Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [176,8,Mod(1,176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(176, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("176.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 176 = 2^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 176.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: | \(54.9797644852\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{14881}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3720 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 22) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(61.4939\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 176.1 |
$q$-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 | ||||||||
\(3\) | −49.4939 | −1.05834 | −0.529172 | − | 0.848515i | \(-0.677497\pi\) | ||||
−0.529172 | + | 0.848515i | \(0.677497\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 104.506 | 0.373893 | 0.186946 | − | 0.982370i | \(-0.440141\pi\) | ||||
0.186946 | + | 0.982370i | \(0.440141\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −43.0861 | −0.0474781 | −0.0237391 | − | 0.999718i | \(-0.507557\pi\) | ||||
−0.0237391 | + | 0.999718i | \(0.507557\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 262.641 | 0.120092 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1331.00 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4494.27 | 0.567359 | 0.283679 | − | 0.958919i | \(-0.408445\pi\) | ||||
0.283679 | + | 0.958919i | \(0.408445\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5172.41 | −0.395707 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6878.55 | −0.339567 | −0.169784 | − | 0.985481i | \(-0.554307\pi\) | ||||
−0.169784 | + | 0.985481i | \(0.554307\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 21063.0 | 0.704503 | 0.352252 | − | 0.935905i | \(-0.385416\pi\) | ||||
0.352252 | + | 0.935905i | \(0.385416\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2132.50 | 0.0502482 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 60259.0 | 1.03270 | 0.516350 | − | 0.856377i | \(-0.327290\pi\) | ||||
0.516350 | + | 0.856377i | \(0.327290\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −67203.5 | −0.860204 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 95243.9 | 0.931245 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −59039.5 | −0.449521 | −0.224760 | − | 0.974414i | \(-0.572160\pi\) | ||||
−0.224760 | + | 0.974414i | \(0.572160\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 88522.5 | 0.533689 | 0.266844 | − | 0.963740i | \(-0.414019\pi\) | ||||
0.266844 | + | 0.963740i | \(0.414019\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 65876.3 | 0.319103 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4502.76 | −0.0177517 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 382131. | 1.24024 | 0.620120 | − | 0.784507i | \(-0.287084\pi\) | ||||
0.620120 | + | 0.784507i | \(0.287084\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −222439. | −0.600461 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 550122. | 1.24657 | 0.623283 | − | 0.781996i | \(-0.285798\pi\) | ||||
0.623283 | + | 0.781996i | \(0.285798\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −693613. | −1.33039 | −0.665193 | − | 0.746671i | \(-0.731651\pi\) | ||||
−0.665193 | + | 0.746671i | \(0.731651\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 27447.6 | 0.0449015 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 126233. | 0.177349 | 0.0886745 | − | 0.996061i | \(-0.471737\pi\) | ||||
0.0886745 | + | 0.996061i | \(0.471737\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −821687. | −0.997746 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 340446. | 0.359379 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.19815e6 | −1.10546 | −0.552732 | − | 0.833359i | \(-0.686415\pi\) | ||||
−0.552732 | + | 0.833359i | \(0.686415\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −139098. | −0.112733 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.04249e6 | −0.745607 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.31641e6 | −0.834469 | −0.417234 | − | 0.908799i | \(-0.637001\pi\) | ||||
−0.417234 | + | 0.908799i | \(0.637001\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 440165. | 0.248291 | 0.124145 | − | 0.992264i | \(-0.460381\pi\) | ||||
0.124145 | + | 0.992264i | \(0.460381\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −11316.2 | −0.00570175 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 469679. | 0.212131 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.56366e6 | −1.44755 | −0.723777 | − | 0.690034i | \(-0.757596\pi\) | ||||
−0.723777 | + | 0.690034i | \(0.757596\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.98245e6 | −1.09295 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.13943e6 | −1.04099 | −0.520494 | − | 0.853865i | \(-0.674252\pi\) | ||||
−0.520494 | + | 0.853865i | \(0.674252\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.07747e6 | −1.22676 | −0.613382 | − | 0.789787i | \(-0.710191\pi\) | ||||
−0.613382 | + | 0.789787i | \(0.710191\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.32616e6 | 0.910392 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 57347.6 | 0.0143152 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.89723e6 | −0.432937 | −0.216468 | − | 0.976290i | \(-0.569454\pi\) | ||||
−0.216468 | + | 0.976290i | \(0.569454\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.28839e6 | −1.10567 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.49257e6 | −1.24636 | −0.623179 | − | 0.782079i | \(-0.714159\pi\) | ||||
−0.623179 | + | 0.782079i | \(0.714159\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −718851. | −0.126962 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.92209e6 | 0.475747 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.23033e6 | 1.38788 | 0.693940 | − | 0.720032i | \(-0.255873\pi\) | ||||
0.693940 | + | 0.720032i | \(0.255873\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −193641. | −0.0269371 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.38132e6 | −0.564826 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.20122e6 | 0.263409 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.38062e7 | −1.53593 | −0.767967 | − | 0.640489i | \(-0.778732\pi\) | ||||
−0.767967 | + | 0.640489i | \(0.778732\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −349576. | −0.0362091 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.59478e6 | 0.636906 | 0.318453 | − | 0.947939i | \(-0.396837\pi\) | ||||
0.318453 | + | 0.947939i | \(0.396837\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.98787e7 | 1.79250 | 0.896249 | − | 0.443551i | \(-0.146282\pi\) | ||||
0.896249 | + | 0.443551i | \(0.146282\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 222859. | 0.0187874 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.09533e7 | −1.65352 | −0.826758 | − | 0.562558i | \(-0.809817\pi\) | ||||
−0.826758 | + | 0.562558i | \(0.809817\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −598244. | −0.0442472 | −0.0221236 | − | 0.999755i | \(-0.507043\pi\) | ||||
−0.0221236 | + | 0.999755i | \(0.507043\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.89131e7 | −1.31260 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.41807e6 | −0.0924535 | −0.0462267 | − | 0.998931i | \(-0.514720\pi\) | ||||
−0.0462267 | + | 0.998931i | \(0.514720\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.29744e6 | 0.386119 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.18038e6 | 0.0681353 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 296370. | 0.0161220 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.77156e6 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.72276e7 | −1.31930 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.51877e7 | −0.695517 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.92988e7 | 0.836023 | 0.418012 | − | 0.908442i | \(-0.362727\pi\) | ||||
0.418012 | + | 0.908442i | \(0.362727\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.43296e7 | 1.40801 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.22451e7 | −1.64182 | −0.820912 | − | 0.571055i | \(-0.806534\pi\) | ||||
−0.820912 | + | 0.571055i | \(0.806534\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −907523. | −0.0334485 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.95358e6 | 0.348186 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.65888e6 | −0.254474 | −0.127237 | − | 0.991872i | \(-0.540611\pi\) | ||||
−0.127237 | + | 0.991872i | \(0.540611\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.46018e7 | 0.461164 | 0.230582 | − | 0.973053i | \(-0.425937\pi\) | ||||
0.230582 | + | 0.973053i | \(0.425937\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.24773e6 | −0.187696 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.98188e6 | −0.171065 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.16999e6 | −0.168072 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.06684e7 | 1.05596 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.54730e7 | −0.878507 | −0.439254 | − | 0.898363i | \(-0.644757\pi\) | ||||
−0.439254 | + | 0.898363i | \(0.644757\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.10281e7 | −0.969754 | −0.484877 | − | 0.874582i | \(-0.661136\pi\) | ||||
−0.484877 | + | 0.874582i | \(0.661136\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.80659e6 | −0.0407793 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.25115e6 | 0.199542 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.66977e7 | −1.37550 | −0.687752 | − | 0.725946i | \(-0.741402\pi\) | ||||
−0.687752 | + | 0.725946i | \(0.741402\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.93009e7 | 1.16996 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.59632e6 | −0.0490307 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.29744e6 | −0.168154 | −0.0840769 | − | 0.996459i | \(-0.526794\pi\) | ||||
−0.0840769 | + | 0.996459i | \(0.526794\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.88448e6 | 0.119310 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.93268e7 | 0.985696 | 0.492848 | − | 0.870115i | \(-0.335956\pi\) | ||||
0.492848 | + | 0.870115i | \(0.335956\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.25500e7 | −0.678104 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.53202e6 | 0.0846053 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.19997e8 | 1.76201 | 0.881004 | − | 0.473108i | \(-0.156868\pi\) | ||||
0.881004 | + | 0.473108i | \(0.156868\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.89553e6 | 0.0408409 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.51543e7 | 0.883155 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.18894e7 | −0.415586 | −0.207793 | − | 0.978173i | \(-0.566628\pi\) | ||||
−0.207793 | + | 0.978173i | \(0.566628\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.14661e7 | 0.269079 | 0.134539 | − | 0.990908i | \(-0.457045\pi\) | ||||
0.134539 | + | 0.990908i | \(0.457045\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.17854e7 | −0.262777 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.99350e7 | 0.463717 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.15535e6 | 0.102383 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.10369e6 | −0.0442138 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.37382e7 | 0.558042 | 0.279021 | − | 0.960285i | \(-0.409990\pi\) | ||||
0.279021 | + | 0.960285i | \(0.409990\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.72101e8 | 1.72319 | 0.861593 | − | 0.507600i | \(-0.169467\pi\) | ||||
0.861593 | + | 0.507600i | \(0.169467\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.32462e7 | −0.224508 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.14526e8 | −1.06726 | −0.533631 | − | 0.845718i | \(-0.679173\pi\) | ||||
−0.533631 | + | 0.845718i | \(0.679173\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.40644e7 | 0.306418 | 0.153209 | − | 0.988194i | \(-0.451039\pi\) | ||||
0.153209 | + | 0.988194i | \(0.451039\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.76379e8 | 1.53201 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.54378e6 | 0.0213424 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.74911e7 | 0.466082 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.58265e7 | 0.124019 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.80349e7 | −0.212416 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.74288e8 | 1.27726 | 0.638628 | − | 0.769516i | \(-0.279502\pi\) | ||||
0.638628 | + | 0.769516i | \(0.279502\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.55382e8 | 1.10172 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.24868e7 | −0.497421 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.81409e6 | −0.0253385 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.01810e8 | 1.29834 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.09141e7 | −0.192656 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.45730e8 | −0.879998 | −0.439999 | − | 0.897998i | \(-0.645021\pi\) | ||||
−0.439999 | + | 0.897998i | \(0.645021\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.76504e7 | −0.103304 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.27102e8 | 0.721211 | 0.360606 | − | 0.932718i | \(-0.382570\pi\) | ||||
0.360606 | + | 0.932718i | \(0.382570\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.29750e8 | −0.713975 | −0.356987 | − | 0.934109i | \(-0.616196\pi\) | ||||
−0.356987 | + | 0.934109i | \(0.616196\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.83835e6 | −0.0151504 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.52210e8 | −0.788310 | −0.394155 | − | 0.919044i | \(-0.628963\pi\) | ||||
−0.394155 | + | 0.919044i | \(0.628963\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.31921e7 | 0.0663095 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.39011e7 | 0.458196 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.43061e8 | 1.15165 | 0.575827 | − | 0.817571i | \(-0.304680\pi\) | ||||
0.575827 | + | 0.817571i | \(0.304680\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.84592e7 | −0.315045 | −0.157522 | − | 0.987515i | \(-0.550351\pi\) | ||||
−0.157522 | + | 0.987515i | \(0.550351\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.34441e7 | 0.238934 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.58713e7 | −0.373050 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.46630e7 | 0.399706 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.21342e8 | 1.31908 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.67292e8 | −0.667755 | −0.333878 | − | 0.942616i | \(-0.608357\pi\) | ||||
−0.333878 | + | 0.942616i | \(0.608357\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.02047e7 | −0.311371 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.55787e7 | 0.134369 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.84789e8 | 1.41402 | 0.707012 | − | 0.707202i | \(-0.250043\pi\) | ||||
0.707012 | + | 0.707202i | \(0.250043\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.64645e7 | −0.0588843 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.55062e7 | −0.0539839 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.09459e8 | −1.72689 | −0.863444 | − | 0.504445i | \(-0.831697\pi\) | ||||
−0.863444 | + | 0.504445i | \(0.831697\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.25214e8 | −0.413325 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.56845e8 | −1.46886 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.51297e8 | −1.72684 | −0.863421 | − | 0.504484i | \(-0.831683\pi\) | ||||
−0.863421 | + | 0.504484i | \(0.831683\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.42271e8 | −1.04467 | −0.522333 | − | 0.852742i | \(-0.674938\pi\) | ||||
−0.522333 | + | 0.852742i | \(0.674938\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.58402e6 | 0.0285088 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.94478e7 | 0.259361 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.10974e8 | −1.44451 | −0.722253 | − | 0.691629i | \(-0.756893\pi\) | ||||
−0.722253 | + | 0.691629i | \(0.756893\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.32497e7 | 0.0640918 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.51750e7 | −0.0407998 | −0.0203999 | − | 0.999792i | \(-0.506494\pi\) | ||||
−0.0203999 | + | 0.999792i | \(0.506494\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.25341e8 | 0.590999 | 0.295500 | − | 0.955343i | \(-0.404514\pi\) | ||||
0.295500 | + | 0.955343i | \(0.404514\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.08947e8 | −0.278777 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.37026e7 | −0.0591846 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.63024e8 | −0.884694 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.83322e8 | 1.62555 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.84004e8 | 0.891864 | 0.445932 | − | 0.895067i | \(-0.352872\pi\) | ||||
0.445932 | + | 0.895067i | \(0.352872\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.37573e8 | −0.312002 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.26770e8 | −0.280781 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.70821e8 | 0.585912 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.98851e7 | 0.0631643 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.26401e8 | −0.674066 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.59999e7 | 0.0928341 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.46289e8 | −1.47205 | −0.736026 | − | 0.676954i | \(-0.763300\pi\) | ||||
−0.736026 | + | 0.676954i | \(0.763300\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.83876e8 | −1.89708 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.40000e8 | −1.20648 | −0.603238 | − | 0.797561i | \(-0.706123\pi\) | ||||
−0.603238 | + | 0.797561i | \(0.706123\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.35452e8 | 0.249677 | 0.124839 | − | 0.992177i | \(-0.460159\pi\) | ||||
0.124839 | + | 0.992177i | \(0.460159\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.18261e6 | −0.00213184 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.75198e7 | 0.171943 | 0.0859717 | − | 0.996298i | \(-0.472601\pi\) | ||||
0.0859717 | + | 0.996298i | \(0.472601\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.85816e7 | 0.135536 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.03706e9 | 1.74999 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.44883e8 | −0.239226 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.02031e8 | −0.488045 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.96094e7 | 0.0468288 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.43886e6 | −0.00842020 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.49842e8 | −0.530242 | −0.265121 | − | 0.964215i | \(-0.585412\pi\) | ||||
−0.265121 | + | 0.964215i | \(0.585412\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.00363e8 | 0.148943 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.72425e8 | −0.541230 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.20870e8 | 1.02601 | 0.513006 | − | 0.858385i | \(-0.328532\pi\) | ||||
0.513006 | + | 0.858385i | \(0.328532\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.01858e7 | 0.0978476 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.17823e8 | −0.160913 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.08865e7 | 0.0948493 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.11684e8 | −0.408647 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.28079e8 | −0.164560 | −0.0822798 | − | 0.996609i | \(-0.526220\pi\) | ||||
−0.0822798 | + | 0.996609i | \(0.526220\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.00379e8 | −0.126402 | −0.0632012 | − | 0.998001i | \(-0.520131\pi\) | ||||
−0.0632012 | + | 0.998001i | \(0.520131\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.28052e8 | 0.528350 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.51413e8 | 0.909216 | 0.454608 | − | 0.890692i | \(-0.349779\pi\) | ||||
0.454608 | + | 0.890692i | \(0.349779\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.28089e8 | −0.389218 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.46685e7 | −0.0170626 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.17064e8 | 1.04609 | 0.523045 | − | 0.852305i | \(-0.324796\pi\) | ||||
0.523045 | + | 0.852305i | \(0.324796\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.50221e8 | −0.503675 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.76814e7 | −0.0962131 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.26121e8 | −0.458678 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.16435e8 | 0.967766 | 0.483883 | − | 0.875133i | \(-0.339226\pi\) | ||||
0.483883 | + | 0.875133i | \(0.339226\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.44485e8 | 0.149703 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.16234e7 | 0.0524854 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.56099e9 | −1.55747 | −0.778736 | − | 0.627352i | \(-0.784139\pi\) | ||||
−0.778736 | + | 0.627352i | \(0.784139\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.51699e8 | 0.736096 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.65340e8 | −0.255040 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.34986e7 | −0.0410429 | −0.0205214 | − | 0.999789i | \(-0.506533\pi\) | ||||
−0.0205214 | + | 0.999789i | \(0.506533\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.55174e8 | −0.884800 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.95422e8 | −0.177737 | −0.0888685 | − | 0.996043i | \(-0.528325\pi\) | ||||
−0.0888685 | + | 0.996043i | \(0.528325\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.99317e6 | 0.00535235 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.82171e8 | −0.159769 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.60846e9 | −1.38543 | −0.692716 | − | 0.721210i | \(-0.743586\pi\) | ||||
−0.692716 | + | 0.721210i | \(0.743586\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.14495e8 | −0.350671 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.09087e9 | 1.73761 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.98272e8 | −0.161872 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.20591e9 | 0.967268 | 0.483634 | − | 0.875270i | \(-0.339317\pi\) | ||||
0.483634 | + | 0.875270i | \(0.339317\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.49168e7 | 0.0354000 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.40689e8 | 0.573628 | 0.286814 | − | 0.957986i | \(-0.407404\pi\) | ||||
0.286814 | + | 0.957986i | \(0.407404\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.97845e8 | 0.302793 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.52669e8 | −0.413402 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.08616e8 | −0.373947 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.37187e7 | 0.00991476 | 0.00495738 | − | 0.999988i | \(-0.498422\pi\) | ||||
0.00495738 | + | 0.999988i | \(0.498422\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.79067e8 | 0.269321 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.67190e7 | 0.0396190 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.78513e8 | −0.466004 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.22700e8 | −0.488070 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.95596e9 | −1.29901 | −0.649503 | − | 0.760359i | \(-0.725023\pi\) | ||||
−0.649503 | + | 0.760359i | \(0.725023\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.31110e9 | −1.50950 | −0.754748 | − | 0.656015i | \(-0.772241\pi\) | ||||
−0.754748 | + | 0.656015i | \(0.772241\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.31539e7 | 0.0212982 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.62262e8 | 0.292097 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.89650e7 | −0.0117884 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.96066e8 | 0.181046 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.03521e9 | 1.22444 | 0.612222 | − | 0.790686i | \(-0.290276\pi\) | ||||
0.612222 | + | 0.790686i | \(0.290276\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.81028e9 | 1.66357 | 0.831786 | − | 0.555096i | \(-0.187318\pi\) | ||||
0.831786 | + | 0.555096i | \(0.187318\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.05377e8 | 0.177878 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.26924e9 | 0.727541 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.58225e9 | −0.892587 | −0.446293 | − | 0.894887i | \(-0.647256\pi\) | ||||
−0.446293 | + | 0.894887i | \(0.647256\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.15809e8 | −0.119821 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.88989e8 | 0.267231 | 0.133615 | − | 0.991033i | \(-0.457341\pi\) | ||||
0.133615 | + | 0.991033i | \(0.457341\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.64626e8 | 0.518918 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.75569e9 | 0.929763 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.81072e9 | 0.944036 | 0.472018 | − | 0.881589i | \(-0.343526\pi\) | ||||
0.472018 | + | 0.881589i | \(0.343526\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.32212e8 | −0.375854 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.03064e9 | 1.02633 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.02366e7 | −0.0100716 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.64311e8 | −0.423607 | −0.211804 | − | 0.977312i | \(-0.567934\pi\) | ||||
−0.211804 | + | 0.977312i | \(0.567934\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.55140e8 | −0.316220 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.85430e8 | 0.230767 | 0.115383 | − | 0.993321i | \(-0.463190\pi\) | ||||
0.115383 | + | 0.993321i | \(0.463190\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.85376e9 | −0.867999 | −0.434000 | − | 0.900913i | \(-0.642898\pi\) | ||||
−0.434000 | + | 0.900913i | \(0.642898\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.57875e8 | −0.211184 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.16192e7 | −0.0143662 | −0.00718310 | − | 0.999974i | \(-0.502286\pi\) | ||||
−0.00718310 | + | 0.999974i | \(0.502286\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.53544e8 | 0.0687272 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.30112e9 | 1.45576 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.23199e8 | 0.401126 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.41551e9 | −0.606017 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.14683e8 | −0.132757 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.11838e9 | 1.29645 | 0.648223 | − | 0.761451i | \(-0.275513\pi\) | ||||
0.648223 | + | 0.761451i | \(0.275513\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.71740e9 | 0.703661 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.28502e8 | 0.0518914 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.44283e9 | −0.574275 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.37608e9 | 1.32453 | 0.662265 | − | 0.749270i | \(-0.269596\pi\) | ||||
0.662265 | + | 0.749270i | \(0.269596\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.60166e8 | 0.177965 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.55043e9 | 1.73487 | 0.867436 | − | 0.497548i | \(-0.165766\pi\) | ||||
0.867436 | + | 0.497548i | \(0.165766\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.06106e8 | 0.152642 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.65328e7 | −0.0135383 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.35266e8 | 0.0494242 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.25733e8 | 0.225443 | 0.112722 | − | 0.993627i | \(-0.464043\pi\) | ||||
0.112722 | + | 0.993627i | \(0.464043\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.93631e9 | −1.04321 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.43240e9 | 1.20257 | 0.601285 | − | 0.799035i | \(-0.294656\pi\) | ||||
0.601285 | + | 0.799035i | \(0.294656\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.89195e8 | 0.238135 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.10596e9 | 0.717667 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.36035e9 | 0.457234 | 0.228617 | − | 0.973516i | \(-0.426580\pi\) | ||||
0.228617 | + | 0.973516i | \(0.426580\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.75682e8 | 0.0582445 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.00613e9 | 0.656066 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.07745e9 | 0.670202 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.68016e8 | −0.0534727 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.93910e9 | −1.86481 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.51109e9 | −0.777912 | −0.388956 | − | 0.921256i | \(-0.627164\pi\) | ||||
−0.388956 | + | 0.921256i | \(0.627164\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.25045e9 | −1.29921 | −0.649605 | − | 0.760272i | \(-0.725066\pi\) | ||||
−0.649605 | + | 0.760272i | \(0.725066\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.43311e8 | −0.0432237 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.08907e8 | −0.181223 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.26323e8 | 0.0664713 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.45744e8 | −0.100213 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.47240e9 | 0.707250 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.18974e9 | −0.618237 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.57833e9 | 0.439833 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.09366e9 | 0.300832 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.06279e9 | 0.288574 | 0.144287 | − | 0.989536i | \(-0.453911\pi\) | ||||
0.144287 | + | 0.989536i | \(0.453911\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.06244e9 | −0.284778 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.25202e7 | −0.0165437 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.28564e9 | 0.858350 | 0.429175 | − | 0.903221i | \(-0.358804\pi\) | ||||
0.429175 | + | 0.903221i | \(0.358804\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.15605e8 | 0.0298178 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.24355e9 | −0.316689 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.17441e7 | 0.0205550 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.97654e9 | −0.490772 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.04436e9 | −0.991645 | −0.495823 | − | 0.868424i | \(-0.665133\pi\) | ||||
−0.495823 | + | 0.868424i | \(0.665133\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.11729e9 | −0.754806 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.53133e8 | −0.108357 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.60197e9 | 0.378333 | 0.189167 | − | 0.981945i | \(-0.439421\pi\) | ||||
0.189167 | + | 0.981945i | \(0.439421\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.48197e8 | −0.0345677 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.27856e8 | 0.0524952 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.94461e9 | −1.35279 | −0.676396 | − | 0.736539i | \(-0.736459\pi\) | ||||
−0.676396 | + | 0.736539i | \(0.736459\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.01942e9 | 0.229154 | 0.114577 | − | 0.993414i | \(-0.463449\pi\) | ||||
0.114577 | + | 0.993414i | \(0.463449\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.65971e9 | −0.590600 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.04961e9 | −0.888334 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.05194e8 | −0.109482 | −0.0547410 | − | 0.998501i | \(-0.517433\pi\) | ||||
−0.0547410 | + | 0.998501i | \(0.517433\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.51792e9 | −1.82372 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.79739e8 | 0.0591748 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.59473e9 | 0.333310 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.23357e8 | 0.0254753 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.05441e8 | −0.123549 | −0.0617744 | − | 0.998090i | \(-0.519676\pi\) | ||||
−0.0617744 | + | 0.998090i | \(0.519676\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.86455e9 | 0.375985 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.66831e9 | 1.12953 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.44359e8 | −0.0481212 | −0.0240606 | − | 0.999711i | \(-0.507659\pi\) | ||||
−0.0240606 | + | 0.999711i | \(0.507659\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.09725e7 | 0.00602790 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.68598e9 | −0.324296 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.76209e9 | −0.905324 | −0.452662 | − | 0.891682i | \(-0.649526\pi\) | ||||
−0.452662 | + | 0.891682i | \(0.649526\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.27387e9 | −0.803083 | −0.401542 | − | 0.915841i | \(-0.631525\pi\) | ||||
−0.401542 | + | 0.915841i | \(0.631525\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.35966e8 | −0.173840 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.85139e8 | 0.0339902 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.40384e9 | −1.16220 | −0.581099 | − | 0.813833i | \(-0.697377\pi\) | ||||
−0.581099 | + | 0.813833i | \(0.697377\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.25901e8 | −0.0225876 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.67324e8 | 0.100621 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.98899e9 | −1.57616 | −0.788078 | − | 0.615575i | \(-0.788924\pi\) | ||||
−0.788078 | + | 0.615575i | \(0.788924\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.84546e9 | −0.493275 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.11391e9 | −0.362316 | −0.181158 | − | 0.983454i | \(-0.557985\pi\) | ||||
−0.181158 | + | 0.983454i | \(0.557985\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.25875e9 | 0.721713 | 0.360856 | − | 0.932621i | \(-0.382484\pi\) | ||||
0.360856 | + | 0.932621i | \(0.382484\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.73930e9 | 0.961698 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.97699e8 | −0.0658940 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.66306e9 | 0.600156 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.38755e9 | 0.224809 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.62850e9 | −0.421145 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.55885e9 | −1.51462 | −0.757309 | − | 0.653057i | \(-0.773486\pi\) | ||||
−0.757309 | + | 0.653057i | \(0.773486\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.62617e9 | −1.35178 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.01685e9 | 0.312583 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.69289e9 | −0.566080 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.24543e8 | −0.125015 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.93190e9 | 1.18953 | 0.594763 | − | 0.803901i | \(-0.297246\pi\) | ||||
0.594763 | + | 0.803901i | \(0.297246\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.67790e9 | 0.545583 | 0.272792 | − | 0.962073i | \(-0.412053\pi\) | ||||
0.272792 | + | 0.962073i | \(0.412053\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.58765e9 | 0.526443 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.34066e9 | 0.484917 | 0.242459 | − | 0.970162i | \(-0.422046\pi\) | ||||
0.242459 | + | 0.970162i | \(0.422046\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.75215e9 | 0.251602 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.88774e8 | 0.0268169 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.23649e10 | 1.73778 | 0.868891 | − | 0.495004i | \(-0.164833\pi\) | ||||
0.868891 | + | 0.495004i | \(0.164833\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.41487e9 | −0.613865 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.07091e9 | −0.147325 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.58087e9 | −1.16797 | −0.583986 | − | 0.811764i | \(-0.698508\pi\) | ||||
−0.583986 | + | 0.811764i | \(0.698508\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.09007e9 | −1.08955 | −0.544775 | − | 0.838582i | \(-0.683385\pi\) | ||||
−0.544775 | + | 0.838582i | \(0.683385\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.53006e9 | 0.203897 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.48417e7 | −0.0125062 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.55766e9 | −0.464220 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.21274e9 | 0.931341 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.85859e8 | −0.0748625 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.38929e10 | −1.75687 | −0.878436 | − | 0.477860i | \(-0.841413\pi\) | ||||
−0.878436 | + | 0.477860i | \(0.841413\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.40072e9 | −0.801061 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.36018e9 | 0.787788 | 0.393894 | − | 0.919156i | \(-0.371128\pi\) | ||||
0.393894 | + | 0.919156i | \(0.371128\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.94855e8 | 0.0729233 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.29077e9 | −0.763289 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.46187e9 | 0.896139 | 0.448069 | − | 0.893999i | \(-0.352112\pi\) | ||||
0.448069 | + | 0.893999i | \(0.352112\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.00400e8 | −0.0951459 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.42182e9 | 0.755631 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.38480e9 | −0.627195 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.01338e10 | 1.16842 | 0.584212 | − | 0.811601i | \(-0.301404\pi\) | ||||
0.584212 | + | 0.811601i | \(0.301404\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.50618e7 | 0.00171914 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.52598e9 | 0.172426 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.78404e9 | −0.423293 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.53345e9 | 0.834303 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.31006e10 | 1.43641 | 0.718206 | − | 0.695831i | \(-0.244964\pi\) | ||||
0.718206 | + | 0.695831i | \(0.244964\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.04883e9 | 0.873754 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.52927e8 | −0.0701782 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.84143e8 | −0.0302391 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.04601e10 | −1.10223 | −0.551116 | − | 0.834429i | \(-0.685798\pi\) | ||||
−0.551116 | + | 0.834429i | \(0.685798\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.98290e8 | −0.0519923 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.33428e9 | 0.551141 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.25143e8 | −0.0639600 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.20300e10 | −1.21885 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.14452e9 | −0.616505 | −0.308253 | − | 0.951305i | \(-0.599744\pi\) | ||||
−0.308253 | + | 0.951305i | \(0.599744\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.56497e8 | −0.0851045 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.38831e9 | 0.333426 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.96766e9 | 0.386680 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.47022e9 | 0.141910 | 0.0709550 | − | 0.997480i | \(-0.477395\pi\) | ||||
0.0709550 | + | 0.997480i | \(0.477395\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.92054e9 | 0.852796 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.77105e9 | 0.451755 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.30989e8 | 0.0591777 | 0.0295888 | − | 0.999562i | \(-0.490580\pi\) | ||||
0.0295888 | + | 0.999562i | \(0.490580\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.25010e9 | 0.394815 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.74324e9 | 0.436454 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.22368e9 | −0.658420 | −0.329210 | − | 0.944257i | \(-0.606782\pi\) | ||||
−0.329210 | + | 0.944257i | \(0.606782\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.68524e9 | −0.423027 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.72789e9 | −0.691194 | −0.345597 | − | 0.938383i | \(-0.612324\pi\) | ||||
−0.345597 | + | 0.938383i | \(0.612324\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.70714e9 | −0.328467 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.70522e9 | −0.149678 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.02793e8 | 0.0785059 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.54417e10 | 1.33032 | 0.665158 | − | 0.746702i | \(-0.268364\pi\) | ||||
0.665158 | + | 0.746702i | \(0.268364\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.27993e9 | 0.706715 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.28769e9 | −0.362584 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.94159e10 | 1.62676 | 0.813378 | − | 0.581735i | \(-0.197626\pi\) | ||||
0.813378 | + | 0.581735i | \(0.197626\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.96964e9 | 0.329538 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.03230e8 | 0.0413924 | 0.0206962 | − | 0.999786i | \(-0.493412\pi\) | ||||
0.0206962 | + | 0.999786i | \(0.493412\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.57760e7 | 0.00210078 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.88800e8 | −0.0152471 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.91632e9 | −0.473443 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.87701e10 | −1.48842 | −0.744208 | − | 0.667948i | \(-0.767173\pi\) | ||||
−0.744208 | + | 0.667948i | \(0.767173\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.90447e10 | −1.49652 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.39166e10 | 1.86239 | 0.931196 | − | 0.364518i | \(-0.118766\pi\) | ||||
0.931196 | + | 0.364518i | \(0.118766\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.94902e9 | −0.459081 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.14892e8 | 0.0623199 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.15872e10 | 0.878210 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.17858e9 | 0.313870 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.62315e9 | −0.418614 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.97032e9 | −0.514291 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.09777e10 | −1.53408 | −0.767038 | − | 0.641602i | \(-0.778270\pi\) | ||||
−0.767038 | + | 0.641602i | \(0.778270\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.52151e10 | 1.82764 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.10991e7 | 0.00438952 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.97822e9 | 0.140870 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.19731e9 | 0.437440 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.55513e10 | 1.08809 | 0.544043 | − | 0.839057i | \(-0.316893\pi\) | ||||
0.544043 | + | 0.839057i | \(0.316893\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.68297e8 | −0.0602219 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.42427e9 | 0.166673 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.42711e9 | 0.369883 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.71332e8 | −0.0183322 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.72858e10 | 1.82759 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.19959e10 | −0.796548 | −0.398274 | − | 0.917266i | \(-0.630391\pi\) | ||||
−0.398274 | + | 0.917266i | \(0.630391\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.18093e10 | −0.777412 | −0.388706 | − | 0.921362i | \(-0.627078\pi\) | ||||
−0.388706 | + | 0.921362i | \(0.627078\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.69403e10 | 1.10562 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.71640e8 | −0.0628715 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.46096e10 | −0.937262 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.08580e7 | −0.00323494 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.96308e10 | −1.23805 | −0.619024 | − | 0.785372i | \(-0.712472\pi\) | ||||
−0.619024 | + | 0.785372i | \(0.712472\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.67601e9 | 0.167336 | 0.0836679 | − | 0.996494i | \(-0.473337\pi\) | ||||
0.0836679 | + | 0.996494i | \(0.473337\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.42712e9 | −0.274494 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.26722e8 | −0.0569745 | −0.0284872 | − | 0.999594i | \(-0.509069\pi\) | ||||
−0.0284872 | + | 0.999594i | \(0.509069\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.94467e10 | −1.79513 | −0.897565 | − | 0.440882i | \(-0.854666\pi\) | ||||
−0.897565 | + | 0.440882i | \(0.854666\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.52900e10 | 1.52878 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.65201e9 | 0.338802 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.20001e9 | 0.368544 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.43123e9 | 0.496995 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.93988e9 | 0.522595 | 0.261297 | − | 0.965258i | \(-0.415850\pi\) | ||||
0.261297 | + | 0.965258i | \(0.415850\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.37642e10 | −0.797931 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.51071e8 | 0.0431802 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.44674e9 | −0.253538 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.63296e7 | −0.00431619 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.11530e10 | −0.625480 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.30268e10 | 1.28080 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.71708e10 | 0.947257 | 0.473628 | − | 0.880725i | \(-0.342944\pi\) | ||||
0.473628 | + | 0.880725i | \(0.342944\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.78130e8 | 0.0316333 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.71458e9 | −0.418677 | −0.209339 | − | 0.977843i | \(-0.567131\pi\) | ||||
−0.209339 | + | 0.977843i | \(0.567131\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.68606e10 | −0.907606 | −0.453803 | − | 0.891102i | \(-0.649933\pi\) | ||||
−0.453803 | + | 0.891102i | \(0.649933\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.17313e9 | 0.0626377 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.42922e10 | 1.28656 | 0.643278 | − | 0.765633i | \(-0.277574\pi\) | ||||
0.643278 | + | 0.765633i | \(0.277574\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.25404e10 | 0.658802 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.79675e10 | 0.936311 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.52521e9 | 0.130535 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.60161e10 | −0.821283 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.62608e9 | −0.184454 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.54379e8 | 0.0330218 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.67740e10 | 1.34034 | 0.670169 | − | 0.742209i | \(-0.266222\pi\) | ||||
0.670169 | + | 0.742209i | \(0.266222\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.90058e10 | −0.943899 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.10654e10 | 0.545197 | 0.272598 | − | 0.962128i | \(-0.412117\pi\) | ||||
0.272598 | + | 0.962128i | \(0.412117\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.06264e10 | −1.00824 | −0.504118 | − | 0.863635i | \(-0.668182\pi\) | ||||
−0.504118 | + | 0.863635i | \(0.668182\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.80903e9 | 0.330205 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.62436e9 | 0.366835 | 0.183417 | − | 0.983035i | \(-0.441284\pi\) | ||||
0.183417 | + | 0.983035i | \(0.441284\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.31512e8 | −0.0396928 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.03884e9 | 0.333372 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.65884e9 | 0.124943 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.33264e9 | −0.155385 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.34040e10 | −0.620097 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.22633e9 | −0.239904 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.24151e9 | 0.375379 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.47913e9 | −0.0668495 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.24334e9 | 0.100606 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.36091e10 | 1.49566 | 0.747828 | − | 0.663893i | \(-0.231097\pi\) | ||||
0.747828 | + | 0.663893i | \(0.231097\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.73206e9 | 0.0764874 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.89170e10 | 1.70540 | 0.852698 | − | 0.522404i | \(-0.174965\pi\) | ||||
0.852698 | + | 0.522404i | \(0.174965\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.64161e9 | 0.375791 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.27671e9 | −0.0982504 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.82017e9 | 0.0779507 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.35993e10 | −1.85300 | −0.926499 | − | 0.376296i | \(-0.877197\pi\) | ||||
−0.926499 | + | 0.376296i | \(0.877197\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.69367e10 | 1.55794 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.41094e10 | −0.590614 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.56805e10 | −1.06686 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.22098e9 | 0.215265 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.06911e10 | −1.25591 | −0.627954 | − | 0.778250i | \(-0.716108\pi\) | ||||
−0.627954 | + | 0.778250i | \(0.716108\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.73072e10 | −0.702915 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.16761e10 | 1.27687 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.56790e8 | 0.0382804 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.51153e9 | 0.139446 | 0.0697232 | − | 0.997566i | \(-0.477788\pi\) | ||||
0.0697232 | + | 0.997566i | \(0.477788\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.70402e9 | −0.264244 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.84266e10 | −0.720911 | −0.360455 | − | 0.932776i | \(-0.617379\pi\) | ||||
−0.360455 | + | 0.932776i | \(0.617379\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.31498e10 | 1.28733 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.28860e8 | −0.0165312 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.78798e9 | −0.336251 | −0.168126 | − | 0.985766i | \(-0.553771\pi\) | ||||
−0.168126 | + | 0.985766i | \(0.553771\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.83253e10 | −0.696015 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.82663e9 | −0.181975 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.85304e10 | 0.693521 | 0.346761 | − | 0.937954i | \(-0.387282\pi\) | ||||
0.346761 | + | 0.937954i | \(0.387282\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.61598e9 | 0.208648 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.88930e9 | −0.143443 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.29991e8 | 0.0120819 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.96764e10 | −0.715176 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.50319e9 | −0.198574 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.79856e10 | 0.644286 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.71498e10 | −1.67682 | −0.838412 | − | 0.545037i | \(-0.816516\pi\) | ||||
−0.838412 | + | 0.545037i | \(0.816516\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.17082e9 | 0.253184 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.76215e9 | 0.307145 | 0.153572 | − | 0.988137i | \(-0.450922\pi\) | ||||
0.153572 | + | 0.988137i | \(0.450922\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.29135e8 | −0.0218952 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.49487e10 | 0.516519 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.33661e9 | −0.217383 | −0.108692 | − | 0.994076i | \(-0.534666\pi\) | ||||
−0.108692 | + | 0.994076i | \(0.534666\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.22856e10 | −0.418462 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.57124e8 | −0.00531374 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.47312e10 | −1.50201 | −0.751006 | − | 0.660295i | \(-0.770431\pi\) | ||||
−0.751006 | + | 0.660295i | \(0.770431\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.19686e10 | −0.399041 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.69190e8 | 0.00891147 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.17964e10 | −1.37389 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.62109e10 | −1.50830 | −0.754148 | − | 0.656705i | \(-0.771950\pi\) | ||||
−0.754148 | + | 0.656705i | \(0.771950\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.73150e10 | 0.561178 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.55994e9 | 0.114567 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.52392e10 | −0.487001 | −0.243501 | − | 0.969901i | \(-0.578296\pi\) | ||||
−0.243501 | + | 0.969901i | \(0.578296\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.63956e10 | 1.15497 |
(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 | 176.8.a.e.1.1 | 2 | ||
4.3 | odd | 2 | 22.8.a.d.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 198.8.a.f.1.2 | 2 | |||
20.19 | odd | 2 | 550.8.a.d.1.1 | 2 | |||
44.43 | even | 2 | 242.8.a.h.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.8.a.d.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
176.8.a.e.1.1 | 2 | 1.1 | even | 1 | trivial | ||
198.8.a.f.1.2 | 2 | 12.11 | even | 2 | |||
242.8.a.h.1.2 | 2 | 44.43 | even | 2 | |||
550.8.a.d.1.1 | 2 | 20.19 | odd | 2 |