Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [350,10,Mod(99,350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(350, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("350.99");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.c (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: | \(180.262542657\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{2305})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1153x^{2} + 331776 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.2 | ||
Root | \(24.5052i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.99 |
Dual form | 350.10.c.j.99.3 |
$q$-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 \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 16.0000i | − 0.707107i | ||||||||
\(3\) | 247.052i | 1.76093i | 0.474108 | + | 0.880467i | \(0.342771\pi\) | ||||
−0.474108 | + | 0.880467i | \(0.657229\pi\) | |||||||
\(4\) | −256.000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3952.83 | 1.24517 | ||||||||
\(7\) | 2401.00i | 0.377964i | ||||||||
\(8\) | 4096.00i | 0.353553i | ||||||||
\(9\) | −41351.7 | −2.10089 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −27940.9 | −0.575405 | −0.287703 | − | 0.957720i | \(-0.592891\pi\) | ||||
−0.287703 | + | 0.957720i | \(0.592891\pi\) | |||||||
\(12\) | − 63245.3i | − 0.880467i | ||||||||
\(13\) | − 60943.3i | − 0.591808i | −0.955218 | − | 0.295904i | \(-0.904379\pi\) | ||||
0.955218 | − | 0.295904i | \(-0.0956209\pi\) | |||||||
\(14\) | 38416.0 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 65536.0 | 0.250000 | ||||||||
\(17\) | − 358867.i | − 1.04211i | −0.853523 | − | 0.521055i | \(-0.825538\pi\) | ||||
0.853523 | − | 0.521055i | \(-0.174462\pi\) | |||||||
\(18\) | 661628.i | 1.48555i | ||||||||
\(19\) | 391593. | 0.689356 | 0.344678 | − | 0.938721i | \(-0.387988\pi\) | ||||
0.344678 | + | 0.938721i | \(0.387988\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −593172. | −0.665570 | ||||||||
\(22\) | 447055.i | 0.406873i | ||||||||
\(23\) | 302894.i | 0.225692i | 0.993612 | + | 0.112846i | \(0.0359967\pi\) | ||||
−0.993612 | + | 0.112846i | \(0.964003\pi\) | |||||||
\(24\) | −1.01193e6 | −0.622584 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −975093. | −0.418472 | ||||||||
\(27\) | − 5.35330e6i | − 1.93859i | ||||||||
\(28\) | − 614656.i | − 0.188982i | ||||||||
\(29\) | −6.73993e6 | −1.76956 | −0.884778 | − | 0.466013i | \(-0.845690\pi\) | ||||
−0.884778 | + | 0.466013i | \(0.845690\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.98262e6 | 0.580056 | 0.290028 | − | 0.957018i | \(-0.406335\pi\) | ||||
0.290028 | + | 0.957018i | \(0.406335\pi\) | |||||||
\(32\) | − 1.04858e6i | − 0.176777i | ||||||||
\(33\) | − 6.90287e6i | − 1.01325i | ||||||||
\(34\) | −5.74188e6 | −0.736884 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.05860e7 | 1.05044 | ||||||||
\(37\) | − 3.49582e6i | − 0.306649i | −0.988176 | − | 0.153324i | \(-0.951002\pi\) | ||||
0.988176 | − | 0.153324i | \(-0.0489979\pi\) | |||||||
\(38\) | − 6.26549e6i | − 0.487449i | ||||||||
\(39\) | 1.50562e7 | 1.04214 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.43724e7 | 1.89969 | 0.949845 | − | 0.312722i | \(-0.101241\pi\) | ||||
0.949845 | + | 0.312722i | \(0.101241\pi\) | |||||||
\(42\) | 9.49075e6i | 0.470629i | ||||||||
\(43\) | 1.45085e7i | 0.647164i | 0.946200 | + | 0.323582i | \(0.104887\pi\) | ||||
−0.946200 | + | 0.323582i | \(0.895113\pi\) | |||||||
\(44\) | 7.15288e6 | 0.287703 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.84631e6 | 0.159588 | ||||||||
\(47\) | − 2.76485e7i | − 0.826479i | −0.910622 | − | 0.413239i | \(-0.864397\pi\) | ||||
0.910622 | − | 0.413239i | \(-0.135603\pi\) | |||||||
\(48\) | 1.61908e7i | 0.440233i | ||||||||
\(49\) | −5.76480e6 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.86589e7 | 1.83509 | ||||||||
\(52\) | 1.56015e7i | 0.295904i | ||||||||
\(53\) | 2.39217e7i | 0.416438i | 0.978082 | + | 0.208219i | \(0.0667666\pi\) | ||||
−0.978082 | + | 0.208219i | \(0.933233\pi\) | |||||||
\(54\) | −8.56529e7 | −1.37079 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −9.83450e6 | −0.133631 | ||||||||
\(57\) | 9.67439e7i | 1.21391i | ||||||||
\(58\) | 1.07839e8i | 1.25127i | ||||||||
\(59\) | 1.20580e8 | 1.29551 | 0.647756 | − | 0.761848i | \(-0.275707\pi\) | ||||
0.647756 | + | 0.761848i | \(0.275707\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.23140e7 | 0.668710 | 0.334355 | − | 0.942447i | \(-0.391482\pi\) | ||||
0.334355 | + | 0.942447i | \(0.391482\pi\) | |||||||
\(62\) | − 4.77219e7i | − 0.410161i | ||||||||
\(63\) | − 9.92855e7i | − 0.794060i | ||||||||
\(64\) | −1.67772e7 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.10446e8 | −0.716476 | ||||||||
\(67\) | 8.70377e7i | 0.527680i | 0.964566 | + | 0.263840i | \(0.0849891\pi\) | ||||
−0.964566 | + | 0.263840i | \(0.915011\pi\) | |||||||
\(68\) | 9.18701e7i | 0.521055i | ||||||||
\(69\) | −7.48307e7 | −0.397428 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.19622e8 | 1.02568 | 0.512842 | − | 0.858483i | \(-0.328593\pi\) | ||||
0.512842 | + | 0.858483i | \(0.328593\pi\) | |||||||
\(72\) | − 1.69377e8i | − 0.742775i | ||||||||
\(73\) | − 2.67792e8i | − 1.10368i | −0.833949 | − | 0.551841i | \(-0.813926\pi\) | ||||
0.833949 | − | 0.551841i | \(-0.186074\pi\) | |||||||
\(74\) | −5.59331e7 | −0.216833 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00248e8 | −0.344678 | ||||||||
\(77\) | − 6.70862e7i | − 0.217483i | ||||||||
\(78\) | − 2.40899e8i | − 0.736901i | ||||||||
\(79\) | −2.85350e7 | −0.0824243 | −0.0412122 | − | 0.999150i | \(-0.513122\pi\) | ||||
−0.0412122 | + | 0.999150i | \(0.513122\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.08619e8 | 1.31283 | ||||||||
\(82\) | − 5.49959e8i | − 1.34328i | ||||||||
\(83\) | 3.83237e8i | 0.886372i | 0.896430 | + | 0.443186i | \(0.146152\pi\) | ||||
−0.896430 | + | 0.443186i | \(0.853848\pi\) | |||||||
\(84\) | 1.51852e8 | 0.332785 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.32136e8 | 0.457614 | ||||||||
\(87\) | − 1.66511e9i | − 3.11607i | ||||||||
\(88\) | − 1.14446e8i | − 0.203437i | ||||||||
\(89\) | −7.21581e8 | −1.21907 | −0.609537 | − | 0.792757i | \(-0.708645\pi\) | ||||
−0.609537 | + | 0.792757i | \(0.708645\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.46325e8 | 0.223683 | ||||||||
\(92\) | − 7.75410e7i | − 0.112846i | ||||||||
\(93\) | 7.36861e8i | 1.02144i | ||||||||
\(94\) | −4.42377e8 | −0.584409 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.59053e8 | 0.311292 | ||||||||
\(97\) | − 6.73736e8i | − 0.772710i | −0.922350 | − | 0.386355i | \(-0.873734\pi\) | ||||
0.922350 | − | 0.386355i | \(-0.126266\pi\) | |||||||
\(98\) | 9.22368e7i | 0.101015i | ||||||||
\(99\) | 1.15541e9 | 1.20886 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.04805e7 | −0.0100216 | −0.00501081 | − | 0.999987i | \(-0.501595\pi\) | ||||
−0.00501081 | + | 0.999987i | \(0.501595\pi\) | |||||||
\(102\) | − 1.41854e9i | − 1.29760i | ||||||||
\(103\) | − 1.39782e9i | − 1.22373i | −0.790963 | − | 0.611864i | \(-0.790420\pi\) | ||||
0.790963 | − | 0.611864i | \(-0.209580\pi\) | |||||||
\(104\) | 2.49624e8 | 0.209236 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.82747e8 | 0.294466 | ||||||||
\(107\) | − 4.84414e8i | − 0.357264i | −0.983916 | − | 0.178632i | \(-0.942833\pi\) | ||||
0.983916 | − | 0.178632i | \(-0.0571672\pi\) | |||||||
\(108\) | 1.37045e9i | 0.969293i | ||||||||
\(109\) | 1.96298e8 | 0.133198 | 0.0665989 | − | 0.997780i | \(-0.478785\pi\) | ||||
0.0665989 | + | 0.997780i | \(0.478785\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.63649e8 | 0.539988 | ||||||||
\(112\) | 1.57352e8i | 0.0944911i | ||||||||
\(113\) | 5.80849e8i | 0.335128i | 0.985861 | + | 0.167564i | \(0.0535901\pi\) | ||||
−0.985861 | + | 0.167564i | \(0.946410\pi\) | |||||||
\(114\) | 1.54790e9 | 0.858364 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.72542e9 | 0.884778 | ||||||||
\(117\) | 2.52011e9i | 1.24332i | ||||||||
\(118\) | − 1.92928e9i | − 0.916066i | ||||||||
\(119\) | 8.61641e8 | 0.393881 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.57725e9 | −0.668909 | ||||||||
\(122\) | − 1.15702e9i | − 0.472850i | ||||||||
\(123\) | 8.49178e9i | 3.34523i | ||||||||
\(124\) | −7.63550e8 | −0.290028 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.58857e9 | −0.561485 | ||||||||
\(127\) | 2.59088e9i | 0.883751i | 0.897076 | + | 0.441876i | \(0.145687\pi\) | ||||
−0.897076 | + | 0.441876i | \(0.854313\pi\) | |||||||
\(128\) | 2.68435e8i | 0.0883883i | ||||||||
\(129\) | −3.58436e9 | −1.13961 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.45598e9 | 0.728626 | 0.364313 | − | 0.931277i | \(-0.381304\pi\) | ||||
0.364313 | + | 0.931277i | \(0.381304\pi\) | |||||||
\(132\) | 1.76713e9i | 0.506625i | ||||||||
\(133\) | 9.40215e8i | 0.260552i | ||||||||
\(134\) | 1.39260e9 | 0.373126 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.46992e9 | 0.368442 | ||||||||
\(137\) | 6.08364e9i | 1.47544i | 0.675108 | + | 0.737719i | \(0.264097\pi\) | ||||
−0.675108 | + | 0.737719i | \(0.735903\pi\) | |||||||
\(138\) | 1.19729e9i | 0.281024i | ||||||||
\(139\) | −2.25249e9 | −0.511796 | −0.255898 | − | 0.966704i | \(-0.582371\pi\) | ||||
−0.255898 | + | 0.966704i | \(0.582371\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.83063e9 | 1.45537 | ||||||||
\(142\) | − 3.51395e9i | − 0.725268i | ||||||||
\(143\) | 1.70281e9i | 0.340530i | ||||||||
\(144\) | −2.71003e9 | −0.525221 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.28466e9 | −0.780421 | ||||||||
\(147\) | − 1.42421e9i | − 0.251562i | ||||||||
\(148\) | 8.94930e8i | 0.153324i | ||||||||
\(149\) | 3.13517e9 | 0.521103 | 0.260551 | − | 0.965460i | \(-0.416096\pi\) | ||||
0.260551 | + | 0.965460i | \(0.416096\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.20938e9 | −0.971969 | −0.485984 | − | 0.873968i | \(-0.661539\pi\) | ||||
−0.485984 | + | 0.873968i | \(0.661539\pi\) | |||||||
\(152\) | 1.60397e9i | 0.243724i | ||||||||
\(153\) | 1.48398e10i | 2.18936i | ||||||||
\(154\) | −1.07338e9 | −0.153784 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.85438e9 | −0.521068 | ||||||||
\(157\) | 1.33378e10i | 1.75201i | 0.482300 | + | 0.876006i | \(0.339802\pi\) | ||||
−0.482300 | + | 0.876006i | \(0.660198\pi\) | |||||||
\(158\) | 4.56560e8i | 0.0582828i | ||||||||
\(159\) | −5.90990e9 | −0.733319 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.27249e8 | −0.0853035 | ||||||||
\(162\) | − 8.13790e9i | − 0.928314i | ||||||||
\(163\) | − 7.33621e9i | − 0.814006i | −0.913427 | − | 0.407003i | \(-0.866574\pi\) | ||||
0.913427 | − | 0.407003i | \(-0.133426\pi\) | |||||||
\(164\) | −8.79934e9 | −0.949845 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.13179e9 | 0.626760 | ||||||||
\(167\) | − 6.42205e9i | − 0.638925i | −0.947599 | − | 0.319462i | \(-0.896498\pi\) | ||||
0.947599 | − | 0.319462i | \(-0.103502\pi\) | |||||||
\(168\) | − 2.42963e9i | − 0.235315i | ||||||||
\(169\) | 6.89041e9 | 0.649763 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.61931e10 | −1.44826 | ||||||||
\(172\) | − 3.71418e9i | − 0.323582i | ||||||||
\(173\) | − 1.91846e10i | − 1.62834i | −0.580626 | − | 0.814171i | \(-0.697192\pi\) | ||||
0.580626 | − | 0.814171i | \(-0.302808\pi\) | |||||||
\(174\) | −2.66418e10 | −2.20339 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.83114e9 | −0.143851 | ||||||||
\(177\) | 2.97896e10i | 2.28131i | ||||||||
\(178\) | 1.15453e10i | 0.862016i | ||||||||
\(179\) | −1.53377e10 | −1.11666 | −0.558330 | − | 0.829619i | \(-0.688558\pi\) | ||||
−0.558330 | + | 0.829619i | \(0.688558\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.73475e10 | −1.20139 | −0.600694 | − | 0.799479i | \(-0.705109\pi\) | ||||
−0.600694 | + | 0.799479i | \(0.705109\pi\) | |||||||
\(182\) | − 2.34120e9i | − 0.158167i | ||||||||
\(183\) | 1.78653e10i | 1.17755i | ||||||||
\(184\) | −1.24066e9 | −0.0797941 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.17898e10 | 0.722267 | ||||||||
\(187\) | 1.00271e10i | 0.599636i | ||||||||
\(188\) | 7.07802e9i | 0.413239i | ||||||||
\(189\) | 1.28533e10 | 0.732717 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.70138e10 | 1.46871 | 0.734355 | − | 0.678765i | \(-0.237485\pi\) | ||||
0.734355 | + | 0.678765i | \(0.237485\pi\) | |||||||
\(192\) | − 4.14485e9i | − 0.220117i | ||||||||
\(193\) | − 2.70232e9i | − 0.140194i | −0.997540 | − | 0.0700970i | \(-0.977669\pi\) | ||||
0.997540 | − | 0.0700970i | \(-0.0223309\pi\) | |||||||
\(194\) | −1.07798e10 | −0.546389 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.47579e9 | 0.0714286 | ||||||||
\(197\) | 2.39047e10i | 1.13080i | 0.824818 | + | 0.565399i | \(0.191278\pi\) | ||||
−0.824818 | + | 0.565399i | \(0.808722\pi\) | |||||||
\(198\) | − 1.84865e10i | − 0.854794i | ||||||||
\(199\) | 2.16111e9 | 0.0976872 | 0.0488436 | − | 0.998806i | \(-0.484446\pi\) | ||||
0.0488436 | + | 0.998806i | \(0.484446\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.15028e10 | −0.929209 | ||||||||
\(202\) | 1.67689e8i | 0.00708635i | ||||||||
\(203\) | − 1.61826e10i | − 0.668829i | ||||||||
\(204\) | −2.26967e10 | −0.917544 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.23652e10 | −0.865306 | ||||||||
\(207\) | − 1.25252e10i | − 0.474153i | ||||||||
\(208\) | − 3.99398e9i | − 0.147952i | ||||||||
\(209\) | −1.09415e10 | −0.396659 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.61055e9 | 0.125401 | 0.0627007 | − | 0.998032i | \(-0.480029\pi\) | ||||
0.0627007 | + | 0.998032i | \(0.480029\pi\) | |||||||
\(212\) | − 6.12395e9i | − 0.208219i | ||||||||
\(213\) | 5.42581e10i | 1.80616i | ||||||||
\(214\) | −7.75062e9 | −0.252624 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.19271e10 | 0.685394 | ||||||||
\(217\) | 7.16126e9i | 0.219240i | ||||||||
\(218\) | − 3.14077e9i | − 0.0941851i | ||||||||
\(219\) | 6.61585e10 | 1.94351 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.18706e10 | −0.616730 | ||||||||
\(222\) | − 1.38184e10i | − 0.381829i | ||||||||
\(223\) | 7.13001e10i | 1.93072i | 0.260929 | + | 0.965358i | \(0.415971\pi\) | ||||
−0.260929 | + | 0.965358i | \(0.584029\pi\) | |||||||
\(224\) | 2.51763e9 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.29359e9 | 0.236971 | ||||||||
\(227\) | 7.15361e10i | 1.78817i | 0.447896 | + | 0.894086i | \(0.352173\pi\) | ||||
−0.447896 | + | 0.894086i | \(0.647827\pi\) | |||||||
\(228\) | − 2.47664e10i | − 0.606955i | ||||||||
\(229\) | 3.56020e10 | 0.855491 | 0.427745 | − | 0.903899i | \(-0.359308\pi\) | ||||
0.427745 | + | 0.903899i | \(0.359308\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.65738e10 | 0.382973 | ||||||||
\(232\) | − 2.76067e10i | − 0.625633i | ||||||||
\(233\) | 3.80069e10i | 0.844814i | 0.906406 | + | 0.422407i | \(0.138815\pi\) | ||||
−0.906406 | + | 0.422407i | \(0.861185\pi\) | |||||||
\(234\) | 4.03218e10 | 0.879161 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.08685e10 | −0.647756 | ||||||||
\(237\) | − 7.04962e9i | − 0.145144i | ||||||||
\(238\) | − 1.37863e10i | − 0.278516i | ||||||||
\(239\) | 8.67126e10 | 1.71906 | 0.859531 | − | 0.511083i | \(-0.170756\pi\) | ||||
0.859531 | + | 0.511083i | \(0.170756\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.18418e9 | −0.156278 | −0.0781391 | − | 0.996942i | \(-0.524898\pi\) | ||||
−0.0781391 | + | 0.996942i | \(0.524898\pi\) | |||||||
\(242\) | 2.52360e10i | 0.472990i | ||||||||
\(243\) | 2.02863e10i | 0.373228i | ||||||||
\(244\) | −1.85124e10 | −0.334355 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.35868e11 | 2.36543 | ||||||||
\(247\) | − 2.38650e10i | − 0.407967i | ||||||||
\(248\) | 1.22168e10i | 0.205081i | ||||||||
\(249\) | −9.46795e10 | −1.56084 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.75467e10 | 1.55125 | 0.775624 | − | 0.631196i | \(-0.217435\pi\) | ||||
0.775624 | + | 0.631196i | \(0.217435\pi\) | |||||||
\(252\) | 2.54171e10i | 0.397030i | ||||||||
\(253\) | − 8.46315e9i | − 0.129864i | ||||||||
\(254\) | 4.14540e10 | 0.624907 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.29497e9 | 0.0625000 | ||||||||
\(257\) | − 4.43042e9i | − 0.0633499i | −0.999498 | − | 0.0316750i | \(-0.989916\pi\) | ||||
0.999498 | − | 0.0316750i | \(-0.0100841\pi\) | |||||||
\(258\) | 5.73497e10i | 0.805828i | ||||||||
\(259\) | 8.39346e9 | 0.115902 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.78708e11 | 3.71763 | ||||||||
\(262\) | − 3.92957e10i | − 0.515216i | ||||||||
\(263\) | 1.20620e11i | 1.55460i | 0.629129 | + | 0.777301i | \(0.283412\pi\) | ||||
−0.629129 | + | 0.777301i | \(0.716588\pi\) | |||||||
\(264\) | 2.82741e10 | 0.358238 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.50434e10 | 0.184238 | ||||||||
\(267\) | − 1.78268e11i | − 2.14671i | ||||||||
\(268\) | − 2.22816e10i | − 0.263840i | ||||||||
\(269\) | −7.59025e10 | −0.883835 | −0.441917 | − | 0.897056i | \(-0.645702\pi\) | ||||
−0.441917 | + | 0.897056i | \(0.645702\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.11397e10 | 0.801217 | 0.400608 | − | 0.916249i | \(-0.368799\pi\) | ||||
0.400608 | + | 0.916249i | \(0.368799\pi\) | |||||||
\(272\) | − 2.35187e10i | − 0.260528i | ||||||||
\(273\) | 3.61499e10i | 0.393890i | ||||||||
\(274\) | 9.73382e10 | 1.04329 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.91567e10 | 0.198714 | ||||||||
\(277\) | 8.61542e10i | 0.879261i | 0.898179 | + | 0.439630i | \(0.144891\pi\) | ||||
−0.898179 | + | 0.439630i | \(0.855109\pi\) | |||||||
\(278\) | 3.60399e10i | 0.361894i | ||||||||
\(279\) | −1.23336e11 | −1.21863 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.00179e11 | −0.958511 | −0.479256 | − | 0.877675i | \(-0.659093\pi\) | ||||
−0.479256 | + | 0.877675i | \(0.659093\pi\) | |||||||
\(282\) | − 1.09290e11i | − 1.02910i | ||||||||
\(283\) | 4.57444e10i | 0.423935i | 0.977277 | + | 0.211967i | \(0.0679871\pi\) | ||||
−0.977277 | + | 0.211967i | \(0.932013\pi\) | |||||||
\(284\) | −5.62233e10 | −0.512842 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.72450e10 | 0.240791 | ||||||||
\(287\) | 8.25282e10i | 0.718015i | ||||||||
\(288\) | 4.33604e10i | 0.371388i | ||||||||
\(289\) | −1.01980e10 | −0.0859950 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.66448e11 | 1.36069 | ||||||||
\(292\) | 6.85546e10i | 0.551841i | ||||||||
\(293\) | 1.01615e10i | 0.0805476i | 0.999189 | + | 0.0402738i | \(0.0128230\pi\) | ||||
−0.999189 | + | 0.0402738i | \(0.987177\pi\) | |||||||
\(294\) | −2.27873e10 | −0.177881 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.43189e10 | 0.108417 | ||||||||
\(297\) | 1.49576e11i | 1.11547i | ||||||||
\(298\) | − 5.01628e10i | − 0.368475i | ||||||||
\(299\) | 1.84594e10 | 0.133566 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.48349e10 | −0.244605 | ||||||||
\(302\) | 9.93501e10i | 0.687286i | ||||||||
\(303\) | − 2.58924e9i | − 0.0176474i | ||||||||
\(304\) | 2.56634e10 | 0.172339 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.37437e11 | 1.54811 | ||||||||
\(307\) | − 3.68957e10i | − 0.237057i | −0.992951 | − | 0.118529i | \(-0.962182\pi\) | ||||
0.992951 | − | 0.118529i | \(-0.0378178\pi\) | |||||||
\(308\) | 1.71741e10i | 0.108741i | ||||||||
\(309\) | 3.45335e11 | 2.15490 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.88558e11 | 1.14294 | 0.571469 | − | 0.820624i | \(-0.306374\pi\) | ||||
0.571469 | + | 0.820624i | \(0.306374\pi\) | |||||||
\(312\) | 6.16701e10i | 0.368450i | ||||||||
\(313\) | − 1.31778e11i | − 0.776058i | −0.921647 | − | 0.388029i | \(-0.873156\pi\) | ||||
0.921647 | − | 0.388029i | \(-0.126844\pi\) | |||||||
\(314\) | 2.13405e11 | 1.23886 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.30495e9 | 0.0412122 | ||||||||
\(317\) | − 1.50686e11i | − 0.838118i | −0.907959 | − | 0.419059i | \(-0.862360\pi\) | ||||
0.907959 | − | 0.419059i | \(-0.137640\pi\) | |||||||
\(318\) | 9.45584e10i | 0.518535i | ||||||||
\(319\) | 1.88320e11 | 1.01821 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.19675e11 | 0.629118 | ||||||||
\(322\) | 1.16360e10i | 0.0603187i | ||||||||
\(323\) | − 1.40530e11i | − 0.718386i | ||||||||
\(324\) | −1.30206e11 | −0.656417 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.17379e11 | −0.575589 | ||||||||
\(327\) | 4.84959e10i | 0.234552i | ||||||||
\(328\) | 1.40789e11i | 0.671642i | ||||||||
\(329\) | 6.63841e10 | 0.312380 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.38877e10 | 0.155173 | 0.0775865 | − | 0.996986i | \(-0.475279\pi\) | ||||
0.0775865 | + | 0.996986i | \(0.475279\pi\) | |||||||
\(332\) | − 9.81087e10i | − 0.443186i | ||||||||
\(333\) | 1.44558e11i | 0.644234i | ||||||||
\(334\) | −1.02753e11 | −0.451788 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.88741e10 | −0.166393 | ||||||||
\(337\) | 1.98312e11i | 0.837555i | 0.908089 | + | 0.418778i | \(0.137541\pi\) | ||||
−0.908089 | + | 0.418778i | \(0.862459\pi\) | |||||||
\(338\) | − 1.10247e11i | − 0.459452i | ||||||||
\(339\) | −1.43500e11 | −0.590138 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.33371e10 | −0.333767 | ||||||||
\(342\) | 2.59089e11i | 1.02407i | ||||||||
\(343\) | − 1.38413e10i | − 0.0539949i | ||||||||
\(344\) | −5.94268e10 | −0.228807 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.06954e11 | −1.15141 | ||||||||
\(347\) | − 1.71762e11i | − 0.635981i | −0.948094 | − | 0.317990i | \(-0.896992\pi\) | ||||
0.948094 | − | 0.317990i | \(-0.103008\pi\) | |||||||
\(348\) | 4.26269e11i | 1.55803i | ||||||||
\(349\) | 1.88189e11 | 0.679014 | 0.339507 | − | 0.940603i | \(-0.389740\pi\) | ||||
0.339507 | + | 0.940603i | \(0.389740\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.26248e11 | −1.14727 | ||||||||
\(352\) | 2.92982e10i | 0.101718i | ||||||||
\(353\) | − 1.97995e11i | − 0.678686i | −0.940663 | − | 0.339343i | \(-0.889795\pi\) | ||||
0.940663 | − | 0.339343i | \(-0.110205\pi\) | |||||||
\(354\) | 4.76633e11 | 1.61313 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.84725e11 | 0.609537 | ||||||||
\(357\) | 2.12870e11i | 0.693598i | ||||||||
\(358\) | 2.45403e11i | 0.789598i | ||||||||
\(359\) | −4.34669e11 | −1.38113 | −0.690563 | − | 0.723272i | \(-0.742637\pi\) | ||||
−0.690563 | + | 0.723272i | \(0.742637\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.69343e11 | −0.524788 | ||||||||
\(362\) | 2.77560e11i | 0.849510i | ||||||||
\(363\) | − 3.89663e11i | − 1.17790i | ||||||||
\(364\) | −3.74592e10 | −0.111841 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.85845e11 | 0.832657 | ||||||||
\(367\) | 6.02066e10i | 0.173240i | 0.996241 | + | 0.0866198i | \(0.0276065\pi\) | ||||
−0.996241 | + | 0.0866198i | \(0.972393\pi\) | |||||||
\(368\) | 1.98505e10i | 0.0564230i | ||||||||
\(369\) | −1.42136e12 | −3.99103 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.74359e10 | −0.157399 | ||||||||
\(372\) | − 1.88637e11i | − 0.510720i | ||||||||
\(373\) | 6.85521e11i | 1.83371i | 0.399219 | + | 0.916855i | \(0.369281\pi\) | ||||
−0.399219 | + | 0.916855i | \(0.630719\pi\) | |||||||
\(374\) | 1.60433e11 | 0.424007 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.13248e11 | 0.292204 | ||||||||
\(377\) | 4.10754e11i | 1.04724i | ||||||||
\(378\) | − 2.05653e11i | − 0.518109i | ||||||||
\(379\) | −5.05522e11 | −1.25853 | −0.629266 | − | 0.777190i | \(-0.716644\pi\) | ||||
−0.629266 | + | 0.777190i | \(0.716644\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.40082e11 | −1.55623 | ||||||||
\(382\) | − 4.32221e11i | − 1.03854i | ||||||||
\(383\) | − 2.02054e11i | − 0.479814i | −0.970796 | − | 0.239907i | \(-0.922883\pi\) | ||||
0.970796 | − | 0.239907i | \(-0.0771170\pi\) | |||||||
\(384\) | −6.63175e10 | −0.155646 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.32371e10 | −0.0991321 | ||||||||
\(387\) | − 5.99952e11i | − 1.35962i | ||||||||
\(388\) | 1.72476e11i | 0.386355i | ||||||||
\(389\) | −5.51954e11 | −1.22216 | −0.611082 | − | 0.791567i | \(-0.709265\pi\) | ||||
−0.611082 | + | 0.791567i | \(0.709265\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.08699e11 | 0.235196 | ||||||||
\(392\) | − 2.36126e10i | − 0.0505076i | ||||||||
\(393\) | 6.06756e11i | 1.28306i | ||||||||
\(394\) | 3.82475e11 | 0.799595 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.95784e11 | −0.604430 | ||||||||
\(397\) | 1.26816e11i | 0.256222i | 0.991760 | + | 0.128111i | \(0.0408914\pi\) | ||||
−0.991760 | + | 0.128111i | \(0.959109\pi\) | |||||||
\(398\) | − 3.45777e10i | − 0.0690753i | ||||||||
\(399\) | −2.32282e11 | −0.458815 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.86957e11 | 1.13359 | 0.566795 | − | 0.823859i | \(-0.308183\pi\) | ||||
0.566795 | + | 0.823859i | \(0.308183\pi\) | |||||||
\(402\) | 3.44045e11i | 0.657050i | ||||||||
\(403\) | − 1.81771e11i | − 0.343282i | ||||||||
\(404\) | 2.68302e9 | 0.00501081 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.58921e11 | −0.472934 | ||||||||
\(407\) | 9.76764e10i | 0.176447i | ||||||||
\(408\) | 3.63147e11i | 0.648801i | ||||||||
\(409\) | 9.08262e10 | 0.160493 | 0.0802465 | − | 0.996775i | \(-0.474429\pi\) | ||||
0.0802465 | + | 0.996775i | \(0.474429\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.50298e12 | −2.59815 | ||||||||
\(412\) | 3.57843e11i | 0.611864i | ||||||||
\(413\) | 2.89513e11i | 0.489658i | ||||||||
\(414\) | −2.00403e11 | −0.335277 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.39037e10 | −0.104618 | ||||||||
\(417\) | − 5.56483e11i | − 0.901238i | ||||||||
\(418\) | 1.75064e11i | 0.280481i | ||||||||
\(419\) | 8.34669e11 | 1.32297 | 0.661487 | − | 0.749957i | \(-0.269926\pi\) | ||||
0.661487 | + | 0.749957i | \(0.269926\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.61360e10 | −0.0250337 | −0.0125169 | − | 0.999922i | \(-0.503984\pi\) | ||||
−0.0125169 | + | 0.999922i | \(0.503984\pi\) | |||||||
\(422\) | − 5.77688e10i | − 0.0886722i | ||||||||
\(423\) | 1.14331e12i | 1.73634i | ||||||||
\(424\) | −9.79832e10 | −0.147233 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.68130e11 | 1.27715 | ||||||||
\(427\) | 1.73626e11i | 0.252749i | ||||||||
\(428\) | 1.24010e11i | 0.178632i | ||||||||
\(429\) | −4.20684e11 | −0.599650 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.81935e11 | −0.672730 | −0.336365 | − | 0.941732i | \(-0.609198\pi\) | ||||
−0.336365 | + | 0.941732i | \(0.609198\pi\) | |||||||
\(432\) | − 3.50834e11i | − 0.484646i | ||||||||
\(433\) | − 6.68314e11i | − 0.913661i | −0.889554 | − | 0.456830i | \(-0.848985\pi\) | ||||
0.889554 | − | 0.456830i | \(-0.151015\pi\) | |||||||
\(434\) | 1.14580e11 | 0.155026 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.02523e10 | −0.0665989 | ||||||||
\(437\) | 1.18611e11i | 0.155582i | ||||||||
\(438\) | − 1.05854e12i | − 1.37427i | ||||||||
\(439\) | 4.79819e11 | 0.616577 | 0.308288 | − | 0.951293i | \(-0.400244\pi\) | ||||
0.308288 | + | 0.951293i | \(0.400244\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.38384e11 | 0.300126 | ||||||||
\(442\) | 3.49929e11i | 0.436094i | ||||||||
\(443\) | 6.53598e11i | 0.806295i | 0.915135 | + | 0.403148i | \(0.132084\pi\) | ||||
−0.915135 | + | 0.403148i | \(0.867916\pi\) | |||||||
\(444\) | −2.21094e11 | −0.269994 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.14080e12 | 1.36522 | ||||||||
\(447\) | 7.74551e11i | 0.917627i | ||||||||
\(448\) | − 4.02821e10i | − 0.0472456i | ||||||||
\(449\) | 1.88660e11 | 0.219064 | 0.109532 | − | 0.993983i | \(-0.465065\pi\) | ||||
0.109532 | + | 0.993983i | \(0.465065\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.60397e11 | −1.09309 | ||||||||
\(452\) | − 1.48697e11i | − 0.167564i | ||||||||
\(453\) | − 1.53404e12i | − 1.71157i | ||||||||
\(454\) | 1.14458e12 | 1.26443 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.96263e11 | −0.429182 | ||||||||
\(457\) | 1.31205e12i | 1.40711i | 0.710639 | + | 0.703556i | \(0.248406\pi\) | ||||
−0.710639 | + | 0.703556i | \(0.751594\pi\) | |||||||
\(458\) | − 5.69633e11i | − 0.604923i | ||||||||
\(459\) | −1.92113e12 | −2.02022 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.16594e12 | 1.20233 | 0.601165 | − | 0.799125i | \(-0.294703\pi\) | ||||
0.601165 | + | 0.799125i | \(0.294703\pi\) | |||||||
\(462\) | − 2.65181e11i | − 0.270803i | ||||||||
\(463\) | 3.87318e10i | 0.0391700i | 0.999808 | + | 0.0195850i | \(0.00623449\pi\) | ||||
−0.999808 | + | 0.0195850i | \(0.993766\pi\) | |||||||
\(464\) | −4.41708e11 | −0.442389 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.08111e11 | 0.597374 | ||||||||
\(467\) | 1.17150e11i | 0.113977i | 0.998375 | + | 0.0569883i | \(0.0181498\pi\) | ||||
−0.998375 | + | 0.0569883i | \(0.981850\pi\) | |||||||
\(468\) | − 6.45149e11i | − 0.621661i | ||||||||
\(469\) | −2.08977e11 | −0.199444 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.29514e12 | −3.08518 | ||||||||
\(472\) | 4.93896e11i | 0.458033i | ||||||||
\(473\) | − 4.05381e11i | − 0.372382i | ||||||||
\(474\) | −1.12794e11 | −0.102632 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.20580e11 | −0.196940 | ||||||||
\(477\) | − 9.89203e11i | − 0.874888i | ||||||||
\(478\) | − 1.38740e12i | − 1.21556i | ||||||||
\(479\) | 1.94734e12 | 1.69018 | 0.845089 | − | 0.534626i | \(-0.179548\pi\) | ||||
0.845089 | + | 0.534626i | \(0.179548\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.13047e11 | −0.181477 | ||||||||
\(482\) | 1.30947e11i | 0.110505i | ||||||||
\(483\) | − 1.79668e11i | − 0.150214i | ||||||||
\(484\) | 4.03776e11 | 0.334454 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 3.24580e11 | 0.263912 | ||||||||
\(487\) | − 1.95983e12i | − 1.57884i | −0.613852 | − | 0.789421i | \(-0.710381\pi\) | ||||
0.613852 | − | 0.789421i | \(-0.289619\pi\) | |||||||
\(488\) | 2.96198e11i | 0.236425i | ||||||||
\(489\) | 1.81243e12 | 1.43341 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.93589e11 | −0.227967 | −0.113984 | − | 0.993483i | \(-0.536361\pi\) | ||||
−0.113984 | + | 0.993483i | \(0.536361\pi\) | |||||||
\(492\) | − 2.17389e12i | − 1.67261i | ||||||||
\(493\) | 2.41874e12i | 1.84407i | ||||||||
\(494\) | −3.81840e11 | −0.288476 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.95469e11 | 0.145014 | ||||||||
\(497\) | 5.27313e11i | 0.387672i | ||||||||
\(498\) | 1.51487e12i | 1.10368i | ||||||||
\(499\) | −1.71390e12 | −1.23746 | −0.618732 | − | 0.785602i | \(-0.712353\pi\) | ||||
−0.618732 | + | 0.785602i | \(0.712353\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.58658e12 | 1.12510 | ||||||||
\(502\) | − 1.56075e12i | − 1.09690i | ||||||||
\(503\) | − 1.61385e12i | − 1.12411i | −0.827101 | − | 0.562053i | \(-0.810012\pi\) | ||||
0.827101 | − | 0.562053i | \(-0.189988\pi\) | |||||||
\(504\) | 4.06673e11 | 0.280743 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.35410e11 | −0.0918279 | ||||||||
\(507\) | 1.70229e12i | 1.14419i | ||||||||
\(508\) | − 6.63265e11i | − 0.441876i | ||||||||
\(509\) | −1.17088e12 | −0.773181 | −0.386590 | − | 0.922252i | \(-0.626347\pi\) | ||||
−0.386590 | + | 0.922252i | \(0.626347\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.42967e11 | 0.417153 | ||||||||
\(512\) | − 6.87195e10i | − 0.0441942i | ||||||||
\(513\) | − 2.09632e12i | − 1.33638i | ||||||||
\(514\) | −7.08868e10 | −0.0447952 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 9.17595e11 | 0.569807 | ||||||||
\(517\) | 7.72526e11i | 0.475560i | ||||||||
\(518\) | − 1.34295e11i | − 0.0819553i | ||||||||
\(519\) | 4.73960e12 | 2.86740 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.91339e12 | 1.73232 | 0.866161 | − | 0.499765i | \(-0.166580\pi\) | ||||
0.866161 | + | 0.499765i | \(0.166580\pi\) | |||||||
\(522\) | − 4.45932e12i | − 2.62876i | ||||||||
\(523\) | − 2.53787e12i | − 1.48324i | −0.670820 | − | 0.741620i | \(-0.734058\pi\) | ||||
0.670820 | − | 0.741620i | \(-0.265942\pi\) | |||||||
\(524\) | −6.28732e11 | −0.364313 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.92992e12 | 1.09927 | ||||||||
\(527\) | − 1.07036e12i | − 0.604482i | ||||||||
\(528\) | − 4.52386e11i | − 0.253313i | ||||||||
\(529\) | 1.70941e12 | 0.949063 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.98620e12 | −2.72172 | ||||||||
\(532\) | − 2.40695e11i | − 0.130276i | ||||||||
\(533\) | − 2.09477e12i | − 1.12425i | ||||||||
\(534\) | −2.85229e12 | −1.51795 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.56506e11 | −0.186563 | ||||||||
\(537\) | − 3.78920e12i | − 1.96636i | ||||||||
\(538\) | 1.21444e12i | 0.624965i | ||||||||
\(539\) | 1.61074e11 | 0.0822008 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.11804e12 | 0.561136 | 0.280568 | − | 0.959834i | \(-0.409477\pi\) | ||||
0.280568 | + | 0.959834i | \(0.409477\pi\) | |||||||
\(542\) | − 1.13823e12i | − 0.566546i | ||||||||
\(543\) | − 4.28574e12i | − 2.11556i | ||||||||
\(544\) | −3.76300e11 | −0.184221 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 5.78398e11 | 0.278522 | ||||||||
\(547\) | 1.99438e12i | 0.952500i | 0.879310 | + | 0.476250i | \(0.158004\pi\) | ||||
−0.879310 | + | 0.476250i | \(0.841996\pi\) | |||||||
\(548\) | − 1.55741e12i | − 0.737719i | ||||||||
\(549\) | −2.99031e12 | −1.40488 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.63931e12 | −1.21985 | ||||||||
\(552\) | − 3.06506e11i | − 0.140512i | ||||||||
\(553\) | − 6.85125e10i | − 0.0311535i | ||||||||
\(554\) | 1.37847e12 | 0.621731 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.76638e11 | 0.255898 | ||||||||
\(557\) | − 4.69088e11i | − 0.206493i | −0.994656 | − | 0.103247i | \(-0.967077\pi\) | ||||
0.994656 | − | 0.103247i | \(-0.0329231\pi\) | |||||||
\(558\) | 1.97338e12i | 0.861702i | ||||||||
\(559\) | 8.84197e11 | 0.382997 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.47721e12 | −1.05592 | ||||||||
\(562\) | 1.60286e12i | 0.677770i | ||||||||
\(563\) | − 1.74518e12i | − 0.732069i | −0.930601 | − | 0.366034i | \(-0.880715\pi\) | ||||
0.930601 | − | 0.366034i | \(-0.119285\pi\) | |||||||
\(564\) | −1.74864e12 | −0.727687 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.31911e11 | 0.299767 | ||||||||
\(567\) | 1.22119e12i | 0.496205i | ||||||||
\(568\) | 8.99572e11i | 0.362634i | ||||||||
\(569\) | 4.13341e12 | 1.65311 | 0.826557 | − | 0.562853i | \(-0.190296\pi\) | ||||
0.826557 | + | 0.562853i | \(0.190296\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.14262e12 | 1.63084 | 0.815422 | − | 0.578867i | \(-0.196505\pi\) | ||||
0.815422 | + | 0.578867i | \(0.196505\pi\) | |||||||
\(572\) | − 4.35920e11i | − 0.170265i | ||||||||
\(573\) | 6.67383e12i | 2.58630i | ||||||||
\(574\) | 1.32045e12 | 0.507713 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.93767e11 | 0.262611 | ||||||||
\(577\) | 4.27130e12i | 1.60424i | 0.597164 | + | 0.802120i | \(0.296294\pi\) | ||||
−0.597164 | + | 0.802120i | \(0.703706\pi\) | |||||||
\(578\) | 1.63167e11i | 0.0608076i | ||||||||
\(579\) | 6.67614e11 | 0.246872 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.20152e11 | −0.335017 | ||||||||
\(582\) | − 2.66316e12i | − 0.962154i | ||||||||
\(583\) | − 6.68394e11i | − 0.239621i | ||||||||
\(584\) | 1.09687e12 | 0.390211 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.62584e11 | 0.0569557 | ||||||||
\(587\) | 5.32282e12i | 1.85042i | 0.379455 | + | 0.925210i | \(0.376111\pi\) | ||||
−0.379455 | + | 0.925210i | \(0.623889\pi\) | |||||||
\(588\) | 3.64597e11i | 0.125781i | ||||||||
\(589\) | 1.16797e12 | 0.399865 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.90570e12 | −1.99126 | ||||||||
\(592\) | − 2.29102e11i | − 0.0766622i | ||||||||
\(593\) | 2.69262e11i | 0.0894190i | 0.999000 | + | 0.0447095i | \(0.0142362\pi\) | ||||
−0.999000 | + | 0.0447095i | \(0.985764\pi\) | |||||||
\(594\) | 2.39322e12 | 0.788758 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.02605e11 | −0.260551 | ||||||||
\(597\) | 5.33906e11i | 0.172021i | ||||||||
\(598\) | − 2.95350e11i | − 0.0944457i | ||||||||
\(599\) | −3.51807e12 | −1.11657 | −0.558283 | − | 0.829651i | \(-0.688540\pi\) | ||||
−0.558283 | + | 0.829651i | \(0.688540\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.97549e12 | −0.617645 | −0.308823 | − | 0.951120i | \(-0.599935\pi\) | ||||
−0.308823 | + | 0.951120i | \(0.599935\pi\) | |||||||
\(602\) | 5.57359e11i | 0.172962i | ||||||||
\(603\) | − 3.59916e12i | − 1.10860i | ||||||||
\(604\) | 1.58960e12 | 0.485984 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.14279e10 | −0.0124786 | ||||||||
\(607\) | − 1.20562e12i | − 0.360464i | −0.983624 | − | 0.180232i | \(-0.942315\pi\) | ||||
0.983624 | − | 0.180232i | \(-0.0576848\pi\) | |||||||
\(608\) | − 4.10615e11i | − 0.121862i | ||||||||
\(609\) | 3.99794e12 | 1.17776 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.68499e12 | −0.489117 | ||||||||
\(612\) | − 3.79899e12i | − 1.09468i | ||||||||
\(613\) | 5.02026e11i | 0.143600i | 0.997419 | + | 0.0717999i | \(0.0228743\pi\) | ||||
−0.997419 | + | 0.0717999i | \(0.977126\pi\) | |||||||
\(614\) | −5.90332e11 | −0.167625 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.74785e11 | 0.0768918 | ||||||||
\(617\) | 5.17852e12i | 1.43854i | 0.694730 | + | 0.719271i | \(0.255524\pi\) | ||||
−0.694730 | + | 0.719271i | \(0.744476\pi\) | |||||||
\(618\) | − 5.52536e12i | − 1.52375i | ||||||||
\(619\) | 4.69963e12 | 1.28664 | 0.643318 | − | 0.765599i | \(-0.277557\pi\) | ||||
0.643318 | + | 0.765599i | \(0.277557\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.62149e12 | 0.437523 | ||||||||
\(622\) | − 3.01693e12i | − 0.808179i | ||||||||
\(623\) | − 1.73252e12i | − 0.460767i | ||||||||
\(624\) | 9.86722e11 | 0.260534 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.10845e12 | −0.548756 | ||||||||
\(627\) | − 2.70312e12i | − 0.698491i | ||||||||
\(628\) | − 3.41449e12i | − 0.876006i | ||||||||
\(629\) | −1.25454e12 | −0.319562 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.53678e12 | −1.39035 | −0.695177 | − | 0.718839i | \(-0.744674\pi\) | ||||
−0.695177 | + | 0.718839i | \(0.744674\pi\) | |||||||
\(632\) | − 1.16879e11i | − 0.0291414i | ||||||||
\(633\) | 8.91994e11i | 0.220823i | ||||||||
\(634\) | −2.41097e12 | −0.592639 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.51293e12 | 0.366660 | ||||||||
\(637\) | 3.51326e11i | 0.0845441i | ||||||||
\(638\) | − 3.01312e12i | − 0.719985i | ||||||||
\(639\) | −9.08175e12 | −2.15484 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.85506e12 | −0.667966 | −0.333983 | − | 0.942579i | \(-0.608393\pi\) | ||||
−0.333983 | + | 0.942579i | \(0.608393\pi\) | |||||||
\(642\) | − 1.91481e12i | − 0.444854i | ||||||||
\(643\) | 7.48209e12i | 1.72613i | 0.505093 | + | 0.863065i | \(0.331458\pi\) | ||||
−0.505093 | + | 0.863065i | \(0.668542\pi\) | |||||||
\(644\) | 1.86176e11 | 0.0426518 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.24848e12 | −0.507976 | ||||||||
\(647\) | − 3.83872e12i | − 0.861225i | −0.902537 | − | 0.430613i | \(-0.858297\pi\) | ||||
0.902537 | − | 0.430613i | \(-0.141703\pi\) | |||||||
\(648\) | 2.08330e12i | 0.464157i | ||||||||
\(649\) | −3.36912e12 | −0.745445 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.76920e12 | −0.386068 | ||||||||
\(652\) | 1.87807e12i | 0.407003i | ||||||||
\(653\) | 1.09261e11i | 0.0235157i | 0.999931 | + | 0.0117578i | \(0.00374272\pi\) | ||||
−0.999931 | + | 0.0117578i | \(0.996257\pi\) | |||||||
\(654\) | 7.75934e11 | 0.165854 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.25263e12 | 0.474922 | ||||||||
\(657\) | 1.10736e13i | 2.31871i | ||||||||
\(658\) | − 1.06215e12i | − 0.220886i | ||||||||
\(659\) | 2.10319e12 | 0.434403 | 0.217202 | − | 0.976127i | \(-0.430307\pi\) | ||||
0.217202 | + | 0.976127i | \(0.430307\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.76045e12 | −0.358688 | −0.179344 | − | 0.983786i | \(-0.557397\pi\) | ||||
−0.179344 | + | 0.983786i | \(0.557397\pi\) | |||||||
\(662\) | − 5.42203e11i | − 0.109724i | ||||||||
\(663\) | − 5.40317e12i | − 1.08602i | ||||||||
\(664\) | −1.56974e12 | −0.313380 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.31293e12 | 0.455542 | ||||||||
\(667\) | − 2.04149e12i | − 0.399374i | ||||||||
\(668\) | 1.64404e12i | 0.319462i | ||||||||
\(669\) | −1.76148e13 | −3.39986 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.02052e12 | −0.384779 | ||||||||
\(672\) | 6.21986e11i | 0.117657i | ||||||||
\(673\) | − 8.52389e12i | − 1.60166i | −0.598892 | − | 0.800830i | \(-0.704392\pi\) | ||||
0.598892 | − | 0.800830i | \(-0.295608\pi\) | |||||||
\(674\) | 3.17299e12 | 0.592241 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.76394e12 | −0.324881 | ||||||||
\(677\) | − 2.88497e12i | − 0.527828i | −0.964546 | − | 0.263914i | \(-0.914986\pi\) | ||||
0.964546 | − | 0.263914i | \(-0.0850135\pi\) | |||||||
\(678\) | 2.29600e12i | 0.417290i | ||||||||
\(679\) | 1.61764e12 | 0.292057 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.76732e13 | −3.14885 | ||||||||
\(682\) | 1.33339e12i | 0.236009i | ||||||||
\(683\) | − 1.03086e13i | − 1.81262i | −0.422616 | − | 0.906309i | \(-0.638888\pi\) | ||||
0.422616 | − | 0.906309i | \(-0.361112\pi\) | |||||||
\(684\) | 4.14542e12 | 0.724130 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.21461e11 | −0.0381802 | ||||||||
\(687\) | 8.79556e12i | 1.50646i | ||||||||
\(688\) | 9.50829e11i | 0.161791i | ||||||||
\(689\) | 1.45787e12 | 0.246451 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.85439e12 | 1.31057 | 0.655287 | − | 0.755380i | \(-0.272548\pi\) | ||||
0.655287 | + | 0.755380i | \(0.272548\pi\) | |||||||
\(692\) | 4.91126e12i | 0.814171i | ||||||||
\(693\) | 2.77413e12i | 0.456906i | ||||||||
\(694\) | −2.74819e12 | −0.449706 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 6.82030e12 | 1.10170 | ||||||||
\(697\) | − 1.23351e13i | − 1.97969i | ||||||||
\(698\) | − 3.01102e12i | − 0.480136i | ||||||||
\(699\) | −9.38969e12 | −1.48766 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.69579e12 | 0.265242 | 0.132621 | − | 0.991167i | \(-0.457661\pi\) | ||||
0.132621 | + | 0.991167i | \(0.457661\pi\) | |||||||
\(702\) | 5.21997e12i | 0.811243i | ||||||||
\(703\) | − 1.36894e12i | − 0.211390i | ||||||||
\(704\) | 4.68771e11 | 0.0719257 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.16793e12 | −0.479904 | ||||||||
\(707\) | − 2.51638e10i | − 0.00378781i | ||||||||
\(708\) | − 7.62613e12i | − 1.14066i | ||||||||
\(709\) | 2.20703e12 | 0.328020 | 0.164010 | − | 0.986459i | \(-0.447557\pi\) | ||||
0.164010 | + | 0.986459i | \(0.447557\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.17997e12 | 0.173164 | ||||||||
\(712\) | − 2.95560e12i | − 0.431008i | ||||||||
\(713\) | 9.03417e11i | 0.130914i | ||||||||
\(714\) | 3.40592e12 | 0.490448 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.92644e12 | 0.558330 | ||||||||
\(717\) | 2.14225e13i | 3.02715i | ||||||||
\(718\) | 6.95470e12i | 0.976604i | ||||||||
\(719\) | 1.46869e12 | 0.204952 | 0.102476 | − | 0.994735i | \(-0.467324\pi\) | ||||
0.102476 | + | 0.994735i | \(0.467324\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.35617e12 | 0.462525 | ||||||||
\(722\) | 2.70948e12i | 0.371081i | ||||||||
\(723\) | − 2.02192e12i | − 0.275195i | ||||||||
\(724\) | 4.44096e12 | 0.600694 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −6.23461e12 | −0.832904 | ||||||||
\(727\) | − 4.97511e11i | − 0.0660538i | −0.999454 | − | 0.0330269i | \(-0.989485\pi\) | ||||
0.999454 | − | 0.0330269i | \(-0.0105147\pi\) | |||||||
\(728\) | 5.99347e11i | 0.0790837i | ||||||||
\(729\) | 4.99938e12 | 0.655605 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.20663e12 | 0.674417 | ||||||||
\(732\) | − 4.57352e12i | − 0.588777i | ||||||||
\(733\) | 5.22437e12i | 0.668445i | 0.942494 | + | 0.334223i | \(0.108474\pi\) | ||||
−0.942494 | + | 0.334223i | \(0.891526\pi\) | |||||||
\(734\) | 9.63306e11 | 0.122499 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.17608e11 | 0.0398971 | ||||||||
\(737\) | − 2.43191e12i | − 0.303630i | ||||||||
\(738\) | 2.27417e13i | 2.82208i | ||||||||
\(739\) | −7.35495e11 | −0.0907152 | −0.0453576 | − | 0.998971i | \(-0.514443\pi\) | ||||
−0.0453576 | + | 0.998971i | \(0.514443\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.89590e12 | 0.718403 | ||||||||
\(742\) | 9.18975e11i | 0.111298i | ||||||||
\(743\) | 1.12076e12i | 0.134916i | 0.997722 | + | 0.0674580i | \(0.0214889\pi\) | ||||
−0.997722 | + | 0.0674580i | \(0.978511\pi\) | |||||||
\(744\) | −3.01818e12 | −0.361133 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.09683e13 | 1.29663 | ||||||||
\(747\) | − 1.58475e13i | − 1.86217i | ||||||||
\(748\) | − 2.56694e12i | − 0.299818i | ||||||||
\(749\) | 1.16308e12 | 0.135033 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.62183e12 | −0.186049 | −0.0930244 | − | 0.995664i | \(-0.529653\pi\) | ||||
−0.0930244 | + | 0.995664i | \(0.529653\pi\) | |||||||
\(752\) | − 1.81197e12i | − 0.206620i | ||||||||
\(753\) | 2.40991e13i | 2.73164i | ||||||||
\(754\) | 6.57206e12 | 0.740509 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.29044e12 | −0.366358 | ||||||||
\(757\) | − 1.55150e12i | − 0.171720i | −0.996307 | − | 0.0858600i | \(-0.972636\pi\) | ||||
0.996307 | − | 0.0858600i | \(-0.0273638\pi\) | |||||||
\(758\) | 8.08836e12i | 0.889916i | ||||||||
\(759\) | 2.09084e12 | 0.228682 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.62863e13 | 1.76032 | 0.880159 | − | 0.474679i | \(-0.157436\pi\) | ||||
0.880159 | + | 0.474679i | \(0.157436\pi\) | |||||||
\(762\) | 1.02413e13i | 1.10042i | ||||||||
\(763\) | 4.71312e11i | 0.0503440i | ||||||||
\(764\) | −6.91554e12 | −0.734355 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.23286e12 | −0.339280 | ||||||||
\(767\) | − 7.34856e12i | − 0.766695i | ||||||||
\(768\) | 1.06108e12i | 0.110058i | ||||||||
\(769\) | 1.32915e13 | 1.37059 | 0.685293 | − | 0.728267i | \(-0.259674\pi\) | ||||
0.685293 | + | 0.728267i | \(0.259674\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.09455e12 | 0.111555 | ||||||||
\(772\) | 6.91794e11i | 0.0700970i | ||||||||
\(773\) | 7.58593e12i | 0.764190i | 0.924123 | + | 0.382095i | \(0.124797\pi\) | ||||
−0.924123 | + | 0.382095i | \(0.875203\pi\) | |||||||
\(774\) | −9.59923e12 | −0.961395 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.75962e12 | 0.273194 | ||||||||
\(777\) | 2.07362e12i | 0.204096i | ||||||||
\(778\) | 8.83126e12i | 0.864200i | ||||||||
\(779\) | 1.34600e13 | 1.30956 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.13645e12 | −0.590184 | ||||||||
\(782\) | − 1.73918e12i | − 0.166309i | ||||||||
\(783\) | 3.60809e13i | 3.43044i | ||||||||
\(784\) | −3.77802e11 | −0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 9.70809e12 | 0.907262 | ||||||||
\(787\) | 3.30985e12i | 0.307554i | 0.988106 | + | 0.153777i | \(0.0491437\pi\) | ||||
−0.988106 | + | 0.153777i | \(0.950856\pi\) | |||||||
\(788\) | − 6.11960e12i | − 0.565399i | ||||||||
\(789\) | −2.97995e13 | −2.73755 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.39462e12 | −0.126666 | ||||||||
\(792\) | 4.73254e12i | 0.427397i | ||||||||
\(793\) | − 4.40706e12i | − 0.395748i | ||||||||
\(794\) | 2.02906e12 | 0.181176 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.53244e11 | −0.0488436 | ||||||||
\(797\) | − 3.26446e12i | − 0.286582i | −0.989681 | − | 0.143291i | \(-0.954232\pi\) | ||||
0.989681 | − | 0.143291i | \(-0.0457685\pi\) | |||||||
\(798\) | 3.71651e12i | 0.324431i | ||||||||
\(799\) | −9.92216e12 | −0.861283 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.98386e13 | 2.56114 | ||||||||
\(802\) | − 9.39131e12i | − 0.801570i | ||||||||
\(803\) | 7.48235e12i | 0.635064i | ||||||||
\(804\) | 5.50473e12 | 0.464605 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.90833e12 | −0.242737 | ||||||||
\(807\) | − 1.87519e13i | − 1.55637i | ||||||||
\(808\) | − 4.29283e10i | − 0.00354318i | ||||||||
\(809\) | −3.46768e12 | −0.284624 | −0.142312 | − | 0.989822i | \(-0.545454\pi\) | ||||
−0.142312 | + | 0.989822i | \(0.545454\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.02915e13 | 0.835381 | 0.417690 | − | 0.908589i | \(-0.362840\pi\) | ||||
0.417690 | + | 0.908589i | \(0.362840\pi\) | |||||||
\(812\) | 4.14274e12i | 0.334415i | ||||||||
\(813\) | 1.75752e13i | 1.41089i | ||||||||
\(814\) | 1.56282e12 | 0.124767 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5.81035e12 | 0.458772 | ||||||||
\(817\) | 5.68143e12i | 0.446127i | ||||||||
\(818\) | − 1.45322e12i | − 0.113486i | ||||||||
\(819\) | −6.05079e12 | −0.469931 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.23700e12 | 0.479106 | 0.239553 | − | 0.970883i | \(-0.422999\pi\) | ||||
0.239553 | + | 0.970883i | \(0.422999\pi\) | |||||||
\(822\) | 2.40476e13i | 1.83717i | ||||||||
\(823\) | − 2.46689e13i | − 1.87435i | −0.348860 | − | 0.937175i | \(-0.613431\pi\) | ||||
0.348860 | − | 0.937175i | \(-0.386569\pi\) | |||||||
\(824\) | 5.72548e12 | 0.432653 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.63221e12 | 0.346240 | ||||||||
\(827\) | − 1.45027e13i | − 1.07814i | −0.842262 | − | 0.539068i | \(-0.818776\pi\) | ||||
0.842262 | − | 0.539068i | \(-0.181224\pi\) | |||||||
\(828\) | 3.20645e12i | 0.237076i | ||||||||
\(829\) | 1.07681e13 | 0.791854 | 0.395927 | − | 0.918282i | \(-0.370423\pi\) | ||||
0.395927 | + | 0.918282i | \(0.370423\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.12846e13 | −1.54832 | ||||||||
\(832\) | 1.02246e12i | 0.0739761i | ||||||||
\(833\) | 2.06880e12i | 0.148873i | ||||||||
\(834\) | −8.90373e12 | −0.637272 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.80102e12 | 0.198330 | ||||||||
\(837\) | − 1.59668e13i | − 1.12449i | ||||||||
\(838\) | − 1.33547e13i | − 0.935484i | ||||||||
\(839\) | 2.36129e13 | 1.64521 | 0.822603 | − | 0.568616i | \(-0.192521\pi\) | ||||
0.822603 | + | 0.568616i | \(0.192521\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.09195e13 | 2.13133 | ||||||||
\(842\) | 2.58176e11i | 0.0177015i | ||||||||
\(843\) | − 2.47494e13i | − 1.68787i | ||||||||
\(844\) | −9.24301e11 | −0.0627007 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.82930e13 | 1.22778 | ||||||||
\(847\) | − 3.78698e12i | − 0.252824i | ||||||||
\(848\) | 1.56773e12i | 0.104109i | ||||||||
\(849\) | −1.13013e13 | −0.746521 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.05886e12 | 0.0692081 | ||||||||
\(852\) | − 1.38901e13i | − 0.903080i | ||||||||
\(853\) | 1.67503e13i | 1.08331i | 0.840601 | + | 0.541655i | \(0.182202\pi\) | ||||
−0.840601 | + | 0.541655i | \(0.817798\pi\) | |||||||
\(854\) | 2.77801e12 | 0.178720 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.98416e12 | 0.126312 | ||||||||
\(857\) | − 1.16182e13i | − 0.735742i | −0.929877 | − | 0.367871i | \(-0.880087\pi\) | ||||
0.929877 | − | 0.367871i | \(-0.119913\pi\) | |||||||
\(858\) | 6.73094e12i | 0.424017i | ||||||||
\(859\) | −1.58818e13 | −0.995246 | −0.497623 | − | 0.867393i | \(-0.665794\pi\) | ||||
−0.497623 | + | 0.867393i | \(0.665794\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.03888e13 | −1.26438 | ||||||||
\(862\) | 7.71096e12i | 0.475692i | ||||||||
\(863\) | − 1.35971e13i | − 0.834446i | −0.908804 | − | 0.417223i | \(-0.863003\pi\) | ||||
0.908804 | − | 0.417223i | \(-0.136997\pi\) | |||||||
\(864\) | −5.61335e12 | −0.342697 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.06930e13 | −0.646056 | ||||||||
\(867\) | − 2.51943e12i | − 0.151431i | ||||||||
\(868\) | − 1.83328e12i | − 0.109620i | ||||||||
\(869\) | 7.97294e11 | 0.0474274 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.30437e12 | 0.312285 | ||||||||
\(872\) | 8.04037e11i | 0.0470925i | ||||||||
\(873\) | 2.78601e13i | 1.62338i | ||||||||
\(874\) | 1.89778e12 | 0.110013 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.69366e13 | −0.971755 | ||||||||
\(877\) | 3.40277e12i | 0.194238i | 0.995273 | + | 0.0971189i | \(0.0309627\pi\) | ||||
−0.995273 | + | 0.0971189i | \(0.969037\pi\) | |||||||
\(878\) | − 7.67711e12i | − 0.435986i | ||||||||
\(879\) | −2.51041e12 | −0.141839 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.30779e12 | 0.520541 | 0.260270 | − | 0.965536i | \(-0.416188\pi\) | ||||
0.260270 | + | 0.965536i | \(0.416188\pi\) | |||||||
\(882\) | − 3.81415e12i | − 0.212221i | ||||||||
\(883\) | − 1.00154e13i | − 0.554430i | −0.960808 | − | 0.277215i | \(-0.910589\pi\) | ||||
0.960808 | − | 0.277215i | \(-0.0894114\pi\) | |||||||
\(884\) | 5.59887e12 | 0.308365 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.04576e13 | 0.570137 | ||||||||
\(887\) | − 2.58440e13i | − 1.40186i | −0.713232 | − | 0.700928i | \(-0.752769\pi\) | ||||
0.713232 | − | 0.700928i | \(-0.247231\pi\) | |||||||
\(888\) | 3.53751e12i | 0.190915i | ||||||||
\(889\) | −6.22070e12 | −0.334027 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.42113e13 | −0.755412 | ||||||||
\(892\) | − 1.82528e13i | − 0.965358i | ||||||||
\(893\) | − 1.08270e13i | − 0.569739i | ||||||||
\(894\) | 1.23928e13 | 0.648860 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −6.44514e11 | −0.0334077 | ||||||||
\(897\) | 4.56043e12i | 0.235201i | ||||||||
\(898\) | − 3.01855e12i | − 0.154901i | ||||||||
\(899\) | −2.01026e13 | −1.02644 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.58471e12 | 0.433974 | ||||||||
\(902\) | 1.53664e13i | 0.772932i | ||||||||
\(903\) | − 8.60604e12i | − 0.430733i | ||||||||
\(904\) | −2.37916e12 | −0.118486 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.45447e13 | −1.21026 | ||||||||
\(907\) | 3.82049e13i | 1.87451i | 0.348650 | + | 0.937253i | \(0.386640\pi\) | ||||
−0.348650 | + | 0.937253i | \(0.613360\pi\) | |||||||
\(908\) | − 1.83133e13i | − 0.894086i | ||||||||
\(909\) | 4.33389e11 | 0.0210543 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.85478e12 | 0.474039 | 0.237020 | − | 0.971505i | \(-0.423829\pi\) | ||||
0.237020 | + | 0.971505i | \(0.423829\pi\) | |||||||
\(912\) | 6.34021e12i | 0.303478i | ||||||||
\(913\) | − 1.07080e13i | − 0.510023i | ||||||||
\(914\) | 2.09929e13 | 0.994979 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.11412e12 | −0.427745 | ||||||||
\(917\) | 5.89682e12i | 0.275395i | ||||||||
\(918\) | 3.07380e13i | 1.42851i | ||||||||
\(919\) | −2.60834e13 | −1.20627 | −0.603135 | − | 0.797639i | \(-0.706082\pi\) | ||||
−0.603135 | + | 0.797639i | \(0.706082\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.11517e12 | 0.417442 | ||||||||
\(922\) | − 1.86551e13i | − 0.850176i | ||||||||
\(923\) | − 1.33845e13i | − 0.607008i | ||||||||
\(924\) | −4.24289e12 | −0.191486 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.19709e11 | 0.0276974 | ||||||||
\(927\) | 5.78024e13i | 2.57091i | ||||||||
\(928\) | 7.06733e12i | 0.312816i | ||||||||
\(929\) | 3.60592e13 | 1.58835 | 0.794174 | − | 0.607690i | \(-0.207904\pi\) | ||||
0.794174 | + | 0.607690i | \(0.207904\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.25746e12 | −0.0984795 | ||||||||
\(932\) | − 9.72977e12i | − 0.422407i | ||||||||
\(933\) | 4.65836e13i | 2.01264i | ||||||||
\(934\) | 1.87440e12 | 0.0805936 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.03224e13 | −0.439581 | ||||||||
\(937\) | 2.75358e13i | 1.16700i | 0.812114 | + | 0.583499i | \(0.198317\pi\) | ||||
−0.812114 | + | 0.583499i | \(0.801683\pi\) | |||||||
\(938\) | 3.34364e12i | 0.141028i | ||||||||
\(939\) | 3.25561e13 | 1.36659 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.60157e12 | −0.316046 | −0.158023 | − | 0.987435i | \(-0.550512\pi\) | ||||
−0.158023 | + | 0.987435i | \(0.550512\pi\) | |||||||
\(942\) | 5.27223e13i | 2.18155i | ||||||||
\(943\) | 1.04112e13i | 0.428745i | ||||||||
\(944\) | 7.90234e12 | 0.323878 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.48610e12 | −0.263314 | ||||||||
\(947\) | − 2.35269e13i | − 0.950582i | −0.879829 | − | 0.475291i | \(-0.842343\pi\) | ||||
0.879829 | − | 0.475291i | \(-0.157657\pi\) | |||||||
\(948\) | 1.80470e12i | 0.0725719i | ||||||||
\(949\) | −1.63201e13 | −0.653168 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.72272e13 | 1.47587 | ||||||||
\(952\) | 3.52928e12i | 0.139258i | ||||||||
\(953\) | − 3.76056e12i | − 0.147684i | −0.997270 | − | 0.0738422i | \(-0.976474\pi\) | ||||
0.997270 | − | 0.0738422i | \(-0.0235261\pi\) | |||||||
\(954\) | −1.58272e13 | −0.618639 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.21984e13 | −0.859531 | ||||||||
\(957\) | 4.65248e13i | 1.79300i | ||||||||
\(958\) | − 3.11575e13i | − 1.19514i | ||||||||
\(959\) | −1.46068e13 | −0.557663 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.75436e13 | −0.663535 | ||||||||
\(962\) | 3.40875e12i | 0.128324i | ||||||||
\(963\) | 2.00313e13i | 0.750571i | ||||||||
\(964\) | 2.09515e12 | 0.0781391 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.87470e12 | −0.106217 | ||||||||
\(967\) | 3.59678e13i | 1.32280i | 0.750033 | + | 0.661400i | \(0.230037\pi\) | ||||
−0.750033 | + | 0.661400i | \(0.769963\pi\) | |||||||
\(968\) | − 6.46042e12i | − 0.236495i | ||||||||
\(969\) | 3.47182e13 | 1.26503 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.20049e13 | −0.433383 | −0.216692 | − | 0.976240i | \(-0.569527\pi\) | ||||
−0.216692 | + | 0.976240i | \(0.569527\pi\) | |||||||
\(972\) | − 5.19328e12i | − 0.186614i | ||||||||
\(973\) | − 5.40823e12i | − 0.193441i | ||||||||
\(974\) | −3.13573e13 | −1.11641 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.73917e12 | 0.167178 | ||||||||
\(977\) | − 4.59954e12i | − 0.161506i | −0.996734 | − | 0.0807530i | \(-0.974268\pi\) | ||||
0.996734 | − | 0.0807530i | \(-0.0257325\pi\) | |||||||
\(978\) | − 2.89988e13i | − 1.01357i | ||||||||
\(979\) | 2.01617e13 | 0.701462 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.11727e12 | −0.279833 | ||||||||
\(982\) | 4.69742e12i | 0.161197i | ||||||||
\(983\) | 3.13830e12i | 0.107202i | 0.998562 | + | 0.0536011i | \(0.0170699\pi\) | ||||
−0.998562 | + | 0.0536011i | \(0.982930\pi\) | |||||||
\(984\) | −3.47823e13 | −1.18272 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.86999e13 | 1.30396 | ||||||||
\(987\) | 1.64003e13i | 0.550080i | ||||||||
\(988\) | 6.10944e12i | 0.203984i | ||||||||
\(989\) | −4.39454e12 | −0.146060 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.38736e13 | 0.456939 | 0.228470 | − | 0.973551i | \(-0.426628\pi\) | ||||
0.228470 | + | 0.973551i | \(0.426628\pi\) | |||||||
\(992\) | − 3.12750e12i | − 0.102540i | ||||||||
\(993\) | 8.37203e12i | 0.273249i | ||||||||
\(994\) | 8.43700e12 | 0.274126 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.42380e13 | 0.780421 | ||||||||
\(997\) | − 1.65453e13i | − 0.530331i | −0.964203 | − | 0.265166i | \(-0.914573\pi\) | ||||
0.964203 | − | 0.265166i | \(-0.0854266\pi\) | |||||||
\(998\) | 2.74224e13i | 0.875019i | ||||||||
\(999\) | −1.87142e13 | −0.594465 |
(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 | 350.10.c.j.99.2 | 4 | ||
5.2 | odd | 4 | 350.10.a.j.1.2 | 2 | |||
5.3 | odd | 4 | 14.10.a.c.1.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 350.10.c.j.99.3 | 4 | ||
15.8 | even | 4 | 126.10.a.o.1.2 | 2 | |||
20.3 | even | 4 | 112.10.a.c.1.2 | 2 | |||
35.3 | even | 12 | 98.10.c.h.79.1 | 4 | |||
35.13 | even | 4 | 98.10.a.e.1.2 | 2 | |||
35.18 | odd | 12 | 98.10.c.j.79.2 | 4 | |||
35.23 | odd | 12 | 98.10.c.j.67.2 | 4 | |||
35.33 | even | 12 | 98.10.c.h.67.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.10.a.c.1.1 | ✓ | 2 | 5.3 | odd | 4 | ||
98.10.a.e.1.2 | 2 | 35.13 | even | 4 | |||
98.10.c.h.67.1 | 4 | 35.33 | even | 12 | |||
98.10.c.h.79.1 | 4 | 35.3 | even | 12 | |||
98.10.c.j.67.2 | 4 | 35.23 | odd | 12 | |||
98.10.c.j.79.2 | 4 | 35.18 | odd | 12 | |||
112.10.a.c.1.2 | 2 | 20.3 | even | 4 | |||
126.10.a.o.1.2 | 2 | 15.8 | even | 4 | |||
350.10.a.j.1.2 | 2 | 5.2 | odd | 4 | |||
350.10.c.j.99.2 | 4 | 1.1 | even | 1 | trivial | ||
350.10.c.j.99.3 | 4 | 5.4 | even | 2 | inner |