Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,6,Mod(1,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.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: | \(17.3214525398\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{41}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.70156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −57.6281 | −1.03088 | −0.515442 | − | 0.856925i | \(-0.672372\pi\) | ||||
−0.515442 | + | 0.856925i | \(0.672372\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 156.884 | 1.21014 | 0.605068 | − | 0.796173i | \(-0.293146\pi\) | ||||
0.605068 | + | 0.796173i | \(0.293146\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 218.025 | 0.543281 | 0.271640 | − | 0.962399i | \(-0.412434\pi\) | ||||
0.271640 | + | 0.962399i | \(0.412434\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −587.537 | −0.964222 | −0.482111 | − | 0.876110i | \(-0.660130\pi\) | ||||
−0.482111 | + | 0.876110i | \(0.660130\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2124.56 | −1.78298 | −0.891491 | − | 0.453038i | \(-0.850340\pi\) | ||||
−0.891491 | + | 0.453038i | \(0.850340\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 29.7687 | 0.0189180 | 0.00945902 | − | 0.999955i | \(-0.496989\pi\) | ||||
0.00945902 | + | 0.999955i | \(0.496989\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3171.49 | −1.25010 | −0.625048 | − | 0.780586i | \(-0.714921\pi\) | ||||
−0.625048 | + | 0.780586i | \(0.714921\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 196.000 | 0.0627200 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3642.13 | −0.804194 | −0.402097 | − | 0.915597i | \(-0.631718\pi\) | ||||
−0.402097 | + | 0.915597i | \(0.631718\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6331.88 | 1.18339 | 0.591696 | − | 0.806162i | \(-0.298459\pi\) | ||||
0.591696 | + | 0.806162i | \(0.298459\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9040.95 | −1.24751 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8435.69 | −1.01302 | −0.506508 | − | 0.862235i | \(-0.669064\pi\) | ||||
−0.506508 | + | 0.862235i | \(0.669064\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10146.4 | −0.942657 | −0.471328 | − | 0.881958i | \(-0.656225\pi\) | ||||
−0.471328 | + | 0.881958i | \(0.656225\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6855.76 | −0.565437 | −0.282718 | − | 0.959203i | \(-0.591236\pi\) | ||||
−0.282718 | + | 0.959203i | \(0.591236\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −24447.8 | −1.61434 | −0.807171 | − | 0.590318i | \(-0.799002\pi\) | ||||
−0.807171 | + | 0.590318i | \(0.799002\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7805.70 | 0.464432 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 25483.2 | 1.24613 | 0.623066 | − | 0.782169i | \(-0.285887\pi\) | ||||
0.623066 | + | 0.782169i | \(0.285887\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12564.4 | −0.560059 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 20696.2 | 0.774034 | 0.387017 | − | 0.922073i | \(-0.373505\pi\) | ||||
0.387017 | + | 0.922073i | \(0.373505\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 45580.2 | 1.56838 | 0.784191 | − | 0.620519i | \(-0.213078\pi\) | ||||
0.784191 | + | 0.620519i | \(0.213078\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 33858.7 | 0.994000 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 19099.3 | 0.519794 | 0.259897 | − | 0.965636i | \(-0.416311\pi\) | ||||
0.259897 | + | 0.965636i | \(0.416311\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −23055.0 | −0.542773 | −0.271387 | − | 0.962470i | \(-0.587482\pi\) | ||||
−0.271387 | + | 0.962470i | \(0.587482\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −89651.6 | −1.96902 | −0.984511 | − | 0.175320i | \(-0.943904\pi\) | ||||
−0.984511 | + | 0.175320i | \(0.943904\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 34204.7 | 0.657444 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −34023.6 | −0.613356 | −0.306678 | − | 0.951813i | \(-0.599218\pi\) | ||||
−0.306678 | + | 0.951813i | \(0.599218\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 108497. | 1.72872 | 0.864359 | − | 0.502875i | \(-0.167724\pi\) | ||||
0.864359 | + | 0.502875i | \(0.167724\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 122435. | 1.83805 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 110055. | 1.47277 | 0.736384 | − | 0.676564i | \(-0.236532\pi\) | ||||
0.736384 | + | 0.676564i | \(0.236532\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −92175.4 | −1.16684 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1715.51 | −0.0195023 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −28832.0 | −0.311132 | −0.155566 | − | 0.987825i | \(-0.549720\pi\) | ||||
−0.155566 | + | 0.987825i | \(0.549720\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 40290.3 | 0.393004 | 0.196502 | − | 0.980503i | \(-0.437042\pi\) | ||||
0.196502 | + | 0.980503i | \(0.437042\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 204547. | 1.89977 | 0.949885 | − | 0.312600i | \(-0.101200\pi\) | ||||
0.949885 | + | 0.312600i | \(0.101200\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −164042. | −1.38515 | −0.692573 | − | 0.721348i | \(-0.743523\pi\) | ||||
−0.692573 | + | 0.721348i | \(0.743523\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −131554. | −1.06057 | −0.530285 | − | 0.847819i | \(-0.677915\pi\) | ||||
−0.530285 | + | 0.847819i | \(0.677915\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 94322.0 | 0.694891 | 0.347446 | − | 0.937700i | \(-0.387049\pi\) | ||||
0.347446 | + | 0.937700i | \(0.387049\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 182767. | 1.28870 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −333311. | −2.15765 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −113516. | −0.704846 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 168793. | 0.966226 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −303144. | −1.66778 | −0.833891 | − | 0.551929i | \(-0.813892\pi\) | ||||
−0.833891 | + | 0.551929i | \(0.813892\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −316573. | −1.61174 | −0.805871 | − | 0.592091i | \(-0.798303\pi\) | ||||
−0.805871 | + | 0.592091i | \(0.798303\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4670.24 | 0.0228934 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 982.957 | 0.00447438 | 0.00223719 | − | 0.999997i | \(-0.499288\pi\) | ||||
0.00223719 | + | 0.999997i | \(0.499288\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 77533.8 | 0.340372 | 0.170186 | − | 0.985412i | \(-0.445563\pi\) | ||||
0.170186 | + | 0.985412i | \(0.445563\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −128098. | −0.523844 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 209889. | 0.829030 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −119209. | −0.439890 | −0.219945 | − | 0.975512i | \(-0.570588\pi\) | ||||
−0.219945 | + | 0.975512i | \(0.570588\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −59568.9 | −0.212607 | −0.106303 | − | 0.994334i | \(-0.533901\pi\) | ||||
−0.106303 | + | 0.994334i | \(0.533901\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −364894. | −1.21994 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 297561. | 0.963446 | 0.481723 | − | 0.876324i | \(-0.340011\pi\) | ||||
0.481723 | + | 0.876324i | \(0.340011\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −497557. | −1.51279 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −98681.9 | −0.290917 | −0.145458 | − | 0.989364i | \(-0.546466\pi\) | ||||
−0.145458 | + | 0.989364i | \(0.546466\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18553.0 | 0.0514782 | 0.0257391 | − | 0.999669i | \(-0.491806\pi\) | ||||
0.0257391 | + | 0.999669i | \(0.491806\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −26092.8 | −0.0702755 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 496652. | 1.26164 | 0.630822 | − | 0.775927i | \(-0.282718\pi\) | ||||
0.630822 | + | 0.775927i | \(0.282718\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 30749.3 | 0.0758998 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 150072. | 0.350080 | 0.175040 | − | 0.984561i | \(-0.443995\pi\) | ||||
0.175040 | + | 0.984561i | \(0.443995\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −73515.6 | −0.166795 | −0.0833976 | − | 0.996516i | \(-0.526577\pi\) | ||||
−0.0833976 | + | 0.996516i | \(0.526577\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 486133. | 1.04430 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −463208. | −0.968661 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 599319. | 1.18871 | 0.594353 | − | 0.804204i | \(-0.297408\pi\) | ||||
0.594353 | + | 0.804204i | \(0.297408\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −723746. | −1.39860 | −0.699299 | − | 0.714829i | \(-0.746504\pi\) | ||||
−0.699299 | + | 0.714829i | \(0.746504\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 416589. | 0.764790 | 0.382395 | − | 0.923999i | \(-0.375099\pi\) | ||||
0.382395 | + | 0.923999i | \(0.375099\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 688177. | 1.23188 | 0.615938 | − | 0.787794i | \(-0.288777\pi\) | ||||
0.615938 | + | 0.787794i | \(0.288777\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −571393. | −0.973184 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 584720. | 0.971769 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6490.32 | 0.0102778 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −321874. | −0.497714 | −0.248857 | − | 0.968540i | \(-0.580055\pi\) | ||||
−0.248857 | + | 0.968540i | \(0.580055\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 395084. | 0.582899 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 993373. | 1.43207 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.24826e6 | 1.71919 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −354474. | −0.477334 | −0.238667 | − | 0.971101i | \(-0.576710\pi\) | ||||
−0.238667 | + | 0.971101i | \(0.576710\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 226523. | 0.291774 | 0.145887 | − | 0.989301i | \(-0.453396\pi\) | ||||
0.145887 | + | 0.989301i | \(0.453396\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.45431e6 | −1.83260 | −0.916299 | − | 0.400494i | \(-0.868839\pi\) | ||||
−0.916299 | + | 0.400494i | \(0.868839\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 423642. | 0.511221 | 0.255611 | − | 0.966780i | \(-0.417723\pi\) | ||||
0.255611 | + | 0.966780i | \(0.417723\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.40888e6 | 1.66420 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 747052. | 0.845972 | 0.422986 | − | 0.906136i | \(-0.360982\pi\) | ||||
0.422986 | + | 0.906136i | \(0.360982\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 611874. | 0.678609 | 0.339305 | − | 0.940677i | \(-0.389808\pi\) | ||||
0.339305 | + | 0.940677i | \(0.389808\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −449828. | −0.478775 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17490.2 | −0.0182412 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 985152. | 0.987004 | 0.493502 | − | 0.869745i | \(-0.335717\pi\) | ||||
0.493502 | + | 0.869745i | \(0.335717\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −691463. | −0.679153 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.38778e6 | −1.31065 | −0.655327 | − | 0.755345i | \(-0.727469\pi\) | ||||
−0.655327 | + | 0.755345i | \(0.727469\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.32343e6 | −1.22589 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −877536. | −0.782304 | −0.391152 | − | 0.920326i | \(-0.627923\pi\) | ||||
−0.391152 | + | 0.920326i | \(0.627923\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.46855e6 | −1.28462 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −911089. | −0.767680 | −0.383840 | − | 0.923400i | \(-0.625399\pi\) | ||||
−0.383840 | + | 0.923400i | \(0.625399\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 620129. | 0.512931 | 0.256465 | − | 0.966553i | \(-0.417442\pi\) | ||||
0.256465 | + | 0.966553i | \(0.417442\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 42732.9 | 0.0340746 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −236728. | −0.185374 | −0.0926871 | − | 0.995695i | \(-0.529546\pi\) | ||||
−0.0926871 | + | 0.995695i | \(0.529546\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.07691e6 | −0.813609 | −0.406804 | − | 0.913515i | \(-0.633357\pi\) | ||||
−0.406804 | + | 0.913515i | \(0.633357\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.05317e6 | 1.52391 | 0.761953 | − | 0.647633i | \(-0.224241\pi\) | ||||
0.761953 | + | 0.647633i | \(0.224241\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.59182e6 | −1.14074 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.09391e6 | 2.17903 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.12866e6 | −1.44856 | −0.724280 | − | 0.689506i | \(-0.757828\pi\) | ||||
−0.724280 | + | 0.689506i | \(0.757828\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.19268e6 | −0.797939 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.86337e6 | 1.20537 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.07556e6 | −0.684256 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.62670e6 | −1.61682 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.54154e6 | −0.933489 | −0.466744 | − | 0.884392i | \(-0.654573\pi\) | ||||
−0.466744 | + | 0.884392i | \(0.654573\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.73639e6 | 1.01800 | 0.508999 | − | 0.860767i | \(-0.330016\pi\) | ||||
0.508999 | + | 0.860767i | \(0.330016\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.27414e6 | 1.31207 | 0.656034 | − | 0.754732i | \(-0.272233\pi\) | ||||
0.656034 | + | 0.754732i | \(0.272233\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 316836. | 0.177087 | 0.0885435 | − | 0.996072i | \(-0.471779\pi\) | ||||
0.0885435 | + | 0.996072i | \(0.471779\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −794076. | −0.436903 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −63245.5 | −0.0337305 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −115157. | −0.0604760 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.83548e6 | −1.95357 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −448791. | −0.225151 | −0.112576 | − | 0.993643i | \(-0.535910\pi\) | ||||
−0.112576 | + | 0.993643i | \(0.535910\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.10066e6 | −0.535847 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.85869e6 | −0.891524 | −0.445762 | − | 0.895151i | \(-0.647067\pi\) | ||||
−0.445762 | + | 0.895151i | \(0.647067\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.38051e6 | 0.642914 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.41216e6 | −0.648111 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 223643. | 0.0997084 | 0.0498542 | − | 0.998757i | \(-0.484124\pi\) | ||||
0.0498542 | + | 0.998757i | \(0.484124\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.33981e6 | 0.588815 | 0.294407 | − | 0.955680i | \(-0.404878\pi\) | ||||
0.294407 | + | 0.955680i | \(0.404878\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.39683e6 | −1.45090 | −0.725449 | − | 0.688276i | \(-0.758368\pi\) | ||||
−0.725449 | + | 0.688276i | \(0.758368\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.32861e6 | 0.559536 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 761965. | 0.312032 | 0.156016 | − | 0.987755i | \(-0.450135\pi\) | ||||
0.156016 | + | 0.987755i | \(0.450135\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.47521e6 | −0.999642 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.16645e6 | 2.02983 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.39712e6 | 0.541461 | 0.270730 | − | 0.962655i | \(-0.412735\pi\) | ||||
0.270730 | + | 0.962655i | \(0.412735\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.99791e6 | 1.50799 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.25243e6 | 1.21042 | 0.605209 | − | 0.796067i | \(-0.293090\pi\) | ||||
0.605209 | + | 0.796067i | \(0.293090\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.13989e6 | 0.775421 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −700188. | −0.250390 | −0.125195 | − | 0.992132i | \(-0.539956\pi\) | ||||
−0.125195 | + | 0.992132i | \(0.539956\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.30721e6 | 0.803693 | 0.401847 | − | 0.915707i | \(-0.368369\pi\) | ||||
0.401847 | + | 0.915707i | \(0.368369\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.97115e6 | −0.677748 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.01126e6 | 0.673899 | 0.336950 | − | 0.941523i | \(-0.390605\pi\) | ||||
0.336950 | + | 0.941523i | \(0.390605\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.73802e6 | 2.22890 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.96072e6 | 0.632299 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −165619. | −0.0527392 | −0.0263696 | − | 0.999652i | \(-0.508395\pi\) | ||||
−0.0263696 | + | 0.999652i | \(0.508395\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.09454e6 | −0.339915 | −0.169958 | − | 0.985451i | \(-0.554363\pi\) | ||||
−0.169958 | + | 0.985451i | \(0.554363\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.72021e6 | −1.14105 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.83919e6 | −0.550352 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.07293e6 | −0.317149 | −0.158574 | − | 0.987347i | \(-0.550690\pi\) | ||||
−0.158574 | + | 0.987347i | \(0.550690\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.24691e6 | 0.936687 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.25250e6 | −1.78211 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −852181. | −0.237135 | −0.118568 | − | 0.992946i | \(-0.537830\pi\) | ||||
−0.118568 | + | 0.992946i | \(0.537830\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.18784e6 | 0.876579 | 0.438290 | − | 0.898834i | \(-0.355584\pi\) | ||||
0.438290 | + | 0.898834i | \(0.355584\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −416414. | −0.111829 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.15083e6 | 1.89796 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.54409e6 | 1.17829 | 0.589147 | − | 0.808026i | \(-0.299464\pi\) | ||||
0.589147 | + | 0.808026i | \(0.299464\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.16131e6 | −1.57926 | −0.789629 | − | 0.613585i | \(-0.789727\pi\) | ||||
−0.789629 | + | 0.613585i | \(0.789727\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −94411.1 | −0.0236494 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 902834. | 0.223587 | 0.111793 | − | 0.993731i | \(-0.464340\pi\) | ||||
0.111793 | + | 0.993731i | \(0.464340\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.68712e6 | 0.892642 | 0.446321 | − | 0.894873i | \(-0.352734\pi\) | ||||
0.446321 | + | 0.894873i | \(0.352734\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.34225e6 | −1.51825 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.71368e6 | −1.80570 | −0.902851 | − | 0.429954i | \(-0.858530\pi\) | ||||
−0.902851 | + | 0.429954i | \(0.858530\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.21218e6 | −0.512128 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.31190e6 | 1.20288 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.79267e6 | 0.849484 | 0.424742 | − | 0.905315i | \(-0.360365\pi\) | ||||
0.424742 | + | 0.905315i | \(0.360365\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.77898e6 | 1.04733 | 0.523664 | − | 0.851925i | \(-0.324565\pi\) | ||||
0.523664 | + | 0.851925i | \(0.324565\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.55903e6 | 0.554782 | 0.277391 | − | 0.960757i | \(-0.410530\pi\) | ||||
0.277391 | + | 0.960757i | \(0.410530\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.22563e6 | −1.74533 | −0.872664 | − | 0.488321i | \(-0.837610\pi\) | ||||
−0.872664 | + | 0.488321i | \(0.837610\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.99639e6 | 0.629022 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.49473e6 | −0.307191 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5834.67 | 0.00118654 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.54369e6 | −0.506554 | −0.253277 | − | 0.967394i | \(-0.581508\pi\) | ||||
−0.253277 | + | 0.967394i | \(0.581508\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.95628e6 | 0.976772 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.66153e6 | 0.320741 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.25686e6 | 0.240139 | 0.120070 | − | 0.992765i | \(-0.461688\pi\) | ||||
0.120070 | + | 0.992765i | \(0.461688\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.89966e6 | −1.85318 | −0.926588 | − | 0.376078i | \(-0.877273\pi\) | ||||
−0.926588 | + | 0.376078i | \(0.877273\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.73794e6 | 1.43386 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.61696e6 | −0.656830 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.04151e6 | −0.546812 | −0.273406 | − | 0.961899i | \(-0.588150\pi\) | ||||
−0.273406 | + | 0.961899i | \(0.588150\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.75985e6 | −0.486368 | −0.243184 | − | 0.969980i | \(-0.578192\pi\) | ||||
−0.243184 | + | 0.969980i | \(0.578192\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.32186e6 | −0.405142 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.44508e6 | 0.247227 | 0.123614 | − | 0.992330i | \(-0.460552\pi\) | ||||
0.123614 | + | 0.992330i | \(0.460552\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.40649e7 | −2.38279 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.17877e7 | −1.95844 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.33024e6 | −0.877041 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.28492e6 | −0.207388 | −0.103694 | − | 0.994609i | \(-0.533066\pi\) | ||||
−0.103694 | + | 0.994609i | \(0.533066\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.38275e6 | −0.380912 | −0.190456 | − | 0.981696i | \(-0.560997\pi\) | ||||
−0.190456 | + | 0.981696i | \(0.560997\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.34525e7 | −2.10997 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.62199e6 | 0.562740 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.96141e6 | 0.908931 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.45342e6 | 1.42792 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.70184e6 | 0.252317 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.22158e6 | 0.326339 | 0.163170 | − | 0.986598i | \(-0.447828\pi\) | ||||
0.163170 | + | 0.986598i | \(0.447828\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.58124e6 | 1.09332 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.81689e6 | −0.259634 | −0.129817 | − | 0.991538i | \(-0.541439\pi\) | ||||
−0.129817 | + | 0.991538i | \(0.541439\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −108422. | −0.0152138 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.33777e6 | −0.742245 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.53109e6 | 0.482248 | 0.241124 | − | 0.970494i | \(-0.422484\pi\) | ||||
0.241124 | + | 0.970494i | \(0.422484\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.02801e6 | 0.545207 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 327456. | 0.0435393 | 0.0217697 | − | 0.999763i | \(-0.493070\pi\) | ||||
0.0217697 | + | 0.999763i | \(0.493070\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.43560e6 | −0.716351 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.06773e6 | −1.04465 | −0.522325 | − | 0.852747i | \(-0.674935\pi\) | ||||
−0.522325 | + | 0.852747i | \(0.674935\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −211349. | −0.0271275 | −0.0135637 | − | 0.999908i | \(-0.504318\pi\) | ||||
−0.0135637 | + | 0.999908i | \(0.504318\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −621612. | −0.0784060 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.60363e6 | −0.200523 | −0.100261 | − | 0.994961i | \(-0.531968\pi\) | ||||
−0.100261 | + | 0.994961i | \(0.531968\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.70216e7 | 2.09199 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.55597e6 | 0.677000 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.92480e6 | −1.18885 | −0.594424 | − | 0.804151i | \(-0.702620\pi\) | ||||
−0.594424 | + | 0.804151i | \(0.702620\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 188492. | 0.0223874 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.74316e6 | −0.670678 | −0.335339 | − | 0.942098i | \(-0.608851\pi\) | ||||
−0.335339 | + | 0.942098i | \(0.608851\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.92081e7 | 2.22429 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.27574e6 | −0.600781 | −0.300391 | − | 0.953816i | \(-0.597117\pi\) | ||||
−0.300391 | + | 0.953816i | \(0.597117\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.14952e6 | 0.468610 | 0.234305 | − | 0.972163i | \(-0.424719\pi\) | ||||
0.234305 | + | 0.972163i | \(0.424719\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.54172e6 | 0.726614 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.58501e7 | −1.74606 | −0.873031 | − | 0.487665i | \(-0.837849\pi\) | ||||
−0.873031 | + | 0.487665i | \(0.837849\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.43640e7 | 1.55658 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.48963e7 | 1.60113 | 0.800565 | − | 0.599246i | \(-0.204533\pi\) | ||||
0.800565 | + | 0.599246i | \(0.204533\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.44790e7 | −1.53118 | −0.765591 | − | 0.643328i | \(-0.777553\pi\) | ||||
−0.765591 | + | 0.643328i | \(0.777553\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.05892e7 | −1.11080 | −0.555402 | − | 0.831582i | \(-0.687435\pi\) | ||||
−0.555402 | + | 0.831582i | \(0.687435\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.72659e7 | 1.78225 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.03397e7 | −1.05879 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.79221e7 | 1.80619 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.93118e6 | −0.493035 | −0.246517 | − | 0.969138i | \(-0.579286\pi\) | ||||
−0.246517 | + | 0.969138i | \(0.579286\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.74696e7 | 1.71929 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.58614e6 | −0.447815 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.90060e7 | 1.82703 | 0.913514 | − | 0.406807i | \(-0.133358\pi\) | ||||
0.913514 | + | 0.406807i | \(0.133358\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.69738e6 | −0.638818 | −0.319409 | − | 0.947617i | \(-0.603484\pi\) | ||||
−0.319409 | + | 0.947617i | \(0.603484\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.62821e7 | −1.52915 | −0.764574 | − | 0.644536i | \(-0.777051\pi\) | ||||
−0.764574 | + | 0.644536i | \(0.777051\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.51228e6 | 0.420518 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.52086e6 | 0.506668 | 0.253334 | − | 0.967379i | \(-0.418473\pi\) | ||||
0.253334 | + | 0.967379i | \(0.418473\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.82435e7 | 1.66152 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −139176. | −0.0124839 | −0.00624197 | − | 0.999981i | \(-0.501987\pi\) | ||||
−0.00624197 | + | 0.999981i | \(0.501987\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.94550e7 | −1.73192 | −0.865960 | − | 0.500113i | \(-0.833292\pi\) | ||||
−0.865960 | + | 0.500113i | \(0.833292\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −269137. | −0.0236004 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.15510e7 | 1.00532 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.93763e6 | 0.852072 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.15012e6 | −0.778734 | −0.389367 | − | 0.921083i | \(-0.627306\pi\) | ||||
−0.389367 | + | 0.921083i | \(0.627306\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.92716e6 | 0.832441 | 0.416220 | − | 0.909264i | \(-0.363354\pi\) | ||||
0.416220 | + | 0.909264i | \(0.363354\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.52328e6 | −0.376513 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.27969e7 | −1.04967 | −0.524835 | − | 0.851204i | \(-0.675873\pi\) | ||||
−0.524835 | + | 0.851204i | \(0.675873\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −56646.0 | −0.00461257 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.49723e7 | −1.20155 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.05692e6 | 0.641909 | 0.320955 | − | 0.947095i | \(-0.395996\pi\) | ||||
0.320955 | + | 0.947095i | \(0.395996\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.46813e6 | −0.350884 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.15567e7 | 1.68074 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.05658e7 | 0.812100 | 0.406050 | − | 0.913851i | \(-0.366906\pi\) | ||||
0.406050 | + | 0.913851i | \(0.366906\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −251120. | −0.0191643 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.32092e6 | 0.475589 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.51822e7 | −1.13428 | −0.567138 | − | 0.823623i | \(-0.691949\pi\) | ||||
−0.567138 | + | 0.823623i | \(0.691949\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.00815e7 | −1.47935 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.38204e6 | 0.540021 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.93525e6 | −0.211750 | −0.105875 | − | 0.994379i | \(-0.533764\pi\) | ||||
−0.105875 | + | 0.994379i | \(0.533764\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.20903e7 | 2.29898 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −713858. | −0.0504390 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.33363e6 | −0.654960 | −0.327480 | − | 0.944858i | \(-0.606199\pi\) | ||||
−0.327480 | + | 0.944858i | \(0.606199\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.45655e7 | 1.00816 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.73250e6 | −0.325335 | −0.162667 | − | 0.986681i | \(-0.552010\pi\) | ||||
−0.162667 | + | 0.986681i | \(0.552010\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.16413e6 | 0.282394 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.42162e7 | −1.63115 | −0.815575 | − | 0.578651i | \(-0.803579\pi\) | ||||
−0.815575 | + | 0.578651i | \(0.803579\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.47448e7 | −1.64441 | −0.822207 | − | 0.569189i | \(-0.807257\pi\) | ||||
−0.822207 | + | 0.569189i | \(0.807257\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.86981e6 | 0.453476 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.57356e7 | −1.67622 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.57065e6 | −0.360418 | −0.180209 | − | 0.983628i | \(-0.557677\pi\) | ||||
−0.180209 | + | 0.983628i | \(0.557677\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.43284e6 | 0.219173 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.72203e6 | −0.172645 | −0.0863224 | − | 0.996267i | \(-0.527511\pi\) | ||||
−0.0863224 | + | 0.996267i | \(0.527511\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.50617e7 | 0.942787 | 0.471393 | − | 0.881923i | \(-0.343751\pi\) | ||||
0.471393 | + | 0.881923i | \(0.343751\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.06388e7 | −1.28344 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.21598e7 | −0.746341 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.13893e6 | 0.557288 | 0.278644 | − | 0.960395i | \(-0.410115\pi\) | ||||
0.278644 | + | 0.960395i | \(0.410115\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.35738e7 | −0.817060 | −0.408530 | − | 0.912745i | \(-0.633959\pi\) | ||||
−0.408530 | + | 0.912745i | \(0.633959\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.24105e6 | 0.0742223 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −302046. | −0.0178332 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.02656e6 | −0.294878 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.71479e7 | −0.993200 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.04292e7 | −1.17575 | −0.587875 | − | 0.808952i | \(-0.700035\pi\) | ||||
−0.587875 | + | 0.808952i | \(0.700035\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.47976e7 | 0.840913 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.67801e7 | −1.51227 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.03966e7 | −1.69504 | −0.847518 | − | 0.530766i | \(-0.821904\pi\) | ||||
−0.847518 | + | 0.530766i | \(0.821904\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.19409e7 | 2.87834 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.95463e7 | −1.06973 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.86733e7 | 1.55951 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.50428e7 | −1.88247 | −0.941234 | − | 0.337755i | \(-0.890333\pi\) | ||||
−0.941234 | + | 0.337755i | \(0.890333\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.55069e7 | 0.827893 | 0.413946 | − | 0.910301i | \(-0.364150\pi\) | ||||
0.413946 | + | 0.910301i | \(0.364150\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.68685e6 | 0.299901 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −204087. | −0.0106970 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.51617e7 | 0.785038 | 0.392519 | − | 0.919744i | \(-0.371604\pi\) | ||||
0.392519 | + | 0.919744i | \(0.371604\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.26532e7 | −0.651180 | −0.325590 | − | 0.945511i | \(-0.605563\pi\) | ||||
−0.325590 | + | 0.945511i | \(0.605563\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.21240e7 | −0.616427 | −0.308213 | − | 0.951317i | \(-0.599731\pi\) | ||||
−0.308213 | + | 0.951317i | \(0.599731\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.79003e7 | −0.904634 | −0.452317 | − | 0.891857i | \(-0.649402\pi\) | ||||
−0.452317 | + | 0.891857i | \(0.649402\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.65837e7 | −0.828073 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.06918e6 | −0.0530680 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.34365e7 | 1.14945 | 0.574723 | − | 0.818348i | \(-0.305110\pi\) | ||||
0.574723 | + | 0.818348i | \(0.305110\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.24603e6 | −0.353273 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.50368e6 | 0.0724458 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.78089e7 | −0.852960 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.67537e7 | 1.26637 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.89092e7 | 1.36039 | 0.680196 | − | 0.733030i | \(-0.261895\pi\) | ||||
0.680196 | + | 0.733030i | \(0.261895\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.06961e7 | −0.497476 | −0.248738 | − | 0.968571i | \(-0.580016\pi\) | ||||
−0.248738 | + | 0.968571i | \(0.580016\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.69703e7 | 1.70950 | 0.854752 | − | 0.519037i | \(-0.173709\pi\) | ||||
0.854752 | + | 0.519037i | \(0.173709\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.83720e7 | 1.75383 | 0.876914 | − | 0.480646i | \(-0.159598\pi\) | ||||
0.876914 | + | 0.480646i | \(0.159598\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.86211e7 | −1.30061 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.41800e6 | −0.333225 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.12216e7 | −0.501197 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.64809e7 | 1.16927 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.66208e7 | 1.60779 | 0.803895 | − | 0.594771i | \(-0.202757\pi\) | ||||
0.803895 | + | 0.594771i | \(0.202757\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.70223e7 | 0.738889 | 0.369445 | − | 0.929253i | \(-0.379548\pi\) | ||||
0.369445 | + | 0.929253i | \(0.379548\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.54409e7 | 1.52969 | 0.764844 | − | 0.644215i | \(-0.222816\pi\) | ||||
0.764844 | + | 0.644215i | \(0.222816\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.20072e7 | 0.512428 | 0.256214 | − | 0.966620i | \(-0.417525\pi\) | ||||
0.256214 | + | 0.966620i | \(0.417525\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.75585e7 | −2.01824 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −727780. | −0.0305402 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.64837e6 | −0.360892 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.30615e7 | −0.951676 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.41406e7 | −2.22183 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.23657e6 | 0.171946 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.42904e6 | −0.340220 | −0.170110 | − | 0.985425i | \(-0.554412\pi\) | ||||
−0.170110 | + | 0.985425i | \(0.554412\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.48847e7 | 0.993430 | 0.496715 | − | 0.867914i | \(-0.334539\pi\) | ||||
0.496715 | + | 0.867914i | \(0.334539\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.36552e7 | 0.939180 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.96653e7 | −1.95043 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.68789e7 | −1.44042 | −0.720210 | − | 0.693757i | \(-0.755954\pi\) | ||||
−0.720210 | + | 0.693757i | \(0.755954\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.35456e7 | 0.523354 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.65339e6 | −0.0635363 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.60910e7 | 0.991863 | 0.495932 | − | 0.868362i | \(-0.334827\pi\) | ||||
0.495932 | + | 0.868362i | \(0.334827\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 232366. | 0.00878613 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.66938e7 | 0.998576 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.84259e6 | 0.291817 | 0.145908 | − | 0.989298i | \(-0.453390\pi\) | ||||
0.145908 | + | 0.989298i | \(0.453390\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.36164e7 | 1.23759 | 0.618796 | − | 0.785552i | \(-0.287621\pi\) | ||||
0.618796 | + | 0.785552i | \(0.287621\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.21793e7 | 1.17841 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.57753e7 | −0.571615 | −0.285808 | − | 0.958287i | \(-0.592262\pi\) | ||||
−0.285808 | + | 0.958287i | \(0.592262\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.26737e7 | 1.89858 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.32737e7 | 0.830104 | 0.415052 | − | 0.909798i | \(-0.363763\pi\) | ||||
0.415052 | + | 0.909798i | \(0.363763\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.45376e7 | −1.22542 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 154211. | 0.00541462 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.14635e7 | 0.400414 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.17081e7 | 1.44179 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.95430e7 | 0.672085 | 0.336043 | − | 0.941847i | \(-0.390911\pi\) | ||||
0.336043 | + | 0.941847i | \(0.390911\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.59842e7 | 1.90554 | 0.952768 | − | 0.303700i | \(-0.0982220\pi\) | ||||
0.952768 | + | 0.303700i | \(0.0982220\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.21638e7 | 0.411897 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.20225e6 | −0.140846 | −0.0704231 | − | 0.997517i | \(-0.522435\pi\) | ||||
−0.0704231 | + | 0.997517i | \(0.522435\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.39947e7 | 0.800127 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.81575e7 | −0.599340 | −0.299670 | − | 0.954043i | \(-0.596877\pi\) | ||||
−0.299670 | + | 0.954043i | \(0.596877\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.40072e7 | −0.788409 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.17429e7 | 0.706851 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.51450e6 | 0.210716 | 0.105358 | − | 0.994434i | \(-0.466401\pi\) | ||||
0.105358 | + | 0.994434i | \(0.466401\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.96583e7 | −1.26992 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.89170e7 | −0.921329 | −0.460664 | − | 0.887574i | \(-0.652389\pi\) | ||||
−0.460664 | + | 0.887574i | \(0.652389\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 108.6.a.b.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 108.6.a.c.1.2 | yes | 2 | ||
4.3 | odd | 2 | 432.6.a.r.1.1 | 2 | |||
9.2 | odd | 6 | 324.6.e.f.109.1 | 4 | |||
9.4 | even | 3 | 324.6.e.g.217.2 | 4 | |||
9.5 | odd | 6 | 324.6.e.f.217.1 | 4 | |||
9.7 | even | 3 | 324.6.e.g.109.2 | 4 | |||
12.11 | even | 2 | 432.6.a.q.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.6.a.b.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
108.6.a.c.1.2 | yes | 2 | 3.2 | odd | 2 | ||
324.6.e.f.109.1 | 4 | 9.2 | odd | 6 | |||
324.6.e.f.217.1 | 4 | 9.5 | odd | 6 | |||
324.6.e.g.109.2 | 4 | 9.7 | even | 3 | |||
324.6.e.g.217.2 | 4 | 9.4 | even | 3 | |||
432.6.a.q.1.2 | 2 | 12.11 | even | 2 | |||
432.6.a.r.1.1 | 2 | 4.3 | odd | 2 |