Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,10,Mod(24,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.24");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.b (of order \(2\), degree \(1\), not 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: | \(12.8758959041\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 1305x^{4} + 433104x^{2} + 16000000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 5^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 24.5 | ||
Root | \(-22.2334i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.24 |
Dual form | 25.10.b.c.24.2 |
$q$-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 \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 21.4187i | 0.946580i | 0.880907 | + | 0.473290i | \(0.156934\pi\) | ||||
−0.880907 | + | 0.473290i | \(0.843066\pi\) | |||||||
\(3\) | 210.171i | 1.49805i | 0.662539 | + | 0.749027i | \(0.269479\pi\) | ||||
−0.662539 | + | 0.749027i | \(0.730521\pi\) | |||||||
\(4\) | 53.2406 | 0.103986 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −4501.59 | −1.41803 | ||||||||
\(7\) | 9905.49i | 1.55932i | 0.626204 | + | 0.779659i | \(0.284608\pi\) | ||||
−0.626204 | + | 0.779659i | \(0.715392\pi\) | |||||||
\(8\) | 12106.7i | 1.04501i | ||||||||
\(9\) | −24489.0 | −1.24417 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 36453.6 | 0.750712 | 0.375356 | − | 0.926881i | \(-0.377520\pi\) | ||||
0.375356 | + | 0.926881i | \(0.377520\pi\) | |||||||
\(12\) | 11189.6i | 0.155776i | ||||||||
\(13\) | − 164867.i | − 1.60099i | −0.599341 | − | 0.800494i | \(-0.704571\pi\) | ||||
0.599341 | − | 0.800494i | \(-0.295429\pi\) | |||||||
\(14\) | −212162. | −1.47602 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −232050. | −0.885201 | ||||||||
\(17\) | 82357.1i | 0.239156i | 0.992825 | + | 0.119578i | \(0.0381541\pi\) | ||||
−0.992825 | + | 0.119578i | \(0.961846\pi\) | |||||||
\(18\) | − 524521.i | − 1.17771i | ||||||||
\(19\) | 609617. | 1.07316 | 0.536582 | − | 0.843848i | \(-0.319715\pi\) | ||||
0.536582 | + | 0.843848i | \(0.319715\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.08185e6 | −2.33594 | ||||||||
\(22\) | 780787.i | 0.710609i | ||||||||
\(23\) | − 1.88578e6i | − 1.40513i | −0.711620 | − | 0.702564i | \(-0.752038\pi\) | ||||
0.711620 | − | 0.702564i | \(-0.247962\pi\) | |||||||
\(24\) | −2.54448e6 | −1.56548 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.53123e6 | 1.51546 | ||||||||
\(27\) | − 1.01008e6i | − 0.365778i | ||||||||
\(28\) | 527374.i | 0.162147i | ||||||||
\(29\) | −339235. | −0.0890657 | −0.0445328 | − | 0.999008i | \(-0.514180\pi\) | ||||
−0.0445328 | + | 0.999008i | \(0.514180\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 547314. | 0.106441 | 0.0532205 | − | 0.998583i | \(-0.483051\pi\) | ||||
0.0532205 | + | 0.998583i | \(0.483051\pi\) | |||||||
\(32\) | 1.22842e6i | 0.207097i | ||||||||
\(33\) | 7.66150e6i | 1.12461i | ||||||||
\(34\) | −1.76398e6 | −0.226380 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.30381e6 | −0.129376 | ||||||||
\(37\) | 5.25687e6i | 0.461126i | 0.973057 | + | 0.230563i | \(0.0740567\pi\) | ||||
−0.973057 | + | 0.230563i | \(0.925943\pi\) | |||||||
\(38\) | 1.30572e7i | 1.01584i | ||||||||
\(39\) | 3.46503e7 | 2.39837 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.05812e6 | 0.113748 | 0.0568739 | − | 0.998381i | \(-0.481887\pi\) | ||||
0.0568739 | + | 0.998381i | \(0.481887\pi\) | |||||||
\(42\) | − 4.45904e7i | − 2.21116i | ||||||||
\(43\) | 6.76158e6i | 0.301606i | 0.988564 | + | 0.150803i | \(0.0481859\pi\) | ||||
−0.988564 | + | 0.150803i | \(0.951814\pi\) | |||||||
\(44\) | 1.94081e6 | 0.0780632 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.03909e7 | 1.33007 | ||||||||
\(47\) | 3.15241e7i | 0.942330i | 0.882045 | + | 0.471165i | \(0.156166\pi\) | ||||
−0.882045 | + | 0.471165i | \(0.843834\pi\) | |||||||
\(48\) | − 4.87703e7i | − 1.32608i | ||||||||
\(49\) | −5.77651e7 | −1.43147 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.73091e7 | −0.358268 | ||||||||
\(52\) | − 8.77761e6i | − 0.166480i | ||||||||
\(53\) | 4.89593e7i | 0.852303i | 0.904652 | + | 0.426151i | \(0.140131\pi\) | ||||
−0.904652 | + | 0.426151i | \(0.859869\pi\) | |||||||
\(54\) | 2.16345e7 | 0.346238 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.19923e8 | −1.62950 | ||||||||
\(57\) | 1.28124e8i | 1.60766i | ||||||||
\(58\) | − 7.26597e6i | − 0.0843078i | ||||||||
\(59\) | −8.77960e7 | −0.943281 | −0.471640 | − | 0.881791i | \(-0.656338\pi\) | ||||
−0.471640 | + | 0.881791i | \(0.656338\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.84654e7 | 0.355701 | 0.177851 | − | 0.984057i | \(-0.443086\pi\) | ||||
0.177851 | + | 0.984057i | \(0.443086\pi\) | |||||||
\(62\) | 1.17227e7i | 0.100755i | ||||||||
\(63\) | − 2.42575e8i | − 1.94005i | ||||||||
\(64\) | −1.45121e8 | −1.08124 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.64099e8 | −1.06453 | ||||||||
\(67\) | − 1.36116e8i | − 0.825227i | −0.910906 | − | 0.412613i | \(-0.864616\pi\) | ||||
0.910906 | − | 0.412613i | \(-0.135384\pi\) | |||||||
\(68\) | 4.38474e6i | 0.0248687i | ||||||||
\(69\) | 3.96337e8 | 2.10496 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.49218e8 | 1.63092 | 0.815462 | − | 0.578810i | \(-0.196483\pi\) | ||||
0.815462 | + | 0.578810i | \(0.196483\pi\) | |||||||
\(72\) | − 2.96481e8i | − 1.30017i | ||||||||
\(73\) | − 1.61345e8i | − 0.664971i | −0.943108 | − | 0.332486i | \(-0.892113\pi\) | ||||
0.943108 | − | 0.332486i | \(-0.107887\pi\) | |||||||
\(74\) | −1.12595e8 | −0.436492 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.24564e7 | 0.111594 | ||||||||
\(77\) | 3.61091e8i | 1.17060i | ||||||||
\(78\) | 7.42163e8i | 2.27025i | ||||||||
\(79\) | 1.26975e8 | 0.366772 | 0.183386 | − | 0.983041i | \(-0.441294\pi\) | ||||
0.183386 | + | 0.983041i | \(0.441294\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.69727e8 | −0.696213 | ||||||||
\(82\) | 4.40822e7i | 0.107671i | ||||||||
\(83\) | 2.87494e8i | 0.664931i | 0.943115 | + | 0.332466i | \(0.107881\pi\) | ||||
−0.943115 | + | 0.332466i | \(0.892119\pi\) | |||||||
\(84\) | −1.10839e8 | −0.242904 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.44824e8 | −0.285494 | ||||||||
\(87\) | − 7.12976e7i | − 0.133425i | ||||||||
\(88\) | 4.41333e8i | 0.784502i | ||||||||
\(89\) | 5.63133e8 | 0.951385 | 0.475692 | − | 0.879612i | \(-0.342198\pi\) | ||||
0.475692 | + | 0.879612i | \(0.342198\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.63309e9 | 2.49645 | ||||||||
\(92\) | − 1.00400e8i | − 0.146113i | ||||||||
\(93\) | 1.15030e8i | 0.159454i | ||||||||
\(94\) | −6.75205e8 | −0.891991 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.58179e8 | −0.310242 | ||||||||
\(97\) | − 4.71704e8i | − 0.541000i | −0.962720 | − | 0.270500i | \(-0.912811\pi\) | ||||
0.962720 | − | 0.270500i | \(-0.0871890\pi\) | |||||||
\(98\) | − 1.23725e9i | − 1.35500i | ||||||||
\(99\) | −8.92711e8 | −0.934012 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.25673e9 | −1.20170 | −0.600851 | − | 0.799361i | \(-0.705172\pi\) | ||||
−0.600851 | + | 0.799361i | \(0.705172\pi\) | |||||||
\(102\) | − 3.70738e8i | − 0.339130i | ||||||||
\(103\) | − 1.95398e9i | − 1.71062i | −0.518119 | − | 0.855309i | \(-0.673367\pi\) | ||||
0.518119 | − | 0.855309i | \(-0.326633\pi\) | |||||||
\(104\) | 1.99599e9 | 1.67305 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.04864e9 | −0.806773 | ||||||||
\(107\) | 2.12306e9i | 1.56580i | 0.622148 | + | 0.782899i | \(0.286260\pi\) | ||||
−0.622148 | + | 0.782899i | \(0.713740\pi\) | |||||||
\(108\) | − 5.37771e7i | − 0.0380356i | ||||||||
\(109\) | 1.18863e8 | 0.0806544 | 0.0403272 | − | 0.999187i | \(-0.487160\pi\) | ||||
0.0403272 | + | 0.999187i | \(0.487160\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.10484e9 | −0.690791 | ||||||||
\(112\) | − 2.29857e9i | − 1.38031i | ||||||||
\(113\) | 1.85455e9i | 1.07001i | 0.844850 | + | 0.535003i | \(0.179689\pi\) | ||||
−0.844850 | + | 0.535003i | \(0.820311\pi\) | |||||||
\(114\) | −2.74425e9 | −1.52178 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.80611e7 | −0.00926154 | ||||||||
\(117\) | 4.03742e9i | 1.99190i | ||||||||
\(118\) | − 1.88047e9i | − 0.892891i | ||||||||
\(119\) | −8.15787e8 | −0.372920 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.02908e9 | −0.436432 | ||||||||
\(122\) | 8.23877e8i | 0.336700i | ||||||||
\(123\) | 4.32557e8i | 0.170400i | ||||||||
\(124\) | 2.91393e7 | 0.0110683 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5.19564e9 | 1.83642 | ||||||||
\(127\) | − 5.39208e9i | − 1.83924i | −0.392805 | − | 0.919622i | \(-0.628495\pi\) | ||||
0.392805 | − | 0.919622i | \(-0.371505\pi\) | |||||||
\(128\) | − 2.47934e9i | − 0.816379i | ||||||||
\(129\) | −1.42109e9 | −0.451823 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.83690e9 | 1.13831 | 0.569154 | − | 0.822231i | \(-0.307271\pi\) | ||||
0.569154 | + | 0.822231i | \(0.307271\pi\) | |||||||
\(132\) | 4.07903e8i | 0.116943i | ||||||||
\(133\) | 6.03856e9i | 1.67340i | ||||||||
\(134\) | 2.91543e9 | 0.781143 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.97072e8 | −0.249920 | ||||||||
\(137\) | − 2.55408e9i | − 0.619430i | −0.950829 | − | 0.309715i | \(-0.899766\pi\) | ||||
0.950829 | − | 0.309715i | \(-0.100234\pi\) | |||||||
\(138\) | 8.48901e9i | 1.99251i | ||||||||
\(139\) | 4.09121e9 | 0.929577 | 0.464789 | − | 0.885422i | \(-0.346130\pi\) | ||||
0.464789 | + | 0.885422i | \(0.346130\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.62547e9 | −1.41166 | ||||||||
\(142\) | 7.47978e9i | 1.54380i | ||||||||
\(143\) | − 6.00999e9i | − 1.20188i | ||||||||
\(144\) | 5.68267e9 | 1.10134 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.45580e9 | 0.629449 | ||||||||
\(147\) | − 1.21406e10i | − 2.14443i | ||||||||
\(148\) | 2.79879e8i | 0.0479504i | ||||||||
\(149\) | 6.13643e9 | 1.01995 | 0.509974 | − | 0.860190i | \(-0.329655\pi\) | ||||
0.509974 | + | 0.860190i | \(0.329655\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.83754e9 | −0.913763 | −0.456882 | − | 0.889528i | \(-0.651034\pi\) | ||||
−0.456882 | + | 0.889528i | \(0.651034\pi\) | |||||||
\(152\) | 7.38046e9i | 1.12147i | ||||||||
\(153\) | − 2.01684e9i | − 0.297550i | ||||||||
\(154\) | −7.73408e9 | −1.10807 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.84480e9 | 0.249396 | ||||||||
\(157\) | − 1.35031e9i | − 0.177371i | −0.996060 | − | 0.0886857i | \(-0.971733\pi\) | ||||
0.996060 | − | 0.0886857i | \(-0.0282667\pi\) | |||||||
\(158\) | 2.71963e9i | 0.347179i | ||||||||
\(159\) | −1.02898e10 | −1.27680 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.86796e10 | 2.19104 | ||||||||
\(162\) | − 5.77720e9i | − 0.659022i | ||||||||
\(163\) | 4.50806e9i | 0.500202i | 0.968220 | + | 0.250101i | \(0.0804638\pi\) | ||||
−0.968220 | + | 0.250101i | \(0.919536\pi\) | |||||||
\(164\) | 1.09575e8 | 0.0118281 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.15773e9 | −0.629411 | ||||||||
\(167\) | 1.81836e10i | 1.80908i | 0.426393 | + | 0.904538i | \(0.359784\pi\) | ||||
−0.426393 | + | 0.904538i | \(0.640216\pi\) | |||||||
\(168\) | − 2.52043e10i | − 2.44109i | ||||||||
\(169\) | −1.65766e10 | −1.56316 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.49289e10 | −1.33520 | ||||||||
\(172\) | 3.59991e8i | 0.0313627i | ||||||||
\(173\) | − 9.77143e9i | − 0.829375i | −0.909964 | − | 0.414687i | \(-0.863891\pi\) | ||||
0.909964 | − | 0.414687i | \(-0.136109\pi\) | |||||||
\(174\) | 1.52710e9 | 0.126298 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −8.45906e9 | −0.664531 | ||||||||
\(177\) | − 1.84522e10i | − 1.41309i | ||||||||
\(178\) | 1.20616e10i | 0.900562i | ||||||||
\(179\) | −6.65866e9 | −0.484784 | −0.242392 | − | 0.970178i | \(-0.577932\pi\) | ||||
−0.242392 | + | 0.970178i | \(0.577932\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.32873e9 | −0.507546 | −0.253773 | − | 0.967264i | \(-0.581672\pi\) | ||||
−0.253773 | + | 0.967264i | \(0.581672\pi\) | |||||||
\(182\) | 3.49785e10i | 2.36309i | ||||||||
\(183\) | 8.08432e9i | 0.532860i | ||||||||
\(184\) | 2.28306e10 | 1.46837 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.46378e9 | −0.150936 | ||||||||
\(187\) | 3.00221e9i | 0.179537i | ||||||||
\(188\) | 1.67836e9i | 0.0979887i | ||||||||
\(189\) | 1.00053e10 | 0.570364 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.06956e9 | 0.438732 | 0.219366 | − | 0.975643i | \(-0.429601\pi\) | ||||
0.219366 | + | 0.975643i | \(0.429601\pi\) | |||||||
\(192\) | − 3.05003e10i | − 1.61975i | ||||||||
\(193\) | − 3.12603e9i | − 0.162176i | −0.996707 | − | 0.0810878i | \(-0.974161\pi\) | ||||
0.996707 | − | 0.0810878i | \(-0.0258394\pi\) | |||||||
\(194\) | 1.01033e10 | 0.512100 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.07545e9 | −0.148853 | ||||||||
\(197\) | − 2.40133e10i | − 1.13594i | −0.823051 | − | 0.567968i | \(-0.807730\pi\) | ||||
0.823051 | − | 0.567968i | \(-0.192270\pi\) | |||||||
\(198\) | − 1.91207e10i | − 0.884117i | ||||||||
\(199\) | −9.73605e9 | −0.440093 | −0.220046 | − | 0.975489i | \(-0.570621\pi\) | ||||
−0.220046 | + | 0.975489i | \(0.570621\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.86077e10 | 1.23623 | ||||||||
\(202\) | − 2.69175e10i | − 1.13751i | ||||||||
\(203\) | − 3.36029e9i | − 0.138882i | ||||||||
\(204\) | −9.21546e8 | −0.0372547 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.18517e10 | 1.61924 | ||||||||
\(207\) | 4.61808e10i | 1.74822i | ||||||||
\(208\) | 3.82574e10i | 1.41720i | ||||||||
\(209\) | 2.22227e10 | 0.805637 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.39305e10 | −0.831151 | −0.415576 | − | 0.909559i | \(-0.636420\pi\) | ||||
−0.415576 | + | 0.909559i | \(0.636420\pi\) | |||||||
\(212\) | 2.60662e9i | 0.0886272i | ||||||||
\(213\) | 7.33956e10i | 2.44321i | ||||||||
\(214\) | −4.54732e10 | −1.48215 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.22287e10 | 0.382242 | ||||||||
\(217\) | 5.42141e9i | 0.165975i | ||||||||
\(218\) | 2.54589e9i | 0.0763459i | ||||||||
\(219\) | 3.39101e10 | 0.996163 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.35779e10 | 0.382885 | ||||||||
\(222\) | − 2.36643e10i | − 0.653890i | ||||||||
\(223\) | − 2.02289e10i | − 0.547773i | −0.961762 | − | 0.273886i | \(-0.911691\pi\) | ||||
0.961762 | − | 0.273886i | \(-0.0883092\pi\) | |||||||
\(224\) | −1.21681e10 | −0.322930 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.97220e10 | −1.01285 | ||||||||
\(227\) | 4.42152e10i | 1.10524i | 0.833434 | + | 0.552618i | \(0.186371\pi\) | ||||
−0.833434 | + | 0.552618i | \(0.813629\pi\) | |||||||
\(228\) | 6.82140e9i | 0.167173i | ||||||||
\(229\) | 4.89483e10 | 1.17619 | 0.588096 | − | 0.808791i | \(-0.299878\pi\) | ||||
0.588096 | + | 0.808791i | \(0.299878\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.58909e10 | −1.75362 | ||||||||
\(232\) | − 4.10702e9i | − 0.0930746i | ||||||||
\(233\) | − 6.68132e10i | − 1.48512i | −0.669781 | − | 0.742559i | \(-0.733612\pi\) | ||||
0.669781 | − | 0.742559i | \(-0.266388\pi\) | |||||||
\(234\) | −8.64761e10 | −1.88549 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.67431e9 | −0.0980876 | ||||||||
\(237\) | 2.66865e10i | 0.549444i | ||||||||
\(238\) | − 1.74731e10i | − 0.352999i | ||||||||
\(239\) | 2.21153e10 | 0.438431 | 0.219216 | − | 0.975676i | \(-0.429650\pi\) | ||||
0.219216 | + | 0.975676i | \(0.429650\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.97637e10 | 1.90500 | 0.952502 | − | 0.304532i | \(-0.0985002\pi\) | ||||
0.952502 | + | 0.304532i | \(0.0985002\pi\) | |||||||
\(242\) | − 2.20416e10i | − 0.413118i | ||||||||
\(243\) | − 7.65703e10i | − 1.40874i | ||||||||
\(244\) | 2.04792e9 | 0.0369878 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −9.26480e9 | −0.161298 | ||||||||
\(247\) | − 1.00506e11i | − 1.71812i | ||||||||
\(248\) | 6.62616e9i | 0.111232i | ||||||||
\(249\) | −6.04229e10 | −0.996104 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.97276e10 | −0.790799 | −0.395399 | − | 0.918509i | \(-0.629394\pi\) | ||||
−0.395399 | + | 0.918509i | \(0.629394\pi\) | |||||||
\(252\) | − 1.29149e10i | − 0.201738i | ||||||||
\(253\) | − 6.87435e10i | − 1.05485i | ||||||||
\(254\) | 1.15491e11 | 1.74099 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.11977e10 | −0.308467 | ||||||||
\(257\) | 5.81308e10i | 0.831204i | 0.909547 | + | 0.415602i | \(0.136429\pi\) | ||||
−0.909547 | + | 0.415602i | \(0.863571\pi\) | |||||||
\(258\) | − 3.04379e10i | − 0.427686i | ||||||||
\(259\) | −5.20718e10 | −0.719041 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.30753e9 | 0.110813 | ||||||||
\(262\) | 8.21814e10i | 1.07750i | ||||||||
\(263\) | 3.23476e10i | 0.416909i | 0.978032 | + | 0.208454i | \(0.0668433\pi\) | ||||
−0.978032 | + | 0.208454i | \(0.933157\pi\) | |||||||
\(264\) | −9.27555e10 | −1.17523 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.29338e11 | −1.58401 | ||||||||
\(267\) | 1.18354e11i | 1.42523i | ||||||||
\(268\) | − 7.24691e9i | − 0.0858116i | ||||||||
\(269\) | −6.24220e9 | −0.0726863 | −0.0363431 | − | 0.999339i | \(-0.511571\pi\) | ||||
−0.0363431 | + | 0.999339i | \(0.511571\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.05816e10 | 0.907557 | 0.453779 | − | 0.891114i | \(-0.350076\pi\) | ||||
0.453779 | + | 0.891114i | \(0.350076\pi\) | |||||||
\(272\) | − 1.91110e10i | − 0.211701i | ||||||||
\(273\) | 3.43228e11i | 3.73982i | ||||||||
\(274\) | 5.47050e10 | 0.586340 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.11012e10 | 0.218885 | ||||||||
\(277\) | − 7.07976e10i | − 0.722536i | −0.932462 | − | 0.361268i | \(-0.882344\pi\) | ||||
0.932462 | − | 0.361268i | \(-0.117656\pi\) | |||||||
\(278\) | 8.76284e10i | 0.879920i | ||||||||
\(279\) | −1.34031e10 | −0.132430 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.15619e10 | 0.780385 | 0.390193 | − | 0.920733i | \(-0.372408\pi\) | ||||
0.390193 | + | 0.920733i | \(0.372408\pi\) | |||||||
\(282\) | − 1.41909e11i | − 1.33625i | ||||||||
\(283\) | − 1.89301e11i | − 1.75434i | −0.480184 | − | 0.877168i | \(-0.659430\pi\) | ||||
0.480184 | − | 0.877168i | \(-0.340570\pi\) | |||||||
\(284\) | 1.85926e10 | 0.169593 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.28726e11 | 1.13768 | ||||||||
\(287\) | 2.03867e10i | 0.177369i | ||||||||
\(288\) | − 3.00828e10i | − 0.257663i | ||||||||
\(289\) | 1.11805e11 | 0.942805 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.91387e10 | 0.810447 | ||||||||
\(292\) | − 8.59011e9i | − 0.0691474i | ||||||||
\(293\) | 5.39489e10i | 0.427640i | 0.976873 | + | 0.213820i | \(0.0685906\pi\) | ||||
−0.976873 | + | 0.213820i | \(0.931409\pi\) | |||||||
\(294\) | 2.60035e11 | 2.02987 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.36433e10 | −0.481881 | ||||||||
\(297\) | − 3.68209e10i | − 0.274594i | ||||||||
\(298\) | 1.31434e11i | 0.965462i | ||||||||
\(299\) | −3.10903e11 | −2.24959 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.69768e10 | −0.470300 | ||||||||
\(302\) | − 1.25032e11i | − 0.864950i | ||||||||
\(303\) | − 2.64129e11i | − 1.80022i | ||||||||
\(304\) | −1.41462e11 | −0.949966 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.31980e10 | 0.281655 | ||||||||
\(307\) | − 1.30037e11i | − 0.835496i | −0.908563 | − | 0.417748i | \(-0.862819\pi\) | ||||
0.908563 | − | 0.417748i | \(-0.137181\pi\) | |||||||
\(308\) | 1.92247e10i | 0.121725i | ||||||||
\(309\) | 4.10671e11 | 2.56260 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.09580e9 | 0.0127036 | 0.00635182 | − | 0.999980i | \(-0.497978\pi\) | ||||
0.00635182 | + | 0.999980i | \(0.497978\pi\) | |||||||
\(312\) | 4.19500e11i | 2.50632i | ||||||||
\(313\) | 2.43788e11i | 1.43570i | 0.696200 | + | 0.717848i | \(0.254873\pi\) | ||||
−0.696200 | + | 0.717848i | \(0.745127\pi\) | |||||||
\(314\) | 2.89217e10 | 0.167896 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.76022e9 | 0.0381390 | ||||||||
\(317\) | − 3.46483e11i | − 1.92715i | −0.267445 | − | 0.963573i | \(-0.586179\pi\) | ||||
0.267445 | − | 0.963573i | \(-0.413821\pi\) | |||||||
\(318\) | − 2.20395e11i | − 1.20859i | ||||||||
\(319\) | −1.23664e10 | −0.0668626 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.46207e11 | −2.34565 | ||||||||
\(322\) | 4.00092e11i | 2.07400i | ||||||||
\(323\) | 5.02063e10i | 0.256653i | ||||||||
\(324\) | −1.43604e10 | −0.0723961 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.65566e10 | −0.473481 | ||||||||
\(327\) | 2.49816e10i | 0.120825i | ||||||||
\(328\) | 2.49170e10i | 0.118868i | ||||||||
\(329\) | −3.12262e11 | −1.46939 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.43303e11 | −0.656189 | −0.328094 | − | 0.944645i | \(-0.606406\pi\) | ||||
−0.328094 | + | 0.944645i | \(0.606406\pi\) | |||||||
\(332\) | 1.53063e10i | 0.0691433i | ||||||||
\(333\) | − 1.28735e11i | − 0.573718i | ||||||||
\(334\) | −3.89470e11 | −1.71244 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.83094e11 | 2.06778 | ||||||||
\(337\) | 3.34820e11i | 1.41409i | 0.707170 | + | 0.707044i | \(0.249972\pi\) | ||||
−0.707170 | + | 0.707044i | \(0.750028\pi\) | |||||||
\(338\) | − 3.55048e11i | − 1.47966i | ||||||||
\(339\) | −3.89773e11 | −1.60293 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.99515e10 | 0.0799064 | ||||||||
\(342\) | − 3.19757e11i | − 1.26387i | ||||||||
\(343\) | − 1.72469e11i | − 0.672804i | ||||||||
\(344\) | −8.18604e10 | −0.315182 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.09291e11 | 0.785070 | ||||||||
\(347\) | − 9.22101e10i | − 0.341425i | −0.985321 | − | 0.170713i | \(-0.945393\pi\) | ||||
0.985321 | − | 0.170713i | \(-0.0546070\pi\) | |||||||
\(348\) | − 3.79592e9i | − 0.0138743i | ||||||||
\(349\) | 4.71738e11 | 1.70211 | 0.851053 | − | 0.525080i | \(-0.175965\pi\) | ||||
0.851053 | + | 0.525080i | \(0.175965\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.66528e11 | −0.585606 | ||||||||
\(352\) | 4.47805e10i | 0.155470i | ||||||||
\(353\) | 4.01029e11i | 1.37464i | 0.726353 | + | 0.687322i | \(0.241214\pi\) | ||||
−0.726353 | + | 0.687322i | \(0.758786\pi\) | |||||||
\(354\) | 3.95222e11 | 1.33760 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.99816e10 | 0.0989303 | ||||||||
\(357\) | − 1.71455e11i | − 0.558654i | ||||||||
\(358\) | − 1.42620e11i | − 0.458887i | ||||||||
\(359\) | 2.36110e10 | 0.0750220 | 0.0375110 | − | 0.999296i | \(-0.488057\pi\) | ||||
0.0375110 | + | 0.999296i | \(0.488057\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.89457e10 | 0.151681 | ||||||||
\(362\) | − 1.56972e11i | − 0.480433i | ||||||||
\(363\) | − 2.16284e11i | − 0.653799i | ||||||||
\(364\) | 8.69465e10 | 0.259595 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.73155e11 | −0.504395 | ||||||||
\(367\) | 1.23035e11i | 0.354022i | 0.984209 | + | 0.177011i | \(0.0566427\pi\) | ||||
−0.984209 | + | 0.177011i | \(0.943357\pi\) | |||||||
\(368\) | 4.37596e11i | 1.24382i | ||||||||
\(369\) | −5.04012e10 | −0.141521 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.84966e11 | −1.32901 | ||||||||
\(372\) | 6.12424e9i | 0.0165809i | ||||||||
\(373\) | 2.39248e11i | 0.639968i | 0.947423 | + | 0.319984i | \(0.103678\pi\) | ||||
−0.947423 | + | 0.319984i | \(0.896322\pi\) | |||||||
\(374\) | −6.43034e10 | −0.169946 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.81653e11 | −0.984745 | ||||||||
\(377\) | 5.59287e10i | 0.142593i | ||||||||
\(378\) | 2.14300e11i | 0.539896i | ||||||||
\(379\) | 5.90629e11 | 1.47041 | 0.735205 | − | 0.677845i | \(-0.237086\pi\) | ||||
0.735205 | + | 0.677845i | \(0.237086\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.13326e12 | 2.75529 | ||||||||
\(382\) | 1.72839e11i | 0.415295i | ||||||||
\(383\) | 5.30525e10i | 0.125983i | 0.998014 | + | 0.0629914i | \(0.0200641\pi\) | ||||
−0.998014 | + | 0.0629914i | \(0.979936\pi\) | |||||||
\(384\) | 5.21087e11 | 1.22298 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.69554e10 | 0.153512 | ||||||||
\(387\) | − 1.65584e11i | − 0.375249i | ||||||||
\(388\) | − 2.51138e10i | − 0.0562562i | ||||||||
\(389\) | −3.10395e11 | −0.687293 | −0.343646 | − | 0.939099i | \(-0.611662\pi\) | ||||
−0.343646 | + | 0.939099i | \(0.611662\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.55307e11 | 0.336045 | ||||||||
\(392\) | − 6.99345e11i | − 1.49591i | ||||||||
\(393\) | 8.06407e11i | 1.70525i | ||||||||
\(394\) | 5.14333e11 | 1.07525 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4.75285e10 | −0.0971238 | ||||||||
\(397\) | − 2.09351e11i | − 0.422979i | −0.977380 | − | 0.211489i | \(-0.932169\pi\) | ||||
0.977380 | − | 0.211489i | \(-0.0678314\pi\) | |||||||
\(398\) | − 2.08533e11i | − 0.416583i | ||||||||
\(399\) | −1.26913e12 | −2.50685 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.43868e11 | 0.857244 | 0.428622 | − | 0.903484i | \(-0.358999\pi\) | ||||
0.428622 | + | 0.903484i | \(0.358999\pi\) | |||||||
\(402\) | 6.12739e11i | 1.17020i | ||||||||
\(403\) | − 9.02338e10i | − 0.170411i | ||||||||
\(404\) | −6.69092e10 | −0.124960 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.19730e10 | 0.131463 | ||||||||
\(407\) | 1.91632e11i | 0.346172i | ||||||||
\(408\) | − 2.09556e11i | − 0.374394i | ||||||||
\(409\) | −4.56031e11 | −0.805823 | −0.402912 | − | 0.915239i | \(-0.632002\pi\) | ||||
−0.402912 | + | 0.915239i | \(0.632002\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.36794e11 | 0.927940 | ||||||||
\(412\) | − 1.04031e11i | − 0.177880i | ||||||||
\(413\) | − 8.69663e11i | − 1.47087i | ||||||||
\(414\) | −9.89132e11 | −1.65483 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.02526e11 | 0.331559 | ||||||||
\(417\) | 8.59856e11i | 1.39256i | ||||||||
\(418\) | 4.75982e11i | 0.762600i | ||||||||
\(419\) | 1.12392e12 | 1.78144 | 0.890720 | − | 0.454552i | \(-0.150201\pi\) | ||||
0.890720 | + | 0.454552i | \(0.150201\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.02822e12 | −1.59521 | −0.797605 | − | 0.603180i | \(-0.793900\pi\) | ||||
−0.797605 | + | 0.603180i | \(0.793900\pi\) | |||||||
\(422\) | − 5.12559e11i | − 0.786751i | ||||||||
\(423\) | − 7.71994e11i | − 1.17242i | ||||||||
\(424\) | −5.92736e11 | −0.890666 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.57204e12 | −2.31270 | ||||||||
\(427\) | 3.81018e11i | 0.554652i | ||||||||
\(428\) | 1.13033e11i | 0.162820i | ||||||||
\(429\) | 1.26313e12 | 1.80048 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.37714e12 | −1.92234 | −0.961171 | − | 0.275953i | \(-0.911007\pi\) | ||||
−0.961171 | + | 0.275953i | \(0.911007\pi\) | |||||||
\(432\) | 2.34389e11i | 0.323787i | ||||||||
\(433\) | − 1.94790e11i | − 0.266299i | −0.991096 | − | 0.133150i | \(-0.957491\pi\) | ||||
0.991096 | − | 0.133150i | \(-0.0425091\pi\) | |||||||
\(434\) | −1.16119e11 | −0.157109 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.32835e9 | 0.00838689 | ||||||||
\(437\) | − 1.14961e12i | − 1.50793i | ||||||||
\(438\) | 7.26309e11i | 0.942948i | ||||||||
\(439\) | 5.32533e11 | 0.684315 | 0.342157 | − | 0.939643i | \(-0.388842\pi\) | ||||
0.342157 | + | 0.939643i | \(0.388842\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.41461e12 | 1.78099 | ||||||||
\(442\) | 2.90821e11i | 0.362432i | ||||||||
\(443\) | − 7.26633e11i | − 0.896393i | −0.893935 | − | 0.448196i | \(-0.852067\pi\) | ||||
0.893935 | − | 0.448196i | \(-0.147933\pi\) | |||||||
\(444\) | −5.88225e10 | −0.0718323 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.33276e11 | 0.518511 | ||||||||
\(447\) | 1.28970e12i | 1.52794i | ||||||||
\(448\) | − 1.43749e12i | − 1.68599i | ||||||||
\(449\) | −9.34830e11 | −1.08549 | −0.542743 | − | 0.839899i | \(-0.682614\pi\) | ||||
−0.542743 | + | 0.839899i | \(0.682614\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.50258e10 | 0.0853918 | ||||||||
\(452\) | 9.87374e10i | 0.111265i | ||||||||
\(453\) | − 1.22688e12i | − 1.36887i | ||||||||
\(454\) | −9.47031e11 | −1.04620 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.55116e12 | −1.68002 | ||||||||
\(457\) | − 1.09190e12i | − 1.17101i | −0.810670 | − | 0.585503i | \(-0.800897\pi\) | ||||
0.810670 | − | 0.585503i | \(-0.199103\pi\) | |||||||
\(458\) | 1.04841e12i | 1.11336i | ||||||||
\(459\) | 8.31870e10 | 0.0874779 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.93683e11 | 1.02469 | 0.512347 | − | 0.858779i | \(-0.328776\pi\) | ||||
0.512347 | + | 0.858779i | \(0.328776\pi\) | |||||||
\(462\) | − 1.62548e12i | − 1.65994i | ||||||||
\(463\) | 6.95734e11i | 0.703605i | 0.936074 | + | 0.351802i | \(0.114431\pi\) | ||||
−0.936074 | + | 0.351802i | \(0.885569\pi\) | |||||||
\(464\) | 7.87197e10 | 0.0788411 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.43105e12 | 1.40578 | ||||||||
\(467\) | 1.87957e12i | 1.82866i | 0.404975 | + | 0.914328i | \(0.367280\pi\) | ||||
−0.404975 | + | 0.914328i | \(0.632720\pi\) | |||||||
\(468\) | 2.14955e11i | 0.207129i | ||||||||
\(469\) | 1.34830e12 | 1.28679 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.83795e11 | 0.265712 | ||||||||
\(472\) | − 1.06292e12i | − 0.985739i | ||||||||
\(473\) | 2.46484e11i | 0.226419i | ||||||||
\(474\) | −5.71589e11 | −0.520093 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.34330e10 | −0.0387783 | ||||||||
\(477\) | − 1.19896e12i | − 1.06041i | ||||||||
\(478\) | 4.73679e11i | 0.415010i | ||||||||
\(479\) | 2.29011e11 | 0.198768 | 0.0993838 | − | 0.995049i | \(-0.468313\pi\) | ||||
0.0993838 | + | 0.995049i | \(0.468313\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.66683e11 | 0.738256 | ||||||||
\(482\) | 2.13681e12i | 1.80324i | ||||||||
\(483\) | 3.92591e12i | 3.28230i | ||||||||
\(484\) | −5.47890e10 | −0.0453826 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.64003e12 | 1.33349 | ||||||||
\(487\) | − 4.81410e11i | − 0.387824i | −0.981019 | − | 0.193912i | \(-0.937882\pi\) | ||||
0.981019 | − | 0.193912i | \(-0.0621177\pi\) | |||||||
\(488\) | 4.65689e11i | 0.371712i | ||||||||
\(489\) | −9.47465e11 | −0.749330 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.70320e12 | −1.32251 | −0.661257 | − | 0.750160i | \(-0.729977\pi\) | ||||
−0.661257 | + | 0.750160i | \(0.729977\pi\) | |||||||
\(492\) | 2.30296e10i | 0.0177192i | ||||||||
\(493\) | − 2.79384e10i | − 0.0213006i | ||||||||
\(494\) | 2.15270e12 | 1.62634 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.27004e11 | −0.0942217 | ||||||||
\(497\) | 3.45917e12i | 2.54313i | ||||||||
\(498\) | − 1.29418e12i | − 0.942892i | ||||||||
\(499\) | −2.06075e12 | −1.48789 | −0.743947 | − | 0.668238i | \(-0.767049\pi\) | ||||
−0.743947 | + | 0.668238i | \(0.767049\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.82168e12 | −2.71010 | ||||||||
\(502\) | − 1.06510e12i | − 0.748555i | ||||||||
\(503\) | 5.97493e11i | 0.416176i | 0.978110 | + | 0.208088i | \(0.0667240\pi\) | ||||
−0.978110 | + | 0.208088i | \(0.933276\pi\) | |||||||
\(504\) | 2.93679e12 | 2.02738 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.47239e12 | 0.998497 | ||||||||
\(507\) | − 3.48392e12i | − 2.34170i | ||||||||
\(508\) | − 2.87077e11i | − 0.191255i | ||||||||
\(509\) | 8.46938e11 | 0.559270 | 0.279635 | − | 0.960106i | \(-0.409787\pi\) | ||||
0.279635 | + | 0.960106i | \(0.409787\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.59820e12 | 1.03690 | ||||||||
\(512\) | − 1.72345e12i | − 1.10837i | ||||||||
\(513\) | − 6.15760e11i | − 0.392540i | ||||||||
\(514\) | −1.24508e12 | −0.786801 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −7.56597e10 | −0.0469830 | ||||||||
\(517\) | 1.14917e12i | 0.707418i | ||||||||
\(518\) | − 1.11531e12i | − 0.680630i | ||||||||
\(519\) | 2.05367e12 | 1.24245 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.31013e11 | 0.434666 | 0.217333 | − | 0.976098i | \(-0.430264\pi\) | ||||
0.217333 | + | 0.976098i | \(0.430264\pi\) | |||||||
\(522\) | 1.77936e11i | 0.104893i | ||||||||
\(523\) | − 1.04453e12i | − 0.610467i | −0.952278 | − | 0.305233i | \(-0.901266\pi\) | ||||
0.952278 | − | 0.305233i | \(-0.0987345\pi\) | |||||||
\(524\) | 2.04279e11 | 0.118368 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.92842e11 | −0.394638 | ||||||||
\(527\) | 4.50751e10i | 0.0254559i | ||||||||
\(528\) | − 1.77785e12i | − 0.995504i | ||||||||
\(529\) | −1.75502e12 | −0.974386 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.15003e12 | 1.17360 | ||||||||
\(532\) | 3.21496e11i | 0.174010i | ||||||||
\(533\) | − 3.39315e11i | − 0.182109i | ||||||||
\(534\) | −2.53500e12 | −1.34909 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.64792e12 | 0.862371 | ||||||||
\(537\) | − 1.39946e12i | − 0.726233i | ||||||||
\(538\) | − 1.33700e11i | − 0.0688034i | ||||||||
\(539\) | −2.10575e12 | −1.07462 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.88034e12 | −0.943733 | −0.471866 | − | 0.881670i | \(-0.656420\pi\) | ||||
−0.471866 | + | 0.881670i | \(0.656420\pi\) | |||||||
\(542\) | 1.72595e12i | 0.859076i | ||||||||
\(543\) | − 1.54029e12i | − 0.760331i | ||||||||
\(544\) | −1.01169e11 | −0.0495284 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −7.35148e12 | −3.54004 | ||||||||
\(547\) | − 1.08624e12i | − 0.518780i | −0.965773 | − | 0.259390i | \(-0.916479\pi\) | ||||
0.965773 | − | 0.259390i | \(-0.0835215\pi\) | |||||||
\(548\) | − 1.35981e11i | − 0.0644117i | ||||||||
\(549\) | −9.41977e11 | −0.442553 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.06804e11 | −0.0955821 | ||||||||
\(552\) | 4.79834e12i | 2.19971i | ||||||||
\(553\) | 1.25775e12i | 0.571914i | ||||||||
\(554\) | 1.51639e12 | 0.683938 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.17819e11 | 0.0966626 | ||||||||
\(557\) | 2.11965e12i | 0.933072i | 0.884502 | + | 0.466536i | \(0.154498\pi\) | ||||
−0.884502 | + | 0.466536i | \(0.845502\pi\) | |||||||
\(558\) | − 2.87078e11i | − 0.125356i | ||||||||
\(559\) | 1.11476e12 | 0.482868 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.30978e11 | −0.268956 | ||||||||
\(562\) | 1.74695e12i | 0.738697i | ||||||||
\(563\) | − 3.04489e12i | − 1.27727i | −0.769509 | − | 0.638636i | \(-0.779499\pi\) | ||||
0.769509 | − | 0.638636i | \(-0.220501\pi\) | |||||||
\(564\) | −3.52744e11 | −0.146792 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.05456e12 | 1.66062 | ||||||||
\(567\) | − 2.67178e12i | − 1.08562i | ||||||||
\(568\) | 4.22788e12i | 1.70433i | ||||||||
\(569\) | −3.25275e12 | −1.30090 | −0.650452 | − | 0.759548i | \(-0.725420\pi\) | ||||
−0.650452 | + | 0.759548i | \(0.725420\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.35916e12 | −0.535066 | −0.267533 | − | 0.963549i | \(-0.586208\pi\) | ||||
−0.267533 | + | 0.963549i | \(0.586208\pi\) | |||||||
\(572\) | − 3.19975e11i | − 0.124978i | ||||||||
\(573\) | 1.69599e12i | 0.657245i | ||||||||
\(574\) | −4.36655e11 | −0.167894 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.55386e12 | 1.34524 | ||||||||
\(577\) | − 2.35782e12i | − 0.885564i | −0.896629 | − | 0.442782i | \(-0.853992\pi\) | ||||
0.896629 | − | 0.442782i | \(-0.146008\pi\) | |||||||
\(578\) | 2.39472e12i | 0.892440i | ||||||||
\(579\) | 6.57002e11 | 0.242948 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.84777e12 | −1.03684 | ||||||||
\(582\) | 2.12342e12i | 0.767154i | ||||||||
\(583\) | 1.78474e12i | 0.639834i | ||||||||
\(584\) | 1.95336e12 | 0.694902 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.15551e12 | −0.404796 | ||||||||
\(587\) | − 2.37065e12i | − 0.824130i | −0.911154 | − | 0.412065i | \(-0.864808\pi\) | ||||
0.911154 | − | 0.412065i | \(-0.135192\pi\) | |||||||
\(588\) | − 6.46371e11i | − 0.222989i | ||||||||
\(589\) | 3.33652e11 | 0.114229 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.04690e12 | 1.70169 | ||||||||
\(592\) | − 1.21986e12i | − 0.408189i | ||||||||
\(593\) | − 4.56707e12i | − 1.51667i | −0.651864 | − | 0.758336i | \(-0.726013\pi\) | ||||
0.651864 | − | 0.758336i | \(-0.273987\pi\) | |||||||
\(594\) | 7.88655e11 | 0.259925 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.26707e11 | 0.106060 | ||||||||
\(597\) | − 2.04624e12i | − 0.659283i | ||||||||
\(598\) | − 6.65912e12i | − 2.12942i | ||||||||
\(599\) | 5.30493e12 | 1.68368 | 0.841839 | − | 0.539729i | \(-0.181473\pi\) | ||||
0.841839 | + | 0.539729i | \(0.181473\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.71307e12 | −0.848255 | −0.424128 | − | 0.905602i | \(-0.639419\pi\) | ||||
−0.424128 | + | 0.905602i | \(0.639419\pi\) | |||||||
\(602\) | − 1.43455e12i | − 0.445177i | ||||||||
\(603\) | 3.33335e12i | 1.02672i | ||||||||
\(604\) | −3.10794e11 | −0.0950182 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.65730e12 | 1.70405 | ||||||||
\(607\) | − 4.00734e12i | − 1.19814i | −0.800698 | − | 0.599069i | \(-0.795538\pi\) | ||||
0.800698 | − | 0.599069i | \(-0.204462\pi\) | |||||||
\(608\) | 7.48868e11i | 0.222249i | ||||||||
\(609\) | 7.06237e11 | 0.208052 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.19728e12 | 1.50866 | ||||||||
\(612\) | − 1.07378e11i | − 0.0309409i | ||||||||
\(613\) | 2.24954e12i | 0.643459i | 0.946832 | + | 0.321730i | \(0.104264\pi\) | ||||
−0.946832 | + | 0.321730i | \(0.895736\pi\) | |||||||
\(614\) | 2.78522e12 | 0.790864 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.37162e12 | −1.22329 | ||||||||
\(617\) | 1.19664e12i | 0.332414i | 0.986091 | + | 0.166207i | \(0.0531519\pi\) | ||||
−0.986091 | + | 0.166207i | \(0.946848\pi\) | |||||||
\(618\) | 8.79602e12i | 2.42571i | ||||||||
\(619\) | 4.36723e12 | 1.19563 | 0.597817 | − | 0.801633i | \(-0.296035\pi\) | ||||
0.597817 | + | 0.801633i | \(0.296035\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.90478e12 | −0.513965 | ||||||||
\(622\) | 4.48893e10i | 0.0120250i | ||||||||
\(623\) | 5.57811e12i | 1.48351i | ||||||||
\(624\) | −8.04060e12 | −2.12304 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −5.22161e12 | −1.35900 | ||||||||
\(627\) | 4.67058e12i | 1.20689i | ||||||||
\(628\) | − 7.18911e10i | − 0.0184441i | ||||||||
\(629\) | −4.32940e11 | −0.110281 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.78790e12 | 0.700077 | 0.350039 | − | 0.936735i | \(-0.386168\pi\) | ||||
0.350039 | + | 0.936735i | \(0.386168\pi\) | |||||||
\(632\) | 1.53725e12i | 0.383281i | ||||||||
\(633\) | − 5.02950e12i | − 1.24511i | ||||||||
\(634\) | 7.42120e12 | 1.82420 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −5.47837e11 | −0.132768 | ||||||||
\(637\) | 9.52355e12i | 2.29177i | ||||||||
\(638\) | − 2.64871e11i | − 0.0632909i | ||||||||
\(639\) | −8.55199e12 | −2.02915 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.28295e12 | −0.534115 | −0.267058 | − | 0.963681i | \(-0.586051\pi\) | ||||
−0.267058 | + | 0.963681i | \(0.586051\pi\) | |||||||
\(642\) | − 9.55716e12i | − 2.22035i | ||||||||
\(643\) | 2.29995e12i | 0.530603i | 0.964166 | + | 0.265301i | \(0.0854715\pi\) | ||||
−0.964166 | + | 0.265301i | \(0.914529\pi\) | |||||||
\(644\) | 9.94512e11 | 0.227837 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.07535e12 | −0.242943 | ||||||||
\(647\) | 1.85647e12i | 0.416503i | 0.978075 | + | 0.208251i | \(0.0667772\pi\) | ||||
−0.978075 | + | 0.208251i | \(0.933223\pi\) | |||||||
\(648\) | − 3.26551e12i | − 0.727550i | ||||||||
\(649\) | −3.20048e12 | −0.708132 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.13942e12 | −0.248640 | ||||||||
\(652\) | 2.40012e11i | 0.0520138i | ||||||||
\(653\) | − 7.75397e12i | − 1.66884i | −0.551129 | − | 0.834420i | \(-0.685803\pi\) | ||||
0.551129 | − | 0.834420i | \(-0.314197\pi\) | |||||||
\(654\) | −5.35073e11 | −0.114370 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.77587e11 | −0.100690 | ||||||||
\(657\) | 3.95117e12i | 0.827336i | ||||||||
\(658\) | − 6.68824e12i | − 1.39090i | ||||||||
\(659\) | −7.42166e12 | −1.53291 | −0.766455 | − | 0.642298i | \(-0.777981\pi\) | ||||
−0.766455 | + | 0.642298i | \(0.777981\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.79783e12 | 1.18130 | 0.590648 | − | 0.806929i | \(-0.298872\pi\) | ||||
0.590648 | + | 0.806929i | \(0.298872\pi\) | |||||||
\(662\) | − 3.06936e12i | − 0.621135i | ||||||||
\(663\) | 2.85369e12i | 0.573583i | ||||||||
\(664\) | −3.48060e12 | −0.694861 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.75734e12 | 0.543070 | ||||||||
\(667\) | 6.39724e11i | 0.125149i | ||||||||
\(668\) | 9.68108e11i | 0.188118i | ||||||||
\(669\) | 4.25153e12 | 0.820593 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.40220e12 | 0.267029 | ||||||||
\(672\) | − 2.55739e12i | − 0.483766i | ||||||||
\(673\) | 6.32456e12i | 1.18840i | 0.804318 | + | 0.594200i | \(0.202531\pi\) | ||||
−0.804318 | + | 0.594200i | \(0.797469\pi\) | |||||||
\(674\) | −7.17139e12 | −1.33855 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.82546e11 | −0.162546 | ||||||||
\(677\) | − 4.95066e12i | − 0.905762i | −0.891571 | − | 0.452881i | \(-0.850396\pi\) | ||||
0.891571 | − | 0.452881i | \(-0.149604\pi\) | |||||||
\(678\) | − 8.34843e12i | − 1.51730i | ||||||||
\(679\) | 4.67246e12 | 0.843591 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.29277e12 | −1.65571 | ||||||||
\(682\) | 4.27336e11i | 0.0756379i | ||||||||
\(683\) | − 7.32611e12i | − 1.28819i | −0.764945 | − | 0.644095i | \(-0.777234\pi\) | ||||
0.764945 | − | 0.644095i | \(-0.222766\pi\) | |||||||
\(684\) | −7.94824e11 | −0.138841 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.69406e12 | 0.636863 | ||||||||
\(687\) | 1.02875e13i | 1.76200i | ||||||||
\(688\) | − 1.56903e12i | − 0.266982i | ||||||||
\(689\) | 8.07176e12 | 1.36453 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.66806e12 | −0.945765 | −0.472882 | − | 0.881126i | \(-0.656786\pi\) | ||||
−0.472882 | + | 0.881126i | \(0.656786\pi\) | |||||||
\(692\) | − 5.20237e11i | − 0.0862430i | ||||||||
\(693\) | − 8.84274e12i | − 1.45642i | ||||||||
\(694\) | 1.97502e12 | 0.323187 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.63178e11 | 0.139431 | ||||||||
\(697\) | 1.69501e11i | 0.0272034i | ||||||||
\(698\) | 1.01040e13i | 1.61118i | ||||||||
\(699\) | 1.40422e13 | 2.22479 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.20985e12 | −0.658470 | −0.329235 | − | 0.944248i | \(-0.606791\pi\) | ||||
−0.329235 | + | 0.944248i | \(0.606791\pi\) | |||||||
\(702\) | − 3.56681e12i | − 0.554323i | ||||||||
\(703\) | 3.20468e12i | 0.494863i | ||||||||
\(704\) | −5.29018e12 | −0.811696 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.58952e12 | −1.30121 | ||||||||
\(707\) | − 1.24486e13i | − 1.87384i | ||||||||
\(708\) | − 9.82407e11i | − 0.146941i | ||||||||
\(709\) | −1.19654e13 | −1.77835 | −0.889176 | − | 0.457566i | \(-0.848721\pi\) | ||||
−0.889176 | + | 0.457566i | \(0.848721\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.10949e12 | −0.456326 | ||||||||
\(712\) | 6.81769e12i | 0.994208i | ||||||||
\(713\) | − 1.03211e12i | − 0.149563i | ||||||||
\(714\) | 3.67234e12 | 0.528811 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.54511e11 | −0.0504105 | ||||||||
\(717\) | 4.64799e12i | 0.656794i | ||||||||
\(718\) | 5.05715e11i | 0.0710143i | ||||||||
\(719\) | 4.07118e11 | 0.0568120 | 0.0284060 | − | 0.999596i | \(-0.490957\pi\) | ||||
0.0284060 | + | 0.999596i | \(0.490957\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.93551e13 | 2.66740 | ||||||||
\(722\) | 1.04835e12i | 0.143579i | ||||||||
\(723\) | 2.09675e13i | 2.85380i | ||||||||
\(724\) | −3.90186e11 | −0.0527774 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.63251e12 | 0.618873 | ||||||||
\(727\) | 6.44424e12i | 0.855592i | 0.903875 | + | 0.427796i | \(0.140710\pi\) | ||||
−0.903875 | + | 0.427796i | \(0.859290\pi\) | |||||||
\(728\) | 1.97713e13i | 2.60882i | ||||||||
\(729\) | 1.07838e13 | 1.41416 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.56864e11 | −0.0721308 | ||||||||
\(732\) | 4.30414e11i | 0.0554098i | ||||||||
\(733\) | − 5.46122e12i | − 0.698749i | −0.936983 | − | 0.349375i | \(-0.886394\pi\) | ||||
0.936983 | − | 0.349375i | \(-0.113606\pi\) | |||||||
\(734\) | −2.63524e12 | −0.335110 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.31654e12 | 0.290998 | ||||||||
\(737\) | − 4.96192e12i | − 0.619507i | ||||||||
\(738\) | − 1.07953e12i | − 0.133961i | ||||||||
\(739\) | 1.88201e12 | 0.232125 | 0.116062 | − | 0.993242i | \(-0.462973\pi\) | ||||
0.116062 | + | 0.993242i | \(0.462973\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.11234e13 | 2.57384 | ||||||||
\(742\) | − 1.03873e13i | − 1.25802i | ||||||||
\(743\) | − 1.36704e13i | − 1.64563i | −0.568312 | − | 0.822813i | \(-0.692403\pi\) | ||||
0.568312 | − | 0.822813i | \(-0.307597\pi\) | |||||||
\(744\) | −1.39263e12 | −0.166632 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −5.12437e12 | −0.605781 | ||||||||
\(747\) | − 7.04042e12i | − 0.827287i | ||||||||
\(748\) | 1.59840e11i | 0.0186693i | ||||||||
\(749\) | −2.10300e13 | −2.44158 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.52585e12 | 0.978043 | 0.489021 | − | 0.872272i | \(-0.337354\pi\) | ||||
0.489021 | + | 0.872272i | \(0.337354\pi\) | |||||||
\(752\) | − 7.31518e12i | − 0.834152i | ||||||||
\(753\) | − 1.04513e13i | − 1.18466i | ||||||||
\(754\) | −1.19792e12 | −0.134976 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.32688e11 | 0.0593096 | ||||||||
\(757\) | − 7.50792e12i | − 0.830975i | −0.909599 | − | 0.415487i | \(-0.863611\pi\) | ||||
0.909599 | − | 0.415487i | \(-0.136389\pi\) | |||||||
\(758\) | 1.26505e13i | 1.39186i | ||||||||
\(759\) | 1.44479e13 | 1.58022 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.61560e13 | −1.74624 | −0.873118 | − | 0.487509i | \(-0.837906\pi\) | ||||
−0.873118 | + | 0.487509i | \(0.837906\pi\) | |||||||
\(762\) | 2.42729e13i | 2.60810i | ||||||||
\(763\) | 1.17740e12i | 0.125766i | ||||||||
\(764\) | 4.29628e11 | 0.0456218 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.13631e12 | −0.119253 | ||||||||
\(767\) | 1.44747e13i | 1.51018i | ||||||||
\(768\) | − 4.45514e12i | − 0.462100i | ||||||||
\(769\) | −1.11830e12 | −0.115317 | −0.0576583 | − | 0.998336i | \(-0.518363\pi\) | ||||
−0.0576583 | + | 0.998336i | \(0.518363\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.22174e13 | −1.24519 | ||||||||
\(772\) | − 1.66432e11i | − 0.0168639i | ||||||||
\(773\) | 1.73165e13i | 1.74442i | 0.489129 | + | 0.872212i | \(0.337315\pi\) | ||||
−0.489129 | + | 0.872212i | \(0.662685\pi\) | |||||||
\(774\) | 3.54659e12 | 0.355203 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5.71078e12 | 0.565351 | ||||||||
\(777\) | − 1.09440e13i | − 1.07716i | ||||||||
\(778\) | − 6.64825e12i | − 0.650578i | ||||||||
\(779\) | 1.25466e12 | 0.122070 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.27302e13 | 1.22435 | ||||||||
\(782\) | 3.32648e12i | 0.318093i | ||||||||
\(783\) | 3.42654e11i | 0.0325783i | ||||||||
\(784\) | 1.34044e13 | 1.26714 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.72722e13 | −1.61416 | ||||||||
\(787\) | − 3.88515e11i | − 0.0361012i | −0.999837 | − | 0.0180506i | \(-0.994254\pi\) | ||||
0.999837 | − | 0.0180506i | \(-0.00574599\pi\) | |||||||
\(788\) | − 1.27848e12i | − 0.118121i | ||||||||
\(789\) | −6.79853e12 | −0.624552 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.83702e13 | −1.66848 | ||||||||
\(792\) | − 1.08078e13i | − 0.976053i | ||||||||
\(793\) | − 6.34166e12i | − 0.569474i | ||||||||
\(794\) | 4.48403e12 | 0.400383 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.18353e11 | −0.0457633 | ||||||||
\(797\) | − 1.08432e12i | − 0.0951910i | −0.998867 | − | 0.0475955i | \(-0.984844\pi\) | ||||
0.998867 | − | 0.0475955i | \(-0.0151558\pi\) | |||||||
\(798\) | − 2.71831e13i | − 2.37294i | ||||||||
\(799\) | −2.59624e12 | −0.225363 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.37906e13 | −1.18368 | ||||||||
\(802\) | 9.50706e12i | 0.811450i | ||||||||
\(803\) | − 5.88161e12i | − 0.499202i | ||||||||
\(804\) | 1.52309e12 | 0.128551 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.93269e12 | 0.161307 | ||||||||
\(807\) | − 1.31193e12i | − 0.108888i | ||||||||
\(808\) | − 1.52149e13i | − 1.25579i | ||||||||
\(809\) | −4.06803e12 | −0.333900 | −0.166950 | − | 0.985965i | \(-0.553392\pi\) | ||||
−0.166950 | + | 0.985965i | \(0.553392\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.87468e12 | 0.395688 | 0.197844 | − | 0.980234i | \(-0.436606\pi\) | ||||
0.197844 | + | 0.980234i | \(0.436606\pi\) | |||||||
\(812\) | − 1.78904e11i | − 0.0144417i | ||||||||
\(813\) | 1.69359e13i | 1.35957i | ||||||||
\(814\) | −4.10449e12 | −0.327680 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.01658e12 | 0.317140 | ||||||||
\(817\) | 4.12198e12i | 0.323673i | ||||||||
\(818\) | − 9.76758e12i | − 0.762777i | ||||||||
\(819\) | −3.99926e13 | −3.10600 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.03829e12 | −0.0797582 | −0.0398791 | − | 0.999205i | \(-0.512697\pi\) | ||||
−0.0398791 | + | 0.999205i | \(0.512697\pi\) | |||||||
\(822\) | 1.14974e13i | 0.878370i | ||||||||
\(823\) | − 1.10923e13i | − 0.842794i | −0.906876 | − | 0.421397i | \(-0.861540\pi\) | ||||
0.906876 | − | 0.421397i | \(-0.138460\pi\) | |||||||
\(824\) | 2.36563e13 | 1.78761 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.86270e13 | 1.39230 | ||||||||
\(827\) | − 1.45526e13i | − 1.08184i | −0.841073 | − | 0.540922i | \(-0.818075\pi\) | ||||
0.841073 | − | 0.540922i | \(-0.181925\pi\) | |||||||
\(828\) | 2.45870e12i | 0.181789i | ||||||||
\(829\) | −1.37985e13 | −1.01470 | −0.507348 | − | 0.861741i | \(-0.669374\pi\) | ||||
−0.507348 | + | 0.861741i | \(0.669374\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.48796e13 | 1.08240 | ||||||||
\(832\) | 2.39256e13i | 1.73104i | ||||||||
\(833\) | − 4.75736e12i | − 0.342345i | ||||||||
\(834\) | −1.84170e13 | −1.31817 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.18315e12 | 0.0837746 | ||||||||
\(837\) | − 5.52829e11i | − 0.0389337i | ||||||||
\(838\) | 2.40728e13i | 1.68628i | ||||||||
\(839\) | −9.20234e11 | −0.0641165 | −0.0320582 | − | 0.999486i | \(-0.510206\pi\) | ||||
−0.0320582 | + | 0.999486i | \(0.510206\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.43921e13 | −0.992067 | ||||||||
\(842\) | − 2.20232e13i | − 1.50999i | ||||||||
\(843\) | 1.71420e13i | 1.16906i | ||||||||
\(844\) | −1.27407e12 | −0.0864277 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.65351e13 | 1.10979 | ||||||||
\(847\) | − 1.01936e13i | − 0.680536i | ||||||||
\(848\) | − 1.13610e13i | − 0.754460i | ||||||||
\(849\) | 3.97855e13 | 2.62809 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.91330e12 | 0.647941 | ||||||||
\(852\) | 3.90762e12i | 0.254059i | ||||||||
\(853\) | 7.46964e12i | 0.483091i | 0.970390 | + | 0.241545i | \(0.0776543\pi\) | ||||
−0.970390 | + | 0.241545i | \(0.922346\pi\) | |||||||
\(854\) | −8.16090e12 | −0.525022 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.57033e13 | −1.63628 | ||||||||
\(857\) | 2.05568e13i | 1.30179i | 0.759166 | + | 0.650897i | \(0.225607\pi\) | ||||
−0.759166 | + | 0.650897i | \(0.774393\pi\) | |||||||
\(858\) | 2.70545e13i | 1.70430i | ||||||||
\(859\) | 1.05923e12 | 0.0663775 | 0.0331888 | − | 0.999449i | \(-0.489434\pi\) | ||||
0.0331888 | + | 0.999449i | \(0.489434\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.28469e12 | −0.265709 | ||||||||
\(862\) | − 2.94965e13i | − 1.81965i | ||||||||
\(863\) | − 1.53023e13i | − 0.939092i | −0.882908 | − | 0.469546i | \(-0.844418\pi\) | ||||
0.882908 | − | 0.469546i | \(-0.155582\pi\) | |||||||
\(864\) | 1.24080e12 | 0.0757514 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.17213e12 | 0.252074 | ||||||||
\(867\) | 2.34982e13i | 1.41237i | ||||||||
\(868\) | 2.88639e11i | 0.0172590i | ||||||||
\(869\) | 4.62869e12 | 0.275340 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.24410e13 | −1.32118 | ||||||||
\(872\) | 1.43904e12i | 0.0842847i | ||||||||
\(873\) | 1.15516e13i | 0.673095i | ||||||||
\(874\) | 2.46230e13 | 1.42738 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.80539e12 | 0.103587 | ||||||||
\(877\) | − 1.74558e11i | − 0.00996416i | −0.999988 | − | 0.00498208i | \(-0.998414\pi\) | ||||
0.999988 | − | 0.00498208i | \(-0.00158585\pi\) | |||||||
\(878\) | 1.14061e13i | 0.647759i | ||||||||
\(879\) | −1.13385e13 | −0.640629 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.59039e12 | 0.480420 | 0.240210 | − | 0.970721i | \(-0.422784\pi\) | ||||
0.240210 | + | 0.970721i | \(0.422784\pi\) | |||||||
\(882\) | 3.02990e13i | 1.68585i | ||||||||
\(883\) | 1.70227e13i | 0.942336i | 0.882043 | + | 0.471168i | \(0.156167\pi\) | ||||
−0.882043 | + | 0.471168i | \(0.843833\pi\) | |||||||
\(884\) | 7.22898e11 | 0.0398145 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.55635e13 | 0.848508 | ||||||||
\(887\) | − 2.01246e13i | − 1.09162i | −0.837909 | − | 0.545810i | \(-0.816222\pi\) | ||||
0.837909 | − | 0.545810i | \(-0.183778\pi\) | |||||||
\(888\) | − 1.33760e13i | − 0.721885i | ||||||||
\(889\) | 5.34112e13 | 2.86797 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.83253e12 | −0.522655 | ||||||||
\(892\) | − 1.07700e12i | − 0.0569604i | ||||||||
\(893\) | 1.92177e13i | 1.01127i | ||||||||
\(894\) | −2.76237e13 | −1.44632 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.45591e13 | 1.27299 | ||||||||
\(897\) | − 6.53428e13i | − 3.37002i | ||||||||
\(898\) | − 2.00228e13i | − 1.02750i | ||||||||
\(899\) | −1.85668e11 | −0.00948023 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.03214e12 | −0.203833 | ||||||||
\(902\) | 1.60695e12i | 0.0808302i | ||||||||
\(903\) | − 1.40766e13i | − 0.704535i | ||||||||
\(904\) | −2.24525e13 | −1.11817 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.62782e13 | 1.29574 | ||||||||
\(907\) | − 2.10130e13i | − 1.03099i | −0.856893 | − | 0.515495i | \(-0.827608\pi\) | ||||
0.856893 | − | 0.515495i | \(-0.172392\pi\) | |||||||
\(908\) | 2.35404e12i | 0.114929i | ||||||||
\(909\) | 3.07761e13 | 1.49512 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.95345e12 | 0.0939656 | 0.0469828 | − | 0.998896i | \(-0.485039\pi\) | ||||
0.0469828 | + | 0.998896i | \(0.485039\pi\) | |||||||
\(912\) | − 2.97312e13i | − 1.42310i | ||||||||
\(913\) | 1.04802e13i | 0.499172i | ||||||||
\(914\) | 2.33870e13 | 1.10845 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.60604e12 | 0.122307 | ||||||||
\(917\) | 3.80064e13i | 1.77499i | ||||||||
\(918\) | 1.78175e12i | 0.0828048i | ||||||||
\(919\) | 2.47656e12 | 0.114533 | 0.0572663 | − | 0.998359i | \(-0.481762\pi\) | ||||
0.0572663 | + | 0.998359i | \(0.481762\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.73301e13 | 1.25162 | ||||||||
\(922\) | 2.12834e13i | 0.969954i | ||||||||
\(923\) | − 5.75744e13i | − 2.61109i | ||||||||
\(924\) | −4.04048e12 | −0.182351 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.49017e13 | −0.666018 | ||||||||
\(927\) | 4.78510e13i | 2.12830i | ||||||||
\(928\) | − 4.16725e11i | − 0.0184452i | ||||||||
\(929\) | −4.40844e13 | −1.94184 | −0.970922 | − | 0.239395i | \(-0.923051\pi\) | ||||
−0.970922 | + | 0.239395i | \(0.923051\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.52146e13 | −1.53621 | ||||||||
\(932\) | − 3.55718e12i | − 0.154431i | ||||||||
\(933\) | 4.40477e11i | 0.0190308i | ||||||||
\(934\) | −4.02578e13 | −1.73097 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.88798e13 | −2.08156 | ||||||||
\(937\) | 4.92250e12i | 0.208621i | 0.994545 | + | 0.104310i | \(0.0332635\pi\) | ||||
−0.994545 | + | 0.104310i | \(0.966736\pi\) | |||||||
\(938\) | 2.88787e13i | 1.21805i | ||||||||
\(939\) | −5.12372e13 | −2.15075 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.54680e13 | −0.643103 | −0.321552 | − | 0.946892i | \(-0.604204\pi\) | ||||
−0.321552 | + | 0.946892i | \(0.604204\pi\) | |||||||
\(942\) | 6.07852e12i | 0.251518i | ||||||||
\(943\) | − 3.88116e12i | − 0.159830i | ||||||||
\(944\) | 2.03731e13 | 0.834993 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.27936e12 | −0.214324 | ||||||||
\(947\) | 5.49107e12i | 0.221862i | 0.993828 | + | 0.110931i | \(0.0353832\pi\) | ||||
−0.993828 | + | 0.110931i | \(0.964617\pi\) | |||||||
\(948\) | 1.42080e12i | 0.0571343i | ||||||||
\(949\) | −2.66004e13 | −1.06461 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.28207e13 | 2.88697 | ||||||||
\(952\) | − 9.87649e12i | − 0.389705i | ||||||||
\(953\) | 1.76932e13i | 0.694845i | 0.937709 | + | 0.347422i | \(0.112943\pi\) | ||||
−0.937709 | + | 0.347422i | \(0.887057\pi\) | |||||||
\(954\) | 2.56802e13 | 1.00376 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.17743e12 | 0.0455905 | ||||||||
\(957\) | − 2.59905e12i | − 0.100164i | ||||||||
\(958\) | 4.90510e12i | 0.188150i | ||||||||
\(959\) | 2.52994e13 | 0.965888 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.61401e13 | −0.988670 | ||||||||
\(962\) | 1.85632e13i | 0.698819i | ||||||||
\(963\) | − 5.19916e13i | − 1.94812i | ||||||||
\(964\) | 5.31148e12 | 0.198093 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −8.40878e13 | −3.10696 | ||||||||
\(967\) | 2.89231e13i | 1.06372i | 0.846834 | + | 0.531858i | \(0.178506\pi\) | ||||
−0.846834 | + | 0.531858i | \(0.821494\pi\) | |||||||
\(968\) | − 1.24588e13i | − 0.456076i | ||||||||
\(969\) | −1.05519e13 | −0.384481 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.69482e13 | 0.972843 | 0.486422 | − | 0.873724i | \(-0.338302\pi\) | ||||
0.486422 | + | 0.873724i | \(0.338302\pi\) | |||||||
\(972\) | − 4.07665e12i | − 0.146489i | ||||||||
\(973\) | 4.05255e13i | 1.44951i | ||||||||
\(974\) | 1.03112e13 | 0.367107 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.92590e12 | −0.314867 | ||||||||
\(977\) | 3.90598e13i | 1.37153i | 0.727824 | + | 0.685764i | \(0.240532\pi\) | ||||
−0.727824 | + | 0.685764i | \(0.759468\pi\) | |||||||
\(978\) | − 2.02934e13i | − 0.709301i | ||||||||
\(979\) | 2.05282e13 | 0.714216 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.91084e12 | −0.100348 | ||||||||
\(982\) | − 3.64804e13i | − 1.25187i | ||||||||
\(983\) | − 9.03830e12i | − 0.308742i | −0.988013 | − | 0.154371i | \(-0.950665\pi\) | ||||
0.988013 | − | 0.154371i | \(-0.0493351\pi\) | |||||||
\(984\) | −5.23684e12 | −0.178070 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.98404e11 | 0.0201627 | ||||||||
\(987\) | − 6.56285e13i | − 2.20123i | ||||||||
\(988\) | − 5.35098e12i | − 0.178660i | ||||||||
\(989\) | 1.27509e13 | 0.423795 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.89096e13 | 1.61088 | 0.805439 | − | 0.592678i | \(-0.201929\pi\) | ||||
0.805439 | + | 0.592678i | \(0.201929\pi\) | |||||||
\(992\) | 6.72333e11i | 0.0220436i | ||||||||
\(993\) | − 3.01181e13i | − 0.983007i | ||||||||
\(994\) | −7.40909e13 | −2.40728 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.21695e12 | −0.103580 | ||||||||
\(997\) | 4.01445e13i | 1.28676i | 0.765547 | + | 0.643380i | \(0.222468\pi\) | ||||
−0.765547 | + | 0.643380i | \(0.777532\pi\) | |||||||
\(998\) | − 4.41384e13i | − 1.40841i | ||||||||
\(999\) | 5.30984e12 | 0.168670 |
(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 | 25.10.b.c.24.5 | 6 | ||
3.2 | odd | 2 | 225.10.b.m.199.2 | 6 | |||
4.3 | odd | 2 | 400.10.c.q.49.2 | 6 | |||
5.2 | odd | 4 | 25.10.a.c.1.2 | ✓ | 3 | ||
5.3 | odd | 4 | 25.10.a.d.1.2 | yes | 3 | ||
5.4 | even | 2 | inner | 25.10.b.c.24.2 | 6 | ||
15.2 | even | 4 | 225.10.a.p.1.2 | 3 | |||
15.8 | even | 4 | 225.10.a.m.1.2 | 3 | |||
15.14 | odd | 2 | 225.10.b.m.199.5 | 6 | |||
20.3 | even | 4 | 400.10.a.u.1.3 | 3 | |||
20.7 | even | 4 | 400.10.a.y.1.1 | 3 | |||
20.19 | odd | 2 | 400.10.c.q.49.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.10.a.c.1.2 | ✓ | 3 | 5.2 | odd | 4 | ||
25.10.a.d.1.2 | yes | 3 | 5.3 | odd | 4 | ||
25.10.b.c.24.2 | 6 | 5.4 | even | 2 | inner | ||
25.10.b.c.24.5 | 6 | 1.1 | even | 1 | trivial | ||
225.10.a.m.1.2 | 3 | 15.8 | even | 4 | |||
225.10.a.p.1.2 | 3 | 15.2 | even | 4 | |||
225.10.b.m.199.2 | 6 | 3.2 | odd | 2 | |||
225.10.b.m.199.5 | 6 | 15.14 | odd | 2 | |||
400.10.a.u.1.3 | 3 | 20.3 | even | 4 | |||
400.10.a.y.1.1 | 3 | 20.7 | even | 4 | |||
400.10.c.q.49.2 | 6 | 4.3 | odd | 2 | |||
400.10.c.q.49.5 | 6 | 20.19 | odd | 2 |