Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [350,10,Mod(1,350)]
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([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("350.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.a (trivial) |
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: | yes |
Analytic conductor: | \(180.262542657\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{2305}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 576 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2\cdot 5 \) |
Twist minimal: | no (minimal twist has level 14) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(24.5052\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 16.0000 | 0.707107 | ||||||||
\(3\) | 247.052 | 1.76093 | 0.880467 | − | 0.474108i | \(-0.157229\pi\) | ||||
0.880467 | + | 0.474108i | \(0.157229\pi\) | |||||||
\(4\) | 256.000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3952.83 | 1.24517 | ||||||||
\(7\) | −2401.00 | −0.377964 | ||||||||
\(8\) | 4096.00 | 0.353553 | ||||||||
\(9\) | 41351.7 | 2.10089 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −27940.9 | −0.575405 | −0.287703 | − | 0.957720i | \(-0.592891\pi\) | ||||
−0.287703 | + | 0.957720i | \(0.592891\pi\) | |||||||
\(12\) | 63245.3 | 0.880467 | ||||||||
\(13\) | −60943.3 | −0.591808 | −0.295904 | − | 0.955218i | \(-0.595621\pi\) | ||||
−0.295904 | + | 0.955218i | \(0.595621\pi\) | |||||||
\(14\) | −38416.0 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 65536.0 | 0.250000 | ||||||||
\(17\) | 358867. | 1.04211 | 0.521055 | − | 0.853523i | \(-0.325538\pi\) | ||||
0.521055 | + | 0.853523i | \(0.325538\pi\) | |||||||
\(18\) | 661628. | 1.48555 | ||||||||
\(19\) | −391593. | −0.689356 | −0.344678 | − | 0.938721i | \(-0.612012\pi\) | ||||
−0.344678 | + | 0.938721i | \(0.612012\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −593172. | −0.665570 | ||||||||
\(22\) | −447055. | −0.406873 | ||||||||
\(23\) | 302894. | 0.225692 | 0.112846 | − | 0.993612i | \(-0.464003\pi\) | ||||
0.112846 | + | 0.993612i | \(0.464003\pi\) | |||||||
\(24\) | 1.01193e6 | 0.622584 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −975093. | −0.418472 | ||||||||
\(27\) | 5.35330e6 | 1.93859 | ||||||||
\(28\) | −614656. | −0.188982 | ||||||||
\(29\) | 6.73993e6 | 1.76956 | 0.884778 | − | 0.466013i | \(-0.154310\pi\) | ||||
0.884778 | + | 0.466013i | \(0.154310\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.98262e6 | 0.580056 | 0.290028 | − | 0.957018i | \(-0.406335\pi\) | ||||
0.290028 | + | 0.957018i | \(0.406335\pi\) | |||||||
\(32\) | 1.04858e6 | 0.176777 | ||||||||
\(33\) | −6.90287e6 | −1.01325 | ||||||||
\(34\) | 5.74188e6 | 0.736884 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.05860e7 | 1.05044 | ||||||||
\(37\) | 3.49582e6 | 0.306649 | 0.153324 | − | 0.988176i | \(-0.451002\pi\) | ||||
0.153324 | + | 0.988176i | \(0.451002\pi\) | |||||||
\(38\) | −6.26549e6 | −0.487449 | ||||||||
\(39\) | −1.50562e7 | −1.04214 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.43724e7 | 1.89969 | 0.949845 | − | 0.312722i | \(-0.101241\pi\) | ||||
0.949845 | + | 0.312722i | \(0.101241\pi\) | |||||||
\(42\) | −9.49075e6 | −0.470629 | ||||||||
\(43\) | 1.45085e7 | 0.647164 | 0.323582 | − | 0.946200i | \(-0.395113\pi\) | ||||
0.323582 | + | 0.946200i | \(0.395113\pi\) | |||||||
\(44\) | −7.15288e6 | −0.287703 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.84631e6 | 0.159588 | ||||||||
\(47\) | 2.76485e7 | 0.826479 | 0.413239 | − | 0.910622i | \(-0.364397\pi\) | ||||
0.413239 | + | 0.910622i | \(0.364397\pi\) | |||||||
\(48\) | 1.61908e7 | 0.440233 | ||||||||
\(49\) | 5.76480e6 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.86589e7 | 1.83509 | ||||||||
\(52\) | −1.56015e7 | −0.295904 | ||||||||
\(53\) | 2.39217e7 | 0.416438 | 0.208219 | − | 0.978082i | \(-0.433233\pi\) | ||||
0.208219 | + | 0.978082i | \(0.433233\pi\) | |||||||
\(54\) | 8.56529e7 | 1.37079 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −9.83450e6 | −0.133631 | ||||||||
\(57\) | −9.67439e7 | −1.21391 | ||||||||
\(58\) | 1.07839e8 | 1.25127 | ||||||||
\(59\) | −1.20580e8 | −1.29551 | −0.647756 | − | 0.761848i | \(-0.724293\pi\) | ||||
−0.647756 | + | 0.761848i | \(0.724293\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.23140e7 | 0.668710 | 0.334355 | − | 0.942447i | \(-0.391482\pi\) | ||||
0.334355 | + | 0.942447i | \(0.391482\pi\) | |||||||
\(62\) | 4.77219e7 | 0.410161 | ||||||||
\(63\) | −9.92855e7 | −0.794060 | ||||||||
\(64\) | 1.67772e7 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.10446e8 | −0.716476 | ||||||||
\(67\) | −8.70377e7 | −0.527680 | −0.263840 | − | 0.964566i | \(-0.584989\pi\) | ||||
−0.263840 | + | 0.964566i | \(0.584989\pi\) | |||||||
\(68\) | 9.18701e7 | 0.521055 | ||||||||
\(69\) | 7.48307e7 | 0.397428 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.19622e8 | 1.02568 | 0.512842 | − | 0.858483i | \(-0.328593\pi\) | ||||
0.512842 | + | 0.858483i | \(0.328593\pi\) | |||||||
\(72\) | 1.69377e8 | 0.742775 | ||||||||
\(73\) | −2.67792e8 | −1.10368 | −0.551841 | − | 0.833949i | \(-0.686074\pi\) | ||||
−0.551841 | + | 0.833949i | \(0.686074\pi\) | |||||||
\(74\) | 5.59331e7 | 0.216833 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00248e8 | −0.344678 | ||||||||
\(77\) | 6.70862e7 | 0.217483 | ||||||||
\(78\) | −2.40899e8 | −0.736901 | ||||||||
\(79\) | 2.85350e7 | 0.0824243 | 0.0412122 | − | 0.999150i | \(-0.486878\pi\) | ||||
0.0412122 | + | 0.999150i | \(0.486878\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.08619e8 | 1.31283 | ||||||||
\(82\) | 5.49959e8 | 1.34328 | ||||||||
\(83\) | 3.83237e8 | 0.886372 | 0.443186 | − | 0.896430i | \(-0.353848\pi\) | ||||
0.443186 | + | 0.896430i | \(0.353848\pi\) | |||||||
\(84\) | −1.51852e8 | −0.332785 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.32136e8 | 0.457614 | ||||||||
\(87\) | 1.66511e9 | 3.11607 | ||||||||
\(88\) | −1.14446e8 | −0.203437 | ||||||||
\(89\) | 7.21581e8 | 1.21907 | 0.609537 | − | 0.792757i | \(-0.291355\pi\) | ||||
0.609537 | + | 0.792757i | \(0.291355\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.46325e8 | 0.223683 | ||||||||
\(92\) | 7.75410e7 | 0.112846 | ||||||||
\(93\) | 7.36861e8 | 1.02144 | ||||||||
\(94\) | 4.42377e8 | 0.584409 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.59053e8 | 0.311292 | ||||||||
\(97\) | 6.73736e8 | 0.772710 | 0.386355 | − | 0.922350i | \(-0.373734\pi\) | ||||
0.386355 | + | 0.922350i | \(0.373734\pi\) | |||||||
\(98\) | 9.22368e7 | 0.101015 | ||||||||
\(99\) | −1.15541e9 | −1.20886 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.04805e7 | −0.0100216 | −0.00501081 | − | 0.999987i | \(-0.501595\pi\) | ||||
−0.00501081 | + | 0.999987i | \(0.501595\pi\) | |||||||
\(102\) | 1.41854e9 | 1.29760 | ||||||||
\(103\) | −1.39782e9 | −1.22373 | −0.611864 | − | 0.790963i | \(-0.709580\pi\) | ||||
−0.611864 | + | 0.790963i | \(0.709580\pi\) | |||||||
\(104\) | −2.49624e8 | −0.209236 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.82747e8 | 0.294466 | ||||||||
\(107\) | 4.84414e8 | 0.357264 | 0.178632 | − | 0.983916i | \(-0.442833\pi\) | ||||
0.178632 | + | 0.983916i | \(0.442833\pi\) | |||||||
\(108\) | 1.37045e9 | 0.969293 | ||||||||
\(109\) | −1.96298e8 | −0.133198 | −0.0665989 | − | 0.997780i | \(-0.521215\pi\) | ||||
−0.0665989 | + | 0.997780i | \(0.521215\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.63649e8 | 0.539988 | ||||||||
\(112\) | −1.57352e8 | −0.0944911 | ||||||||
\(113\) | 5.80849e8 | 0.335128 | 0.167564 | − | 0.985861i | \(-0.446410\pi\) | ||||
0.167564 | + | 0.985861i | \(0.446410\pi\) | |||||||
\(114\) | −1.54790e9 | −0.858364 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.72542e9 | 0.884778 | ||||||||
\(117\) | −2.52011e9 | −1.24332 | ||||||||
\(118\) | −1.92928e9 | −0.916066 | ||||||||
\(119\) | −8.61641e8 | −0.393881 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.57725e9 | −0.668909 | ||||||||
\(122\) | 1.15702e9 | 0.472850 | ||||||||
\(123\) | 8.49178e9 | 3.34523 | ||||||||
\(124\) | 7.63550e8 | 0.290028 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.58857e9 | −0.561485 | ||||||||
\(127\) | −2.59088e9 | −0.883751 | −0.441876 | − | 0.897076i | \(-0.645687\pi\) | ||||
−0.441876 | + | 0.897076i | \(0.645687\pi\) | |||||||
\(128\) | 2.68435e8 | 0.0883883 | ||||||||
\(129\) | 3.58436e9 | 1.13961 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.45598e9 | 0.728626 | 0.364313 | − | 0.931277i | \(-0.381304\pi\) | ||||
0.364313 | + | 0.931277i | \(0.381304\pi\) | |||||||
\(132\) | −1.76713e9 | −0.506625 | ||||||||
\(133\) | 9.40215e8 | 0.260552 | ||||||||
\(134\) | −1.39260e9 | −0.373126 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.46992e9 | 0.368442 | ||||||||
\(137\) | −6.08364e9 | −1.47544 | −0.737719 | − | 0.675108i | \(-0.764097\pi\) | ||||
−0.737719 | + | 0.675108i | \(0.764097\pi\) | |||||||
\(138\) | 1.19729e9 | 0.281024 | ||||||||
\(139\) | 2.25249e9 | 0.511796 | 0.255898 | − | 0.966704i | \(-0.417629\pi\) | ||||
0.255898 | + | 0.966704i | \(0.417629\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.83063e9 | 1.45537 | ||||||||
\(142\) | 3.51395e9 | 0.725268 | ||||||||
\(143\) | 1.70281e9 | 0.340530 | ||||||||
\(144\) | 2.71003e9 | 0.525221 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.28466e9 | −0.780421 | ||||||||
\(147\) | 1.42421e9 | 0.251562 | ||||||||
\(148\) | 8.94930e8 | 0.153324 | ||||||||
\(149\) | −3.13517e9 | −0.521103 | −0.260551 | − | 0.965460i | \(-0.583904\pi\) | ||||
−0.260551 | + | 0.965460i | \(0.583904\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.20938e9 | −0.971969 | −0.485984 | − | 0.873968i | \(-0.661539\pi\) | ||||
−0.485984 | + | 0.873968i | \(0.661539\pi\) | |||||||
\(152\) | −1.60397e9 | −0.243724 | ||||||||
\(153\) | 1.48398e10 | 2.18936 | ||||||||
\(154\) | 1.07338e9 | 0.153784 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.85438e9 | −0.521068 | ||||||||
\(157\) | −1.33378e10 | −1.75201 | −0.876006 | − | 0.482300i | \(-0.839802\pi\) | ||||
−0.876006 | + | 0.482300i | \(0.839802\pi\) | |||||||
\(158\) | 4.56560e8 | 0.0582828 | ||||||||
\(159\) | 5.90990e9 | 0.733319 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.27249e8 | −0.0853035 | ||||||||
\(162\) | 8.13790e9 | 0.928314 | ||||||||
\(163\) | −7.33621e9 | −0.814006 | −0.407003 | − | 0.913427i | \(-0.633426\pi\) | ||||
−0.407003 | + | 0.913427i | \(0.633426\pi\) | |||||||
\(164\) | 8.79934e9 | 0.949845 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.13179e9 | 0.626760 | ||||||||
\(167\) | 6.42205e9 | 0.638925 | 0.319462 | − | 0.947599i | \(-0.396498\pi\) | ||||
0.319462 | + | 0.947599i | \(0.396498\pi\) | |||||||
\(168\) | −2.42963e9 | −0.235315 | ||||||||
\(169\) | −6.89041e9 | −0.649763 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.61931e10 | −1.44826 | ||||||||
\(172\) | 3.71418e9 | 0.323582 | ||||||||
\(173\) | −1.91846e10 | −1.62834 | −0.814171 | − | 0.580626i | \(-0.802808\pi\) | ||||
−0.814171 | + | 0.580626i | \(0.802808\pi\) | |||||||
\(174\) | 2.66418e10 | 2.20339 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.83114e9 | −0.143851 | ||||||||
\(177\) | −2.97896e10 | −2.28131 | ||||||||
\(178\) | 1.15453e10 | 0.862016 | ||||||||
\(179\) | 1.53377e10 | 1.11666 | 0.558330 | − | 0.829619i | \(-0.311442\pi\) | ||||
0.558330 | + | 0.829619i | \(0.311442\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.73475e10 | −1.20139 | −0.600694 | − | 0.799479i | \(-0.705109\pi\) | ||||
−0.600694 | + | 0.799479i | \(0.705109\pi\) | |||||||
\(182\) | 2.34120e9 | 0.158167 | ||||||||
\(183\) | 1.78653e10 | 1.17755 | ||||||||
\(184\) | 1.24066e9 | 0.0797941 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.17898e10 | 0.722267 | ||||||||
\(187\) | −1.00271e10 | −0.599636 | ||||||||
\(188\) | 7.07802e9 | 0.413239 | ||||||||
\(189\) | −1.28533e10 | −0.732717 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.70138e10 | 1.46871 | 0.734355 | − | 0.678765i | \(-0.237485\pi\) | ||||
0.734355 | + | 0.678765i | \(0.237485\pi\) | |||||||
\(192\) | 4.14485e9 | 0.220117 | ||||||||
\(193\) | −2.70232e9 | −0.140194 | −0.0700970 | − | 0.997540i | \(-0.522331\pi\) | ||||
−0.0700970 | + | 0.997540i | \(0.522331\pi\) | |||||||
\(194\) | 1.07798e10 | 0.546389 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.47579e9 | 0.0714286 | ||||||||
\(197\) | −2.39047e10 | −1.13080 | −0.565399 | − | 0.824818i | \(-0.691278\pi\) | ||||
−0.565399 | + | 0.824818i | \(0.691278\pi\) | |||||||
\(198\) | −1.84865e10 | −0.854794 | ||||||||
\(199\) | −2.16111e9 | −0.0976872 | −0.0488436 | − | 0.998806i | \(-0.515554\pi\) | ||||
−0.0488436 | + | 0.998806i | \(0.515554\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.15028e10 | −0.929209 | ||||||||
\(202\) | −1.67689e8 | −0.00708635 | ||||||||
\(203\) | −1.61826e10 | −0.668829 | ||||||||
\(204\) | 2.26967e10 | 0.917544 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.23652e10 | −0.865306 | ||||||||
\(207\) | 1.25252e10 | 0.474153 | ||||||||
\(208\) | −3.99398e9 | −0.147952 | ||||||||
\(209\) | 1.09415e10 | 0.396659 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.61055e9 | 0.125401 | 0.0627007 | − | 0.998032i | \(-0.480029\pi\) | ||||
0.0627007 | + | 0.998032i | \(0.480029\pi\) | |||||||
\(212\) | 6.12395e9 | 0.208219 | ||||||||
\(213\) | 5.42581e10 | 1.80616 | ||||||||
\(214\) | 7.75062e9 | 0.252624 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.19271e10 | 0.685394 | ||||||||
\(217\) | −7.16126e9 | −0.219240 | ||||||||
\(218\) | −3.14077e9 | −0.0941851 | ||||||||
\(219\) | −6.61585e10 | −1.94351 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.18706e10 | −0.616730 | ||||||||
\(222\) | 1.38184e10 | 0.381829 | ||||||||
\(223\) | 7.13001e10 | 1.93072 | 0.965358 | − | 0.260929i | \(-0.0840287\pi\) | ||||
0.965358 | + | 0.260929i | \(0.0840287\pi\) | |||||||
\(224\) | −2.51763e9 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.29359e9 | 0.236971 | ||||||||
\(227\) | −7.15361e10 | −1.78817 | −0.894086 | − | 0.447896i | \(-0.852173\pi\) | ||||
−0.894086 | + | 0.447896i | \(0.852173\pi\) | |||||||
\(228\) | −2.47664e10 | −0.606955 | ||||||||
\(229\) | −3.56020e10 | −0.855491 | −0.427745 | − | 0.903899i | \(-0.640692\pi\) | ||||
−0.427745 | + | 0.903899i | \(0.640692\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.65738e10 | 0.382973 | ||||||||
\(232\) | 2.76067e10 | 0.625633 | ||||||||
\(233\) | 3.80069e10 | 0.844814 | 0.422407 | − | 0.906406i | \(-0.361185\pi\) | ||||
0.422407 | + | 0.906406i | \(0.361185\pi\) | |||||||
\(234\) | −4.03218e10 | −0.879161 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.08685e10 | −0.647756 | ||||||||
\(237\) | 7.04962e9 | 0.145144 | ||||||||
\(238\) | −1.37863e10 | −0.278516 | ||||||||
\(239\) | −8.67126e10 | −1.71906 | −0.859531 | − | 0.511083i | \(-0.829244\pi\) | ||||
−0.859531 | + | 0.511083i | \(0.829244\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.18418e9 | −0.156278 | −0.0781391 | − | 0.996942i | \(-0.524898\pi\) | ||||
−0.0781391 | + | 0.996942i | \(0.524898\pi\) | |||||||
\(242\) | −2.52360e10 | −0.472990 | ||||||||
\(243\) | 2.02863e10 | 0.373228 | ||||||||
\(244\) | 1.85124e10 | 0.334355 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.35868e11 | 2.36543 | ||||||||
\(247\) | 2.38650e10 | 0.407967 | ||||||||
\(248\) | 1.22168e10 | 0.205081 | ||||||||
\(249\) | 9.46795e10 | 1.56084 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.75467e10 | 1.55125 | 0.775624 | − | 0.631196i | \(-0.217435\pi\) | ||||
0.775624 | + | 0.631196i | \(0.217435\pi\) | |||||||
\(252\) | −2.54171e10 | −0.397030 | ||||||||
\(253\) | −8.46315e9 | −0.129864 | ||||||||
\(254\) | −4.14540e10 | −0.624907 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.29497e9 | 0.0625000 | ||||||||
\(257\) | 4.43042e9 | 0.0633499 | 0.0316750 | − | 0.999498i | \(-0.489916\pi\) | ||||
0.0316750 | + | 0.999498i | \(0.489916\pi\) | |||||||
\(258\) | 5.73497e10 | 0.805828 | ||||||||
\(259\) | −8.39346e9 | −0.115902 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.78708e11 | 3.71763 | ||||||||
\(262\) | 3.92957e10 | 0.515216 | ||||||||
\(263\) | 1.20620e11 | 1.55460 | 0.777301 | − | 0.629129i | \(-0.216588\pi\) | ||||
0.777301 | + | 0.629129i | \(0.216588\pi\) | |||||||
\(264\) | −2.82741e10 | −0.358238 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.50434e10 | 0.184238 | ||||||||
\(267\) | 1.78268e11 | 2.14671 | ||||||||
\(268\) | −2.22816e10 | −0.263840 | ||||||||
\(269\) | 7.59025e10 | 0.883835 | 0.441917 | − | 0.897056i | \(-0.354298\pi\) | ||||
0.441917 | + | 0.897056i | \(0.354298\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.11397e10 | 0.801217 | 0.400608 | − | 0.916249i | \(-0.368799\pi\) | ||||
0.400608 | + | 0.916249i | \(0.368799\pi\) | |||||||
\(272\) | 2.35187e10 | 0.260528 | ||||||||
\(273\) | 3.61499e10 | 0.393890 | ||||||||
\(274\) | −9.73382e10 | −1.04329 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.91567e10 | 0.198714 | ||||||||
\(277\) | −8.61542e10 | −0.879261 | −0.439630 | − | 0.898179i | \(-0.644891\pi\) | ||||
−0.439630 | + | 0.898179i | \(0.644891\pi\) | |||||||
\(278\) | 3.60399e10 | 0.361894 | ||||||||
\(279\) | 1.23336e11 | 1.21863 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.00179e11 | −0.958511 | −0.479256 | − | 0.877675i | \(-0.659093\pi\) | ||||
−0.479256 | + | 0.877675i | \(0.659093\pi\) | |||||||
\(282\) | 1.09290e11 | 1.02910 | ||||||||
\(283\) | 4.57444e10 | 0.423935 | 0.211967 | − | 0.977277i | \(-0.432013\pi\) | ||||
0.211967 | + | 0.977277i | \(0.432013\pi\) | |||||||
\(284\) | 5.62233e10 | 0.512842 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.72450e10 | 0.240791 | ||||||||
\(287\) | −8.25282e10 | −0.718015 | ||||||||
\(288\) | 4.33604e10 | 0.371388 | ||||||||
\(289\) | 1.01980e10 | 0.0859950 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.66448e11 | 1.36069 | ||||||||
\(292\) | −6.85546e10 | −0.551841 | ||||||||
\(293\) | 1.01615e10 | 0.0805476 | 0.0402738 | − | 0.999189i | \(-0.487177\pi\) | ||||
0.0402738 | + | 0.999189i | \(0.487177\pi\) | |||||||
\(294\) | 2.27873e10 | 0.177881 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.43189e10 | 0.108417 | ||||||||
\(297\) | −1.49576e11 | −1.11547 | ||||||||
\(298\) | −5.01628e10 | −0.368475 | ||||||||
\(299\) | −1.84594e10 | −0.133566 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.48349e10 | −0.244605 | ||||||||
\(302\) | −9.93501e10 | −0.687286 | ||||||||
\(303\) | −2.58924e9 | −0.0176474 | ||||||||
\(304\) | −2.56634e10 | −0.172339 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.37437e11 | 1.54811 | ||||||||
\(307\) | 3.68957e10 | 0.237057 | 0.118529 | − | 0.992951i | \(-0.462182\pi\) | ||||
0.118529 | + | 0.992951i | \(0.462182\pi\) | |||||||
\(308\) | 1.71741e10 | 0.108741 | ||||||||
\(309\) | −3.45335e11 | −2.15490 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.88558e11 | 1.14294 | 0.571469 | − | 0.820624i | \(-0.306374\pi\) | ||||
0.571469 | + | 0.820624i | \(0.306374\pi\) | |||||||
\(312\) | −6.16701e10 | −0.368450 | ||||||||
\(313\) | −1.31778e11 | −0.776058 | −0.388029 | − | 0.921647i | \(-0.626844\pi\) | ||||
−0.388029 | + | 0.921647i | \(0.626844\pi\) | |||||||
\(314\) | −2.13405e11 | −1.23886 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.30495e9 | 0.0412122 | ||||||||
\(317\) | 1.50686e11 | 0.838118 | 0.419059 | − | 0.907959i | \(-0.362360\pi\) | ||||
0.419059 | + | 0.907959i | \(0.362360\pi\) | |||||||
\(318\) | 9.45584e10 | 0.518535 | ||||||||
\(319\) | −1.88320e11 | −1.01821 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.19675e11 | 0.629118 | ||||||||
\(322\) | −1.16360e10 | −0.0603187 | ||||||||
\(323\) | −1.40530e11 | −0.718386 | ||||||||
\(324\) | 1.30206e11 | 0.656417 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.17379e11 | −0.575589 | ||||||||
\(327\) | −4.84959e10 | −0.234552 | ||||||||
\(328\) | 1.40789e11 | 0.671642 | ||||||||
\(329\) | −6.63841e10 | −0.312380 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.38877e10 | 0.155173 | 0.0775865 | − | 0.996986i | \(-0.475279\pi\) | ||||
0.0775865 | + | 0.996986i | \(0.475279\pi\) | |||||||
\(332\) | 9.81087e10 | 0.443186 | ||||||||
\(333\) | 1.44558e11 | 0.644234 | ||||||||
\(334\) | 1.02753e11 | 0.451788 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.88741e10 | −0.166393 | ||||||||
\(337\) | −1.98312e11 | −0.837555 | −0.418778 | − | 0.908089i | \(-0.637541\pi\) | ||||
−0.418778 | + | 0.908089i | \(0.637541\pi\) | |||||||
\(338\) | −1.10247e11 | −0.459452 | ||||||||
\(339\) | 1.43500e11 | 0.590138 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.33371e10 | −0.333767 | ||||||||
\(342\) | −2.59089e11 | −1.02407 | ||||||||
\(343\) | −1.38413e10 | −0.0539949 | ||||||||
\(344\) | 5.94268e10 | 0.228807 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.06954e11 | −1.15141 | ||||||||
\(347\) | 1.71762e11 | 0.635981 | 0.317990 | − | 0.948094i | \(-0.396992\pi\) | ||||
0.317990 | + | 0.948094i | \(0.396992\pi\) | |||||||
\(348\) | 4.26269e11 | 1.55803 | ||||||||
\(349\) | −1.88189e11 | −0.679014 | −0.339507 | − | 0.940603i | \(-0.610260\pi\) | ||||
−0.339507 | + | 0.940603i | \(0.610260\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.26248e11 | −1.14727 | ||||||||
\(352\) | −2.92982e10 | −0.101718 | ||||||||
\(353\) | −1.97995e11 | −0.678686 | −0.339343 | − | 0.940663i | \(-0.610205\pi\) | ||||
−0.339343 | + | 0.940663i | \(0.610205\pi\) | |||||||
\(354\) | −4.76633e11 | −1.61313 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.84725e11 | 0.609537 | ||||||||
\(357\) | −2.12870e11 | −0.693598 | ||||||||
\(358\) | 2.45403e11 | 0.789598 | ||||||||
\(359\) | 4.34669e11 | 1.38113 | 0.690563 | − | 0.723272i | \(-0.257363\pi\) | ||||
0.690563 | + | 0.723272i | \(0.257363\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.69343e11 | −0.524788 | ||||||||
\(362\) | −2.77560e11 | −0.849510 | ||||||||
\(363\) | −3.89663e11 | −1.17790 | ||||||||
\(364\) | 3.74592e10 | 0.111841 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.85845e11 | 0.832657 | ||||||||
\(367\) | −6.02066e10 | −0.173240 | −0.0866198 | − | 0.996241i | \(-0.527607\pi\) | ||||
−0.0866198 | + | 0.996241i | \(0.527607\pi\) | |||||||
\(368\) | 1.98505e10 | 0.0564230 | ||||||||
\(369\) | 1.42136e12 | 3.99103 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.74359e10 | −0.157399 | ||||||||
\(372\) | 1.88637e11 | 0.510720 | ||||||||
\(373\) | 6.85521e11 | 1.83371 | 0.916855 | − | 0.399219i | \(-0.130719\pi\) | ||||
0.916855 | + | 0.399219i | \(0.130719\pi\) | |||||||
\(374\) | −1.60433e11 | −0.424007 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.13248e11 | 0.292204 | ||||||||
\(377\) | −4.10754e11 | −1.04724 | ||||||||
\(378\) | −2.05653e11 | −0.518109 | ||||||||
\(379\) | 5.05522e11 | 1.25853 | 0.629266 | − | 0.777190i | \(-0.283356\pi\) | ||||
0.629266 | + | 0.777190i | \(0.283356\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.40082e11 | −1.55623 | ||||||||
\(382\) | 4.32221e11 | 1.03854 | ||||||||
\(383\) | −2.02054e11 | −0.479814 | −0.239907 | − | 0.970796i | \(-0.577117\pi\) | ||||
−0.239907 | + | 0.970796i | \(0.577117\pi\) | |||||||
\(384\) | 6.63175e10 | 0.155646 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.32371e10 | −0.0991321 | ||||||||
\(387\) | 5.99952e11 | 1.35962 | ||||||||
\(388\) | 1.72476e11 | 0.386355 | ||||||||
\(389\) | 5.51954e11 | 1.22216 | 0.611082 | − | 0.791567i | \(-0.290735\pi\) | ||||
0.611082 | + | 0.791567i | \(0.290735\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.08699e11 | 0.235196 | ||||||||
\(392\) | 2.36126e10 | 0.0505076 | ||||||||
\(393\) | 6.06756e11 | 1.28306 | ||||||||
\(394\) | −3.82475e11 | −0.799595 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.95784e11 | −0.604430 | ||||||||
\(397\) | −1.26816e11 | −0.256222 | −0.128111 | − | 0.991760i | \(-0.540891\pi\) | ||||
−0.128111 | + | 0.991760i | \(0.540891\pi\) | |||||||
\(398\) | −3.45777e10 | −0.0690753 | ||||||||
\(399\) | 2.32282e11 | 0.458815 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.86957e11 | 1.13359 | 0.566795 | − | 0.823859i | \(-0.308183\pi\) | ||||
0.566795 | + | 0.823859i | \(0.308183\pi\) | |||||||
\(402\) | −3.44045e11 | −0.657050 | ||||||||
\(403\) | −1.81771e11 | −0.343282 | ||||||||
\(404\) | −2.68302e9 | −0.00501081 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.58921e11 | −0.472934 | ||||||||
\(407\) | −9.76764e10 | −0.176447 | ||||||||
\(408\) | 3.63147e11 | 0.648801 | ||||||||
\(409\) | −9.08262e10 | −0.160493 | −0.0802465 | − | 0.996775i | \(-0.525571\pi\) | ||||
−0.0802465 | + | 0.996775i | \(0.525571\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.50298e12 | −2.59815 | ||||||||
\(412\) | −3.57843e11 | −0.611864 | ||||||||
\(413\) | 2.89513e11 | 0.489658 | ||||||||
\(414\) | 2.00403e11 | 0.335277 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.39037e10 | −0.104618 | ||||||||
\(417\) | 5.56483e11 | 0.901238 | ||||||||
\(418\) | 1.75064e11 | 0.280481 | ||||||||
\(419\) | −8.34669e11 | −1.32297 | −0.661487 | − | 0.749957i | \(-0.730074\pi\) | ||||
−0.661487 | + | 0.749957i | \(0.730074\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.61360e10 | −0.0250337 | −0.0125169 | − | 0.999922i | \(-0.503984\pi\) | ||||
−0.0125169 | + | 0.999922i | \(0.503984\pi\) | |||||||
\(422\) | 5.77688e10 | 0.0886722 | ||||||||
\(423\) | 1.14331e12 | 1.73634 | ||||||||
\(424\) | 9.79832e10 | 0.147233 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.68130e11 | 1.27715 | ||||||||
\(427\) | −1.73626e11 | −0.252749 | ||||||||
\(428\) | 1.24010e11 | 0.178632 | ||||||||
\(429\) | 4.20684e11 | 0.599650 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.81935e11 | −0.672730 | −0.336365 | − | 0.941732i | \(-0.609198\pi\) | ||||
−0.336365 | + | 0.941732i | \(0.609198\pi\) | |||||||
\(432\) | 3.50834e11 | 0.484646 | ||||||||
\(433\) | −6.68314e11 | −0.913661 | −0.456830 | − | 0.889554i | \(-0.651015\pi\) | ||||
−0.456830 | + | 0.889554i | \(0.651015\pi\) | |||||||
\(434\) | −1.14580e11 | −0.155026 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.02523e10 | −0.0665989 | ||||||||
\(437\) | −1.18611e11 | −0.155582 | ||||||||
\(438\) | −1.05854e12 | −1.37427 | ||||||||
\(439\) | −4.79819e11 | −0.616577 | −0.308288 | − | 0.951293i | \(-0.599756\pi\) | ||||
−0.308288 | + | 0.951293i | \(0.599756\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.38384e11 | 0.300126 | ||||||||
\(442\) | −3.49929e11 | −0.436094 | ||||||||
\(443\) | 6.53598e11 | 0.806295 | 0.403148 | − | 0.915135i | \(-0.367916\pi\) | ||||
0.403148 | + | 0.915135i | \(0.367916\pi\) | |||||||
\(444\) | 2.21094e11 | 0.269994 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.14080e12 | 1.36522 | ||||||||
\(447\) | −7.74551e11 | −0.917627 | ||||||||
\(448\) | −4.02821e10 | −0.0472456 | ||||||||
\(449\) | −1.88660e11 | −0.219064 | −0.109532 | − | 0.993983i | \(-0.534935\pi\) | ||||
−0.109532 | + | 0.993983i | \(0.534935\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.60397e11 | −1.09309 | ||||||||
\(452\) | 1.48697e11 | 0.167564 | ||||||||
\(453\) | −1.53404e12 | −1.71157 | ||||||||
\(454\) | −1.14458e12 | −1.26443 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.96263e11 | −0.429182 | ||||||||
\(457\) | −1.31205e12 | −1.40711 | −0.703556 | − | 0.710639i | \(-0.748406\pi\) | ||||
−0.703556 | + | 0.710639i | \(0.748406\pi\) | |||||||
\(458\) | −5.69633e11 | −0.604923 | ||||||||
\(459\) | 1.92113e12 | 2.02022 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.16594e12 | 1.20233 | 0.601165 | − | 0.799125i | \(-0.294703\pi\) | ||||
0.601165 | + | 0.799125i | \(0.294703\pi\) | |||||||
\(462\) | 2.65181e11 | 0.270803 | ||||||||
\(463\) | 3.87318e10 | 0.0391700 | 0.0195850 | − | 0.999808i | \(-0.493766\pi\) | ||||
0.0195850 | + | 0.999808i | \(0.493766\pi\) | |||||||
\(464\) | 4.41708e11 | 0.442389 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.08111e11 | 0.597374 | ||||||||
\(467\) | −1.17150e11 | −0.113977 | −0.0569883 | − | 0.998375i | \(-0.518150\pi\) | ||||
−0.0569883 | + | 0.998375i | \(0.518150\pi\) | |||||||
\(468\) | −6.45149e11 | −0.621661 | ||||||||
\(469\) | 2.08977e11 | 0.199444 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.29514e12 | −3.08518 | ||||||||
\(472\) | −4.93896e11 | −0.458033 | ||||||||
\(473\) | −4.05381e11 | −0.372382 | ||||||||
\(474\) | 1.12794e11 | 0.102632 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.20580e11 | −0.196940 | ||||||||
\(477\) | 9.89203e11 | 0.874888 | ||||||||
\(478\) | −1.38740e12 | −1.21556 | ||||||||
\(479\) | −1.94734e12 | −1.69018 | −0.845089 | − | 0.534626i | \(-0.820452\pi\) | ||||
−0.845089 | + | 0.534626i | \(0.820452\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.13047e11 | −0.181477 | ||||||||
\(482\) | −1.30947e11 | −0.110505 | ||||||||
\(483\) | −1.79668e11 | −0.150214 | ||||||||
\(484\) | −4.03776e11 | −0.334454 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 3.24580e11 | 0.263912 | ||||||||
\(487\) | 1.95983e12 | 1.57884 | 0.789421 | − | 0.613852i | \(-0.210381\pi\) | ||||
0.789421 | + | 0.613852i | \(0.210381\pi\) | |||||||
\(488\) | 2.96198e11 | 0.236425 | ||||||||
\(489\) | −1.81243e12 | −1.43341 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.93589e11 | −0.227967 | −0.113984 | − | 0.993483i | \(-0.536361\pi\) | ||||
−0.113984 | + | 0.993483i | \(0.536361\pi\) | |||||||
\(492\) | 2.17389e12 | 1.67261 | ||||||||
\(493\) | 2.41874e12 | 1.84407 | ||||||||
\(494\) | 3.81840e11 | 0.288476 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.95469e11 | 0.145014 | ||||||||
\(497\) | −5.27313e11 | −0.387672 | ||||||||
\(498\) | 1.51487e12 | 1.10368 | ||||||||
\(499\) | 1.71390e12 | 1.23746 | 0.618732 | − | 0.785602i | \(-0.287647\pi\) | ||||
0.618732 | + | 0.785602i | \(0.287647\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.58658e12 | 1.12510 | ||||||||
\(502\) | 1.56075e12 | 1.09690 | ||||||||
\(503\) | −1.61385e12 | −1.12411 | −0.562053 | − | 0.827101i | \(-0.689988\pi\) | ||||
−0.562053 | + | 0.827101i | \(0.689988\pi\) | |||||||
\(504\) | −4.06673e11 | −0.280743 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.35410e11 | −0.0918279 | ||||||||
\(507\) | −1.70229e12 | −1.14419 | ||||||||
\(508\) | −6.63265e11 | −0.441876 | ||||||||
\(509\) | 1.17088e12 | 0.773181 | 0.386590 | − | 0.922252i | \(-0.373653\pi\) | ||||
0.386590 | + | 0.922252i | \(0.373653\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.42967e11 | 0.417153 | ||||||||
\(512\) | 6.87195e10 | 0.0441942 | ||||||||
\(513\) | −2.09632e12 | −1.33638 | ||||||||
\(514\) | 7.08868e10 | 0.0447952 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 9.17595e11 | 0.569807 | ||||||||
\(517\) | −7.72526e11 | −0.475560 | ||||||||
\(518\) | −1.34295e11 | −0.0819553 | ||||||||
\(519\) | −4.73960e12 | −2.86740 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.91339e12 | 1.73232 | 0.866161 | − | 0.499765i | \(-0.166580\pi\) | ||||
0.866161 | + | 0.499765i | \(0.166580\pi\) | |||||||
\(522\) | 4.45932e12 | 2.62876 | ||||||||
\(523\) | −2.53787e12 | −1.48324 | −0.741620 | − | 0.670820i | \(-0.765942\pi\) | ||||
−0.741620 | + | 0.670820i | \(0.765942\pi\) | |||||||
\(524\) | 6.28732e11 | 0.364313 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.92992e12 | 1.09927 | ||||||||
\(527\) | 1.07036e12 | 0.604482 | ||||||||
\(528\) | −4.52386e11 | −0.253313 | ||||||||
\(529\) | −1.70941e12 | −0.949063 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.98620e12 | −2.72172 | ||||||||
\(532\) | 2.40695e11 | 0.130276 | ||||||||
\(533\) | −2.09477e12 | −1.12425 | ||||||||
\(534\) | 2.85229e12 | 1.51795 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.56506e11 | −0.186563 | ||||||||
\(537\) | 3.78920e12 | 1.96636 | ||||||||
\(538\) | 1.21444e12 | 0.624965 | ||||||||
\(539\) | −1.61074e11 | −0.0822008 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.11804e12 | 0.561136 | 0.280568 | − | 0.959834i | \(-0.409477\pi\) | ||||
0.280568 | + | 0.959834i | \(0.409477\pi\) | |||||||
\(542\) | 1.13823e12 | 0.566546 | ||||||||
\(543\) | −4.28574e12 | −2.11556 | ||||||||
\(544\) | 3.76300e11 | 0.184221 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 5.78398e11 | 0.278522 | ||||||||
\(547\) | −1.99438e12 | −0.952500 | −0.476250 | − | 0.879310i | \(-0.658004\pi\) | ||||
−0.476250 | + | 0.879310i | \(0.658004\pi\) | |||||||
\(548\) | −1.55741e12 | −0.737719 | ||||||||
\(549\) | 2.99031e12 | 1.40488 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.63931e12 | −1.21985 | ||||||||
\(552\) | 3.06506e11 | 0.140512 | ||||||||
\(553\) | −6.85125e10 | −0.0311535 | ||||||||
\(554\) | −1.37847e12 | −0.621731 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.76638e11 | 0.255898 | ||||||||
\(557\) | 4.69088e11 | 0.206493 | 0.103247 | − | 0.994656i | \(-0.467077\pi\) | ||||
0.103247 | + | 0.994656i | \(0.467077\pi\) | |||||||
\(558\) | 1.97338e12 | 0.861702 | ||||||||
\(559\) | −8.84197e11 | −0.382997 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.47721e12 | −1.05592 | ||||||||
\(562\) | −1.60286e12 | −0.677770 | ||||||||
\(563\) | −1.74518e12 | −0.732069 | −0.366034 | − | 0.930601i | \(-0.619285\pi\) | ||||
−0.366034 | + | 0.930601i | \(0.619285\pi\) | |||||||
\(564\) | 1.74864e12 | 0.727687 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.31911e11 | 0.299767 | ||||||||
\(567\) | −1.22119e12 | −0.496205 | ||||||||
\(568\) | 8.99572e11 | 0.362634 | ||||||||
\(569\) | −4.13341e12 | −1.65311 | −0.826557 | − | 0.562853i | \(-0.809704\pi\) | ||||
−0.826557 | + | 0.562853i | \(0.809704\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.14262e12 | 1.63084 | 0.815422 | − | 0.578867i | \(-0.196505\pi\) | ||||
0.815422 | + | 0.578867i | \(0.196505\pi\) | |||||||
\(572\) | 4.35920e11 | 0.170265 | ||||||||
\(573\) | 6.67383e12 | 2.58630 | ||||||||
\(574\) | −1.32045e12 | −0.507713 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.93767e11 | 0.262611 | ||||||||
\(577\) | −4.27130e12 | −1.60424 | −0.802120 | − | 0.597164i | \(-0.796294\pi\) | ||||
−0.802120 | + | 0.597164i | \(0.796294\pi\) | |||||||
\(578\) | 1.63167e11 | 0.0608076 | ||||||||
\(579\) | −6.67614e11 | −0.246872 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.20152e11 | −0.335017 | ||||||||
\(582\) | 2.66316e12 | 0.962154 | ||||||||
\(583\) | −6.68394e11 | −0.239621 | ||||||||
\(584\) | −1.09687e12 | −0.390211 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.62584e11 | 0.0569557 | ||||||||
\(587\) | −5.32282e12 | −1.85042 | −0.925210 | − | 0.379455i | \(-0.876111\pi\) | ||||
−0.925210 | + | 0.379455i | \(0.876111\pi\) | |||||||
\(588\) | 3.64597e11 | 0.125781 | ||||||||
\(589\) | −1.16797e12 | −0.399865 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.90570e12 | −1.99126 | ||||||||
\(592\) | 2.29102e11 | 0.0766622 | ||||||||
\(593\) | 2.69262e11 | 0.0894190 | 0.0447095 | − | 0.999000i | \(-0.485764\pi\) | ||||
0.0447095 | + | 0.999000i | \(0.485764\pi\) | |||||||
\(594\) | −2.39322e12 | −0.788758 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.02605e11 | −0.260551 | ||||||||
\(597\) | −5.33906e11 | −0.172021 | ||||||||
\(598\) | −2.95350e11 | −0.0944457 | ||||||||
\(599\) | 3.51807e12 | 1.11657 | 0.558283 | − | 0.829651i | \(-0.311460\pi\) | ||||
0.558283 | + | 0.829651i | \(0.311460\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.97549e12 | −0.617645 | −0.308823 | − | 0.951120i | \(-0.599935\pi\) | ||||
−0.308823 | + | 0.951120i | \(0.599935\pi\) | |||||||
\(602\) | −5.57359e11 | −0.172962 | ||||||||
\(603\) | −3.59916e12 | −1.10860 | ||||||||
\(604\) | −1.58960e12 | −0.485984 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.14279e10 | −0.0124786 | ||||||||
\(607\) | 1.20562e12 | 0.360464 | 0.180232 | − | 0.983624i | \(-0.442315\pi\) | ||||
0.180232 | + | 0.983624i | \(0.442315\pi\) | |||||||
\(608\) | −4.10615e11 | −0.121862 | ||||||||
\(609\) | −3.99794e12 | −1.17776 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.68499e12 | −0.489117 | ||||||||
\(612\) | 3.79899e12 | 1.09468 | ||||||||
\(613\) | 5.02026e11 | 0.143600 | 0.0717999 | − | 0.997419i | \(-0.477126\pi\) | ||||
0.0717999 | + | 0.997419i | \(0.477126\pi\) | |||||||
\(614\) | 5.90332e11 | 0.167625 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.74785e11 | 0.0768918 | ||||||||
\(617\) | −5.17852e12 | −1.43854 | −0.719271 | − | 0.694730i | \(-0.755524\pi\) | ||||
−0.719271 | + | 0.694730i | \(0.755524\pi\) | |||||||
\(618\) | −5.52536e12 | −1.52375 | ||||||||
\(619\) | −4.69963e12 | −1.28664 | −0.643318 | − | 0.765599i | \(-0.722443\pi\) | ||||
−0.643318 | + | 0.765599i | \(0.722443\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.62149e12 | 0.437523 | ||||||||
\(622\) | 3.01693e12 | 0.808179 | ||||||||
\(623\) | −1.73252e12 | −0.460767 | ||||||||
\(624\) | −9.86722e11 | −0.260534 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.10845e12 | −0.548756 | ||||||||
\(627\) | 2.70312e12 | 0.698491 | ||||||||
\(628\) | −3.41449e12 | −0.876006 | ||||||||
\(629\) | 1.25454e12 | 0.319562 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.53678e12 | −1.39035 | −0.695177 | − | 0.718839i | \(-0.744674\pi\) | ||||
−0.695177 | + | 0.718839i | \(0.744674\pi\) | |||||||
\(632\) | 1.16879e11 | 0.0291414 | ||||||||
\(633\) | 8.91994e11 | 0.220823 | ||||||||
\(634\) | 2.41097e12 | 0.592639 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.51293e12 | 0.366660 | ||||||||
\(637\) | −3.51326e11 | −0.0845441 | ||||||||
\(638\) | −3.01312e12 | −0.719985 | ||||||||
\(639\) | 9.08175e12 | 2.15484 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.85506e12 | −0.667966 | −0.333983 | − | 0.942579i | \(-0.608393\pi\) | ||||
−0.333983 | + | 0.942579i | \(0.608393\pi\) | |||||||
\(642\) | 1.91481e12 | 0.444854 | ||||||||
\(643\) | 7.48209e12 | 1.72613 | 0.863065 | − | 0.505093i | \(-0.168542\pi\) | ||||
0.863065 | + | 0.505093i | \(0.168542\pi\) | |||||||
\(644\) | −1.86176e11 | −0.0426518 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.24848e12 | −0.507976 | ||||||||
\(647\) | 3.83872e12 | 0.861225 | 0.430613 | − | 0.902537i | \(-0.358297\pi\) | ||||
0.430613 | + | 0.902537i | \(0.358297\pi\) | |||||||
\(648\) | 2.08330e12 | 0.464157 | ||||||||
\(649\) | 3.36912e12 | 0.745445 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.76920e12 | −0.386068 | ||||||||
\(652\) | −1.87807e12 | −0.407003 | ||||||||
\(653\) | 1.09261e11 | 0.0235157 | 0.0117578 | − | 0.999931i | \(-0.496257\pi\) | ||||
0.0117578 | + | 0.999931i | \(0.496257\pi\) | |||||||
\(654\) | −7.75934e11 | −0.165854 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.25263e12 | 0.474922 | ||||||||
\(657\) | −1.10736e13 | −2.31871 | ||||||||
\(658\) | −1.06215e12 | −0.220886 | ||||||||
\(659\) | −2.10319e12 | −0.434403 | −0.217202 | − | 0.976127i | \(-0.569693\pi\) | ||||
−0.217202 | + | 0.976127i | \(0.569693\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.76045e12 | −0.358688 | −0.179344 | − | 0.983786i | \(-0.557397\pi\) | ||||
−0.179344 | + | 0.983786i | \(0.557397\pi\) | |||||||
\(662\) | 5.42203e11 | 0.109724 | ||||||||
\(663\) | −5.40317e12 | −1.08602 | ||||||||
\(664\) | 1.56974e12 | 0.313380 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.31293e12 | 0.455542 | ||||||||
\(667\) | 2.04149e12 | 0.399374 | ||||||||
\(668\) | 1.64404e12 | 0.319462 | ||||||||
\(669\) | 1.76148e13 | 3.39986 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.02052e12 | −0.384779 | ||||||||
\(672\) | −6.21986e11 | −0.117657 | ||||||||
\(673\) | −8.52389e12 | −1.60166 | −0.800830 | − | 0.598892i | \(-0.795608\pi\) | ||||
−0.800830 | + | 0.598892i | \(0.795608\pi\) | |||||||
\(674\) | −3.17299e12 | −0.592241 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.76394e12 | −0.324881 | ||||||||
\(677\) | 2.88497e12 | 0.527828 | 0.263914 | − | 0.964546i | \(-0.414986\pi\) | ||||
0.263914 | + | 0.964546i | \(0.414986\pi\) | |||||||
\(678\) | 2.29600e12 | 0.417290 | ||||||||
\(679\) | −1.61764e12 | −0.292057 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.76732e13 | −3.14885 | ||||||||
\(682\) | −1.33339e12 | −0.236009 | ||||||||
\(683\) | −1.03086e13 | −1.81262 | −0.906309 | − | 0.422616i | \(-0.861112\pi\) | ||||
−0.906309 | + | 0.422616i | \(0.861112\pi\) | |||||||
\(684\) | −4.14542e12 | −0.724130 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.21461e11 | −0.0381802 | ||||||||
\(687\) | −8.79556e12 | −1.50646 | ||||||||
\(688\) | 9.50829e11 | 0.161791 | ||||||||
\(689\) | −1.45787e12 | −0.246451 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.85439e12 | 1.31057 | 0.655287 | − | 0.755380i | \(-0.272548\pi\) | ||||
0.655287 | + | 0.755380i | \(0.272548\pi\) | |||||||
\(692\) | −4.91126e12 | −0.814171 | ||||||||
\(693\) | 2.77413e12 | 0.456906 | ||||||||
\(694\) | 2.74819e12 | 0.449706 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 6.82030e12 | 1.10170 | ||||||||
\(697\) | 1.23351e13 | 1.97969 | ||||||||
\(698\) | −3.01102e12 | −0.480136 | ||||||||
\(699\) | 9.38969e12 | 1.48766 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.69579e12 | 0.265242 | 0.132621 | − | 0.991167i | \(-0.457661\pi\) | ||||
0.132621 | + | 0.991167i | \(0.457661\pi\) | |||||||
\(702\) | −5.21997e12 | −0.811243 | ||||||||
\(703\) | −1.36894e12 | −0.211390 | ||||||||
\(704\) | −4.68771e11 | −0.0719257 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.16793e12 | −0.479904 | ||||||||
\(707\) | 2.51638e10 | 0.00378781 | ||||||||
\(708\) | −7.62613e12 | −1.14066 | ||||||||
\(709\) | −2.20703e12 | −0.328020 | −0.164010 | − | 0.986459i | \(-0.552443\pi\) | ||||
−0.164010 | + | 0.986459i | \(0.552443\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.17997e12 | 0.173164 | ||||||||
\(712\) | 2.95560e12 | 0.431008 | ||||||||
\(713\) | 9.03417e11 | 0.130914 | ||||||||
\(714\) | −3.40592e12 | −0.490448 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.92644e12 | 0.558330 | ||||||||
\(717\) | −2.14225e13 | −3.02715 | ||||||||
\(718\) | 6.95470e12 | 0.976604 | ||||||||
\(719\) | −1.46869e12 | −0.204952 | −0.102476 | − | 0.994735i | \(-0.532676\pi\) | ||||
−0.102476 | + | 0.994735i | \(0.532676\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.35617e12 | 0.462525 | ||||||||
\(722\) | −2.70948e12 | −0.371081 | ||||||||
\(723\) | −2.02192e12 | −0.275195 | ||||||||
\(724\) | −4.44096e12 | −0.600694 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −6.23461e12 | −0.832904 | ||||||||
\(727\) | 4.97511e11 | 0.0660538 | 0.0330269 | − | 0.999454i | \(-0.489485\pi\) | ||||
0.0330269 | + | 0.999454i | \(0.489485\pi\) | |||||||
\(728\) | 5.99347e11 | 0.0790837 | ||||||||
\(729\) | −4.99938e12 | −0.655605 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.20663e12 | 0.674417 | ||||||||
\(732\) | 4.57352e12 | 0.588777 | ||||||||
\(733\) | 5.22437e12 | 0.668445 | 0.334223 | − | 0.942494i | \(-0.391526\pi\) | ||||
0.334223 | + | 0.942494i | \(0.391526\pi\) | |||||||
\(734\) | −9.63306e11 | −0.122499 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.17608e11 | 0.0398971 | ||||||||
\(737\) | 2.43191e12 | 0.303630 | ||||||||
\(738\) | 2.27417e13 | 2.82208 | ||||||||
\(739\) | 7.35495e11 | 0.0907152 | 0.0453576 | − | 0.998971i | \(-0.485557\pi\) | ||||
0.0453576 | + | 0.998971i | \(0.485557\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.89590e12 | 0.718403 | ||||||||
\(742\) | −9.18975e11 | −0.111298 | ||||||||
\(743\) | 1.12076e12 | 0.134916 | 0.0674580 | − | 0.997722i | \(-0.478511\pi\) | ||||
0.0674580 | + | 0.997722i | \(0.478511\pi\) | |||||||
\(744\) | 3.01818e12 | 0.361133 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.09683e13 | 1.29663 | ||||||||
\(747\) | 1.58475e13 | 1.86217 | ||||||||
\(748\) | −2.56694e12 | −0.299818 | ||||||||
\(749\) | −1.16308e12 | −0.135033 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.62183e12 | −0.186049 | −0.0930244 | − | 0.995664i | \(-0.529653\pi\) | ||||
−0.0930244 | + | 0.995664i | \(0.529653\pi\) | |||||||
\(752\) | 1.81197e12 | 0.206620 | ||||||||
\(753\) | 2.40991e13 | 2.73164 | ||||||||
\(754\) | −6.57206e12 | −0.740509 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.29044e12 | −0.366358 | ||||||||
\(757\) | 1.55150e12 | 0.171720 | 0.0858600 | − | 0.996307i | \(-0.472636\pi\) | ||||
0.0858600 | + | 0.996307i | \(0.472636\pi\) | |||||||
\(758\) | 8.08836e12 | 0.889916 | ||||||||
\(759\) | −2.09084e12 | −0.228682 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.62863e13 | 1.76032 | 0.880159 | − | 0.474679i | \(-0.157436\pi\) | ||||
0.880159 | + | 0.474679i | \(0.157436\pi\) | |||||||
\(762\) | −1.02413e13 | −1.10042 | ||||||||
\(763\) | 4.71312e11 | 0.0503440 | ||||||||
\(764\) | 6.91554e12 | 0.734355 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.23286e12 | −0.339280 | ||||||||
\(767\) | 7.34856e12 | 0.766695 | ||||||||
\(768\) | 1.06108e12 | 0.110058 | ||||||||
\(769\) | −1.32915e13 | −1.37059 | −0.685293 | − | 0.728267i | \(-0.740326\pi\) | ||||
−0.685293 | + | 0.728267i | \(0.740326\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.09455e12 | 0.111555 | ||||||||
\(772\) | −6.91794e11 | −0.0700970 | ||||||||
\(773\) | 7.58593e12 | 0.764190 | 0.382095 | − | 0.924123i | \(-0.375203\pi\) | ||||
0.382095 | + | 0.924123i | \(0.375203\pi\) | |||||||
\(774\) | 9.59923e12 | 0.961395 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.75962e12 | 0.273194 | ||||||||
\(777\) | −2.07362e12 | −0.204096 | ||||||||
\(778\) | 8.83126e12 | 0.864200 | ||||||||
\(779\) | −1.34600e13 | −1.30956 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.13645e12 | −0.590184 | ||||||||
\(782\) | 1.73918e12 | 0.166309 | ||||||||
\(783\) | 3.60809e13 | 3.43044 | ||||||||
\(784\) | 3.77802e11 | 0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 9.70809e12 | 0.907262 | ||||||||
\(787\) | −3.30985e12 | −0.307554 | −0.153777 | − | 0.988106i | \(-0.549144\pi\) | ||||
−0.153777 | + | 0.988106i | \(0.549144\pi\) | |||||||
\(788\) | −6.11960e12 | −0.565399 | ||||||||
\(789\) | 2.97995e13 | 2.73755 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.39462e12 | −0.126666 | ||||||||
\(792\) | −4.73254e12 | −0.427397 | ||||||||
\(793\) | −4.40706e12 | −0.395748 | ||||||||
\(794\) | −2.02906e12 | −0.181176 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.53244e11 | −0.0488436 | ||||||||
\(797\) | 3.26446e12 | 0.286582 | 0.143291 | − | 0.989681i | \(-0.454232\pi\) | ||||
0.143291 | + | 0.989681i | \(0.454232\pi\) | |||||||
\(798\) | 3.71651e12 | 0.324431 | ||||||||
\(799\) | 9.92216e12 | 0.861283 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.98386e13 | 2.56114 | ||||||||
\(802\) | 9.39131e12 | 0.801570 | ||||||||
\(803\) | 7.48235e12 | 0.635064 | ||||||||
\(804\) | −5.50473e12 | −0.464605 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.90833e12 | −0.242737 | ||||||||
\(807\) | 1.87519e13 | 1.55637 | ||||||||
\(808\) | −4.29283e10 | −0.00354318 | ||||||||
\(809\) | 3.46768e12 | 0.284624 | 0.142312 | − | 0.989822i | \(-0.454546\pi\) | ||||
0.142312 | + | 0.989822i | \(0.454546\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.02915e13 | 0.835381 | 0.417690 | − | 0.908589i | \(-0.362840\pi\) | ||||
0.417690 | + | 0.908589i | \(0.362840\pi\) | |||||||
\(812\) | −4.14274e12 | −0.334415 | ||||||||
\(813\) | 1.75752e13 | 1.41089 | ||||||||
\(814\) | −1.56282e12 | −0.124767 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5.81035e12 | 0.458772 | ||||||||
\(817\) | −5.68143e12 | −0.446127 | ||||||||
\(818\) | −1.45322e12 | −0.113486 | ||||||||
\(819\) | 6.05079e12 | 0.469931 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.23700e12 | 0.479106 | 0.239553 | − | 0.970883i | \(-0.422999\pi\) | ||||
0.239553 | + | 0.970883i | \(0.422999\pi\) | |||||||
\(822\) | −2.40476e13 | −1.83717 | ||||||||
\(823\) | −2.46689e13 | −1.87435 | −0.937175 | − | 0.348860i | \(-0.886569\pi\) | ||||
−0.937175 | + | 0.348860i | \(0.886569\pi\) | |||||||
\(824\) | −5.72548e12 | −0.432653 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.63221e12 | 0.346240 | ||||||||
\(827\) | 1.45027e13 | 1.07814 | 0.539068 | − | 0.842262i | \(-0.318776\pi\) | ||||
0.539068 | + | 0.842262i | \(0.318776\pi\) | |||||||
\(828\) | 3.20645e12 | 0.237076 | ||||||||
\(829\) | −1.07681e13 | −0.791854 | −0.395927 | − | 0.918282i | \(-0.629577\pi\) | ||||
−0.395927 | + | 0.918282i | \(0.629577\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.12846e13 | −1.54832 | ||||||||
\(832\) | −1.02246e12 | −0.0739761 | ||||||||
\(833\) | 2.06880e12 | 0.148873 | ||||||||
\(834\) | 8.90373e12 | 0.637272 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.80102e12 | 0.198330 | ||||||||
\(837\) | 1.59668e13 | 1.12449 | ||||||||
\(838\) | −1.33547e13 | −0.935484 | ||||||||
\(839\) | −2.36129e13 | −1.64521 | −0.822603 | − | 0.568616i | \(-0.807479\pi\) | ||||
−0.822603 | + | 0.568616i | \(0.807479\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.09195e13 | 2.13133 | ||||||||
\(842\) | −2.58176e11 | −0.0177015 | ||||||||
\(843\) | −2.47494e13 | −1.68787 | ||||||||
\(844\) | 9.24301e11 | 0.0627007 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.82930e13 | 1.22778 | ||||||||
\(847\) | 3.78698e12 | 0.252824 | ||||||||
\(848\) | 1.56773e12 | 0.104109 | ||||||||
\(849\) | 1.13013e13 | 0.746521 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.05886e12 | 0.0692081 | ||||||||
\(852\) | 1.38901e13 | 0.903080 | ||||||||
\(853\) | 1.67503e13 | 1.08331 | 0.541655 | − | 0.840601i | \(-0.317798\pi\) | ||||
0.541655 | + | 0.840601i | \(0.317798\pi\) | |||||||
\(854\) | −2.77801e12 | −0.178720 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.98416e12 | 0.126312 | ||||||||
\(857\) | 1.16182e13 | 0.735742 | 0.367871 | − | 0.929877i | \(-0.380087\pi\) | ||||
0.367871 | + | 0.929877i | \(0.380087\pi\) | |||||||
\(858\) | 6.73094e12 | 0.424017 | ||||||||
\(859\) | 1.58818e13 | 0.995246 | 0.497623 | − | 0.867393i | \(-0.334206\pi\) | ||||
0.497623 | + | 0.867393i | \(0.334206\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.03888e13 | −1.26438 | ||||||||
\(862\) | −7.71096e12 | −0.475692 | ||||||||
\(863\) | −1.35971e13 | −0.834446 | −0.417223 | − | 0.908804i | \(-0.636997\pi\) | ||||
−0.417223 | + | 0.908804i | \(0.636997\pi\) | |||||||
\(864\) | 5.61335e12 | 0.342697 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.06930e13 | −0.646056 | ||||||||
\(867\) | 2.51943e12 | 0.151431 | ||||||||
\(868\) | −1.83328e12 | −0.109620 | ||||||||
\(869\) | −7.97294e11 | −0.0474274 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.30437e12 | 0.312285 | ||||||||
\(872\) | −8.04037e11 | −0.0470925 | ||||||||
\(873\) | 2.78601e13 | 1.62338 | ||||||||
\(874\) | −1.89778e12 | −0.110013 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.69366e13 | −0.971755 | ||||||||
\(877\) | −3.40277e12 | −0.194238 | −0.0971189 | − | 0.995273i | \(-0.530963\pi\) | ||||
−0.0971189 | + | 0.995273i | \(0.530963\pi\) | |||||||
\(878\) | −7.67711e12 | −0.435986 | ||||||||
\(879\) | 2.51041e12 | 0.141839 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.30779e12 | 0.520541 | 0.260270 | − | 0.965536i | \(-0.416188\pi\) | ||||
0.260270 | + | 0.965536i | \(0.416188\pi\) | |||||||
\(882\) | 3.81415e12 | 0.212221 | ||||||||
\(883\) | −1.00154e13 | −0.554430 | −0.277215 | − | 0.960808i | \(-0.589411\pi\) | ||||
−0.277215 | + | 0.960808i | \(0.589411\pi\) | |||||||
\(884\) | −5.59887e12 | −0.308365 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.04576e13 | 0.570137 | ||||||||
\(887\) | 2.58440e13 | 1.40186 | 0.700928 | − | 0.713232i | \(-0.252769\pi\) | ||||
0.700928 | + | 0.713232i | \(0.252769\pi\) | |||||||
\(888\) | 3.53751e12 | 0.190915 | ||||||||
\(889\) | 6.22070e12 | 0.334027 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.42113e13 | −0.755412 | ||||||||
\(892\) | 1.82528e13 | 0.965358 | ||||||||
\(893\) | −1.08270e13 | −0.569739 | ||||||||
\(894\) | −1.23928e13 | −0.648860 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −6.44514e11 | −0.0334077 | ||||||||
\(897\) | −4.56043e12 | −0.235201 | ||||||||
\(898\) | −3.01855e12 | −0.154901 | ||||||||
\(899\) | 2.01026e13 | 1.02644 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.58471e12 | 0.433974 | ||||||||
\(902\) | −1.53664e13 | −0.772932 | ||||||||
\(903\) | −8.60604e12 | −0.430733 | ||||||||
\(904\) | 2.37916e12 | 0.118486 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.45447e13 | −1.21026 | ||||||||
\(907\) | −3.82049e13 | −1.87451 | −0.937253 | − | 0.348650i | \(-0.886640\pi\) | ||||
−0.937253 | + | 0.348650i | \(0.886640\pi\) | |||||||
\(908\) | −1.83133e13 | −0.894086 | ||||||||
\(909\) | −4.33389e11 | −0.0210543 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.85478e12 | 0.474039 | 0.237020 | − | 0.971505i | \(-0.423829\pi\) | ||||
0.237020 | + | 0.971505i | \(0.423829\pi\) | |||||||
\(912\) | −6.34021e12 | −0.303478 | ||||||||
\(913\) | −1.07080e13 | −0.510023 | ||||||||
\(914\) | −2.09929e13 | −0.994979 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.11412e12 | −0.427745 | ||||||||
\(917\) | −5.89682e12 | −0.275395 | ||||||||
\(918\) | 3.07380e13 | 1.42851 | ||||||||
\(919\) | 2.60834e13 | 1.20627 | 0.603135 | − | 0.797639i | \(-0.293918\pi\) | ||||
0.603135 | + | 0.797639i | \(0.293918\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.11517e12 | 0.417442 | ||||||||
\(922\) | 1.86551e13 | 0.850176 | ||||||||
\(923\) | −1.33845e13 | −0.607008 | ||||||||
\(924\) | 4.24289e12 | 0.191486 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.19709e11 | 0.0276974 | ||||||||
\(927\) | −5.78024e13 | −2.57091 | ||||||||
\(928\) | 7.06733e12 | 0.312816 | ||||||||
\(929\) | −3.60592e13 | −1.58835 | −0.794174 | − | 0.607690i | \(-0.792096\pi\) | ||||
−0.794174 | + | 0.607690i | \(0.792096\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.25746e12 | −0.0984795 | ||||||||
\(932\) | 9.72977e12 | 0.422407 | ||||||||
\(933\) | 4.65836e13 | 2.01264 | ||||||||
\(934\) | −1.87440e12 | −0.0805936 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.03224e13 | −0.439581 | ||||||||
\(937\) | −2.75358e13 | −1.16700 | −0.583499 | − | 0.812114i | \(-0.698317\pi\) | ||||
−0.583499 | + | 0.812114i | \(0.698317\pi\) | |||||||
\(938\) | 3.34364e12 | 0.141028 | ||||||||
\(939\) | −3.25561e13 | −1.36659 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.60157e12 | −0.316046 | −0.158023 | − | 0.987435i | \(-0.550512\pi\) | ||||
−0.158023 | + | 0.987435i | \(0.550512\pi\) | |||||||
\(942\) | −5.27223e13 | −2.18155 | ||||||||
\(943\) | 1.04112e13 | 0.428745 | ||||||||
\(944\) | −7.90234e12 | −0.323878 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.48610e12 | −0.263314 | ||||||||
\(947\) | 2.35269e13 | 0.950582 | 0.475291 | − | 0.879829i | \(-0.342343\pi\) | ||||
0.475291 | + | 0.879829i | \(0.342343\pi\) | |||||||
\(948\) | 1.80470e12 | 0.0725719 | ||||||||
\(949\) | 1.63201e13 | 0.653168 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.72272e13 | 1.47587 | ||||||||
\(952\) | −3.52928e12 | −0.139258 | ||||||||
\(953\) | −3.76056e12 | −0.147684 | −0.0738422 | − | 0.997270i | \(-0.523526\pi\) | ||||
−0.0738422 | + | 0.997270i | \(0.523526\pi\) | |||||||
\(954\) | 1.58272e13 | 0.618639 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.21984e13 | −0.859531 | ||||||||
\(957\) | −4.65248e13 | −1.79300 | ||||||||
\(958\) | −3.11575e13 | −1.19514 | ||||||||
\(959\) | 1.46068e13 | 0.557663 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.75436e13 | −0.663535 | ||||||||
\(962\) | −3.40875e12 | −0.128324 | ||||||||
\(963\) | 2.00313e13 | 0.750571 | ||||||||
\(964\) | −2.09515e12 | −0.0781391 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.87470e12 | −0.106217 | ||||||||
\(967\) | −3.59678e13 | −1.32280 | −0.661400 | − | 0.750033i | \(-0.730037\pi\) | ||||
−0.661400 | + | 0.750033i | \(0.730037\pi\) | |||||||
\(968\) | −6.46042e12 | −0.236495 | ||||||||
\(969\) | −3.47182e13 | −1.26503 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.20049e13 | −0.433383 | −0.216692 | − | 0.976240i | \(-0.569527\pi\) | ||||
−0.216692 | + | 0.976240i | \(0.569527\pi\) | |||||||
\(972\) | 5.19328e12 | 0.186614 | ||||||||
\(973\) | −5.40823e12 | −0.193441 | ||||||||
\(974\) | 3.13573e13 | 1.11641 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.73917e12 | 0.167178 | ||||||||
\(977\) | 4.59954e12 | 0.161506 | 0.0807530 | − | 0.996734i | \(-0.474268\pi\) | ||||
0.0807530 | + | 0.996734i | \(0.474268\pi\) | |||||||
\(978\) | −2.89988e13 | −1.01357 | ||||||||
\(979\) | −2.01617e13 | −0.701462 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.11727e12 | −0.279833 | ||||||||
\(982\) | −4.69742e12 | −0.161197 | ||||||||
\(983\) | 3.13830e12 | 0.107202 | 0.0536011 | − | 0.998562i | \(-0.482930\pi\) | ||||
0.0536011 | + | 0.998562i | \(0.482930\pi\) | |||||||
\(984\) | 3.47823e13 | 1.18272 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.86999e13 | 1.30396 | ||||||||
\(987\) | −1.64003e13 | −0.550080 | ||||||||
\(988\) | 6.10944e12 | 0.203984 | ||||||||
\(989\) | 4.39454e12 | 0.146060 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.38736e13 | 0.456939 | 0.228470 | − | 0.973551i | \(-0.426628\pi\) | ||||
0.228470 | + | 0.973551i | \(0.426628\pi\) | |||||||
\(992\) | 3.12750e12 | 0.102540 | ||||||||
\(993\) | 8.37203e12 | 0.273249 | ||||||||
\(994\) | −8.43700e12 | −0.274126 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.42380e13 | 0.780421 | ||||||||
\(997\) | 1.65453e13 | 0.530331 | 0.265166 | − | 0.964203i | \(-0.414573\pi\) | ||||
0.265166 | + | 0.964203i | \(0.414573\pi\) | |||||||
\(998\) | 2.74224e13 | 0.875019 | ||||||||
\(999\) | 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.a.j.1.2 | 2 | ||
5.2 | odd | 4 | 350.10.c.j.99.3 | 4 | |||
5.3 | odd | 4 | 350.10.c.j.99.2 | 4 | |||
5.4 | even | 2 | 14.10.a.c.1.1 | ✓ | 2 | ||
15.14 | odd | 2 | 126.10.a.o.1.2 | 2 | |||
20.19 | odd | 2 | 112.10.a.c.1.2 | 2 | |||
35.4 | even | 6 | 98.10.c.j.79.2 | 4 | |||
35.9 | even | 6 | 98.10.c.j.67.2 | 4 | |||
35.19 | odd | 6 | 98.10.c.h.67.1 | 4 | |||
35.24 | odd | 6 | 98.10.c.h.79.1 | 4 | |||
35.34 | odd | 2 | 98.10.a.e.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.10.a.c.1.1 | ✓ | 2 | 5.4 | even | 2 | ||
98.10.a.e.1.2 | 2 | 35.34 | odd | 2 | |||
98.10.c.h.67.1 | 4 | 35.19 | odd | 6 | |||
98.10.c.h.79.1 | 4 | 35.24 | odd | 6 | |||
98.10.c.j.67.2 | 4 | 35.9 | even | 6 | |||
98.10.c.j.79.2 | 4 | 35.4 | even | 6 | |||
112.10.a.c.1.2 | 2 | 20.19 | odd | 2 | |||
126.10.a.o.1.2 | 2 | 15.14 | odd | 2 | |||
350.10.a.j.1.2 | 2 | 1.1 | even | 1 | trivial | ||
350.10.c.j.99.2 | 4 | 5.3 | odd | 4 | |||
350.10.c.j.99.3 | 4 | 5.2 | odd | 4 |