Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [272,10,Mod(1,272)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(272, 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("272.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 272 = 2^{4} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 272.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: | \(140.089747437\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 1596x^{3} + 5754x^{2} + 488987x - 2711704 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 17) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(33.6330\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 272.1 |
$q$-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 | ||||||||
\(3\) | 85.9747 | 0.612809 | 0.306404 | − | 0.951901i | \(-0.400874\pi\) | ||||
0.306404 | + | 0.951901i | \(0.400874\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1460.58 | −1.04511 | −0.522553 | − | 0.852607i | \(-0.675020\pi\) | ||||
−0.522553 | + | 0.852607i | \(0.675020\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 446.232 | 0.0702456 | 0.0351228 | − | 0.999383i | \(-0.488818\pi\) | ||||
0.0351228 | + | 0.999383i | \(0.488818\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −12291.3 | −0.624465 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2565.20 | −0.0528268 | −0.0264134 | − | 0.999651i | \(-0.508409\pi\) | ||||
−0.0264134 | + | 0.999651i | \(0.508409\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 70467.9 | 0.684299 | 0.342150 | − | 0.939645i | \(-0.388845\pi\) | ||||
0.342150 | + | 0.939645i | \(0.388845\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −125573. | −0.640450 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −83521.0 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 474111. | 0.834620 | 0.417310 | − | 0.908764i | \(-0.362973\pi\) | ||||
0.417310 | + | 0.908764i | \(0.362973\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 38364.6 | 0.0430471 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.74586e6 | −1.30087 | −0.650437 | − | 0.759561i | \(-0.725414\pi\) | ||||
−0.650437 | + | 0.759561i | \(0.725414\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 180168. | 0.0922461 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.74899e6 | −0.995487 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 501157. | 0.131578 | 0.0657889 | − | 0.997834i | \(-0.479044\pi\) | ||||
0.0657889 | + | 0.997834i | \(0.479044\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 510635. | 0.0993077 | 0.0496538 | − | 0.998766i | \(-0.484188\pi\) | ||||
0.0496538 | + | 0.998766i | \(0.484188\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −220542. | −0.0323727 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −651757. | −0.0734141 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.74847e6 | −0.328811 | −0.164406 | − | 0.986393i | \(-0.552571\pi\) | ||||
−0.164406 | + | 0.986393i | \(0.552571\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.05845e6 | 0.419345 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.04327e7 | −1.68195 | −0.840975 | − | 0.541074i | \(-0.818018\pi\) | ||||
−0.840975 | + | 0.541074i | \(0.818018\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.15222e7 | 0.960017 | 0.480008 | − | 0.877264i | \(-0.340634\pi\) | ||||
0.480008 | + | 0.877264i | \(0.340634\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.79525e7 | 0.652632 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.43306e6 | −0.102622 | −0.0513111 | − | 0.998683i | \(-0.516340\pi\) | ||||
−0.0513111 | + | 0.998683i | \(0.516340\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.01545e7 | −0.995066 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.18069e6 | −0.148628 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.87800e7 | −0.501013 | −0.250506 | − | 0.968115i | \(-0.580597\pi\) | ||||
−0.250506 | + | 0.968115i | \(0.580597\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.74668e6 | 0.0552096 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.07615e7 | 0.511462 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.37313e8 | 1.47529 | 0.737643 | − | 0.675191i | \(-0.235939\pi\) | ||||
0.737643 | + | 0.675191i | \(0.235939\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.21854e8 | 1.12682 | 0.563410 | − | 0.826177i | \(-0.309489\pi\) | ||||
0.563410 | + | 0.826177i | \(0.309489\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.48479e6 | −0.0438659 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.02924e8 | −0.715165 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.31665e7 | 0.504210 | 0.252105 | − | 0.967700i | \(-0.418877\pi\) | ||||
0.252105 | + | 0.967700i | \(0.418877\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.50100e8 | −0.797187 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.48492e8 | −0.693490 | −0.346745 | − | 0.937960i | \(-0.612713\pi\) | ||||
−0.346745 | + | 0.937960i | \(0.612713\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.45029e8 | 0.597726 | 0.298863 | − | 0.954296i | \(-0.403393\pi\) | ||||
0.298863 | + | 0.954296i | \(0.403393\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.54899e7 | 0.0565292 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.14467e6 | −0.00371085 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.22172e8 | 1.21946 | 0.609729 | − | 0.792610i | \(-0.291278\pi\) | ||||
0.609729 | + | 0.792610i | \(0.291278\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.58742e6 | 0.0144221 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.36072e7 | 0.123986 | 0.0619929 | − | 0.998077i | \(-0.480254\pi\) | ||||
0.0619929 | + | 0.998077i | \(0.480254\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.21989e8 | 0.253475 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.30868e7 | 0.0806321 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.26167e8 | 1.56471 | 0.782355 | − | 0.622832i | \(-0.214018\pi\) | ||||
0.782355 | + | 0.622832i | \(0.214018\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.14450e7 | 0.0480690 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.39017e7 | 0.0608566 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.92477e8 | −0.872266 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.44334e9 | 1.65538 | 0.827688 | − | 0.561189i | \(-0.189656\pi\) | ||||
0.827688 | + | 0.561189i | \(0.189656\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.15298e7 | 0.0329885 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.73497e9 | 1.65900 | 0.829498 | − | 0.558510i | \(-0.188627\pi\) | ||||
0.829498 | + | 0.558510i | \(0.188627\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.15796e9 | 1.01374 | 0.506871 | − | 0.862022i | \(-0.330802\pi\) | ||||
0.506871 | + | 0.862022i | \(0.330802\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.60346e7 | −0.0449888 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.18767e8 | −0.456352 | −0.228176 | − | 0.973620i | \(-0.573276\pi\) | ||||
−0.228176 | + | 0.973620i | \(0.573276\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.81586e9 | −1.23215 | −0.616074 | − | 0.787688i | \(-0.711278\pi\) | ||||
−0.616074 | + | 0.787688i | \(0.711278\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.22274e8 | −0.201498 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.89208e9 | −1.66862 | −0.834310 | − | 0.551296i | \(-0.814134\pi\) | ||||
−0.834310 | + | 0.551296i | \(0.814134\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.54997e9 | 1.35955 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.66145e8 | −0.427321 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.72697e7 | −0.0170371 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.35137e9 | −0.997209 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.61644e9 | −1.03071 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.58954e9 | 0.948699 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.38692e9 | −0.473081 | −0.236540 | − | 0.971622i | \(-0.576014\pi\) | ||||
−0.236540 | + | 0.971622i | \(0.576014\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.85037e9 | 0.588307 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.87855e9 | −1.74401 | −0.872006 | − | 0.489496i | \(-0.837181\pi\) | ||||
−0.872006 | + | 0.489496i | \(0.837181\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.11563e8 | 0.0586284 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.01511e9 | 1.04039 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.25574e9 | 0.547075 | 0.273538 | − | 0.961861i | \(-0.411806\pi\) | ||||
0.273538 | + | 0.961861i | \(0.411806\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.06541e9 | 0.469289 | 0.234645 | − | 0.972081i | \(-0.424607\pi\) | ||||
0.234645 | + | 0.972081i | \(0.424607\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.95156e8 | −0.0628878 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.80764e8 | −0.0361493 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.31980e8 | −0.137513 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.45227e9 | −0.609785 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.00126e9 | −0.498845 | −0.249422 | − | 0.968395i | \(-0.580241\pi\) | ||||
−0.249422 | + | 0.968395i | \(0.580241\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.05501e10 | 1.65143 | 0.825714 | − | 0.564089i | \(-0.190773\pi\) | ||||
0.825714 | + | 0.564089i | \(0.190773\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.02659e9 | 0.151455 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.45823e8 | −0.103787 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.51695e9 | 1.11876 | 0.559378 | − | 0.828912i | \(-0.311040\pi\) | ||||
0.559378 | + | 0.828912i | \(0.311040\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.47435e9 | −0.307025 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.79059e8 | −0.0913806 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.90475e9 | 0.766133 | 0.383066 | − | 0.923721i | \(-0.374868\pi\) | ||||
0.383066 | + | 0.923721i | \(0.374868\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.22120e8 | 0.0338329 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.18088e9 | 0.813909 | 0.406954 | − | 0.913448i | \(-0.366591\pi\) | ||||
0.406954 | + | 0.913448i | \(0.366591\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.63878e9 | −0.531735 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.82746e9 | −0.521191 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.96517e9 | 0.166799 | 0.0833995 | − | 0.996516i | \(-0.473422\pi\) | ||||
0.0833995 | + | 0.996516i | \(0.473422\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.03968e7 | 0.00647988 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.18054e10 | 0.904069 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.51083e10 | 1.82801 | 0.914006 | − | 0.405701i | \(-0.132972\pi\) | ||||
0.914006 | + | 0.405701i | \(0.132972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.03563e9 | −0.210230 | −0.105115 | − | 0.994460i | \(-0.533521\pi\) | ||||
−0.105115 | + | 0.994460i | \(0.533521\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.04763e10 | 0.690526 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.47494e9 | 0.343642 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.14248e8 | 0.0128124 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.22668e9 | −0.0699286 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.15580e10 | 1.71577 | 0.857885 | − | 0.513841i | \(-0.171778\pi\) | ||||
0.857885 | + | 0.513841i | \(0.171778\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.29526e9 | 0.119076 | 0.0595379 | − | 0.998226i | \(-0.481037\pi\) | ||||
0.0595379 | + | 0.998226i | \(0.481037\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.84886e9 | −0.438260 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.65359e10 | 1.25527 | 0.627633 | − | 0.778509i | \(-0.284024\pi\) | ||||
0.627633 | + | 0.778509i | \(0.284024\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.45778e10 | 0.658949 | 0.329475 | − | 0.944164i | \(-0.393128\pi\) | ||||
0.329475 | + | 0.944164i | \(0.393128\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.15021e9 | 0.308985 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.23632e8 | 0.00924276 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.44494e10 | 1.75782 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.14590e10 | 0.812350 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.21619e9 | −0.0440903 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.31184e10 | −1.49759 | −0.748793 | − | 0.662804i | \(-0.769366\pi\) | ||||
−0.748793 | + | 0.662804i | \(0.769366\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.27665e10 | −0.424977 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.14349e10 | −1.00332 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.27861e8 | 0.00697593 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.24688e10 | 0.366292 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.88555e9 | −0.165967 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.81093e10 | 1.03195 | 0.515975 | − | 0.856604i | \(-0.327430\pi\) | ||||
0.515975 | + | 0.856604i | \(0.327430\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.21451e9 | −0.0576045 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.78123e10 | 0.695216 | 0.347608 | − | 0.937640i | \(-0.386994\pi\) | ||||
0.347608 | + | 0.937640i | \(0.386994\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.54756e10 | 0.852452 | 0.426226 | − | 0.904617i | \(-0.359843\pi\) | ||||
0.426226 | + | 0.904617i | \(0.359843\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.84130e7 | −0.00227404 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.62674e10 | 1.02843 | 0.514213 | − | 0.857662i | \(-0.328084\pi\) | ||||
0.514213 | + | 0.857662i | \(0.328084\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.01426e9 | 0.107251 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.62961e10 | 0.747295 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.33772e10 | −1.65294 | −0.826469 | − | 0.562982i | \(-0.809654\pi\) | ||||
−0.826469 | + | 0.562982i | \(0.809654\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.31412e9 | −0.139664 | −0.0698321 | − | 0.997559i | \(-0.522246\pi\) | ||||
−0.0698321 | + | 0.997559i | \(0.522246\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.45887e10 | 1.00432 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.86488e10 | 1.03995 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.34096e10 | 0.571130 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.60886e9 | 0.0759795 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.50519e10 | −1.51157 | −0.755786 | − | 0.654818i | \(-0.772745\pi\) | ||||
−0.755786 | + | 0.654818i | \(0.772745\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.47849e9 | 0.0687210 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.04880e10 | 0.155332 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.20648e10 | −1.03044 | −0.515222 | − | 0.857057i | \(-0.672290\pi\) | ||||
−0.515222 | + | 0.857057i | \(0.672290\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.67269e9 | −0.0230975 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.15989e9 | −0.0821658 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.71832e10 | 0.221464 | 0.110732 | − | 0.993850i | \(-0.464680\pi\) | ||||
0.110732 | + | 0.993850i | \(0.464680\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.20354e10 | 0.523612 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.96269e10 | 0.958869 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.10544e10 | 0.128721 | 0.0643605 | − | 0.997927i | \(-0.479499\pi\) | ||||
0.0643605 | + | 0.997927i | \(0.479499\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.41142e11 | 1.58963 | 0.794813 | − | 0.606855i | \(-0.207569\pi\) | ||||
0.794813 | + | 0.606855i | \(0.207569\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.70347e9 | 0.0294571 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.62168e8 | −0.00487307 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.12712e11 | −1.15030 | −0.575151 | − | 0.818047i | \(-0.695057\pi\) | ||||
−0.575151 | + | 0.818047i | \(0.695057\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.27639e9 | −0.0620142 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.86687e10 | 0.465662 | 0.232831 | − | 0.972517i | \(-0.425201\pi\) | ||||
0.232831 | + | 0.972517i | \(0.425201\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.21207e11 | 1.12328 | 0.561640 | − | 0.827382i | \(-0.310171\pi\) | ||||
0.561640 | + | 0.827382i | \(0.310171\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.95355e10 | −0.534532 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.35800e10 | −0.118150 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.97576e9 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.24091e11 | 1.01443 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.65141e10 | 0.765044 | 0.382522 | − | 0.923946i | \(-0.375056\pi\) | ||||
0.382522 | + | 0.923946i | \(0.375056\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.00556e11 | −1.54183 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.05170e9 | 0.0525884 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.23027e11 | −0.890187 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.60389e9 | 0.0674370 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.49163e11 | 1.01665 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.77977e11 | −1.17765 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.31572e11 | 0.845360 | 0.422680 | − | 0.906279i | \(-0.361089\pi\) | ||||
0.422680 | + | 0.906279i | \(0.361089\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.95556e10 | 0.621230 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.19848e9 | −0.0193875 | −0.00969376 | − | 0.999953i | \(-0.503086\pi\) | ||||
−0.00969376 | + | 0.999953i | \(0.503086\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.59936e11 | −0.941882 | −0.470941 | − | 0.882165i | \(-0.656086\pi\) | ||||
−0.470941 | + | 0.882165i | \(0.656086\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.01097e9 | 0.0458445 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.77437e10 | 0.376792 | 0.188396 | − | 0.982093i | \(-0.439671\pi\) | ||||
0.188396 | + | 0.982093i | \(0.439671\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.28557e9 | −0.00695083 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.31983e10 | −0.279657 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.95982e10 | −0.202425 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.26961e10 | 0.0631239 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.56118e11 | −0.755071 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.53194e9 | −0.00720876 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.23890e11 | −0.567295 | −0.283647 | − | 0.958929i | \(-0.591544\pi\) | ||||
−0.283647 | + | 0.958929i | \(0.591544\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.60738e10 | 0.205331 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.21471e11 | −0.526953 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.66091e11 | −0.701476 | −0.350738 | − | 0.936474i | \(-0.614069\pi\) | ||||
−0.350738 | + | 0.936474i | \(0.614069\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.48646e11 | −1.02254 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.30988e9 | −0.00524611 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.59253e10 | −0.140145 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.19233e11 | 0.833144 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.59340e11 | 1.33052 | 0.665262 | − | 0.746610i | \(-0.268320\pi\) | ||||
0.665262 | + | 0.746610i | \(0.268320\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.55698e11 | 1.64423 | 0.822116 | − | 0.569321i | \(-0.192794\pi\) | ||||
0.822116 | + | 0.569321i | \(0.192794\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.93715e11 | −0.681211 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.35070e11 | −0.805772 | −0.402886 | − | 0.915250i | \(-0.631993\pi\) | ||||
−0.402886 | + | 0.915250i | \(0.631993\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.16884e11 | 0.724770 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.20425e9 | −0.0104405 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.46696e10 | −0.269031 | −0.134516 | − | 0.990911i | \(-0.542948\pi\) | ||||
−0.134516 | + | 0.990911i | \(0.542948\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.79067e10 | −0.303410 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.02158e11 | −0.611099 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.11827e11 | −0.624687 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.10781e10 | −0.0894246 | −0.0447123 | − | 0.999000i | \(-0.514237\pi\) | ||||
−0.0447123 | + | 0.999000i | \(0.514237\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.74059e11 | 1.05032 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.28425e10 | −0.0351940 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.64364e11 | −1.77712 | −0.888559 | − | 0.458763i | \(-0.848293\pi\) | ||||
−0.888559 | + | 0.458763i | \(0.848293\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.22635e11 | 0.581371 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.53155e10 | 0.0900386 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.05029e11 | 0.261475 | 0.130738 | − | 0.991417i | \(-0.458265\pi\) | ||||
0.130738 | + | 0.991417i | \(0.458265\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.19240e11 | −0.289908 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.90072e11 | −1.63870 | −0.819351 | − | 0.573293i | \(-0.805666\pi\) | ||||
−0.819351 | + | 0.573293i | \(0.805666\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.67189e9 | 0.00387823 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.64537e11 | −0.599497 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.43485e11 | 0.317712 | 0.158856 | − | 0.987302i | \(-0.449219\pi\) | ||||
0.158856 | + | 0.987302i | \(0.449219\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.45816e11 | 0.315508 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.05407e11 | −1.06875 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.16615e11 | −1.27446 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.59121e11 | −0.927620 | −0.463810 | − | 0.885935i | \(-0.653518\pi\) | ||||
−0.463810 | + | 0.885935i | \(0.653518\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.81891e10 | 0.0359280 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.18477e11 | −0.228815 | −0.114408 | − | 0.993434i | \(-0.536497\pi\) | ||||
−0.114408 | + | 0.993434i | \(0.536497\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.59834e10 | 0.0679562 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.16088e9 | −0.0150726 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.61558e9 | 0.0173700 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.44816e11 | 0.609301 | 0.304651 | − | 0.952464i | \(-0.401460\pi\) | ||||
0.304651 | + | 0.952464i | \(0.401460\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.93937e11 | 0.335253 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.12732e10 | 0.103632 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.82976e10 | −0.129578 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.77573e11 | 0.287585 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.06432e12 | −1.68697 | −0.843487 | − | 0.537150i | \(-0.819501\pi\) | ||||
−0.843487 | + | 0.537150i | \(0.819501\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.40482e11 | 1.30394 | 0.651972 | − | 0.758243i | \(-0.273942\pi\) | ||||
0.651972 | + | 0.758243i | \(0.273942\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.21970e10 | 0.0640840 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.50478e10 | −0.0223730 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.43750e10 | 0.0791542 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.55411e10 | −0.0221526 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.86921e11 | 1.09846 | 0.549229 | − | 0.835672i | \(-0.314922\pi\) | ||||
0.549229 | + | 0.835672i | \(0.314922\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.27832e11 | −0.995029 | −0.497514 | − | 0.867456i | \(-0.665754\pi\) | ||||
−0.497514 | + | 0.867456i | \(0.665754\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.29317e10 | −0.0842690 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.27733e11 | −1.08573 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.63619e11 | 0.724261 | 0.362130 | − | 0.932127i | \(-0.382050\pi\) | ||||
0.362130 | + | 0.932127i | \(0.382050\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.93553e11 | 0.621384 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.48083e11 | −0.306041 | −0.153021 | − | 0.988223i | \(-0.548900\pi\) | ||||
−0.153021 | + | 0.988223i | \(0.548900\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.35274e12 | −1.63529 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.58033e11 | −0.305697 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.36225e12 | −1.58178 | −0.790891 | − | 0.611957i | \(-0.790383\pi\) | ||||
−0.790891 | + | 0.611957i | \(0.790383\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.80660e10 | 0.0888520 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.07040e11 | 1.01201 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.59279e10 | −0.0502372 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.81977e11 | 1.05312 | 0.526560 | − | 0.850138i | \(-0.323481\pi\) | ||||
0.526560 | + | 0.850138i | \(0.323481\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.29598e11 | 0.241441 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.36336e11 | 0.759314 | 0.379657 | − | 0.925127i | \(-0.376042\pi\) | ||||
0.379657 | + | 0.925127i | \(0.376042\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.79548e11 | −0.181579 | −0.0907894 | − | 0.995870i | \(-0.528939\pi\) | ||||
−0.0907894 | + | 0.995870i | \(0.528939\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.41219e10 | −0.0636016 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.13676e11 | −0.110596 | −0.0552982 | − | 0.998470i | \(-0.517611\pi\) | ||||
−0.0552982 | + | 0.998470i | \(0.517611\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.71115e10 | 0.0354186 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.32242e11 | 0.685584 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.52088e10 | −0.0507146 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.54197e10 | 0.0769904 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.53745e11 | 0.312865 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.35347e11 | 0.464649 | 0.232325 | − | 0.972638i | \(-0.425367\pi\) | ||||
0.232325 | + | 0.972638i | \(0.425367\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.64147e11 | −0.225005 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.69794e10 | −0.0559989 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.10812e12 | −1.73004 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.30784e11 | −0.749840 | −0.374920 | − | 0.927057i | \(-0.622330\pi\) | ||||
−0.374920 | + | 0.927057i | \(0.622330\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.93634e11 | 0.469493 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.40150e12 | −1.08824 | −0.544122 | − | 0.839006i | \(-0.683137\pi\) | ||||
−0.544122 | + | 0.839006i | \(0.683137\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.18571e10 | −0.0319123 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.60517e10 | −0.0344765 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.62617e10 | −0.0487146 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.65319e11 | −0.696977 | −0.348488 | − | 0.937313i | \(-0.613305\pi\) | ||||
−0.348488 | + | 0.937313i | \(0.613305\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.03348e11 | 0.498771 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.35251e12 | 0.942076 | 0.471038 | − | 0.882113i | \(-0.343879\pi\) | ||||
0.471038 | + | 0.882113i | \(0.343879\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.53406e12 | −1.73383 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.84792e11 | −0.325852 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.24943e12 | −0.825053 | −0.412527 | − | 0.910946i | \(-0.635354\pi\) | ||||
−0.412527 | + | 0.910946i | \(0.635354\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.47166e10 | 0.0419876 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.30332e12 | −0.830853 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.69130e12 | −1.05947 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.80649e9 | 0.00542120 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.68955e11 | 0.102216 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.83113e11 | 0.168341 | 0.0841706 | − | 0.996451i | \(-0.473176\pi\) | ||||
0.0841706 | + | 0.996451i | \(0.473176\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.03608e11 | −0.352774 | −0.176387 | − | 0.984321i | \(-0.556441\pi\) | ||||
−0.176387 | + | 0.984321i | \(0.556441\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.91209e9 | 0.00397093 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.26487e10 | −0.0240857 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.24689e12 | 0.692271 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.68776e12 | −0.921265 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.14453e12 | −1.15096 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.03758e11 | 0.476936 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.15868e12 | 1.12022 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.03004e11 | 0.0525661 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.92682e11 | −0.397843 | −0.198921 | − | 0.980015i | \(-0.563744\pi\) | ||||
−0.198921 | + | 0.980015i | \(0.563744\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.60987e11 | −0.128831 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.65221e12 | 1.28773 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.81013e10 | −0.0277487 | −0.0138744 | − | 0.999904i | \(-0.504416\pi\) | ||||
−0.0138744 | + | 0.999904i | \(0.504416\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.49775e12 | −0.703660 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.37604e11 | 0.109817 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.88386e11 | 0.0856616 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.70707e11 | 0.210587 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.04975e11 | −0.354351 | −0.177176 | − | 0.984179i | \(-0.556696\pi\) | ||||
−0.177176 | + | 0.984179i | \(0.556696\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.51662e12 | 0.656939 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.84199e10 | 0.00785154 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.22746e12 | 1.35386 | 0.676929 | − | 0.736048i | \(-0.263310\pi\) | ||||
0.676929 | + | 0.736048i | \(0.263310\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.22411e12 | 1.74388 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.49329e9 | 0.00101309 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.00792e12 | −0.803048 | −0.401524 | − | 0.915848i | \(-0.631519\pi\) | ||||
−0.401524 | + | 0.915848i | \(0.631519\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.16004e11 | −0.124403 | −0.0622013 | − | 0.998064i | \(-0.519812\pi\) | ||||
−0.0622013 | + | 0.998064i | \(0.519812\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.71319e12 | 1.05144 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.14549e11 | −0.120001 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.81033e12 | −0.679932 | −0.339966 | − | 0.940438i | \(-0.610416\pi\) | ||||
−0.339966 | + | 0.940438i | \(0.610416\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.97334e11 | 0.0729707 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.39212e10 | 0.00870945 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.38264e10 | 0.0264669 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.26507e12 | 0.446596 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.94820e12 | −1.02491 | −0.512455 | − | 0.858714i | \(-0.671264\pi\) | ||||
−0.512455 | + | 0.858714i | \(0.671264\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.42098e11 | 0.0828842 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.28142e12 | 0.769238 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.46478e12 | 1.48270 | 0.741350 | − | 0.671118i | \(-0.234186\pi\) | ||||
0.741350 | + | 0.671118i | \(0.234186\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.44354e10 | 0.0178055 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.25332e12 | 0.403810 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.15817e12 | −1.00234 | −0.501170 | − | 0.865349i | \(-0.667097\pi\) | ||||
−0.501170 | + | 0.865349i | \(0.667097\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.98536e12 | 1.87135 | 0.935675 | − | 0.352863i | \(-0.114792\pi\) | ||||
0.935675 | + | 0.352863i | \(0.114792\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.02223e12 | −0.314862 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.43436e12 | 1.04219 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.60857e11 | −0.0480939 | −0.0240469 | − | 0.999711i | \(-0.507655\pi\) | ||||
−0.0240469 | + | 0.999711i | \(0.507655\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.92267e10 | 0.00566405 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.41920e11 | −0.0702243 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.87119e12 | −1.39336 | −0.696679 | − | 0.717383i | \(-0.745340\pi\) | ||||
−0.696679 | + | 0.717383i | \(0.745340\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.82152e12 | 1.07721 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.48094e12 | 0.966970 | 0.483485 | − | 0.875353i | \(-0.339371\pi\) | ||||
0.483485 | + | 0.875353i | \(0.339371\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.25847e12 | −0.618310 | −0.309155 | − | 0.951012i | \(-0.600046\pi\) | ||||
−0.309155 | + | 0.951012i | \(0.600046\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.79935e12 | 1.29500 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.13285e11 | 0.109914 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.13413e12 | −1.08374 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.04561e11 | −0.0270189 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.13076e11 | 0.0797484 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.76730e12 | 1.69935 | 0.849676 | − | 0.527305i | \(-0.176797\pi\) | ||||
0.849676 | + | 0.527305i | \(0.176797\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.70709e12 | −0.917734 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.02571e12 | 0.494419 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.82960e12 | −0.680923 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.82516e12 | 0.433060 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.28070e12 | 1.70338 | 0.851691 | − | 0.524045i | \(-0.175578\pi\) | ||||
0.851691 | + | 0.524045i | \(0.175578\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.62565e12 | 1.52855 | 0.764274 | − | 0.644892i | \(-0.223098\pi\) | ||||
0.764274 | + | 0.644892i | \(0.223098\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.70261e12 | −0.614843 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.36313e12 | 1.42758 | 0.713792 | − | 0.700358i | \(-0.246976\pi\) | ||||
0.713792 | + | 0.700358i | \(0.246976\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.52234e11 | −0.0779346 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.95903e10 | 0.00427491 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.95209e12 | 1.28103 | 0.640516 | − | 0.767945i | \(-0.278720\pi\) | ||||
0.640516 | + | 0.767945i | \(0.278720\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.58609e12 | 1.82268 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.78260e12 | −0.373259 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.45445e12 | 1.12659 | 0.563296 | − | 0.826255i | \(-0.309533\pi\) | ||||
0.563296 | + | 0.826255i | \(0.309533\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.82523e12 | −0.575634 | −0.287817 | − | 0.957685i | \(-0.592930\pi\) | ||||
−0.287817 | + | 0.957685i | \(0.592930\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.06008e11 | −0.101706 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.09005e11 | −0.0612728 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.74951e11 | −0.171166 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.27643e12 | 0.632388 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.12579e11 | −0.0595263 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.66233e12 | −0.500259 | −0.250129 | − | 0.968212i | \(-0.580473\pi\) | ||||
−0.250129 | + | 0.968212i | \(0.580473\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.95280e11 | −0.0918298 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.37169e12 | −1.16575 | −0.582875 | − | 0.812562i | \(-0.698072\pi\) | ||||
−0.582875 | + | 0.812562i | \(0.698072\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.44065e11 | 0.116283 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.39115e12 | 0.426035 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.29274e12 | −1.28232 | −0.641161 | − | 0.767406i | \(-0.721547\pi\) | ||||
−0.641161 | + | 0.767406i | \(0.721547\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.29469e12 | −0.571752 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.05000e12 | 0.522390 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.02806e12 | −0.342843 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.91264e12 | −1.48715 | −0.743576 | − | 0.668652i | \(-0.766872\pi\) | ||||
−0.743576 | + | 0.668652i | \(0.766872\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.40696e10 | 0.00231730 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.01670e12 | −0.490457 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.54177e12 | 0.407933 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.97782e12 | 0.630229 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.09782e12 | 0.484534 | 0.242267 | − | 0.970210i | \(-0.422109\pi\) | ||||
0.242267 | + | 0.970210i | \(0.422109\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.77719e12 | −0.274432 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.31099e11 | 0.0657244 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.74197e11 | 0.116537 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.42374e12 | 0.806104 | 0.403052 | − | 0.915177i | \(-0.367949\pi\) | ||||
0.403052 | + | 0.915177i | \(0.367949\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.18906e12 | −0.761509 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.91499e11 | −0.129187 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.64020e11 | 0.0377799 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.16833e12 | −1.01294 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.08993e12 | 0.710284 | 0.355142 | − | 0.934812i | \(-0.384433\pi\) | ||||
0.355142 | + | 0.934812i | \(0.384433\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.16720e11 | 0.0712109 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.28829e11 | −0.0855875 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.02925e10 | 0.0121375 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.07173e12 | −1.07167 | −0.535836 | − | 0.844322i | \(-0.680003\pi\) | ||||
−0.535836 | + | 0.844322i | \(0.680003\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.58327e12 | 0.601037 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.79756e12 | −0.232838 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.29376e12 | 0.805272 | 0.402636 | − | 0.915360i | \(-0.368094\pi\) | ||||
0.402636 | + | 0.915360i | \(0.368094\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.04232e12 | 0.637290 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.13339e11 | −0.0266358 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.33473e11 | 0.115134 | 0.0575668 | − | 0.998342i | \(-0.481666\pi\) | ||||
0.0575668 | + | 0.998342i | \(0.481666\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.87238e12 | 0.349993 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.42665e13 | 1.71739 | 0.858694 | − | 0.512489i | \(-0.171276\pi\) | ||||
0.858694 | + | 0.512489i | \(0.171276\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.38358e12 | 0.521346 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.58905e11 | −0.0774248 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.76113e11 | −0.0320567 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.42997e13 | −1.64039 | −0.820197 | − | 0.572081i | \(-0.806136\pi\) | ||||
−0.820197 | + | 0.572081i | \(0.806136\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.17206e12 | −0.926305 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.54092e13 | −1.72592 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.04819e12 | −0.669413 | −0.334706 | − | 0.942322i | \(-0.608637\pi\) | ||||
−0.334706 | + | 0.942322i | \(0.608637\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.85037e11 | 0.0421128 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.22191e12 | 0.564414 | 0.282207 | − | 0.959353i | \(-0.408933\pi\) | ||||
0.282207 | + | 0.959353i | \(0.408933\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.10294e11 | −0.0865530 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.49941e12 | −0.158287 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.67612e12 | 1.00954 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.85529e12 | −0.913134 | −0.456567 | − | 0.889689i | \(-0.650921\pi\) | ||||
−0.456567 | + | 0.889689i | \(0.650921\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.19575e12 | −0.631465 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.21750e12 | 0.525599 | 0.262799 | − | 0.964850i | \(-0.415354\pi\) | ||||
0.262799 | + | 0.964850i | \(0.415354\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.20002e10 | 0.00916075 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.43809e11 | −0.0141544 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.44285e13 | −1.40379 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.80911e11 | 0.0366348 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.37767e12 | −0.130984 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.24397e13 | −1.16922 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.22879e13 | 1.14181 | 0.570903 | − | 0.821017i | \(-0.306593\pi\) | ||||
0.570903 | + | 0.821017i | \(0.306593\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.47732e12 | 0.135715 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.29054e12 | −0.117213 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.58678e12 | 0.771082 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.61399e12 | 0.320874 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.04691e13 | 0.919063 | 0.459532 | − | 0.888161i | \(-0.348017\pi\) | ||||
0.459532 | + | 0.888161i | \(0.348017\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.86733e11 | 0.0248895 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.13838e13 | −0.977107 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.72029e11 | −0.0315760 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.13788e12 | 0.0955024 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.50398e11 | 0.0788814 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.43675e13 | −1.17927 | −0.589634 | − | 0.807671i | \(-0.700728\pi\) | ||||
−0.589634 | + | 0.807671i | \(0.700728\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.55011e12 | 0.125825 | 0.0629127 | − | 0.998019i | \(-0.479961\pi\) | ||||
0.0629127 | + | 0.998019i | \(0.479961\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.21347e13 | 0.974137 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.00849e13 | −0.800690 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.02039e13 | 0.801249 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.86501e11 | −0.0300174 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.37949e13 | −1.05968 | −0.529839 | − | 0.848098i | \(-0.677748\pi\) | ||||
−0.529839 | + | 0.848098i | \(0.677748\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.07251e13 | 0.814899 | 0.407449 | − | 0.913228i | \(-0.366418\pi\) | ||||
0.407449 | + | 0.913228i | \(0.366418\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.97347e10 | −0.00298626 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.65480e13 | −1.23019 | −0.615093 | − | 0.788454i | \(-0.710882\pi\) | ||||
−0.615093 | + | 0.788454i | \(0.710882\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.03812e13 | 0.763398 | 0.381699 | − | 0.924287i | \(-0.375339\pi\) | ||||
0.381699 | + | 0.924287i | \(0.375339\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.69040e12 | −0.704916 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.35374e12 | 0.241339 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.19488e13 | −0.850621 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.40373e12 | −0.0988595 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.25038e12 | 0.435489 | 0.217745 | − | 0.976006i | \(-0.430130\pi\) | ||||
0.217745 | + | 0.976006i | \(0.430130\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.42560e13 | −0.982687 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.18428e12 | 0.285362 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.23589e12 | 0.555719 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.04925e12 | −0.0700496 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.04207e13 | 0.688356 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.54432e12 | 0.427742 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.08264e13 | −1.34693 | −0.673464 | − | 0.739220i | \(-0.735194\pi\) | ||||
−0.673464 | + | 0.739220i | \(0.735194\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.51147e12 | 0.544700 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.34103e12 | 0.148249 | 0.0741246 | − | 0.997249i | \(-0.476384\pi\) | ||||
0.0741246 | + | 0.997249i | \(0.476384\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.14439e13 | 0.717139 | 0.358569 | − | 0.933503i | \(-0.383265\pi\) | ||||
0.358569 | + | 0.933503i | \(0.383265\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.16754e12 | −0.0724031 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.65044e13 | 1.01286 | 0.506431 | − | 0.862281i | \(-0.330965\pi\) | ||||
0.506431 | + | 0.862281i | \(0.330965\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.87029e12 | −0.174323 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.99739e11 | 0.0360476 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.08295e12 | −0.0644201 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.86056e12 | 0.345031 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.77406e13 | −1.03372 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.15554e12 | 0.0666419 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.42710e11 | −0.00814620 | −0.00407310 | − | 0.999992i | \(-0.501297\pi\) | ||||
−0.00407310 | + | 0.999992i | \(0.501297\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.29777e12 | 0.468826 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.11785e13 | 1.18441 | 0.592206 | − | 0.805786i | \(-0.298257\pi\) | ||||
0.592206 | + | 0.805786i | \(0.298257\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.83970e13 | −1.01841 | −0.509207 | − | 0.860644i | \(-0.670061\pi\) | ||||
−0.509207 | + | 0.860644i | \(0.670061\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.72427e13 | −0.944847 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.18951e13 | 0.645225 | 0.322613 | − | 0.946531i | \(-0.395439\pi\) | ||||
0.322613 | + | 0.946531i | \(0.395439\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.18888e11 | −0.0332318 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.43329e10 | −0.000761874 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.62765e12 | −0.0856505 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.66727e13 | −1.91047 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.05772e13 | −0.545514 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.55908e11 | 0.0130667 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.40373e12 | 0.121513 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.25692e11 | 0.0413260 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.43377e12 | 0.219713 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.91571e13 | −1.92122 | −0.960612 | − | 0.277893i | \(-0.910364\pi\) | ||||
−0.960612 | + | 0.277893i | \(0.910364\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.13251e13 | −1.03599 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.83393e13 | 1.36319 | 0.681595 | − | 0.731730i | \(-0.261287\pi\) | ||||
0.681595 | + | 0.731730i | \(0.261287\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.37513e11 | −0.00654977 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.53015e13 | −0.721672 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.62319e12 | −0.122509 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.73995e13 | 0.804668 | 0.402334 | − | 0.915493i | \(-0.368199\pi\) | ||||
0.402334 | + | 0.915493i | \(0.368199\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.13119e13 | 0.518044 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.04639e13 | −0.474554 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.75356e11 | −0.0303316 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.42329e13 | −0.633047 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.95509e13 | −1.74215 | −0.871074 | − | 0.491151i | \(-0.836576\pi\) | ||||
−0.871074 | + | 0.491151i | \(0.836576\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.90377e13 | −0.830501 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.74988e11 | −0.0118808 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.12926e11 | −0.0133903 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.31185e13 | 1.82741 | 0.913704 | − | 0.406381i | \(-0.133210\pi\) | ||||
0.913704 | + | 0.406381i | \(0.133210\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.37504e13 | −0.577194 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.23028e13 | 0.511505 | 0.255753 | − | 0.966742i | \(-0.417677\pi\) | ||||
0.255753 | + | 0.966742i | \(0.417677\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.31313e13 | 2.18800 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.79167e12 | 0.0730828 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.99251e13 | −1.61314 | −0.806568 | − | 0.591142i | \(-0.798677\pi\) | ||||
−0.806568 | + | 0.591142i | \(0.798677\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.02199e13 | 0.409024 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.82424e12 | 0.230902 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.12885e13 | −1.62148 | −0.810739 | − | 0.585408i | \(-0.800934\pi\) | ||||
−0.810739 | + | 0.585408i | \(0.800934\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.60930e13 | −1.79316 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.10526e11 | −0.00425953 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.00658e12 | 0.0384296 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.61789e13 | −0.990138 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.60548e12 | 0.284976 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.35241e12 | −0.124447 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.74952e13 | 1.37898 | 0.689488 | − | 0.724297i | \(-0.257836\pi\) | ||||
0.689488 | + | 0.724297i | \(0.257836\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.40444e12 | −0.124048 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.85734e13 | 0.670508 | 0.335254 | − | 0.942128i | \(-0.391178\pi\) | ||||
0.335254 | + | 0.942128i | \(0.391178\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.21653e11 | 0.0329655 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.09154e12 | 0.0386829 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.09643e13 | −1.78954 | −0.894769 | − | 0.446530i | \(-0.852660\pi\) | ||||
−0.894769 | + | 0.446530i | \(0.852660\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.37580e12 | −0.0826586 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.23194e13 | 0.769434 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.27845e12 | −0.0436710 | −0.0218355 | − | 0.999762i | \(-0.506951\pi\) | ||||
−0.0218355 | + | 0.999762i | \(0.506951\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.87578e13 | −1.31189 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.31708e11 | −0.00441759 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.75748e13 | −1.24886 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.53850e13 | −0.506719 | −0.253360 | − | 0.967372i | \(-0.581536\pi\) | ||||
−0.253360 | + | 0.967372i | \(0.581536\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.06514e13 | −0.347643 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.12920e13 | −0.688672 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.56093e13 | 1.14139 | 0.570696 | − | 0.821162i | \(-0.306674\pi\) | ||||
0.570696 | + | 0.821162i | \(0.306674\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.03045e13 | 0.327327 |
(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 | 272.10.a.f.1.4 | 5 | ||
4.3 | odd | 2 | 17.10.a.a.1.5 | ✓ | 5 | ||
12.11 | even | 2 | 153.10.a.c.1.1 | 5 | |||
68.67 | odd | 2 | 289.10.a.a.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.10.a.a.1.5 | ✓ | 5 | 4.3 | odd | 2 | ||
153.10.a.c.1.1 | 5 | 12.11 | even | 2 | |||
272.10.a.f.1.4 | 5 | 1.1 | even | 1 | trivial | ||
289.10.a.a.1.5 | 5 | 68.67 | odd | 2 |