Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [112,10,Mod(1,112)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(112, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("112.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 112 = 2^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 112.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: | \(57.6840136504\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
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 | \(\chi\) | \(=\) | 112.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 247.052 | 1.76093 | 0.880467 | − | 0.474108i | \(-0.157229\pi\) | ||||
0.880467 | + | 0.474108i | \(0.157229\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2373.22 | −1.69814 | −0.849069 | − | 0.528283i | \(-0.822836\pi\) | ||||
−0.849069 | + | 0.528283i | \(0.822836\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2401.00 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 41351.7 | 2.10089 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 27940.9 | 0.575405 | 0.287703 | − | 0.957720i | \(-0.407109\pi\) | ||||
0.287703 | + | 0.957720i | \(0.407109\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 60943.3 | 0.591808 | 0.295904 | − | 0.955218i | \(-0.404379\pi\) | ||||
0.295904 | + | 0.955218i | \(0.404379\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −586309. | −2.99031 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −358867. | −1.04211 | −0.521055 | − | 0.853523i | \(-0.674462\pi\) | ||||
−0.521055 | + | 0.853523i | \(0.674462\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 391593. | 0.689356 | 0.344678 | − | 0.938721i | \(-0.387988\pi\) | ||||
0.344678 | + | 0.938721i | \(0.387988\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −593172. | −0.665570 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 302894. | 0.225692 | 0.112846 | − | 0.993612i | \(-0.464003\pi\) | ||||
0.112846 | + | 0.993612i | \(0.464003\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.67904e6 | 1.88367 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.35330e6 | 1.93859 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 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 | \(-0.593665\pi\) | ||||
−0.290028 | + | 0.957018i | \(0.593665\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.90287e6 | 1.01325 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.69810e6 | 0.641835 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.49582e6 | −0.306649 | −0.153324 | − | 0.988176i | \(-0.548998\pi\) | ||||
−0.153324 | + | 0.988176i | \(0.548998\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.50562e7 | 1.04214 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.43724e7 | 1.89969 | 0.949845 | − | 0.312722i | \(-0.101241\pi\) | ||||
0.949845 | + | 0.312722i | \(0.101241\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.45085e7 | 0.647164 | 0.323582 | − | 0.946200i | \(-0.395113\pi\) | ||||
0.323582 | + | 0.946200i | \(0.395113\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.81367e7 | −3.56759 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.76485e7 | 0.826479 | 0.413239 | − | 0.910622i | \(-0.364397\pi\) | ||||
0.413239 | + | 0.910622i | \(0.364397\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.76480e6 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.86589e7 | −1.83509 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.39217e7 | −0.416438 | −0.208219 | − | 0.978082i | \(-0.566767\pi\) | ||||
−0.208219 | + | 0.978082i | \(0.566767\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.63100e7 | −0.977117 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.67439e7 | 1.21391 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 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 | \(0.391482\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.92855e7 | −0.794060 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.44632e8 | −1.00497 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.70377e7 | −0.527680 | −0.263840 | − | 0.964566i | \(-0.584989\pi\) | ||||
−0.263840 | + | 0.964566i | \(0.584989\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.48307e7 | 0.397428 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.19622e8 | −1.02568 | −0.512842 | − | 0.858483i | \(-0.671407\pi\) | ||||
−0.512842 | + | 0.858483i | \(0.671407\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.67792e8 | 1.10368 | 0.551841 | − | 0.833949i | \(-0.313926\pi\) | ||||
0.551841 | + | 0.833949i | \(0.313926\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.08915e8 | 3.31702 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.70862e7 | −0.217483 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −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 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.83237e8 | 0.886372 | 0.443186 | − | 0.896430i | \(-0.353848\pi\) | ||||
0.443186 | + | 0.896430i | \(0.353848\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.51671e8 | 1.76965 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.66511e9 | 3.11607 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 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 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.36861e8 | −1.02144 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.29336e8 | −1.17062 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.73736e8 | −0.772710 | −0.386355 | − | 0.922350i | \(-0.626266\pi\) | ||||
−0.386355 | + | 0.922350i | \(0.626266\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.15541e9 | 1.20886 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.04805e7 | −0.0100216 | −0.00501081 | − | 0.999987i | \(-0.501595\pi\) | ||||
−0.00501081 | + | 0.999987i | \(0.501595\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.39782e9 | −1.22373 | −0.611864 | − | 0.790963i | \(-0.709580\pi\) | ||||
−0.611864 | + | 0.790963i | \(0.709580\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.40773e9 | 1.13023 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.84414e8 | 0.357264 | 0.178632 | − | 0.983916i | \(-0.442833\pi\) | ||||
0.178632 | + | 0.983916i | \(0.442833\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −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 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.80849e8 | −0.335128 | −0.167564 | − | 0.985861i | \(-0.553590\pi\) | ||||
−0.167564 | + | 0.985861i | \(0.553590\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.18835e8 | −0.383256 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.52011e9 | 1.24332 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.61641e8 | 0.393881 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.57725e9 | −0.668909 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.49178e9 | 3.34523 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.09598e9 | −1.50059 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.59088e9 | −0.883751 | −0.441876 | − | 0.897076i | \(-0.645687\pi\) | ||||
−0.441876 | + | 0.897076i | \(0.645687\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.58436e9 | 1.13961 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.45598e9 | −0.728626 | −0.364313 | − | 0.931277i | \(-0.618696\pi\) | ||||
−0.364313 | + | 0.931277i | \(0.618696\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.40215e8 | −0.260552 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.27046e10 | −3.29198 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.08364e9 | 1.47544 | 0.737719 | − | 0.675108i | \(-0.235903\pi\) | ||||
0.737719 | + | 0.675108i | \(0.235903\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −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 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.70281e9 | 0.340530 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.59953e10 | −3.00495 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.42421e9 | 0.251562 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −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 | \(-0.338461\pi\) | ||||
0.485984 | + | 0.873968i | \(0.338461\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.48398e10 | −2.18936 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.07840e9 | 0.985014 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.33378e10 | 1.75201 | 0.876006 | − | 0.482300i | \(-0.160198\pi\) | ||||
0.876006 | + | 0.482300i | \(0.160198\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.90990e9 | −0.733319 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.27249e8 | −0.0853035 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.33621e9 | −0.814006 | −0.407003 | − | 0.913427i | \(-0.633426\pi\) | ||||
−0.407003 | + | 0.913427i | \(0.633426\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.63820e10 | −1.72064 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.42205e9 | 0.638925 | 0.319462 | − | 0.947599i | \(-0.396498\pi\) | ||||
0.319462 | + | 0.947599i | \(0.396498\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.89041e9 | −0.649763 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.61931e10 | 1.44826 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.91846e10 | 1.62834 | 0.814171 | − | 0.580626i | \(-0.197192\pi\) | ||||
0.814171 | + | 0.580626i | \(0.197192\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.83338e9 | −0.711960 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.97896e10 | 2.28131 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −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 | \(0.705109\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.78653e10 | 1.17755 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.29634e9 | 0.520732 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.00271e10 | −0.599636 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.28533e10 | −0.732717 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.70138e10 | −1.46871 | −0.734355 | − | 0.678765i | \(-0.762515\pi\) | ||||
−0.734355 | + | 0.678765i | \(0.762515\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.70232e9 | 0.140194 | 0.0700970 | − | 0.997540i | \(-0.477669\pi\) | ||||
0.0700970 | + | 0.997540i | \(0.477669\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.57316e10 | −1.76969 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.39047e10 | 1.13080 | 0.565399 | − | 0.824818i | \(-0.308722\pi\) | ||||
0.565399 | + | 0.824818i | \(0.308722\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 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 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.61826e10 | −0.668829 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.15732e10 | −3.22593 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.25252e10 | 0.474153 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.09415e10 | 0.396659 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.61055e9 | −0.125401 | −0.0627007 | − | 0.998032i | \(-0.519971\pi\) | ||||
−0.0627007 | + | 0.998032i | \(0.519971\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.42581e10 | −1.80616 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.44319e10 | −1.09897 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.16126e9 | 0.219240 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.61585e10 | 1.94351 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.18706e10 | −0.616730 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.13001e10 | 1.93072 | 0.965358 | − | 0.260929i | \(-0.0840287\pi\) | ||||
0.965358 | + | 0.260929i | \(0.0840287\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.52135e11 | 3.95737 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.15361e10 | −1.78817 | −0.894086 | − | 0.447896i | \(-0.852173\pi\) | ||||
−0.894086 | + | 0.447896i | \(0.852173\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −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 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.80069e10 | −0.844814 | −0.422407 | − | 0.906406i | \(-0.638815\pi\) | ||||
−0.422407 | + | 0.906406i | \(0.638815\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.56160e10 | −1.40347 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.04962e9 | −0.145144 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 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 | \(0.524898\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.02863e10 | 0.373228 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.36811e10 | −0.242591 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.38650e10 | 0.407967 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.46795e10 | 1.56084 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.75467e10 | −1.55125 | −0.775624 | − | 0.631196i | \(-0.782565\pi\) | ||||
−0.775624 | + | 0.631196i | \(0.782565\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.46315e9 | 0.129864 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.10407e11 | 3.11623 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.43042e9 | −0.0633499 | −0.0316750 | − | 0.999498i | \(-0.510084\pi\) | ||||
−0.0316750 | + | 0.999498i | \(0.510084\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.39346e9 | 0.115902 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.78708e11 | 3.71763 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.20620e11 | 1.55460 | 0.777301 | − | 0.629129i | \(-0.216588\pi\) | ||||
0.777301 | + | 0.629129i | \(0.216588\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.67714e10 | 0.707168 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.78268e11 | 2.14671 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 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 | \(-0.631201\pi\) | ||||
−0.400608 | + | 0.916249i | \(0.631201\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.61499e10 | −0.393890 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.02796e11 | 1.08387 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.61542e10 | 0.879261 | 0.439630 | − | 0.898179i | \(-0.355109\pi\) | ||||
0.439630 | + | 0.898179i | \(0.355109\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.23336e11 | −1.21863 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.00179e11 | −0.958511 | −0.479256 | − | 0.877675i | \(-0.659093\pi\) | ||||
−0.479256 | + | 0.877675i | \(0.659093\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.57444e10 | 0.423935 | 0.211967 | − | 0.977277i | \(-0.432013\pi\) | ||||
0.211967 | + | 0.977277i | \(0.432013\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.29594e11 | −2.06139 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.25282e10 | −0.718015 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.01980e10 | 0.0859950 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.66448e11 | −1.36069 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.01615e10 | −0.0805476 | −0.0402738 | − | 0.999189i | \(-0.512823\pi\) | ||||
−0.0402738 | + | 0.999189i | \(0.512823\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.86163e11 | −2.19996 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.49576e11 | 1.11547 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.84594e10 | 0.133566 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.48349e10 | −0.244605 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.58924e9 | −0.0176474 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.71617e11 | −1.13556 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.68957e10 | 0.237057 | 0.118529 | − | 0.992951i | \(-0.462182\pi\) | ||||
0.118529 | + | 0.992951i | \(0.462182\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.45335e11 | −2.15490 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.88558e11 | −1.14294 | −0.571469 | − | 0.820624i | \(-0.693626\pi\) | ||||
−0.571469 | + | 0.820624i | \(0.693626\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.31778e11 | 0.776058 | 0.388029 | − | 0.921647i | \(-0.373156\pi\) | ||||
0.388029 | + | 0.921647i | \(0.373156\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.35626e11 | 1.34842 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.50686e11 | −0.838118 | −0.419059 | − | 0.907959i | \(-0.637640\pi\) | ||||
−0.419059 | + | 0.907959i | \(0.637640\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.88320e11 | 1.01821 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.19675e11 | 0.629118 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.40530e11 | −0.718386 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.24213e11 | 1.11477 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.84959e10 | −0.234552 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.63841e10 | −0.312380 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.38877e10 | −0.155173 | −0.0775865 | − | 0.996986i | \(-0.524721\pi\) | ||||
−0.0775865 | + | 0.996986i | \(0.524721\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.44558e11 | −0.644234 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.06559e11 | 0.896073 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.98312e11 | 0.837555 | 0.418778 | − | 0.908089i | \(-0.362459\pi\) | ||||
0.418778 | + | 0.908089i | \(0.362459\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.43500e11 | −0.590138 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.33371e10 | −0.333767 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.38413e10 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.77590e11 | −0.674888 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.71762e11 | 0.635981 | 0.317990 | − | 0.948094i | \(-0.396992\pi\) | ||||
0.317990 | + | 0.948094i | \(0.396992\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −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 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.97995e11 | 0.678686 | 0.339343 | − | 0.940663i | \(-0.389795\pi\) | ||||
0.339343 | + | 0.940663i | \(0.389795\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.21211e11 | 1.74175 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.12870e11 | 0.693598 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −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 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.89663e11 | −1.17790 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.35528e11 | −1.87420 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.02066e10 | −0.173240 | −0.0866198 | − | 0.996241i | \(-0.527607\pi\) | ||||
−0.0866198 | + | 0.996241i | \(0.527607\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.42136e12 | 3.99103 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.74359e10 | 0.157399 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.85521e11 | −1.83371 | −0.916855 | − | 0.399219i | \(-0.869281\pi\) | ||||
−0.916855 | + | 0.399219i | \(0.869281\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.01192e12 | −2.64244 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.10754e11 | 1.04724 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −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 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.02054e11 | −0.479814 | −0.239907 | − | 0.970796i | \(-0.577117\pi\) | ||||
−0.239907 | + | 0.970796i | \(0.577117\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.59210e11 | 0.369316 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.99952e11 | 1.35962 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 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 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.06756e11 | −1.28306 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.77197e10 | 0.139968 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.26816e11 | 0.256222 | 0.128111 | − | 0.991760i | \(-0.459109\pi\) | ||||
0.128111 | + | 0.991760i | \(0.459109\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.32282e11 | −0.458815 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.86957e11 | 1.13359 | 0.566795 | − | 0.823859i | \(-0.308183\pi\) | ||||
0.566795 | + | 0.823859i | \(0.308183\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.81771e11 | −0.343282 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.20706e12 | −2.22937 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.76764e10 | −0.176447 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −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 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.89513e11 | −0.489658 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.09505e11 | −1.50518 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.56483e11 | −0.901238 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 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 | \(0.503984\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.14331e12 | 1.73634 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.32029e12 | −1.96299 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.73626e11 | −0.252749 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.20684e11 | 0.599650 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.81935e11 | 0.672730 | 0.336365 | − | 0.941732i | \(-0.390802\pi\) | ||||
0.336365 | + | 0.941732i | \(0.390802\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.68314e11 | 0.913661 | 0.456830 | − | 0.889554i | \(-0.348985\pi\) | ||||
0.456830 | + | 0.889554i | \(0.348985\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.95168e12 | −5.29151 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.18611e11 | 0.155582 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 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 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.53598e11 | 0.806295 | 0.403148 | − | 0.915135i | \(-0.367916\pi\) | ||||
0.403148 | + | 0.915135i | \(0.367916\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.71247e12 | −2.07016 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.74551e11 | −0.917627 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −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 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.53404e12 | 1.71157 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.47261e11 | 0.379844 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.31205e12 | 1.40711 | 0.703556 | − | 0.710639i | \(-0.251594\pi\) | ||||
0.703556 | + | 0.710639i | \(0.251594\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.92113e12 | −2.02022 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.16594e12 | 1.20233 | 0.601165 | − | 0.799125i | \(-0.294703\pi\) | ||||
0.601165 | + | 0.799125i | \(0.294703\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.87318e10 | 0.0391700 | 0.0195850 | − | 0.999808i | \(-0.493766\pi\) | ||||
0.0195850 | + | 0.999808i | \(0.493766\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.74873e12 | 1.73454 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.17150e11 | −0.113977 | −0.0569883 | − | 0.998375i | \(-0.518150\pi\) | ||||
−0.0569883 | + | 0.998375i | \(0.518150\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.08977e11 | 0.199444 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.29514e12 | 3.08518 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.05381e11 | 0.372382 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.44069e12 | 1.29852 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.89203e11 | −0.874888 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 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 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.79668e11 | −0.150214 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.59892e12 | 1.31217 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.95983e12 | 1.57884 | 0.789421 | − | 0.613852i | \(-0.210381\pi\) | ||||
0.789421 | + | 0.613852i | \(0.210381\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.81243e12 | −1.43341 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.93589e11 | 0.227967 | 0.113984 | − | 0.993483i | \(-0.463639\pi\) | ||||
0.113984 | + | 0.993483i | \(0.463639\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.41874e12 | −1.84407 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.74203e12 | −2.05281 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.27313e11 | 0.387672 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −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 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.61385e12 | −1.12411 | −0.562053 | − | 0.827101i | \(-0.689988\pi\) | ||||
−0.562053 | + | 0.827101i | \(0.689988\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.48726e10 | 0.0170181 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.70229e12 | −1.14419 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 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 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.09632e12 | 1.33638 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.31734e12 | 2.07806 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.72526e11 | 0.475560 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.73960e12 | 2.86740 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.91339e12 | 1.73232 | 0.866161 | − | 0.499765i | \(-0.166580\pi\) | ||||
0.866161 | + | 0.499765i | \(0.166580\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.53787e12 | −1.48324 | −0.741620 | − | 0.670820i | \(-0.765942\pi\) | ||||
−0.741620 | + | 0.670820i | \(0.765942\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.18230e12 | −1.25371 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.07036e12 | 0.604482 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.70941e12 | −0.949063 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.98620e12 | 2.72172 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.09477e12 | 1.12425 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.14962e12 | −0.606683 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.78920e12 | −1.96636 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.61074e11 | 0.0822008 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.11804e12 | 0.561136 | 0.280568 | − | 0.959834i | \(-0.409477\pi\) | ||||
0.280568 | + | 0.959834i | \(0.409477\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.28574e12 | −2.11556 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.65859e11 | 0.226188 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.99438e12 | −0.952500 | −0.476250 | − | 0.879310i | \(-0.658004\pi\) | ||||
−0.476250 | + | 0.879310i | \(0.658004\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.99031e12 | 1.40488 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.63931e12 | 1.21985 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.85125e10 | 0.0311535 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.04963e12 | 0.916973 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.69088e11 | −0.206493 | −0.103247 | − | 0.994656i | \(-0.532923\pi\) | ||||
−0.103247 | + | 0.994656i | \(0.532923\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.84197e11 | 0.382997 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.47721e12 | −1.05592 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.74518e12 | −0.732069 | −0.366034 | − | 0.930601i | \(-0.619285\pi\) | ||||
−0.366034 | + | 0.930601i | \(0.619285\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.37848e12 | 0.569093 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.22119e12 | −0.496205 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −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 | \(-0.803495\pi\) | ||||
−0.815422 | + | 0.578867i | \(0.803495\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.67383e12 | −2.58630 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.11436e12 | 0.425129 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.27130e12 | 1.60424 | 0.802120 | − | 0.597164i | \(-0.203706\pi\) | ||||
0.802120 | + | 0.597164i | \(0.203706\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.67614e11 | 0.246872 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.20152e11 | −0.335017 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.68394e11 | −0.239621 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.98078e12 | −2.11133 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.32282e12 | −1.85042 | −0.925210 | − | 0.379455i | \(-0.876111\pi\) | ||||
−0.925210 | + | 0.379455i | \(0.876111\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.16797e12 | −0.399865 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.90570e12 | 1.99126 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.69262e11 | −0.0894190 | −0.0447095 | − | 0.999000i | \(-0.514236\pi\) | ||||
−0.0447095 | + | 0.999000i | \(0.514236\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.04486e12 | −0.668864 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.33906e11 | 0.172021 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −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 | \(0.599935\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.59916e12 | −1.10860 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.74316e12 | 1.13590 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.20562e12 | 0.360464 | 0.180232 | − | 0.983624i | \(-0.442315\pi\) | ||||
0.180232 | + | 0.983624i | \(0.442315\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.99794e12 | −1.17776 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.68499e12 | 0.489117 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.02026e11 | −0.143600 | −0.0717999 | − | 0.997419i | \(-0.522874\pi\) | ||||
−0.0717999 | + | 0.997419i | \(0.522874\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.01528e13 | −5.68065 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.17852e12 | 1.43854 | 0.719271 | − | 0.694730i | \(-0.244476\pi\) | ||||
0.719271 | + | 0.694730i | \(0.244476\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 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 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.73252e12 | −0.460767 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.53502e12 | 0.664541 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.70312e12 | 0.698491 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.25454e12 | 0.319562 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.53678e12 | 1.39035 | 0.695177 | − | 0.718839i | \(-0.255326\pi\) | ||||
0.695177 | + | 0.718839i | \(0.255326\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.91994e11 | −0.220823 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.14872e12 | 1.50073 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.51326e11 | 0.0845441 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.08175e12 | −2.15484 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.85506e12 | −0.667966 | −0.333983 | − | 0.942579i | \(-0.608393\pi\) | ||||
−0.333983 | + | 0.942579i | \(0.608393\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.48209e12 | 1.72613 | 0.863065 | − | 0.505093i | \(-0.168542\pi\) | ||||
0.863065 | + | 0.505093i | \(0.168542\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.50646e12 | −1.93522 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.83872e12 | 0.861225 | 0.430613 | − | 0.902537i | \(-0.358297\pi\) | ||||
0.430613 | + | 0.902537i | \(0.358297\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.36912e12 | 0.745445 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.76920e12 | 0.386068 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.09261e11 | −0.0235157 | −0.0117578 | − | 0.999931i | \(-0.503743\pi\) | ||||
−0.0117578 | + | 0.999931i | \(0.503743\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.82859e12 | 1.23731 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.10736e13 | 2.31871 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 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 | \(0.557397\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.40317e12 | −1.08602 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.23134e12 | 0.442453 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.04149e12 | 0.399374 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.76148e13 | 3.39986 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.02052e12 | 0.384779 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.52389e12 | 1.60166 | 0.800830 | − | 0.598892i | \(-0.204392\pi\) | ||||
0.800830 | + | 0.598892i | \(0.204392\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.96950e13 | 3.65165 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.88497e12 | −0.527828 | −0.263914 | − | 0.964546i | \(-0.585014\pi\) | ||||
−0.263914 | + | 0.964546i | \(0.585014\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.61764e12 | 0.292057 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.76732e13 | −3.14885 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.03086e13 | −1.81262 | −0.906309 | − | 0.422616i | \(-0.861112\pi\) | ||||
−0.906309 | + | 0.422616i | \(0.861112\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.44378e13 | −2.50550 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.79556e12 | −1.50646 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.45787e12 | −0.246451 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.85439e12 | −1.31057 | −0.655287 | − | 0.755380i | \(-0.727452\pi\) | ||||
−0.655287 | + | 0.755380i | \(0.727452\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.77413e12 | −0.456906 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.34566e12 | 0.869099 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.23351e13 | −1.97969 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.38969e12 | −1.48766 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.69579e12 | 0.265242 | 0.132621 | − | 0.991167i | \(-0.457661\pi\) | ||||
0.132621 | + | 0.991167i | \(0.457661\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.36894e12 | −0.211390 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.62106e13 | −2.47142 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.51638e10 | 0.00378781 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −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 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.03417e11 | −0.130914 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.04115e12 | −0.578266 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.14225e13 | 3.02715 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 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 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.02192e12 | −0.275195 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.47965e13 | 3.33326 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.97511e11 | 0.0660538 | 0.0330269 | − | 0.999454i | \(-0.489485\pi\) | ||||
0.0330269 | + | 0.999454i | \(0.489485\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.99938e12 | −0.655605 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.20663e12 | −0.674417 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.22437e12 | −0.668445 | −0.334223 | − | 0.942494i | \(-0.608474\pi\) | ||||
−0.334223 | + | 0.942494i | \(0.608474\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.37995e12 | −0.427187 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.43191e12 | −0.303630 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −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 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.12076e12 | 0.134916 | 0.0674580 | − | 0.997722i | \(-0.478511\pi\) | ||||
0.0674580 | + | 0.997722i | \(0.478511\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.44045e12 | 0.884904 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.58475e13 | 1.86217 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.16308e12 | −0.135033 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.62183e12 | 0.186049 | 0.0930244 | − | 0.995664i | \(-0.470347\pi\) | ||||
0.0930244 | + | 0.995664i | \(0.470347\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.40991e13 | −2.73164 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.47362e13 | −1.65054 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.55150e12 | −0.171720 | −0.0858600 | − | 0.996307i | \(-0.527364\pi\) | ||||
−0.0858600 | + | 0.996307i | \(0.527364\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.09084e12 | 0.228682 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.62863e13 | 1.76032 | 0.880159 | − | 0.474679i | \(-0.157436\pi\) | ||||
0.880159 | + | 0.474679i | \(0.157436\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.71312e11 | 0.0503440 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.52181e13 | 3.71783 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.34856e12 | 0.766695 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −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 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.58593e12 | −0.764190 | −0.382095 | − | 0.924123i | \(-0.624797\pi\) | ||||
−0.382095 | + | 0.924123i | \(0.624797\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.09732e13 | −1.09263 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.07362e12 | 0.204096 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.34600e13 | 1.30956 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.13645e12 | −0.590184 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.60809e13 | 3.43044 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.16536e13 | −2.97516 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.30985e12 | −0.307554 | −0.153777 | − | 0.988106i | \(-0.549144\pi\) | ||||
−0.153777 | + | 0.988106i | \(0.549144\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.97995e13 | 2.73755 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.39462e12 | 0.126666 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.40706e12 | 0.395748 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.40255e13 | 1.24528 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.26446e12 | −0.286582 | −0.143291 | − | 0.989681i | \(-0.545768\pi\) | ||||
−0.143291 | + | 0.989681i | \(0.545768\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.92216e12 | −0.861283 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.98386e13 | 2.56114 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.48235e12 | 0.635064 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.72592e12 | 0.144857 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.87519e13 | 1.55637 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 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 | \(-0.637160\pi\) | ||||
−0.417690 | + | 0.908589i | \(0.637160\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.75752e13 | −1.41089 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.74104e13 | 1.38229 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.68143e12 | 0.446127 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.05079e12 | −0.469931 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.23700e12 | 0.479106 | 0.239553 | − | 0.970883i | \(-0.422999\pi\) | ||||
0.239553 | + | 0.970883i | \(0.422999\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.46689e13 | −1.87435 | −0.937175 | − | 0.348860i | \(-0.886569\pi\) | ||||
−0.937175 | + | 0.348860i | \(0.886569\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.53959e13 | 1.90863 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.45027e13 | 1.07814 | 0.539068 | − | 0.842262i | \(-0.318776\pi\) | ||||
0.539068 | + | 0.842262i | \(0.318776\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −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 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.06880e12 | −0.148873 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.52409e13 | −1.08498 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.59668e13 | −1.12449 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 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 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.47494e13 | −1.68787 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.63524e13 | 1.10339 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.78698e12 | 0.252824 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.13013e13 | 0.746521 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.05886e12 | −0.0692081 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.67503e13 | −1.08331 | −0.541655 | − | 0.840601i | \(-0.682202\pi\) | ||||
−0.541655 | + | 0.840601i | \(0.682202\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.84297e13 | −2.45934 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.16182e13 | −0.735742 | −0.367871 | − | 0.929877i | \(-0.619913\pi\) | ||||
−0.367871 | + | 0.929877i | \(0.619913\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −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 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.35971e13 | −0.834446 | −0.417223 | − | 0.908804i | \(-0.636997\pi\) | ||||
−0.417223 | + | 0.908804i | \(0.636997\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.55293e13 | −2.76515 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.51943e12 | 0.151431 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.97294e11 | −0.0474274 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.30437e12 | −0.312285 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.78601e13 | −1.62338 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.83445e12 | 0.567170 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.40277e12 | 0.194238 | 0.0971189 | − | 0.995273i | \(-0.469037\pi\) | ||||
0.0971189 | + | 0.995273i | \(0.469037\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.51041e12 | −0.141839 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.30779e12 | 0.520541 | 0.260270 | − | 0.965536i | \(-0.416188\pi\) | ||||
0.260270 | + | 0.965536i | \(0.416188\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.00154e13 | −0.554430 | −0.277215 | − | 0.960808i | \(-0.589411\pi\) | ||||
−0.277215 | + | 0.960808i | \(0.589411\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.06972e13 | −3.87398 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.58440e13 | 1.40186 | 0.700928 | − | 0.713232i | \(-0.252769\pi\) | ||||
0.700928 | + | 0.713232i | \(0.252769\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.22070e12 | 0.334027 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.42113e13 | 0.755412 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.08270e13 | 0.569739 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.63997e13 | 1.89624 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.56043e12 | 0.235201 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.01026e13 | −1.02644 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.58471e12 | 0.433974 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.60604e12 | −0.430733 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.11694e13 | 2.04012 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.82049e13 | −1.87451 | −0.937253 | − | 0.348650i | \(-0.886640\pi\) | ||||
−0.937253 | + | 0.348650i | \(0.886640\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.33389e11 | −0.0210543 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.85478e12 | −0.474039 | −0.237020 | − | 0.971505i | \(-0.576171\pi\) | ||||
−0.237020 | + | 0.971505i | \(0.576171\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.07080e13 | 0.510023 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.23983e13 | −1.99965 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.89682e12 | 0.275395 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −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 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.33845e13 | −0.607008 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.28613e13 | −0.577625 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.78024e13 | −2.57091 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −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 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.65836e13 | −2.01264 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.37965e13 | 1.01826 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.75358e13 | 1.16700 | 0.583499 | − | 0.812114i | \(-0.301683\pi\) | ||||
0.583499 | + | 0.812114i | \(0.301683\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.25561e13 | 1.36659 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.60157e12 | −0.316046 | −0.158023 | − | 0.987435i | \(-0.550512\pi\) | ||||
−0.158023 | + | 0.987435i | \(0.550512\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.04112e13 | 0.428745 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.05037e13 | 1.24425 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.35269e13 | 0.950582 | 0.475291 | − | 0.879829i | \(-0.342343\pi\) | ||||
0.475291 | + | 0.879829i | \(0.342343\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.63201e13 | 0.653168 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.72272e13 | −1.47587 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.76056e12 | 0.147684 | 0.0738422 | − | 0.997270i | \(-0.476474\pi\) | ||||
0.0738422 | + | 0.997270i | \(0.476474\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.41098e13 | 2.49407 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.65248e13 | 1.79300 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.46068e13 | −0.557663 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.75436e13 | −0.663535 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.00313e13 | 0.750571 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.41320e12 | −0.238068 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.59678e13 | −1.32280 | −0.661400 | − | 0.750033i | \(-0.730037\pi\) | ||||
−0.661400 | + | 0.750033i | \(0.730037\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.47182e13 | −1.26503 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.20049e13 | 0.433383 | 0.216692 | − | 0.976240i | \(-0.430473\pi\) | ||||
0.216692 | + | 0.976240i | \(0.430473\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.40823e12 | 0.193441 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.53923e13 | 1.96304 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.59954e12 | −0.161506 | −0.0807530 | − | 0.996734i | \(-0.525732\pi\) | ||||
−0.0807530 | + | 0.996734i | \(0.525732\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.01617e13 | 0.701462 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.11727e12 | −0.279833 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.13830e12 | 0.107202 | 0.0536011 | − | 0.998562i | \(-0.482930\pi\) | ||||
0.0536011 | + | 0.998562i | \(0.482930\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.67310e13 | −1.92025 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.64003e13 | −0.550080 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.39454e12 | 0.146060 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.38736e13 | −0.456939 | −0.228470 | − | 0.973551i | \(-0.573372\pi\) | ||||
−0.228470 | + | 0.973551i | \(0.573372\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.37203e12 | −0.273249 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.12878e12 | −0.165886 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.65453e13 | −0.530331 | −0.265166 | − | 0.964203i | \(-0.585427\pi\) | ||||
−0.265166 | + | 0.964203i | \(0.585427\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −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 | 112.10.a.c.1.2 | 2 | ||
4.3 | odd | 2 | 14.10.a.c.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 126.10.a.o.1.2 | 2 | |||
20.3 | even | 4 | 350.10.c.j.99.3 | 4 | |||
20.7 | even | 4 | 350.10.c.j.99.2 | 4 | |||
20.19 | odd | 2 | 350.10.a.j.1.2 | 2 | |||
28.3 | even | 6 | 98.10.c.h.79.1 | 4 | |||
28.11 | odd | 6 | 98.10.c.j.79.2 | 4 | |||
28.19 | even | 6 | 98.10.c.h.67.1 | 4 | |||
28.23 | odd | 6 | 98.10.c.j.67.2 | 4 | |||
28.27 | even | 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 | 4.3 | odd | 2 | ||
98.10.a.e.1.2 | 2 | 28.27 | even | 2 | |||
98.10.c.h.67.1 | 4 | 28.19 | even | 6 | |||
98.10.c.h.79.1 | 4 | 28.3 | even | 6 | |||
98.10.c.j.67.2 | 4 | 28.23 | odd | 6 | |||
98.10.c.j.79.2 | 4 | 28.11 | odd | 6 | |||
112.10.a.c.1.2 | 2 | 1.1 | even | 1 | trivial | ||
126.10.a.o.1.2 | 2 | 12.11 | even | 2 | |||
350.10.a.j.1.2 | 2 | 20.19 | odd | 2 | |||
350.10.c.j.99.2 | 4 | 20.7 | even | 4 | |||
350.10.c.j.99.3 | 4 | 20.3 | even | 4 |