||||||
\(299\) | 3.70989e14i | 0.519200i | ||||||||
\(300\) | 3.93725e14 | 0.540090 | ||||||||
\(301\) | 5.78921e13i | 0.0778431i | ||||||||
\(302\) | 4.01563e14i | 0.529312i | ||||||||
\(303\) | 2.44140e14i | 0.315488i | ||||||||
\(304\) | 3.98144e14i | 0.504428i | ||||||||
\(305\) | 2.67501e14i | 0.332297i | ||||||||
\(306\) | 7.81480e14i | 0.951895i | ||||||||
\(307\) | − | 1.27235e15i | − | 1.51977i | −0.650058 | − | 0.759884i | \(-0.725256\pi\) | ||
0.650058 | − | 0.759884i | \(-0.274744\pi\) | |||||||
\(308\) | 3.79260e13 | 0.0444255 | ||||||||
\(309\) | 5.47866e14i | 0.629395i | ||||||||
\(310\) | 7.80954e13 | 0.0879944 | ||||||||
\(311\) | 5.35532e14i | 0.591866i | 0.955209 | + | 0.295933i | \(0.0956305\pi\) | ||||
−0.955209 | + | 0.295933i | \(0.904370\pi\) | |||||||
\(312\) | 5.00281e14 | 0.542358 | ||||||||
\(313\) | −1.02530e15 | −1.09039 | −0.545197 | − | 0.838308i | \(-0.683545\pi\) | ||||
−0.545197 | + | 0.838308i | \(0.683545\pi\) | |||||||
\(314\) | 5.01712e14 | 0.523452 | ||||||||
\(315\) | − | 2.22633e13i | − | 0.0227891i | ||||||
\(316\) | 1.05789e15i | 1.06247i | ||||||||
\(317\) | −1.37443e15 | −1.35446 | −0.677232 | − | 0.735769i | \(-0.736821\pi\) | ||||
−0.677232 | + | 0.735769i | \(0.736821\pi\) | |||||||
\(318\) | −1.72745e15 | −1.67048 | ||||||||
\(319\) | −1.10650e15 | −1.05004 | ||||||||
\(320\) | 1.53379e14i | 0.142846i | ||||||||
\(321\) | − | 8.66532e14i | − | 0.792053i | ||||||
\(322\) | − | 6.92756e13i | − | 0.0621505i | ||||||
\(323\) | 8.33674e14i | 0.734144i | ||||||||
\(324\) | 9.55100e14 | 0.825617 | ||||||||
\(325\) | − | 8.48293e14i | − | 0.719856i | ||||||
\(326\) | 1.96129e15 | 1.63394 | ||||||||
\(327\) | −2.60239e15 | −2.12856 | ||||||||
\(328\) | 5.34349e14i | 0.429124i | ||||||||
\(329\) | − | 3.38276e13i | − | 0.0266744i | ||||||
\(330\) | −7.62833e14 | −0.590671 | ||||||||
\(331\) | − | 1.08760e15i | − | 0.826993i | −0.910506 | − | 0.413496i | \(-0.864307\pi\) | ||
0.910506 | − | 0.413496i | \(-0.135693\pi\) | |||||||
\(332\) | −8.87664e14 | − | 6.01252e13i | −0.662857 | − | 0.0448981i | ||||
\(333\) | 2.58258e14 | 0.189404 | ||||||||
\(334\) | 2.43808e14i | 0.175618i | ||||||||
\(335\) | 5.81791e13 | 0.0411621 | ||||||||
\(336\) | −2.04526e14 | −0.142139 | ||||||||
\(337\) | − | 1.50998e15i | − | 1.03084i | −0.856938 | − | 0.515419i | \(-0.827636\pi\) | ||
0.856938 | − | 0.515419i | \(-0.172364\pi\) | |||||||
\(338\) | 2.10019e14i | 0.140851i | ||||||||
\(339\) | −9.67658e14 | −0.637564 | ||||||||
\(340\) | 1.02771e15i | 0.665267i | ||||||||
\(341\) | 1.30439e14 | 0.0829626 | ||||||||
\(342\) | −3.52958e14 | −0.220580 | ||||||||
\(343\) | 3.16739e14 | 0.194508 | ||||||||
\(344\) | −5.71563e14 | −0.344916 | ||||||||
\(345\) | 5.56205e14i | 0.329853i | ||||||||
\(346\) | − | 2.97995e15i | − | 1.73681i | ||||||
\(347\) | 1.63823e15i | 0.938422i | 0.883086 | + | 0.469211i | \(0.155462\pi\) | ||||
−0.883086 | + | 0.469211i | \(0.844538\pi\) | |||||||
\(348\) | −2.15363e15 | −1.21254 | ||||||||
\(349\) | 2.37222e15 | 1.31281 | 0.656405 | − | 0.754409i | \(-0.272076\pi\) | ||||
0.656405 | + | 0.754409i | \(0.272076\pi\) | |||||||
\(350\) | 1.58403e14i | 0.0861700i | ||||||||
\(351\) | − | 1.37136e15i | − | 0.733345i | ||||||
\(352\) | 1.49009e15i | 0.783352i | ||||||||
\(353\) | −8.55675e14 | −0.442243 | −0.221121 | − | 0.975246i | \(-0.570972\pi\) | ||||
−0.221121 | + | 0.975246i | \(0.570972\pi\) | |||||||
\(354\) | 3.06485e14i | 0.155736i | ||||||||
\(355\) | −1.24490e15 | −0.621961 | ||||||||
\(356\) | 2.30869e15i | 1.13414i | ||||||||
\(357\) | −4.28256e14 | −0.206868 | ||||||||
\(358\) | −2.81478e15 | −1.33704 | ||||||||
\(359\) | −3.30003e15 | −1.54153 | −0.770763 | − | 0.637122i | \(-0.780125\pi\) | ||||
−0.770763 | + | 0.637122i | \(0.780125\pi\) | |||||||
\(360\) | 2.19804e14 | 0.100977 | ||||||||
\(361\) | 1.83678e15 | 0.829879 | ||||||||
\(362\) | 1.42763e15 | 0.634404 | ||||||||
\(363\) | 1.44699e15 | 0.632448 | ||||||||
\(364\) | − | 1.59041e14i | − | 0.0683754i | ||||||
\(365\) | 6.34414e14 | 0.268297 | ||||||||
\(366\) | 2.17854e15i | 0.906316i | ||||||||
\(367\) | 4.29828e15i | 1.75913i | 0.475779 | + | 0.879565i | \(0.342166\pi\) | ||||
−0.475779 | + | 0.879565i | \(0.657834\pi\) | |||||||
\(368\) | 1.49741e15 | 0.602911 | ||||||||
\(369\) | −1.03711e15 | −0.410833 | ||||||||
\(370\) | 8.50830e14 | 0.331614 | ||||||||
\(371\) | − | 2.77420e14i | − | 0.106389i | ||||||
\(372\) | 2.53880e14 | 0.0958010 | ||||||||
\(373\) | 3.19315e14 | 0.118568 | 0.0592839 | − | 0.998241i | \(-0.481118\pi\) | ||||
0.0592839 | + | 0.998241i | \(0.481118\pi\) | |||||||
\(374\) | 4.30022e15i | 1.57131i | ||||||||
\(375\) | − | 3.13249e15i | − | 1.12643i | ||||||
\(376\) | 3.33976e14 | 0.118192 | ||||||||
\(377\) | 4.64006e15i | 1.61613i | ||||||||
\(378\) | 2.56076e14i | 0.0877847i | ||||||||
\(379\) | 2.52108e15i | 0.850651i | 0.905041 | + | 0.425325i | \(0.139840\pi\) | ||||
−0.905041 | + | 0.425325i | \(0.860160\pi\) | |||||||
\(380\) | −4.64168e14 | −0.154161 | ||||||||
\(381\) | 4.58541e13 | 0.0149909 | ||||||||
\(382\) | 5.06781e14i | 0.163095i | ||||||||
\(383\) | 5.80400e14 | 0.183880 | 0.0919401 | − | 0.995765i | \(-0.470693\pi\) | ||||
0.0919401 | + | 0.995765i | \(0.470693\pi\) | |||||||
\(384\) | − | 3.11621e15i | − | 0.971940i | ||||||
\(385\) | − | 1.22508e14i | − | 0.0376182i | ||||||
\(386\) | − | 3.69417e15i | − | 1.11684i | ||||||
\(387\) | − | 1.10933e15i | − | 0.330215i | ||||||
\(388\) | − | 4.14379e15i | − | 1.21453i | ||||||
\(389\) | 1.62500e15i | 0.468982i | 0.972118 | + | 0.234491i | \(0.0753423\pi\) | ||||
−0.972118 | + | 0.234491i | \(0.924658\pi\) | |||||||
\(390\) | 3.19890e15i | 0.909103i | ||||||||
\(391\) | 3.13542e15 | 0.877477 | ||||||||
\(392\) | 1.55607e15i | 0.428856i | ||||||||
\(393\) | −8.60224e15 | −2.33483 | ||||||||
\(394\) | − | 2.80050e15i | − | 0.748615i | ||||||
\(395\) | 3.41716e15 | 0.899670 | ||||||||
\(396\) | −7.26741e14 | −0.188455 | ||||||||
\(397\) | 4.82490e15 | 1.23238 | 0.616191 | − | 0.787597i | \(-0.288675\pi\) | ||||
0.616191 | + | 0.787597i | \(0.288675\pi\) | |||||||
\(398\) | 3.25511e15i | 0.818969i | ||||||||
\(399\) | − | 1.93423e14i | − | 0.0479371i | ||||||
\(400\) | −3.42393e15 | −0.835920 | ||||||||
\(401\) | −2.47784e15 | −0.595947 | −0.297973 | − | 0.954574i | \(-0.596311\pi\) | ||||
−0.297973 | + | 0.954574i | \(0.596311\pi\) | |||||||
\(402\) | 4.73813e14 | 0.112267 | ||||||||
\(403\) | − | 5.46991e14i | − | 0.127688i | ||||||
\(404\) | 7.66264e14i | 0.176234i | ||||||||
\(405\) | − | 3.08514e15i | − | 0.699109i | ||||||
\(406\) | − | 8.66447e14i | − | 0.193458i | ||||||
\(407\) | 1.42111e15 | 0.312651 | ||||||||
\(408\) | − | 4.22813e15i | − | 0.916616i | ||||||
\(409\) | −3.09892e15 | −0.662019 | −0.331009 | − | 0.943627i | \(-0.607389\pi\) | ||||
−0.331009 | + | 0.943627i | \(0.607389\pi\) | |||||||
\(410\) | −3.41674e15 | −0.719299 | ||||||||
\(411\) | − | 8.23966e15i | − | 1.70946i | ||||||
\(412\) | 1.71955e15i | 0.351585i | ||||||||
\(413\) | −4.92201e13 | −0.00991841 | ||||||||
\(414\) | 1.32747e15i | 0.263646i | ||||||||
\(415\) | −1.94215e14 | + | 2.86731e15i | −0.0380184 | + | 0.561288i | ||||
\(416\) | 6.24862e15 | 1.20566 | ||||||||
\(417\) | − | 1.08211e16i | − | 2.05804i | ||||||
\(418\) | −1.94221e15 | −0.364115 | ||||||||
\(419\) | −3.66816e15 | −0.677897 | −0.338949 | − | 0.940805i | \(-0.610071\pi\) | ||||
−0.338949 | + | 0.940805i | \(0.610071\pi\) | |||||||
\(420\) | − | 2.38442e14i | − | 0.0434396i | ||||||
\(421\) | − | 7.75594e15i | − | 1.39297i | −0.717571 | − | 0.696485i | \(-0.754746\pi\) | ||
0.717571 | − | 0.696485i | \(-0.245254\pi\) | |||||||
\(422\) | 6.78540e15 | 1.20144 | ||||||||
\(423\) | 6.48207e14i | 0.113154i | ||||||||
\(424\) | 2.73895e15 | 0.471399 | ||||||||
\(425\) | −7.16936e15 | −1.21660 | ||||||||
\(426\) | −1.01385e16 | −1.69635 | ||||||||
\(427\) | −3.49864e14 | −0.0577208 | ||||||||
\(428\) | − | 2.71972e15i | − | 0.442447i | ||||||
\(429\) | 5.34299e15i | 0.857118i | ||||||||
\(430\) | − | 3.65470e15i | − | 0.578150i | ||||||
\(431\) | −8.42234e15 | −1.31392 | −0.656960 | − | 0.753925i | \(-0.728158\pi\) | ||||
−0.656960 | + | 0.753925i | \(0.728158\pi\) | |||||||
\(432\) | −5.53515e15 | −0.851583 | ||||||||
\(433\) | − | 8.73975e15i | − | 1.32609i | −0.748582 | − | 0.663043i | \(-0.769265\pi\) | ||
0.748582 | − | 0.663043i | \(-0.230735\pi\) | |||||||
\(434\) | 1.02141e14i | 0.0152848i | ||||||||
\(435\) | 6.95660e15i | 1.02674i | ||||||||
\(436\) | −8.16792e15 | −1.18903 | ||||||||
\(437\) | 1.41613e15i | 0.203335i | ||||||||
\(438\) | 5.16669e15 | 0.731759 | ||||||||
\(439\) | − | 8.46221e15i | − | 1.18222i | −0.806592 | − | 0.591108i | \(-0.798691\pi\) | ||
0.806592 | − | 0.591108i | \(-0.201309\pi\) | |||||||
\(440\) | 1.20951e15 | 0.166683 | ||||||||
\(441\) | −3.02013e15 | −0.410577 | ||||||||
\(442\) | 1.80327e16 | 2.41840 | ||||||||
\(443\) | −3.92705e15 | −0.519570 | −0.259785 | − | 0.965666i | \(-0.583652\pi\) | ||||
−0.259785 | + | 0.965666i | \(0.583652\pi\) | |||||||
\(444\) | 2.76596e15 | 0.361034 | ||||||||
\(445\) | 7.45749e15 | 0.960356 | ||||||||
\(446\) | 1.09521e16 | 1.39151 | ||||||||
\(447\) | − | 5.27639e15i | − | 0.661442i | ||||||
\(448\) | −2.00605e14 | −0.0248126 | ||||||||
\(449\) | 4.53577e15i | 0.553570i | 0.960932 | + | 0.276785i | \(0.0892690\pi\) | ||||
−0.960932 | + | 0.276785i | \(0.910731\pi\) | |||||||
\(450\) | − | 3.03534e15i | − | 0.365538i | ||||||
\(451\) | −5.70684e15 | −0.678167 | ||||||||
\(452\) | −3.03711e15 | −0.356148 | ||||||||
\(453\) | 4.21679e15 | 0.487970 | ||||||||
\(454\) | 8.00900e15i | 0.914625i | ||||||||
\(455\) | −5.13729e14 | −0.0578983 | ||||||||
\(456\) | 1.90965e15 | 0.212405 | ||||||||
\(457\) | 9.26229e15i | 1.01677i | 0.861131 | + | 0.508383i | \(0.169757\pi\) | ||||
−0.861131 | + | 0.508383i | \(0.830243\pi\) | |||||||
\(458\) | 1.57412e16i | 1.70547i | ||||||||
\(459\) | −1.15901e16 | −1.23939 | ||||||||
\(460\) | 1.74572e15i | 0.184259i | ||||||||
\(461\) | 3.53752e15i | 0.368548i | 0.982875 | + | 0.184274i | \(0.0589934\pi\) | ||||
−0.982875 | + | 0.184274i | \(0.941007\pi\) | |||||||
\(462\) | − | 9.97707e14i | − | 0.102601i | ||||||
\(463\) | −2.91140e15 | −0.295540 | −0.147770 | − | 0.989022i | \(-0.547209\pi\) | ||||
−0.147770 | + | 0.989022i | \(0.547209\pi\) | |||||||
\(464\) | 1.87285e16 | 1.87670 | ||||||||
\(465\) | − | 8.20076e14i | − | 0.0811215i | ||||||
\(466\) | 1.08680e16 | 1.06129 | ||||||||
\(467\) | 1.95529e16i | 1.88499i | 0.334217 | + | 0.942496i | \(0.391528\pi\) | ||||
−0.334217 | + | 0.942496i | \(0.608472\pi\) | |||||||
\(468\) | 3.04755e15i | 0.290052i | ||||||||
\(469\) | 7.60923e13i | 0.00714996i | ||||||||
\(470\) | 2.13551e15i | 0.198114i | ||||||||
\(471\) | − | 5.26845e15i | − | 0.482567i | ||||||
\(472\) | − | 4.85945e14i | − | 0.0439476i | ||||||
\(473\) | − | 6.10429e15i | − | 0.545090i | ||||||
\(474\) | 2.78295e16 | 2.45378 | ||||||||
\(475\) | − | 3.23807e15i | − | 0.281919i | ||||||
\(476\) | −1.34414e15 | −0.115558 | ||||||||
\(477\) | 5.31596e15i | 0.451306i | ||||||||
\(478\) | 1.54944e16 | 1.29899 | ||||||||
\(479\) | 3.05099e15 | 0.252597 | 0.126298 | − | 0.991992i | \(-0.459690\pi\) | ||||
0.126298 | + | 0.991992i | \(0.459690\pi\) | |||||||
\(480\) | 9.36824e15 | 0.765968 | ||||||||
\(481\) | − | 5.95933e15i | − | 0.481202i | ||||||
\(482\) | − | 4.70432e15i | − | 0.375158i | ||||||
\(483\) | −7.27460e14 | −0.0572962 | ||||||||
\(484\) | 4.54155e15 | 0.353290 | ||||||||
\(485\) | −1.33852e16 | −1.02843 | ||||||||
\(486\) | − | 1.32883e16i | − | 1.00844i | ||||||
\(487\) | 1.53515e16i | 1.15074i | 0.817894 | + | 0.575369i | \(0.195142\pi\) | ||||
−0.817894 | + | 0.575369i | \(0.804858\pi\) | |||||||
\(488\) | − | 3.45418e15i | − | 0.255756i | ||||||
\(489\) | − | 2.05955e16i | − | 1.50632i | ||||||
\(490\) | −9.94982e15 | −0.718850 | ||||||||
\(491\) | − | 6.82025e15i | − | 0.486756i | −0.969932 | − | 0.243378i | \(-0.921744\pi\) | ||
0.969932 | − | 0.243378i | \(-0.0782556\pi\) | |||||||
\(492\) | −1.11075e16 | −0.783113 | ||||||||
\(493\) | 3.92155e16 | 2.73134 | ||||||||
\(494\) | 8.14455e15i | 0.560410i | ||||||||
\(495\) | 2.34750e15i | 0.159579i | ||||||||
\(496\) | −2.20780e15 | −0.148275 | ||||||||
\(497\) | − | 1.62820e15i | − | 0.108036i | ||||||
\(498\) | −1.58169e15 | + | 2.33515e16i | −0.103692 | + | 1.53087i | ||||
\(499\) | −1.70492e16 | −1.10434 | −0.552168 | − | 0.833733i | \(-0.686199\pi\) | ||||
−0.552168 | + | 0.833733i | \(0.686199\pi\) | |||||||
\(500\) | − | 9.83172e15i | − | 0.629230i | ||||||
\(501\) | 2.56022e15 | 0.161901 | ||||||||
\(502\) | 2.21386e16 | 1.38333 | ||||||||
\(503\) | 2.11569e16i | 1.30631i | 0.757226 | + | 0.653153i | \(0.226554\pi\) | ||||
−0.757226 | + | 0.653153i | \(0.773446\pi\) | |||||||
\(504\) | 2.87481e14i | 0.0175398i | ||||||||
\(505\) | 2.47517e15 | 0.149230 | ||||||||
\(506\) | 7.30459e15i | 0.435204i | ||||||||
\(507\) | 2.20540e15 | 0.129850 | ||||||||
\(508\) | 1.43919e14 | 0.00837404 | ||||||||
\(509\) | −5.23984e15 | −0.301308 | −0.150654 | − | 0.988587i | \(-0.548138\pi\) | ||||
−0.150654 | + | 0.988587i | \(0.548138\pi\) | |||||||
\(510\) | 2.70356e16 | 1.53644 | ||||||||
\(511\) | 8.29748e14i | 0.0466037i | ||||||||
\(512\) | − | 1.56817e16i | − | 0.870510i | ||||||
\(513\) | − | 5.23469e15i | − | 0.287202i | ||||||
\(514\) | 5.09700e15 | 0.276398 | ||||||||
\(515\) | 5.55444e15 | 0.297712 | ||||||||
\(516\) | − | 1.18810e16i | − | 0.629442i | ||||||
\(517\) | 3.56686e15i | 0.186785i | ||||||||
\(518\) | 1.11280e15i | 0.0576020i | ||||||||
\(519\) | −3.12923e16 | −1.60116 | ||||||||
\(520\) | − | 5.07200e15i | − | 0.256542i | ||||||
\(521\) | 3.31130e15 | 0.165566 | 0.0827832 | − | 0.996568i | \(-0.473619\pi\) | ||||
0.0827832 | + | 0.996568i | \(0.473619\pi\) | |||||||
\(522\) | 1.66029e16i | 0.820658i | ||||||||
\(523\) | −3.70738e15 | −0.181158 | −0.0905788 | − | 0.995889i | \(-0.528872\pi\) | ||||
−0.0905788 | + | 0.995889i | \(0.528872\pi\) | |||||||
\(524\) | −2.69992e16 | −1.30426 | ||||||||
\(525\) | 1.66339e15 | 0.0794396 | ||||||||
\(526\) | −4.77217e15 | −0.225321 | ||||||||
\(527\) | −4.62290e15 | −0.215800 | ||||||||
\(528\) | 2.15657e16 | 0.995313 | ||||||||
\(529\) | −1.65886e16 | −0.756966 | ||||||||
\(530\) | 1.75134e16i | 0.790160i | ||||||||
\(531\) | 9.43160e14 | 0.0420744 | ||||||||
\(532\) | − | 6.07084e14i | − | 0.0267780i | ||||||
\(533\) | 2.39314e16i | 1.04377i | ||||||||
\(534\) | 6.07341e16 | 2.61930 | ||||||||
\(535\) | −8.78517e15 | −0.374651 | ||||||||
\(536\) | −7.51252e14 | −0.0316808 | ||||||||
\(537\) | 2.95578e16i | 1.23261i | ||||||||
\(538\) | −3.58851e16 | −1.47986 | ||||||||
\(539\) | −1.66188e16 | −0.677744 | ||||||||
\(540\) | − | 6.45303e15i | − | 0.260256i | ||||||
\(541\) | 1.22352e16i | 0.488009i | 0.969774 | + | 0.244004i | \(0.0784611\pi\) | ||||
−0.969774 | + | 0.244004i | \(0.921539\pi\) | |||||||
\(542\) | −2.66698e16 | −1.05202 | ||||||||
\(543\) | − | 1.49915e16i | − | 0.584853i | ||||||
\(544\) | − | 5.28104e16i | − | 2.03763i | ||||||
\(545\) | 2.63838e16i | 1.00684i | ||||||||
\(546\) | −4.18383e15 | −0.157913 | ||||||||
\(547\) | −4.07221e16 | −1.52022 | −0.760109 | − | 0.649795i | \(-0.774855\pi\) | ||||
−0.760109 | + | 0.649795i | \(0.774855\pi\) | |||||||
\(548\) | − | 2.58612e16i | − | 0.954916i | ||||||
\(549\) | 6.70413e15 | 0.244855 | ||||||||
\(550\) | − | 1.67024e16i | − | 0.603398i | ||||||
\(551\) | 1.77118e16i | 0.632928i | ||||||||
\(552\) | − | 7.18214e15i | − | 0.253875i | ||||||
\(553\) | 4.46930e15i | 0.156275i | ||||||||
\(554\) | 1.90464e16i | 0.658802i | ||||||||
\(555\) | − | 8.93452e15i | − | 0.305713i | ||||||
\(556\) | − | 3.39633e16i | − | 1.14964i | ||||||
\(557\) | −4.14237e15 | −0.138713 | −0.0693566 | − | 0.997592i | \(-0.522095\pi\) | ||||
−0.0693566 | + | 0.997592i | \(0.522095\pi\) | |||||||
\(558\) | − | 1.95723e15i | − | 0.0648391i | ||||||
\(559\) | −2.55980e16 | −0.838949 | ||||||||
\(560\) | 2.07354e15i | 0.0672334i | ||||||||
\(561\) | 4.51564e16 | 1.44858 | ||||||||
\(562\) | −5.58417e16 | −1.77231 | ||||||||
\(563\) | 3.88681e16 | 1.22051 | 0.610257 | − | 0.792204i | \(-0.291066\pi\) | ||||
0.610257 | + | 0.792204i | \(0.291066\pi\) | |||||||
\(564\) | 6.94233e15i | 0.215690i | ||||||||
\(565\) | 9.81041e15i | 0.301576i | ||||||||
\(566\) | −3.02516e16 | −0.920130 | ||||||||
\(567\) | 4.03505e15 | 0.121437 | ||||||||
\(568\) | 1.60750e16 | 0.478698 | ||||||||
\(569\) | 4.28307e16i | 1.26206i | 0.775757 | + | 0.631032i | \(0.217368\pi\) | ||||
−0.775757 | + | 0.631032i | \(0.782632\pi\) | |||||||
\(570\) | 1.22107e16i | 0.356034i | ||||||||
\(571\) | − | 3.54697e16i | − | 1.02339i | −0.859168 | − | 0.511694i | \(-0.829018\pi\) | ||
0.859168 | − | 0.511694i | \(-0.170982\pi\) | |||||||
\(572\) | 1.67696e16i | 0.478793i | ||||||||
\(573\) | 5.32168e15 | 0.150356 | ||||||||
\(574\) | − | 4.46875e15i | − | 0.124944i | ||||||
\(575\) | −1.21783e16 | −0.336960 | ||||||||
\(576\) | 3.84401e15 | 0.105257 | ||||||||
\(577\) | − | 3.39986e16i | − | 0.921312i | −0.887579 | − | 0.460656i | \(-0.847614\pi\) | ||
0.887579 | − | 0.460656i | \(-0.152386\pi\) | |||||||
\(578\) | − | 1.04299e17i | − | 2.79713i | ||||||
\(579\) | −3.87923e16 | −1.02961 | ||||||||
\(580\) | 2.18342e16i | 0.573546i | ||||||||
\(581\) | −3.75015e15 | − | 2.54013e14i | −0.0974970 | − | 0.00660388i | ||||
\(582\) | −1.09009e17 | −2.80496 | ||||||||
\(583\) | 2.92519e16i | 0.744977i | ||||||||
\(584\) | −8.19202e15 | −0.206497 | ||||||||
\(585\) | 9.84413e15 | 0.245608 | ||||||||
\(586\) | − | 7.36414e16i | − | 1.81860i | ||||||
\(587\) | − | 3.24372e16i | − | 0.792894i | −0.918058 | − | 0.396447i | \(-0.870243\pi\) | ||
0.918058 | − | 0.396447i | \(-0.129757\pi\) | |||||||
\(588\) | −3.23458e16 | −0.782625 | ||||||||
\(589\) | − | 2.08795e15i | − | 0.0500068i | ||||||
\(590\) | 3.10724e15 | 0.0736652 | ||||||||
\(591\) | −2.94079e16 | −0.690144 | ||||||||
\(592\) | −2.40534e16 | −0.558787 | ||||||||
\(593\) | 3.20871e16 | 0.737909 | 0.368955 | − | 0.929447i | \(-0.379716\pi\) | ||||
0.368955 | + | 0.929447i | \(0.379716\pi\) | |||||||
\(594\) | − | 2.70013e16i | − | 0.614704i | ||||||
\(595\) | 4.34179e15i | 0.0978514i | ||||||||
\(596\) | − | 1.65606e16i | − | 0.369487i | ||||||
\(597\) | 3.41818e16 | 0.755003 | ||||||||
\(598\) | 3.06314e16 | 0.669823 | ||||||||
\(599\) | 3.72205e16i | 0.805789i | 0.915246 | + | 0.402894i | \(0.131996\pi\) | ||||
−0.915246 | + | 0.402894i | \(0.868004\pi\) | |||||||
\(600\) | 1.64225e16i | 0.351990i | ||||||||
\(601\) | − | 4.23168e16i | − | 0.897980i | −0.893537 | − | 0.448990i | \(-0.851784\pi\) | ||
0.893537 | − | 0.448990i | \(-0.148216\pi\) | |||||||
\(602\) | 4.77997e15 | 0.100426 | ||||||||
\(603\) | − | 1.45809e15i | − | 0.0303305i | ||||||
\(604\) | 1.32349e16 | 0.272584 | ||||||||
\(605\) | − | 1.46700e16i | − | 0.299156i | ||||||
\(606\) | 2.01579e16 | 0.407013 | ||||||||
\(607\) | −8.65379e16 | −1.73011 | −0.865056 | − | 0.501675i | \(-0.832718\pi\) | ||||
−0.865056 | + | 0.501675i | \(0.832718\pi\) | |||||||
\(608\) | 2.38520e16 | 0.472175 | ||||||||
\(609\) | −9.09852e15 | −0.178347 | ||||||||
\(610\) | 2.20867e16 | 0.428699 | ||||||||
\(611\) | 1.49575e16 | 0.287482 | ||||||||
\(612\) | 2.57564e16 | 0.490205 | ||||||||
\(613\) | 3.85088e16i | 0.725768i | 0.931834 | + | 0.362884i | \(0.118208\pi\) | ||||
−0.931834 | + | 0.362884i | \(0.881792\pi\) | |||||||
\(614\) | −1.05054e17 | −1.96066 | ||||||||
\(615\) | 3.58791e16i | 0.663117i | ||||||||
\(616\) | 1.58191e15i | 0.0289532i | ||||||||
\(617\) | 1.03870e17 | 1.88270 | 0.941348 | − | 0.337436i | \(-0.109560\pi\) | ||||
0.941348 | + | 0.337436i | \(0.109560\pi\) | |||||||
\(618\) | 4.52356e16 | 0.811987 | ||||||||
\(619\) | 3.32620e16 | 0.591295 | 0.295648 | − | 0.955297i | \(-0.404465\pi\) | ||||
0.295648 | + | 0.955297i | \(0.404465\pi\) | |||||||
\(620\) | − | 2.57391e15i | − | 0.0453151i | ||||||
\(621\) | −1.96875e16 | −0.343274 | ||||||||
\(622\) | 4.42172e16 | 0.763570 | ||||||||
\(623\) | 9.75363e15i | 0.166816i | ||||||||
\(624\) | − | 9.04346e16i | − | 1.53189i | ||||||
\(625\) | 8.98219e15 | 0.150696 | ||||||||
\(626\) | 8.46555e16i | 1.40673i | ||||||||
\(627\) | 2.03950e16i | 0.335675i | ||||||||
\(628\) | − | 1.65357e16i | − | 0.269566i | ||||||
\(629\) | −5.03654e16 | −0.813258 | ||||||||
\(630\) | −1.83821e15 | −0.0294004 | ||||||||
\(631\) | − | 5.99569e16i | − | 0.949867i | −0.880022 | − | 0.474934i | \(-0.842472\pi\) | ||
0.880022 | − | 0.474934i | \(-0.157528\pi\) | |||||||
\(632\) | −4.41250e16 | −0.692440 | ||||||||
\(633\) | − | 7.12532e16i | − | 1.10760i | ||||||
\(634\) | 1.13483e17i | 1.74740i | ||||||||
\(635\) | − | 4.64883e14i | − | 0.00709090i | ||||||
\(636\) | 5.69342e16i | 0.860262i | ||||||||
\(637\) | 6.96899e16i | 1.04312i | ||||||||
\(638\) | 9.13603e16i | 1.35467i | ||||||||
\(639\) | 3.11997e16i | 0.458294i | ||||||||
\(640\) | −3.15931e16 | −0.459740 | ||||||||
\(641\) | 6.84764e16i | 0.987172i | 0.869697 | + | 0.493586i | \(0.164314\pi\) | ||||
−0.869697 | + | 0.493586i | \(0.835686\pi\) | |||||||
\(642\) | −7.15468e16 | −1.02183 | ||||||||
\(643\) | − | 5.37067e16i | − | 0.759911i | −0.925005 | − | 0.379956i | \(-0.875939\pi\) | ||
0.925005 | − | 0.379956i | \(-0.124061\pi\) | |||||||
\(644\) | −2.28322e15 | −0.0320061 | ||||||||
\(645\) | −3.83778e16 | −0.532993 | ||||||||
\(646\) | 6.88338e16 | 0.947124 | ||||||||
\(647\) | − | 2.97579e16i | − | 0.405674i | −0.979213 | − | 0.202837i | \(-0.934984\pi\) | ||
0.979213 | − | 0.202837i | \(-0.0650161\pi\) | |||||||
\(648\) | 3.98376e16i | 0.538076i | ||||||||
\(649\) | 5.18989e15 | 0.0694528 | ||||||||
\(650\) | −7.00408e16 | −0.928691 | ||||||||
\(651\) | 1.07257e15 | 0.0140910 | ||||||||
\(652\) | − | 6.46414e16i | − | 0.841444i | ||||||
\(653\) | 7.89588e16i | 1.01841i | 0.860646 | + | 0.509204i | \(0.170060\pi\) | ||||
−0.860646 | + | 0.509204i | \(0.829940\pi\) | |||||||
\(654\) | 2.14871e17i | 2.74607i | ||||||||
\(655\) | 8.72121e16i | 1.10441i | ||||||||
\(656\) | 9.65931e16 | 1.21206 | ||||||||
\(657\) | − | 1.58997e16i | − | 0.197696i | ||||||
\(658\) | −2.79303e15 | −0.0344129 | ||||||||
\(659\) | 8.92868e16 | 1.09012 | 0.545061 | − | 0.838397i | \(-0.316507\pi\) | ||||
0.545061 | + | 0.838397i | \(0.316507\pi\) | |||||||
\(660\) | 2.51419e16i | 0.304182i | ||||||||
\(661\) | 8.72098e16i | 1.04558i | 0.852462 | + | 0.522789i | \(0.175109\pi\) | ||||
−0.852462 | + | 0.522789i | \(0.824891\pi\) | |||||||
\(662\) | −8.97998e16 | −1.06691 | ||||||||
\(663\) | − | 1.89361e17i | − | 2.22951i | ||||||
\(664\) | 2.50785e15 | − | 3.70248e16i | 0.0292612 | − | 0.432001i | ||||
\(665\) | −1.96099e15 | −0.0226749 | ||||||||
\(666\) | − | 2.13235e16i | − | 0.244351i | ||||||
\(667\) | 6.66137e16 | 0.756499 | ||||||||
\(668\) | 8.03556e15 | 0.0904394 | ||||||||
\(669\) | − | 1.15007e17i | − | 1.28283i | ||||||
\(670\) | − | 4.80366e15i | − | 0.0531036i | ||||||
\(671\) | 3.68905e16 | 0.404185 | ||||||||
\(672\) | 1.22527e16i | 0.133050i | ||||||||
\(673\) | 7.04351e16 | 0.758052 | 0.379026 | − | 0.925386i | \(-0.376259\pi\) | ||||
0.379026 | + | 0.925386i | \(0.376259\pi\) | |||||||
\(674\) | −1.24674e17 | −1.32989 | ||||||||
\(675\) | 4.50168e16 | 0.475940 | ||||||||
\(676\) | 6.92194e15 | 0.0725350 | ||||||||
\(677\) | − | 8.04172e16i | − | 0.835251i | −0.908619 | − | 0.417625i | \(-0.862862\pi\) | ||
0.908619 | − | 0.417625i | \(-0.137138\pi\) | |||||||
\(678\) | 7.98964e16i | 0.822525i | ||||||||
\(679\) | − | 1.75064e16i | − | 0.178640i | ||||||
\(680\) | −4.28661e16 | −0.433571 | ||||||||
\(681\) | 8.41021e16 | 0.843187 | ||||||||
\(682\) | − | 1.07700e16i | − | 0.107031i | ||||||
\(683\) | 6.95506e16i | 0.685136i | 0.939493 | + | 0.342568i | \(0.111297\pi\) | ||||
−0.939493 | + | 0.342568i | \(0.888703\pi\) | |||||||
\(684\) | 1.16330e16i | 0.113594i | ||||||||
\(685\) | −8.35362e16 | −0.808595 | ||||||||
\(686\) | − | 2.61521e16i | − | 0.250936i | ||||||
\(687\) | 1.65298e17 | 1.57227 | ||||||||
\(688\) | 1.03320e17i | 0.974214i | ||||||||
\(689\) | 1.22666e17 | 1.14660 | ||||||||
\(690\) | 4.59241e16 | 0.425546 | ||||||||
\(691\) | −1.81056e16 | −0.166320 | −0.0831601 | − | 0.996536i | \(-0.526501\pi\) | ||||
−0.0831601 | + | 0.996536i | \(0.526501\pi\) | |||||||
\(692\) | −9.82148e16 | −0.894418 | ||||||||
\(693\) | −3.07029e15 | −0.0277192 | ||||||||
\(694\) | 1.35264e17 | 1.21067 | ||||||||
\(695\) | −1.09707e17 | −0.973479 | ||||||||
\(696\) | − | 8.98288e16i | − | 0.790242i | ||||||
\(697\) | 2.02256e17 | 1.76403 | ||||||||
\(698\) | − | 1.95866e17i | − | 1.69366i | ||||||
\(699\) | − | 1.14124e17i | − | 0.978394i | ||||||
\(700\) | 5.22075e15 | 0.0443756 | ||||||||
\(701\) | −1.01202e17 | −0.852869 | −0.426435 | − | 0.904518i | \(-0.640231\pi\) | ||||
−0.426435 | + | 0.904518i | \(0.640231\pi\) | |||||||
\(702\) | −1.13229e17 | −0.946093 | ||||||||
\(703\) | − | 2.27477e16i | − | 0.188454i | ||||||
\(704\) | 2.11522e16 | 0.173748 | ||||||||
\(705\) | 2.24249e16 | 0.182640 | ||||||||
\(706\) | 7.06504e16i | 0.570540i | ||||||||
\(707\) | 3.23726e15i | 0.0259216i | ||||||||
\(708\) | 1.01013e16 | 0.0802006 | ||||||||
\(709\) | − | 3.20927e16i | − | 0.252655i | −0.991989 | − | 0.126328i | \(-0.959681\pi\) | ||
0.991989 | − | 0.126328i | \(-0.0403191\pi\) | |||||||
\(710\) | 1.02787e17i | 0.802396i | ||||||||
\(711\) | − | 8.56411e16i | − | 0.662926i | ||||||
\(712\) | −9.62967e16 | −0.739148 | ||||||||
\(713\) | −7.85272e15 | −0.0597700 | ||||||||
\(714\) | 3.53597e16i | 0.266882i | ||||||||
\(715\) | 5.41689e16 | 0.405428 | ||||||||
\(716\) | 9.27709e16i | 0.688547i | ||||||||
\(717\) | − | 1.62706e17i | − | 1.19753i | ||||||
\(718\) | 2.72473e17i | 1.98873i | ||||||||
\(719\) | − | 1.65694e17i | − | 1.19931i | −0.800257 | − | 0.599657i | \(-0.795304\pi\) | ||
0.800257 | − | 0.599657i | \(-0.204696\pi\) | |||||||
\(720\) | − | 3.97334e16i | − | 0.285208i | ||||||
\(721\) | 7.26463e15i | 0.0517133i | ||||||||
\(722\) | − | 1.51657e17i | − | 1.07063i | ||||||
\(723\) | −4.93998e16 | −0.345856 | ||||||||
\(724\) | − | 4.70528e16i | − | 0.326704i | ||||||
\(725\) | −1.52317e17 | −1.04887 | ||||||||
\(726\) | − | 1.19473e17i | − | 0.815925i | ||||||
\(727\) | −2.61537e16 | −0.177144 | −0.0885721 | − | 0.996070i | \(-0.528230\pi\) | ||||
−0.0885721 | + | 0.996070i | \(0.528230\pi\) | |||||||
\(728\) | 6.63366e15 | 0.0445620 | ||||||||
\(729\) | 4.69825e16 | 0.313019 | ||||||||
\(730\) | − | 5.23815e16i | − | 0.346131i | ||||||
\(731\) | 2.16342e17i | 1.41787i | ||||||||
\(732\) | 7.18016e16 | 0.466732 | ||||||||
\(733\) | 1.30814e17 | 0.843393 | 0.421696 | − | 0.906737i | \(-0.361435\pi\) | ||||
0.421696 | + | 0.906737i | \(0.361435\pi\) | |||||||
\(734\) | 3.54895e17 | 2.26947 | ||||||||
\(735\) | 1.04483e17i | 0.662704i | ||||||||
\(736\) | − | 8.97066e16i | − | 0.564362i | ||||||
\(737\) | − | 8.02336e15i | − | 0.0500669i | ||||||
\(738\) | 8.56306e16i | 0.530018i | ||||||||
\(739\) | −1.47989e17 | −0.908581 | −0.454291 | − | 0.890854i | \(-0.650107\pi\) | ||||
−0.454291 | + | 0.890854i | \(0.650107\pi\) | |||||||
\(740\) | − | 2.80421e16i | − | 0.170774i | ||||||
\(741\) | 8.55256e16 | 0.516639 | ||||||||
\(742\) | −2.29057e16 | −0.137253 | ||||||||
\(743\) | 1.13182e17i | 0.672738i | 0.941730 | + | 0.336369i | \(0.109199\pi\) | ||||
−0.941730 | + | 0.336369i | \(0.890801\pi\) | |||||||
\(744\) | 1.05894e16i | 0.0624360i | ||||||||
\(745\) | −5.34937e16 | −0.312871 | ||||||||
\(746\) | − | 2.63649e16i | − | 0.152965i | ||||||
\(747\) | 7.18607e16 | + | 4.86742e15i | 0.413588 | + | 0.0280140i | ||||
\(748\) | 1.41729e17 | 0.809187 | ||||||||
\(749\) | − | 1.14901e16i | − | 0.0650778i | ||||||
\(750\) | −2.58640e17 | −1.45321 | ||||||||
\(751\) | −2.65556e15 | −0.0148019 | −0.00740093 | − | 0.999973i | \(-0.502356\pi\) | ||||
−0.00740093 | + | 0.999973i | \(0.502356\pi\) | |||||||
\(752\) | − | 6.03721e16i | − | 0.333833i | ||||||
\(753\) | − | 2.32476e17i | − | 1.27529i | ||||||
\(754\) | 3.83115e17 | 2.08498 | ||||||||
\(755\) | − | 4.27512e16i | − | 0.230816i | ||||||
\(756\) | 8.43991e15 | 0.0452071 | ||||||||
\(757\) | 1.40938e17 | 0.748948 | 0.374474 | − | 0.927237i | \(-0.377823\pi\) | ||||
0.374474 | + | 0.927237i | \(0.377823\pi\) | |||||||
\(758\) | 2.08158e17 | 1.09743 | ||||||||
\(759\) | 7.67051e16 | 0.401212 | ||||||||
\(760\) | − | 1.93606e16i | − | 0.100470i | ||||||
\(761\) | 2.44400e16i | 0.125833i | 0.998019 | + | 0.0629163i | \(0.0200401\pi\) | ||||
−0.998019 | + | 0.0629163i | \(0.979960\pi\) | |||||||
\(762\) | − | 3.78603e15i | − | 0.0193399i | ||||||
\(763\) | −3.45073e16 | −0.174890 | ||||||||
\(764\) | 1.67028e16 | 0.0839902 | ||||||||
\(765\) | − | 8.31978e16i | − | 0.415091i | ||||||
\(766\) | − | 4.79218e16i | − | 0.237225i | ||||||
\(767\) | − | 2.17635e16i | − | 0.106895i | ||||||
\(768\) | −3.19263e17 | −1.55590 | ||||||||
\(769\) | − | 1.25665e17i | − | 0.607653i | −0.952727 | − | 0.303827i | \(-0.901736\pi\) | ||
0.952727 | − | 0.303827i | \(-0.0982644\pi\) | |||||||
\(770\) | −1.01151e16 | −0.0485315 | ||||||||
\(771\) | − | 5.35233e16i | − | 0.254810i | ||||||
\(772\) | −1.21754e17 | −0.575150 | ||||||||
\(773\) | −6.69139e16 | −0.313646 | −0.156823 | − | 0.987627i | \(-0.550125\pi\) | ||||
−0.156823 | + | 0.987627i | \(0.550125\pi\) | |||||||
\(774\) | −9.15942e16 | −0.426012 | ||||||||
\(775\) | 1.79558e16 | 0.0828694 | ||||||||
\(776\) | 1.72839e17 | 0.791539 | ||||||||
\(777\) | 1.16854e16 | 0.0531030 | ||||||||
\(778\) | 1.34171e17 | 0.605037 | ||||||||
\(779\) | 9.13498e16i | 0.408774i | ||||||||
\(780\) | 1.05431e17 | 0.468168 | ||||||||
\(781\) | 1.71681e17i | 0.756512i | ||||||||
\(782\) | − | 2.58882e17i | − | 1.13204i | ||||||
\(783\) | −2.46237e17 | −1.06852 | ||||||||
\(784\) | 2.81286e17 | 1.21130 | ||||||||
\(785\) | −5.34132e16 | −0.228261 | ||||||||
\(786\) | 7.10260e17i | 3.01219i | ||||||||
\(787\) | −2.30222e17 | −0.968946 | −0.484473 | − | 0.874806i | \(-0.660989\pi\) | ||||
−0.484473 | + | 0.874806i | \(0.660989\pi\) | |||||||
\(788\) | −9.23005e16 | −0.385520 | ||||||||
\(789\) | 5.01123e16i | 0.207722i | ||||||||
\(790\) | − | 2.82144e17i | − | 1.16067i | ||||||
\(791\) | −1.28310e16 | −0.0523844 | ||||||||
\(792\) | − | 3.03127e16i | − | 0.122821i | ||||||
\(793\) | − | 1.54699e17i | − | 0.622082i | ||||||
\(794\) | − | 3.98377e17i | − | 1.58991i | ||||||
\(795\) | 1.83907e17 | 0.728445 | ||||||||
\(796\) | 1.07284e17 | 0.421751 | ||||||||
\(797\) | − | 4.85656e17i | − | 1.89487i | −0.319954 | − | 0.947433i | \(-0.603667\pi\) | ||
0.319954 | − | 0.947433i | \(-0.396333\pi\) | |||||||
\(798\) | −1.59704e16 | −0.0618440 | ||||||||
\(799\) | − | 1.26413e17i | − | 0.485861i | ||||||
\(800\) | 2.05120e17i | 0.782472i | ||||||||
\(801\) | − | 1.86900e17i | − | 0.707643i | ||||||
\(802\) | 2.04588e17i | 0.768835i | ||||||||
\(803\) | − | 8.74907e16i | − | 0.326339i | ||||||
\(804\) | − | 1.56162e16i | − | 0.0578148i | ||||||
\(805\) | 7.37521e15i | 0.0271019i | ||||||||
\(806\) | −4.51633e16 | −0.164731 | ||||||||
\(807\) | 3.76827e17i | 1.36427i | ||||||||
\(808\) | −3.19612e16 | −0.114856 | ||||||||
\(809\) | 4.20012e17i | 1.49820i | 0.662455 | + | 0.749101i | \(0.269514\pi\) | ||||
−0.662455 | + | 0.749101i | \(0.730486\pi\) | |||||||
\(810\) | −2.54730e17 | −0.901925 | ||||||||
\(811\) | 4.38197e17 | 1.54008 | 0.770041 | − | 0.637994i | \(-0.220236\pi\) | ||||
0.770041 | + | 0.637994i | \(0.220236\pi\) | |||||||
\(812\) | −2.85568e16 | −0.0996263 | ||||||||
\(813\) | 2.80058e17i | 0.969850i | ||||||||
\(814\) | − | 1.17336e17i | − | 0.403353i | ||||||
\(815\) | −2.08803e17 | −0.712510 | ||||||||
\(816\) | −7.64309e17 | −2.58898 | ||||||||
\(817\) | −9.77117e16 | −0.328560 | ||||||||
\(818\) | 2.55868e17i | 0.854075i | ||||||||
\(819\) | 1.28751e16i | 0.0426626i | ||||||||
\(820\) | 1.12611e17i | 0.370423i | ||||||||
\(821\) | − | 6.94386e16i | − | 0.226747i | −0.993552 | − | 0.113374i | \(-0.963834\pi\) | ||
0.993552 | − | 0.113374i | \(-0.0361657\pi\) | |||||||
\(822\) | −6.80322e17 | −2.20538 | ||||||||
\(823\) | − | 3.60013e16i | − | 0.115856i | −0.998321 | − | 0.0579281i | \(-0.981551\pi\) | ||
0.998321 | − | 0.0579281i | \(-0.0184494\pi\) | |||||||
\(824\) | −7.17230e16 | −0.229137 | ||||||||
\(825\) | −1.75392e17 | −0.556269 | ||||||||
\(826\) | 4.06395e15i | 0.0127958i | ||||||||
\(827\) | − | 1.79611e17i | − | 0.561435i | −0.959790 | − | 0.280718i | \(-0.909428\pi\) | ||
0.959790 | − | 0.280718i | \(-0.0905724\pi\) | |||||||
\(828\) | 4.37513e16 | 0.135772 | ||||||||
\(829\) | 3.57922e17i | 1.10271i | 0.834271 | + | 0.551355i | \(0.185889\pi\) | ||||
−0.834271 | + | 0.551355i | \(0.814111\pi\) | |||||||
\(830\) | 2.36745e17 | + | 1.60357e16i | 0.724122 | + | 0.0490478i | ||||
\(831\) | 2.00006e17 | 0.607346 | ||||||||
\(832\) | − | 8.87009e16i | − | 0.267416i | ||||||
\(833\) | 5.88986e17 | 1.76293 | ||||||||
\(834\) | −8.93461e17 | −2.65509 | ||||||||
\(835\) | − | 2.59563e16i | − | 0.0765814i | ||||||
\(836\) | 6.40124e16i | 0.187511i | ||||||||
\(837\) | 2.90275e16 | 0.0844222 | ||||||||
\(838\) | 3.02868e17i | 0.874560i | ||||||||
\(839\) | −2.38812e16 | −0.0684676 | −0.0342338 | − | 0.999414i | \(-0.510899\pi\) | ||||
−0.0342338 | + | 0.999414i | \(0.510899\pi\) | |||||||
\(840\) | 9.94550e15 | 0.0283107 | ||||||||
\(841\) | 4.79339e17 | 1.35477 | ||||||||
\(842\) | −6.40383e17 | −1.79708 | ||||||||
\(843\) | 5.86391e17i | 1.63389i | ||||||||
\(844\) | − | 2.23637e17i | − | 0.618713i | ||||||
\(845\) | − | 2.23591e16i | − | 0.0614205i | ||||||
\(846\) | 5.35204e16 | 0.145981 | ||||||||
\(847\) | 1.91868e16 | 0.0519641 | ||||||||
\(848\) | − | 4.95113e17i | − | 1.33146i | ||||||
\(849\) | 3.17670e17i | 0.848263i | ||||||||
\(850\) | 5.91951e17i | 1.56954i | ||||||||
\(851\) | −8.55535e16 | −0.225248 | ||||||||
\(852\) | 3.34150e17i | 0.873582i | ||||||||
\(853\) | 4.46852e17 | 1.16003 | 0.580016 | − | 0.814605i | \(-0.303046\pi\) | ||||
0.580016 | + | 0.814605i | \(0.303046\pi\) | |||||||
\(854\) | 2.88872e16i | 0.0744660i | ||||||||
\(855\) | 3.75766e16 | 0.0961880 | ||||||||
\(856\) | 1.13441e17 | 0.288354 | ||||||||
\(857\) | −1.68717e17 | −0.425866 | −0.212933 | − | 0.977067i | \(-0.568302\pi\) | ||||
−0.212933 | + | 0.977067i | \(0.568302\pi\) | |||||||
\(858\) | 4.41154e17 | 1.10577 | ||||||||
\(859\) | 2.66618e17 | 0.663638 | 0.331819 | − | 0.943343i | \(-0.392338\pi\) | ||||
0.331819 | + | 0.943343i | \(0.392338\pi\) | |||||||
\(860\) | −1.20454e17 | −0.297734 | ||||||||
\(861\) | −4.69261e16 | −0.115185 | ||||||||
\(862\) | 6.95406e17i | 1.69510i | ||||||||
\(863\) | −2.47135e17 | −0.598232 | −0.299116 | − | 0.954217i | \(-0.596692\pi\) | ||||
−0.299116 | + | 0.954217i | \(0.596692\pi\) | |||||||
\(864\) | 3.31599e17i | 0.797134i | ||||||||
\(865\) | 3.17251e17i | 0.757367i | ||||||||
\(866\) | −7.21613e17 | −1.71079 | ||||||||
\(867\) | −1.09524e18 | −2.57865 | ||||||||
\(868\) | 3.36641e15 | 0.00787134 | ||||||||
\(869\) | − | 4.71254e17i | − | 1.09430i | ||||||
\(870\) | 5.74385e17 | 1.32461 | ||||||||
\(871\) | −3.36455e16 | −0.0770582 | ||||||||
\(872\) | − | 3.40688e17i | − | 0.774921i | ||||||
\(873\) | 3.35460e17i | 0.757801i | ||||||||
\(874\) | 1.16925e17 | 0.262324 | ||||||||
\(875\) | − | 4.15365e16i | − | 0.0925510i | ||||||
\(876\) | − | 1.70287e17i | − | 0.376839i | ||||||
\(877\) | 1.99061e17i | 0.437512i | 0.975780 | + | 0.218756i | \(0.0701998\pi\) | ||||
−0.975780 | + | 0.218756i | \(0.929800\pi\) | |||||||
\(878\) | −6.98698e17 | −1.52518 | ||||||||
\(879\) | −7.73305e17 | −1.67655 | ||||||||
\(880\) | − | 2.18639e17i | − | 0.470796i | ||||||
\(881\) | −7.66604e17 | −1.63951 | −0.819757 | − | 0.572711i | \(-0.805892\pi\) | ||||
−0.819757 | + | 0.572711i | \(0.805892\pi\) | |||||||
\(882\) | 2.49363e17i | 0.529688i | ||||||||
\(883\) | 7.74010e16i | 0.163299i | 0.996661 | + | 0.0816493i | \(0.0260187\pi\) | ||||
−0.996661 | + | 0.0816493i | \(0.973981\pi\) | |||||||
\(884\) | − | 5.94333e17i | − | 1.24542i | ||||||
\(885\) | − | 3.26289e16i | − | 0.0679115i | ||||||
\(886\) | 3.24244e17i | 0.670301i | ||||||||
\(887\) | − | 9.06963e17i | − | 1.86229i | −0.364646 | − | 0.931146i | \(-0.618810\pi\) | ||
0.364646 | − | 0.931146i | \(-0.381190\pi\) | |||||||
\(888\) | 1.15369e17i | 0.235295i | ||||||||
\(889\) | 6.08019e14 | 0.00123170 | ||||||||
\(890\) | − | 6.15741e17i | − | 1.23896i | ||||||
\(891\) | −4.25465e17 | −0.850350 | ||||||||
\(892\) | − | 3.60964e17i | − | 0.716596i | ||||||
\(893\) | 5.70950e16 | 0.112587 | ||||||||
\(894\) | −4.35655e17 | −0.853331 | ||||||||
\(895\) | 2.99666e17 | 0.583042 | ||||||||
\(896\) | − | 4.13206e16i | − | 0.0798579i | ||||||
\(897\) | − | 3.21659e17i | − | 0.617506i | ||||||
\(898\) | 3.74504e17 | 0.714165 | ||||||||
\(899\) | −9.82160e16 | −0.186048 | ||||||||
\(900\) | −1.00040e17 | −0.188244 | ||||||||
\(901\) | − | 1.03672e18i | − | 1.93781i | ||||||
\(902\) | 4.71196e17i | 0.874908i | ||||||||
\(903\) | − | 5.01942e16i | − | 0.0925821i | ||||||
\(904\) | − | 1.26679e17i | − | 0.232111i | ||||||
\(905\) | −1.51989e17 | −0.276643 | ||||||||
\(906\) | − | 3.48167e17i | − | 0.629533i | ||||||
\(907\) | 7.91790e17 | 1.42222 | 0.711109 | − | 0.703082i | \(-0.248193\pi\) | ||||
0.711109 | + | 0.703082i | \(0.248193\pi\) | |||||||
\(908\) | 2.63965e17 | 0.471011 | ||||||||
\(909\) | − | 6.20328e16i | − | 0.109961i | ||||||
\(910\) | 4.24170e16i | 0.0746950i | ||||||||
\(911\) | 5.82123e17 | 1.01837 | 0.509184 | − | 0.860658i | \(-0.329947\pi\) | ||||
0.509184 | + | 0.860658i | \(0.329947\pi\) | |||||||
\(912\) | − | 3.45203e17i | − | 0.599937i | ||||||
\(913\) | 3.95425e17 | + | 2.67838e16i | 0.682714 | + | 0.0462431i | ||||
\(914\) | 7.64758e17 | 1.31174 | ||||||||
\(915\) | − | 2.31932e17i | − | 0.395215i | ||||||
\(916\) | 5.18807e17 | 0.878280 | ||||||||
\(917\) | −1.14065e17 | −0.191838 | ||||||||
\(918\) | 9.56954e17i | 1.59895i | ||||||||
\(919\) | − | 2.87542e16i | − | 0.0477319i | −0.999715 | − | 0.0238659i | \(-0.992403\pi\) | ||
0.999715 | − | 0.0238659i | \(-0.00759749\pi\) | |||||||
\(920\) | −7.28148e16 | −0.120086 | ||||||||
\(921\) | 1.10317e18i | 1.80753i | ||||||||
\(922\) | 2.92082e17 | 0.475466 | ||||||||
\(923\) | 7.19936e17 | 1.16435 | ||||||||
\(924\) | −3.28830e16 | −0.0528371 | ||||||||
\(925\) | 1.95624e17 | 0.312300 | ||||||||
\(926\) | 2.40385e17i | 0.381278i | ||||||||
\(927\) | − | 1.39206e17i | − | 0.219371i | ||||||
\(928\) | − | 1.12198e18i | − | 1.75670i | ||||||
\(929\) | −1.17405e17 | −0.182639 | −0.0913196 | − | 0.995822i | \(-0.529108\pi\) | ||||
−0.0913196 | + | 0.995822i | \(0.529108\pi\) | |||||||
\(930\) | −6.77111e16 | −0.104655 | ||||||||
\(931\) | 2.66018e17i | 0.408519i | ||||||||
\(932\) | − | 3.58192e17i | − | 0.546538i | ||||||
\(933\) | − | 4.64323e17i | − | 0.703931i | ||||||
\(934\) | 1.61442e18 | 2.43184 | ||||||||
\(935\) | − | 4.57809e17i | − | 0.685196i | ||||||
\(936\) | −1.27115e17 | −0.189034 | ||||||||
\(937\) | − | 2.25774e17i | − | 0.333608i | −0.985990 | − | 0.166804i | \(-0.946655\pi\) | ||
0.985990 | − | 0.166804i | \(-0.0533446\pi\) | |||||||
\(938\) | 6.28270e15 | 0.00922421 | ||||||||
\(939\) | 8.88964e17 | 1.29685 | ||||||||
\(940\) | 7.03835e16 | 0.102024 | ||||||||
\(941\) | −8.96450e17 | −1.29119 | −0.645593 | − | 0.763682i | \(-0.723390\pi\) | ||||
−0.645593 | + | 0.763682i | \(0.723390\pi\) | |||||||
\(942\) | −4.35000e17 | −0.622563 | ||||||||
\(943\) | 3.43564e17 | 0.488582 | ||||||||
\(944\) | −8.78432e16 | −0.124130 | ||||||||
\(945\) | − | 2.72624e16i | − | 0.0382801i | ||||||
\(946\) | −5.04012e17 | −0.703224 | ||||||||
\(947\) | 1.08483e18i | 1.50405i | 0.659136 | + | 0.752023i | \(0.270922\pi\) | ||||
−0.659136 | + | 0.752023i | \(0.729078\pi\) | |||||||
\(948\) | − | 9.17221e17i | − | 1.26364i | ||||||
\(949\) | −3.66888e17 | −0.502269 | ||||||||
\(950\) | −2.67357e17 | −0.363706 | ||||||||
\(951\) | 1.19167e18 | 1.61092 | ||||||||
\(952\) | − | 5.60645e16i | − | 0.0753123i | ||||||
\(953\) | 8.98711e16 | 0.119967 | 0.0599836 | − | 0.998199i | \(-0.480895\pi\) | ||||
0.0599836 | + | 0.998199i | \(0.480895\pi\) | |||||||
\(954\) | 4.38922e17 | 0.582233 | ||||||||
\(955\) | − | 5.39529e16i | − | 0.0711204i | ||||||
\(956\) | − | 5.10672e17i | − | 0.668952i | ||||||
\(957\) | 9.59370e17 | 1.24886 | ||||||||
\(958\) | − | 2.51911e17i | − | 0.325877i | ||||||
\(959\) | − | 1.09257e17i | − | 0.140455i | ||||||
\(960\) | − | 1.32985e17i | − | 0.169893i | ||||||
\(961\) | −7.76085e17 | −0.985301 | ||||||||
\(962\) | −4.92043e17 | −0.620802 | ||||||||
\(963\) | 2.20174e17i | 0.276064i | ||||||||
\(964\) | −1.55048e17 | −0.193198 | ||||||||
\(965\) | 3.93288e17i | 0.487020i | ||||||||
\(966\) | 6.00640e16i | 0.0739183i | ||||||||
\(967\) | 1.55492e18i | 1.90174i | 0.309598 | + | 0.950868i | \(0.399806\pi\) | ||||
−0.309598 | + | 0.950868i | \(0.600194\pi\) | |||||||
\(968\) | 1.89430e17i | 0.230248i | ||||||||
\(969\) | − | 7.22821e17i | − | 0.873148i | ||||||
\(970\) | 1.10517e18i | 1.32678i | ||||||||
\(971\) | − | 7.37837e17i | − | 0.880330i | −0.897917 | − | 0.440165i | \(-0.854920\pi\) | ||
0.897917 | − | 0.440165i | \(-0.145080\pi\) | |||||||
\(972\) | −4.37962e17 | −0.519325 | ||||||||
\(973\) | − | 1.43486e17i | − | 0.169096i | ||||||
\(974\) | 1.26752e18 | 1.48458 | ||||||||
\(975\) | 7.35496e17i | 0.856155i | ||||||||
\(976\) | −6.24403e17 | −0.722381 | ||||||||
\(977\) | −1.08800e18 | −1.25101 | −0.625504 | − | 0.780221i | \(-0.715106\pi\) | ||||
−0.625504 | + | 0.780221i | \(0.715106\pi\) | |||||||
\(978\) | −1.70050e18 | −1.94332 | ||||||||
\(979\) | − | 1.02845e18i | − | 1.16811i | ||||||
\(980\) | 3.27932e17i | 0.370192i | ||||||||
\(981\) | 6.61233e17 | 0.741891 | ||||||||
\(982\) | −5.63127e17 | −0.627967 | ||||||||
\(983\) | 9.43822e17 | 1.04609 | 0.523045 | − | 0.852305i | \(-0.324796\pi\) | ||||
0.523045 | + | 0.852305i | \(0.324796\pi\) | |||||||
\(984\) | − | 4.63297e17i | − | 0.510375i | ||||||
\(985\) | 2.98147e17i | 0.326447i | ||||||||
\(986\) | − | 3.23790e18i | − | 3.52373i | ||||||
\(987\) | 2.93295e16i | 0.0317250i | ||||||||
\(988\) | 2.68433e17 | 0.288598 | ||||||||
\(989\) | 3.67491e17i | 0.392707i | ||||||||
\(990\) | 1.93826e17 | 0.205873 | ||||||||
\(991\) | 8.75161e17 | 0.923945 | 0.461972 | − | 0.886894i | \(-0.347142\pi\) | ||||
0.461972 | + | 0.886894i | \(0.347142\pi\) | |||||||
\(992\) | 1.32264e17i | 0.138795i | ||||||||
\(993\) | 9.42983e17i | 0.983577i | ||||||||
\(994\) | −1.34435e17 | −0.139378 | ||||||||
\(995\) | − | 3.46545e17i | − | 0.357126i | ||||||
\(996\) | 7.69632e17 | + | 5.21304e16i | 0.788364 | + | 0.0533992i | ||||
\(997\) | −7.41865e17 | −0.755360 | −0.377680 | − | 0.925936i | \(-0.623278\pi\) | ||||
−0.377680 | + | 0.925936i | \(0.623278\pi\) | |||||||
\(998\) | 1.40770e18i | 1.42471i | ||||||||
\(999\) | 3.16248e17 | 0.318152 |
(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 | 83.13.b.c.82.19 | ✓ | 80 | |
83.82 | odd | 2 | inner | 83.13.b.c.82.62 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
83.13.b.c.82.19 | ✓ | 80 | 1.1 | even | 1 | trivial | |
83.13.b.c.82.62 | yes | 80 | 83.82 | odd | 2 | inner |