Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [550,8,Mod(1,550)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(550, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("550.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 550 = 2 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 550.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: | \(171.811764016\) |
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 | \(\chi\) | \(=\) | 550.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.00000 | −0.707107 | ||||||||
\(3\) | −49.4939 | −1.05834 | −0.529172 | − | 0.848515i | \(-0.677497\pi\) | ||||
−0.529172 | + | 0.848515i | \(0.677497\pi\) | |||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 395.951 | 0.748362 | ||||||||
\(7\) | −43.0861 | −0.0474781 | −0.0237391 | − | 0.999718i | \(-0.507557\pi\) | ||||
−0.0237391 | + | 0.999718i | \(0.507557\pi\) | |||||||
\(8\) | −512.000 | −0.353553 | ||||||||
\(9\) | 262.641 | 0.120092 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1331.00 | 0.301511 | ||||||||
\(12\) | −3167.61 | −0.529172 | ||||||||
\(13\) | −4494.27 | −0.567359 | −0.283679 | − | 0.958919i | \(-0.591555\pi\) | ||||
−0.283679 | + | 0.958919i | \(0.591555\pi\) | |||||||
\(14\) | 344.689 | 0.0335721 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | 6878.55 | 0.339567 | 0.169784 | − | 0.985481i | \(-0.445693\pi\) | ||||
0.169784 | + | 0.985481i | \(0.445693\pi\) | |||||||
\(18\) | −2101.13 | −0.0849179 | ||||||||
\(19\) | −21063.0 | −0.704503 | −0.352252 | − | 0.935905i | \(-0.614584\pi\) | ||||
−0.352252 | + | 0.935905i | \(0.614584\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2132.50 | 0.0502482 | ||||||||
\(22\) | −10648.0 | −0.213201 | ||||||||
\(23\) | 60259.0 | 1.03270 | 0.516350 | − | 0.856377i | \(-0.327290\pi\) | ||||
0.516350 | + | 0.856377i | \(0.327290\pi\) | |||||||
\(24\) | 25340.9 | 0.374181 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 35954.2 | 0.401183 | ||||||||
\(27\) | 95243.9 | 0.931245 | ||||||||
\(28\) | −2757.51 | −0.0237391 | ||||||||
\(29\) | −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 | \(-0.585981\pi\) | ||||
−0.266844 | + | 0.963740i | \(0.585981\pi\) | |||||||
\(32\) | −32768.0 | −0.176777 | ||||||||
\(33\) | −65876.3 | −0.319103 | ||||||||
\(34\) | −55028.4 | −0.240110 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 16809.0 | 0.0600460 | ||||||||
\(37\) | −382131. | −1.24024 | −0.620120 | − | 0.784507i | \(-0.712916\pi\) | ||||
−0.620120 | + | 0.784507i | \(0.712916\pi\) | |||||||
\(38\) | 168504. | 0.498159 | ||||||||
\(39\) | 222439. | 0.600461 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 550122. | 1.24657 | 0.623283 | − | 0.781996i | \(-0.285798\pi\) | ||||
0.623283 | + | 0.781996i | \(0.285798\pi\) | |||||||
\(42\) | −17060.0 | −0.0355309 | ||||||||
\(43\) | −693613. | −1.33039 | −0.665193 | − | 0.746671i | \(-0.731651\pi\) | ||||
−0.665193 | + | 0.746671i | \(0.731651\pi\) | |||||||
\(44\) | 85184.0 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −482072. | −0.730230 | ||||||||
\(47\) | 126233. | 0.177349 | 0.0886745 | − | 0.996061i | \(-0.471737\pi\) | ||||
0.0886745 | + | 0.996061i | \(0.471737\pi\) | |||||||
\(48\) | −202727. | −0.264586 | ||||||||
\(49\) | −821687. | −0.997746 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −340446. | −0.359379 | ||||||||
\(52\) | −287634. | −0.283679 | ||||||||
\(53\) | 1.19815e6 | 1.10546 | 0.552732 | − | 0.833359i | \(-0.313585\pi\) | ||||
0.552732 | + | 0.833359i | \(0.313585\pi\) | |||||||
\(54\) | −761951. | −0.658490 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 22060.1 | 0.0167861 | ||||||||
\(57\) | 1.04249e6 | 0.745607 | ||||||||
\(58\) | 472316. | 0.317859 | ||||||||
\(59\) | 1.31641e6 | 0.834469 | 0.417234 | − | 0.908799i | \(-0.362999\pi\) | ||||
0.417234 | + | 0.908799i | \(0.362999\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 440165. | 0.248291 | 0.124145 | − | 0.992264i | \(-0.460381\pi\) | ||||
0.124145 | + | 0.992264i | \(0.460381\pi\) | |||||||
\(62\) | 708180. | 0.377375 | ||||||||
\(63\) | −11316.2 | −0.00570175 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 527011. | 0.225640 | ||||||||
\(67\) | −3.56366e6 | −1.44755 | −0.723777 | − | 0.690034i | \(-0.757596\pi\) | ||||
−0.723777 | + | 0.690034i | \(0.757596\pi\) | |||||||
\(68\) | 440227. | 0.169784 | ||||||||
\(69\) | −2.98245e6 | −1.09295 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.13943e6 | 1.04099 | 0.520494 | − | 0.853865i | \(-0.325748\pi\) | ||||
0.520494 | + | 0.853865i | \(0.325748\pi\) | |||||||
\(72\) | −134472. | −0.0424590 | ||||||||
\(73\) | 4.07747e6 | 1.22676 | 0.613382 | − | 0.789787i | \(-0.289809\pi\) | ||||
0.613382 | + | 0.789787i | \(0.289809\pi\) | |||||||
\(74\) | 3.05705e6 | 0.876982 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.34803e6 | −0.352252 | ||||||||
\(77\) | −57347.6 | −0.0143152 | ||||||||
\(78\) | −1.77951e6 | −0.424590 | ||||||||
\(79\) | 1.89723e6 | 0.432937 | 0.216468 | − | 0.976290i | \(-0.430546\pi\) | ||||
0.216468 | + | 0.976290i | \(0.430546\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.28839e6 | −1.10567 | ||||||||
\(82\) | −4.40097e6 | −0.881455 | ||||||||
\(83\) | −6.49257e6 | −1.24636 | −0.623179 | − | 0.782079i | \(-0.714159\pi\) | ||||
−0.623179 | + | 0.782079i | \(0.714159\pi\) | |||||||
\(84\) | 136480. | 0.0251241 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.54890e6 | 0.940725 | ||||||||
\(87\) | 2.92209e6 | 0.475747 | ||||||||
\(88\) | −681472. | −0.106600 | ||||||||
\(89\) | 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 | ||||||||
\(92\) | 3.85658e6 | 0.516350 | ||||||||
\(93\) | 4.38132e6 | 0.564826 | ||||||||
\(94\) | −1.00986e6 | −0.125405 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.62181e6 | 0.187091 | ||||||||
\(97\) | 1.38062e7 | 1.53593 | 0.767967 | − | 0.640489i | \(-0.221268\pi\) | ||||
0.767967 | + | 0.640489i | \(0.221268\pi\) | |||||||
\(98\) | 6.57349e6 | 0.705513 | ||||||||
\(99\) | 349576. | 0.0362091 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.59478e6 | 0.636906 | 0.318453 | − | 0.947939i | \(-0.396837\pi\) | ||||
0.318453 | + | 0.947939i | \(0.396837\pi\) | |||||||
\(102\) | 2.72357e6 | 0.254119 | ||||||||
\(103\) | 1.98787e7 | 1.79250 | 0.896249 | − | 0.443551i | \(-0.146282\pi\) | ||||
0.896249 | + | 0.443551i | \(0.146282\pi\) | |||||||
\(104\) | 2.30107e6 | 0.200592 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.58517e6 | −0.781681 | ||||||||
\(107\) | −2.09533e7 | −1.65352 | −0.826758 | − | 0.562558i | \(-0.809817\pi\) | ||||
−0.826758 | + | 0.562558i | \(0.809817\pi\) | |||||||
\(108\) | 6.09561e6 | 0.465623 | ||||||||
\(109\) | −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 | ||||||||
\(112\) | −176481. | −0.0118695 | ||||||||
\(113\) | 1.41807e6 | 0.0924535 | 0.0462267 | − | 0.998931i | \(-0.485280\pi\) | ||||
0.0462267 | + | 0.998931i | \(0.485280\pi\) | |||||||
\(114\) | −8.33992e6 | −0.527224 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.77853e6 | −0.224760 | ||||||||
\(117\) | −1.18038e6 | −0.0681353 | ||||||||
\(118\) | −1.05313e7 | −0.590058 | ||||||||
\(119\) | −296370. | −0.0161220 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.77156e6 | 0.0909091 | ||||||||
\(122\) | −3.52132e6 | −0.175568 | ||||||||
\(123\) | −2.72276e7 | −1.31930 | ||||||||
\(124\) | −5.66544e6 | −0.266844 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 90529.5 | 0.00403175 | ||||||||
\(127\) | 1.92988e7 | 0.836023 | 0.418012 | − | 0.908442i | \(-0.362727\pi\) | ||||
0.418012 | + | 0.908442i | \(0.362727\pi\) | |||||||
\(128\) | −2.09715e6 | −0.0883883 | ||||||||
\(129\) | 3.43296e7 | 1.40801 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.22451e7 | 1.64182 | 0.820912 | − | 0.571055i | \(-0.193466\pi\) | ||||
0.820912 | + | 0.571055i | \(0.193466\pi\) | |||||||
\(132\) | −4.21608e6 | −0.159551 | ||||||||
\(133\) | 907523. | 0.0334485 | ||||||||
\(134\) | 2.85093e7 | 1.02358 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.52182e6 | −0.120055 | ||||||||
\(137\) | 7.65888e6 | 0.254474 | 0.127237 | − | 0.991872i | \(-0.459389\pi\) | ||||
0.127237 | + | 0.991872i | \(0.459389\pi\) | |||||||
\(138\) | 2.38596e7 | 0.772834 | ||||||||
\(139\) | −1.46018e7 | −0.461164 | −0.230582 | − | 0.973053i | \(-0.574063\pi\) | ||||
−0.230582 | + | 0.973053i | \(0.574063\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.24773e6 | −0.187696 | ||||||||
\(142\) | −2.51154e7 | −0.736090 | ||||||||
\(143\) | −5.98188e6 | −0.171065 | ||||||||
\(144\) | 1.07578e6 | 0.0300230 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.26198e7 | −0.867453 | ||||||||
\(147\) | 4.06684e7 | 1.05596 | ||||||||
\(148\) | −2.44564e7 | −0.620120 | ||||||||
\(149\) | −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 | \(-0.338864\pi\) | ||||
0.484877 | + | 0.874582i | \(0.338864\pi\) | |||||||
\(152\) | 1.07843e7 | 0.249080 | ||||||||
\(153\) | 1.80659e6 | 0.0407793 | ||||||||
\(154\) | 458780. | 0.0101224 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.42361e7 | 0.300230 | ||||||||
\(157\) | 6.66977e7 | 1.37550 | 0.687752 | − | 0.725946i | \(-0.258598\pi\) | ||||
0.687752 | + | 0.725946i | \(0.258598\pi\) | |||||||
\(158\) | −1.51778e7 | −0.306133 | ||||||||
\(159\) | −5.93009e7 | −1.16996 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.59632e6 | −0.0490307 | ||||||||
\(162\) | 4.23071e7 | 0.781827 | ||||||||
\(163\) | −9.29744e6 | −0.168154 | −0.0840769 | − | 0.996459i | \(-0.526794\pi\) | ||||
−0.0840769 | + | 0.996459i | \(0.526794\pi\) | |||||||
\(164\) | 3.52078e7 | 0.623283 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.19405e7 | 0.881309 | ||||||||
\(167\) | 5.93268e7 | 0.985696 | 0.492848 | − | 0.870115i | \(-0.335956\pi\) | ||||
0.492848 | + | 0.870115i | \(0.335956\pi\) | |||||||
\(168\) | −1.09184e6 | −0.0177654 | ||||||||
\(169\) | −4.25500e7 | −0.678104 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.53202e6 | −0.0846053 | ||||||||
\(172\) | −4.43912e7 | −0.665193 | ||||||||
\(173\) | −1.19997e8 | −1.76201 | −0.881004 | − | 0.473108i | \(-0.843132\pi\) | ||||
−0.881004 | + | 0.473108i | \(0.843132\pi\) | |||||||
\(174\) | −2.33767e7 | −0.336404 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.45178e6 | 0.0753778 | ||||||||
\(177\) | −6.51543e7 | −0.883155 | ||||||||
\(178\) | −7.38426e7 | −0.981380 | ||||||||
\(179\) | 3.18894e7 | 0.415586 | 0.207793 | − | 0.978173i | \(-0.433372\pi\) | ||||
0.207793 | + | 0.978173i | \(0.433372\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.14661e7 | 0.269079 | 0.134539 | − | 0.990908i | \(-0.457045\pi\) | ||||
0.134539 | + | 0.990908i | \(0.457045\pi\) | |||||||
\(182\) | −1.54913e6 | −0.0190474 | ||||||||
\(183\) | −2.17854e7 | −0.262777 | ||||||||
\(184\) | −3.08526e7 | −0.365115 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.50506e7 | −0.399392 | ||||||||
\(187\) | 9.15535e6 | 0.102383 | ||||||||
\(188\) | 8.07888e6 | 0.0886745 | ||||||||
\(189\) | −4.10369e6 | −0.0442138 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.37382e7 | −0.558042 | −0.279021 | − | 0.960285i | \(-0.590010\pi\) | ||||
−0.279021 | + | 0.960285i | \(0.590010\pi\) | |||||||
\(192\) | −1.29745e7 | −0.132293 | ||||||||
\(193\) | −1.72101e8 | −1.72319 | −0.861593 | − | 0.507600i | \(-0.830533\pi\) | ||||
−0.861593 | + | 0.507600i | \(0.830533\pi\) | |||||||
\(194\) | −1.10450e8 | −1.08607 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.25879e7 | −0.498873 | ||||||||
\(197\) | 1.14526e8 | 1.06726 | 0.533631 | − | 0.845718i | \(-0.320827\pi\) | ||||
0.533631 | + | 0.845718i | \(0.320827\pi\) | |||||||
\(198\) | −2.79661e6 | −0.0256037 | ||||||||
\(199\) | −3.40644e7 | −0.306418 | −0.153209 | − | 0.988194i | \(-0.548961\pi\) | ||||
−0.153209 | + | 0.988194i | \(0.548961\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.76379e8 | 1.53201 | ||||||||
\(202\) | −5.27583e7 | −0.450361 | ||||||||
\(203\) | 2.54378e6 | 0.0213424 | ||||||||
\(204\) | −2.17885e7 | −0.179689 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.59030e8 | −1.26749 | ||||||||
\(207\) | 1.58265e7 | 0.124019 | ||||||||
\(208\) | −1.84085e7 | −0.141840 | ||||||||
\(209\) | −2.80349e7 | −0.212416 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.74288e8 | −1.27726 | −0.638628 | − | 0.769516i | \(-0.720498\pi\) | ||||
−0.638628 | + | 0.769516i | \(0.720498\pi\) | |||||||
\(212\) | 7.66814e7 | 0.552732 | ||||||||
\(213\) | −1.55382e8 | −1.10172 | ||||||||
\(214\) | 1.67626e8 | 1.16921 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.87649e7 | −0.329245 | ||||||||
\(217\) | 3.81409e6 | 0.0253385 | ||||||||
\(218\) | 4.78596e6 | 0.0312875 | ||||||||
\(219\) | −2.01810e8 | −1.29834 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.09141e7 | −0.192656 | ||||||||
\(222\) | −1.51305e8 | −0.928149 | ||||||||
\(223\) | −1.45730e8 | −0.879998 | −0.439999 | − | 0.897998i | \(-0.645021\pi\) | ||||
−0.439999 | + | 0.897998i | \(0.645021\pi\) | |||||||
\(224\) | 1.41184e6 | 0.00839303 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.13446e7 | −0.0653745 | ||||||||
\(227\) | 1.27102e8 | 0.721211 | 0.360606 | − | 0.932718i | \(-0.382570\pi\) | ||||
0.360606 | + | 0.932718i | \(0.382570\pi\) | |||||||
\(228\) | 6.67194e7 | 0.372804 | ||||||||
\(229\) | −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 | ||||||||
\(232\) | 3.02282e7 | 0.158930 | ||||||||
\(233\) | 1.52210e8 | 0.788310 | 0.394155 | − | 0.919044i | \(-0.371037\pi\) | ||||
0.394155 | + | 0.919044i | \(0.371037\pi\) | |||||||
\(234\) | 9.44306e6 | 0.0481789 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 8.42504e7 | 0.417234 | ||||||||
\(237\) | −9.39011e7 | −0.458196 | ||||||||
\(238\) | 2.37096e6 | 0.0114000 | ||||||||
\(239\) | −2.43061e8 | −1.15165 | −0.575827 | − | 0.817571i | \(-0.695320\pi\) | ||||
−0.575827 | + | 0.817571i | \(0.695320\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.84592e7 | −0.315045 | −0.157522 | − | 0.987515i | \(-0.550351\pi\) | ||||
−0.157522 | + | 0.987515i | \(0.550351\pi\) | |||||||
\(242\) | −1.41725e7 | −0.0642824 | ||||||||
\(243\) | 5.34441e7 | 0.238934 | ||||||||
\(244\) | 2.81705e7 | 0.124145 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.17821e8 | 0.932883 | ||||||||
\(247\) | 9.46630e7 | 0.399706 | ||||||||
\(248\) | 4.53235e7 | 0.188687 | ||||||||
\(249\) | 3.21342e8 | 1.31908 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.67292e8 | 0.667755 | 0.333878 | − | 0.942616i | \(-0.391643\pi\) | ||||
0.333878 | + | 0.942616i | \(0.391643\pi\) | |||||||
\(252\) | −724236. | −0.00285087 | ||||||||
\(253\) | 8.02047e7 | 0.311371 | ||||||||
\(254\) | −1.54391e8 | −0.591158 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | −3.84789e8 | −1.41402 | −0.707012 | − | 0.707202i | \(-0.749957\pi\) | ||||
−0.707012 | + | 0.707202i | \(0.749957\pi\) | |||||||
\(258\) | −2.74637e8 | −0.995611 | ||||||||
\(259\) | 1.64645e7 | 0.0588843 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.55062e7 | −0.0539839 | ||||||||
\(262\) | −3.37960e8 | −1.16094 | ||||||||
\(263\) | −5.09459e8 | −1.72689 | −0.863444 | − | 0.504445i | \(-0.831697\pi\) | ||||
−0.863444 | + | 0.504445i | \(0.831697\pi\) | |||||||
\(264\) | 3.37287e7 | 0.112820 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7.26018e6 | −0.0236517 | ||||||||
\(267\) | −4.56845e8 | −1.46886 | ||||||||
\(268\) | −2.28074e8 | −0.723777 | ||||||||
\(269\) | −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 | \(-0.325062\pi\) | ||||
0.522333 | + | 0.852742i | \(0.325062\pi\) | |||||||
\(272\) | 2.81745e7 | 0.0848918 | ||||||||
\(273\) | −9.58402e6 | −0.0285088 | ||||||||
\(274\) | −6.12710e7 | −0.179940 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.90877e8 | −0.546476 | ||||||||
\(277\) | 5.10974e8 | 1.44451 | 0.722253 | − | 0.691629i | \(-0.243107\pi\) | ||||
0.722253 | + | 0.691629i | \(0.243107\pi\) | |||||||
\(278\) | 1.16815e8 | 0.326092 | ||||||||
\(279\) | −2.32497e7 | −0.0640918 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.51750e7 | −0.0407998 | −0.0203999 | − | 0.999792i | \(-0.506494\pi\) | ||||
−0.0203999 | + | 0.999792i | \(0.506494\pi\) | |||||||
\(282\) | 4.99819e7 | 0.132721 | ||||||||
\(283\) | 2.25341e8 | 0.590999 | 0.295500 | − | 0.955343i | \(-0.404514\pi\) | ||||
0.295500 | + | 0.955343i | \(0.404514\pi\) | |||||||
\(284\) | 2.00923e8 | 0.520494 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.78550e7 | 0.120961 | ||||||||
\(287\) | −2.37026e7 | −0.0591846 | ||||||||
\(288\) | −8.60623e6 | −0.0212295 | ||||||||
\(289\) | −3.63024e8 | −0.884694 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.83322e8 | −1.62555 | ||||||||
\(292\) | 2.60958e8 | 0.613382 | ||||||||
\(293\) | −3.84004e8 | −0.891864 | −0.445932 | − | 0.895067i | \(-0.647128\pi\) | ||||
−0.445932 | + | 0.895067i | \(0.647128\pi\) | |||||||
\(294\) | −3.25347e8 | −0.746675 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.95651e8 | 0.438491 | ||||||||
\(297\) | 1.26770e8 | 0.280781 | ||||||||
\(298\) | 2.83784e8 | 0.621199 | ||||||||
\(299\) | −2.70821e8 | −0.585912 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.98851e7 | 0.0631643 | ||||||||
\(302\) | −3.28225e8 | −0.685720 | ||||||||
\(303\) | −3.26401e8 | −0.674066 | ||||||||
\(304\) | −8.62741e7 | −0.176126 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.44527e7 | −0.0288353 | ||||||||
\(307\) | −7.46289e8 | −1.47205 | −0.736026 | − | 0.676954i | \(-0.763300\pi\) | ||||
−0.736026 | + | 0.676954i | \(0.763300\pi\) | |||||||
\(308\) | −3.67024e6 | −0.00715760 | ||||||||
\(309\) | −9.83876e8 | −1.89708 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.40000e8 | 1.20648 | 0.603238 | − | 0.797561i | \(-0.293877\pi\) | ||||
0.603238 | + | 0.797561i | \(0.293877\pi\) | |||||||
\(312\) | −1.13889e8 | −0.212295 | ||||||||
\(313\) | −1.35452e8 | −0.249677 | −0.124839 | − | 0.992177i | \(-0.539841\pi\) | ||||
−0.124839 | + | 0.992177i | \(0.539841\pi\) | |||||||
\(314\) | −5.33581e8 | −0.972628 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.21423e8 | 0.216468 | ||||||||
\(317\) | −9.75198e7 | −0.171943 | −0.0859717 | − | 0.996298i | \(-0.527399\pi\) | ||||
−0.0859717 | + | 0.996298i | \(0.527399\pi\) | |||||||
\(318\) | 4.74407e8 | 0.827287 | ||||||||
\(319\) | −7.85816e7 | −0.135536 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.03706e9 | 1.74999 | ||||||||
\(322\) | 2.07706e7 | 0.0346700 | ||||||||
\(323\) | −1.44883e8 | −0.239226 | ||||||||
\(324\) | −3.38457e8 | −0.552835 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.43795e7 | 0.118903 | ||||||||
\(327\) | 2.96094e7 | 0.0468288 | ||||||||
\(328\) | −2.81662e8 | −0.440728 | ||||||||
\(329\) | −5.43886e6 | −0.00842020 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.49842e8 | 0.530242 | 0.265121 | − | 0.964215i | \(-0.414588\pi\) | ||||
0.265121 | + | 0.964215i | \(0.414588\pi\) | |||||||
\(332\) | −4.15524e8 | −0.623179 | ||||||||
\(333\) | −1.00363e8 | −0.148943 | ||||||||
\(334\) | −4.74614e8 | −0.696992 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 8.73470e6 | 0.0125621 | ||||||||
\(337\) | −7.20870e8 | −1.02601 | −0.513006 | − | 0.858385i | \(-0.671468\pi\) | ||||
−0.513006 | + | 0.858385i | \(0.671468\pi\) | |||||||
\(338\) | 3.40400e8 | 0.479492 | ||||||||
\(339\) | −7.01858e7 | −0.0978476 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.17823e8 | −0.160913 | ||||||||
\(342\) | 4.42562e7 | 0.0598250 | ||||||||
\(343\) | 7.08865e7 | 0.0948493 | ||||||||
\(344\) | 3.55130e8 | 0.470362 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.59974e8 | 1.24593 | ||||||||
\(347\) | −1.28079e8 | −0.164560 | −0.0822798 | − | 0.996609i | \(-0.526220\pi\) | ||||
−0.0822798 | + | 0.996609i | \(0.526220\pi\) | |||||||
\(348\) | 1.87014e8 | 0.237874 | ||||||||
\(349\) | −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 | ||||||||
\(352\) | −4.36142e7 | −0.0533002 | ||||||||
\(353\) | −7.51413e8 | −0.909216 | −0.454608 | − | 0.890692i | \(-0.650221\pi\) | ||||
−0.454608 | + | 0.890692i | \(0.650221\pi\) | |||||||
\(354\) | 5.21235e8 | 0.624485 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.90741e8 | 0.693940 | ||||||||
\(357\) | 1.46685e7 | 0.0170626 | ||||||||
\(358\) | −2.55115e8 | −0.293864 | ||||||||
\(359\) | −9.17064e8 | −1.04609 | −0.523045 | − | 0.852305i | \(-0.675204\pi\) | ||||
−0.523045 | + | 0.852305i | \(0.675204\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.50221e8 | −0.503675 | ||||||||
\(362\) | −1.71729e8 | −0.190267 | ||||||||
\(363\) | −8.76814e7 | −0.0962131 | ||||||||
\(364\) | 1.23930e7 | 0.0134686 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.74283e8 | 0.185811 | ||||||||
\(367\) | 9.16435e8 | 0.967766 | 0.483883 | − | 0.875133i | \(-0.339226\pi\) | ||||
0.483883 | + | 0.875133i | \(0.339226\pi\) | |||||||
\(368\) | 2.46821e8 | 0.258175 | ||||||||
\(369\) | 1.44485e8 | 0.149703 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.16234e7 | −0.0524854 | ||||||||
\(372\) | 2.80405e8 | 0.282413 | ||||||||
\(373\) | 1.56099e9 | 1.55747 | 0.778736 | − | 0.627352i | \(-0.215861\pi\) | ||||
0.778736 | + | 0.627352i | \(0.215861\pi\) | |||||||
\(374\) | −7.32428e7 | −0.0723960 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.46311e7 | −0.0627024 | ||||||||
\(377\) | 2.65340e8 | 0.255040 | ||||||||
\(378\) | 3.28295e7 | 0.0312639 | ||||||||
\(379\) | 4.34986e7 | 0.0410429 | 0.0205214 | − | 0.999789i | \(-0.493467\pi\) | ||||
0.0205214 | + | 0.999789i | \(0.493467\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.55174e8 | −0.884800 | ||||||||
\(382\) | 4.29906e8 | 0.394595 | ||||||||
\(383\) | −1.95422e8 | −0.177737 | −0.0888685 | − | 0.996043i | \(-0.528325\pi\) | ||||
−0.0888685 | + | 0.996043i | \(0.528325\pi\) | |||||||
\(384\) | 1.03796e8 | 0.0935453 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.37681e9 | 1.21848 | ||||||||
\(387\) | −1.82171e8 | −0.159769 | ||||||||
\(388\) | 8.83596e8 | 0.767967 | ||||||||
\(389\) | −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 | ||||||||
\(392\) | 4.20704e8 | 0.352756 | ||||||||
\(393\) | −2.09087e9 | −1.73761 | ||||||||
\(394\) | −9.16205e8 | −0.754668 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.23728e7 | 0.0181046 | ||||||||
\(397\) | −1.20591e9 | −0.967268 | −0.483634 | − | 0.875270i | \(-0.660683\pi\) | ||||
−0.483634 | + | 0.875270i | \(0.660683\pi\) | |||||||
\(398\) | 2.72515e8 | 0.216670 | ||||||||
\(399\) | −4.49168e7 | −0.0354000 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.40689e8 | 0.573628 | 0.286814 | − | 0.957986i | \(-0.407404\pi\) | ||||
0.286814 | + | 0.957986i | \(0.407404\pi\) | |||||||
\(402\) | −1.41104e9 | −1.08330 | ||||||||
\(403\) | 3.97845e8 | 0.302793 | ||||||||
\(404\) | 4.22066e8 | 0.318453 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.03502e7 | −0.0150914 | ||||||||
\(407\) | −5.08616e8 | −0.373947 | ||||||||
\(408\) | 1.74308e8 | 0.127060 | ||||||||
\(409\) | 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 | ||||||||
\(412\) | 1.27224e9 | 0.896249 | ||||||||
\(413\) | −5.67190e7 | −0.0396190 | ||||||||
\(414\) | −1.26612e8 | −0.0876948 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.47268e8 | 0.100296 | ||||||||
\(417\) | 7.22700e8 | 0.488070 | ||||||||
\(418\) | 2.24279e8 | 0.150201 | ||||||||
\(419\) | 1.95596e9 | 1.29901 | 0.649503 | − | 0.760359i | \(-0.274977\pi\) | ||||
0.649503 | + | 0.760359i | \(0.274977\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.31110e9 | −1.50950 | −0.754748 | − | 0.656015i | \(-0.772241\pi\) | ||||
−0.754748 | + | 0.656015i | \(0.772241\pi\) | |||||||
\(422\) | 1.39430e9 | 0.903156 | ||||||||
\(423\) | 3.31539e7 | 0.0212982 | ||||||||
\(424\) | −6.13451e8 | −0.390840 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.24306e9 | 0.779037 | ||||||||
\(427\) | −1.89650e7 | −0.0117884 | ||||||||
\(428\) | −1.34101e9 | −0.826758 | ||||||||
\(429\) | 2.96066e8 | 0.181046 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.03521e9 | −1.22444 | −0.612222 | − | 0.790686i | \(-0.709724\pi\) | ||||
−0.612222 | + | 0.790686i | \(0.709724\pi\) | |||||||
\(432\) | 3.90119e8 | 0.232811 | ||||||||
\(433\) | −2.81028e9 | −1.66357 | −0.831786 | − | 0.555096i | \(-0.812682\pi\) | ||||
−0.831786 | + | 0.555096i | \(0.812682\pi\) | |||||||
\(434\) | −3.05127e7 | −0.0179171 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.82876e7 | −0.0221236 | ||||||||
\(437\) | −1.26924e9 | −0.727541 | ||||||||
\(438\) | 1.61448e9 | 0.918063 | ||||||||
\(439\) | 1.58225e9 | 0.892587 | 0.446293 | − | 0.894887i | \(-0.352744\pi\) | ||||
0.446293 | + | 0.894887i | \(0.352744\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.15809e8 | −0.119821 | ||||||||
\(442\) | 2.47313e8 | 0.136229 | ||||||||
\(443\) | 4.88989e8 | 0.267231 | 0.133615 | − | 0.991033i | \(-0.457341\pi\) | ||||
0.133615 | + | 0.991033i | \(0.457341\pi\) | |||||||
\(444\) | 1.21044e9 | 0.656301 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.16584e9 | 0.622253 | ||||||||
\(447\) | 1.75569e9 | 0.929763 | ||||||||
\(448\) | −1.12948e7 | −0.00593477 | ||||||||
\(449\) | 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 | ||||||||
\(452\) | 9.07565e7 | 0.0462267 | ||||||||
\(453\) | −2.03064e9 | −1.02633 | ||||||||
\(454\) | −1.01682e9 | −0.509973 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.33755e8 | −0.263612 | ||||||||
\(457\) | 8.64311e8 | 0.423607 | 0.211804 | − | 0.977312i | \(-0.432066\pi\) | ||||
0.211804 | + | 0.977312i | \(0.432066\pi\) | |||||||
\(458\) | 1.03800e9 | 0.504857 | ||||||||
\(459\) | 6.55140e8 | 0.316220 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.85430e8 | 0.230767 | 0.115383 | − | 0.993321i | \(-0.463190\pi\) | ||||
0.115383 | + | 0.993321i | \(0.463190\pi\) | |||||||
\(462\) | −2.27068e7 | −0.0107130 | ||||||||
\(463\) | −1.85376e9 | −0.867999 | −0.434000 | − | 0.900913i | \(-0.642898\pi\) | ||||
−0.434000 | + | 0.900913i | \(0.642898\pi\) | |||||||
\(464\) | −2.41826e8 | −0.112380 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.21768e9 | −0.557419 | ||||||||
\(467\) | −3.16192e7 | −0.0143662 | −0.00718310 | − | 0.999974i | \(-0.502286\pi\) | ||||
−0.00718310 | + | 0.999974i | \(0.502286\pi\) | |||||||
\(468\) | −7.55445e7 | −0.0340677 | ||||||||
\(469\) | 1.53544e8 | 0.0687272 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.30112e9 | −1.45576 | ||||||||
\(472\) | −6.74003e8 | −0.295029 | ||||||||
\(473\) | −9.23199e8 | −0.401126 | ||||||||
\(474\) | 7.51209e8 | 0.323994 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.89677e7 | −0.00806101 | ||||||||
\(477\) | 3.14683e8 | 0.132757 | ||||||||
\(478\) | 1.94449e9 | 0.814343 | ||||||||
\(479\) | −3.11838e9 | −1.29645 | −0.648223 | − | 0.761451i | \(-0.724487\pi\) | ||||
−0.648223 | + | 0.761451i | \(0.724487\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.71740e9 | 0.703661 | ||||||||
\(482\) | 5.47674e8 | 0.222770 | ||||||||
\(483\) | 1.28502e8 | 0.0518914 | ||||||||
\(484\) | 1.13380e8 | 0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −4.27553e8 | −0.168952 | ||||||||
\(487\) | 3.37608e9 | 1.32453 | 0.662265 | − | 0.749270i | \(-0.269596\pi\) | ||||
0.662265 | + | 0.749270i | \(0.269596\pi\) | |||||||
\(488\) | −2.25364e8 | −0.0877840 | ||||||||
\(489\) | 4.60166e8 | 0.177965 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.55043e9 | −1.73487 | −0.867436 | − | 0.497548i | \(-0.834234\pi\) | ||||
−0.867436 | + | 0.497548i | \(0.834234\pi\) | |||||||
\(492\) | −1.74257e9 | −0.659648 | ||||||||
\(493\) | −4.06106e8 | −0.152642 | ||||||||
\(494\) | −7.57304e8 | −0.282635 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.62588e8 | −0.133422 | ||||||||
\(497\) | −1.35266e8 | −0.0494242 | ||||||||
\(498\) | −2.57074e9 | −0.932728 | ||||||||
\(499\) | −6.25733e8 | −0.225443 | −0.112722 | − | 0.993627i | \(-0.535957\pi\) | ||||
−0.112722 | + | 0.993627i | \(0.535957\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.93631e9 | −1.04321 | ||||||||
\(502\) | −1.33834e9 | −0.472174 | ||||||||
\(503\) | 3.43240e9 | 1.20257 | 0.601285 | − | 0.799035i | \(-0.294656\pi\) | ||||
0.601285 | + | 0.799035i | \(0.294656\pi\) | |||||||
\(504\) | 5.79389e6 | 0.00201587 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.41638e8 | −0.220173 | ||||||||
\(507\) | 2.10596e9 | 0.717667 | ||||||||
\(508\) | 1.23513e9 | 0.418012 | ||||||||
\(509\) | 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 | ||||||||
\(512\) | −1.34218e8 | −0.0441942 | ||||||||
\(513\) | −2.00613e9 | −0.656066 | ||||||||
\(514\) | 3.07831e9 | 0.999866 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.19709e9 | 0.704003 | ||||||||
\(517\) | 1.68016e8 | 0.0534727 | ||||||||
\(518\) | −1.31716e8 | −0.0416375 | ||||||||
\(519\) | 5.93910e9 | 1.86481 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.51109e9 | −0.777912 | −0.388956 | − | 0.921256i | \(-0.627164\pi\) | ||||
−0.388956 | + | 0.921256i | \(0.627164\pi\) | |||||||
\(522\) | 1.24050e8 | 0.0381724 | ||||||||
\(523\) | −4.25045e9 | −1.29921 | −0.649605 | − | 0.760272i | \(-0.725066\pi\) | ||||
−0.649605 | + | 0.760272i | \(0.725066\pi\) | |||||||
\(524\) | 2.70368e9 | 0.820912 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.07567e9 | 1.22109 | ||||||||
\(527\) | −6.08907e8 | −0.181223 | ||||||||
\(528\) | −2.69829e8 | −0.0797757 | ||||||||
\(529\) | 2.26323e8 | 0.0664713 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.45744e8 | 0.100213 | ||||||||
\(532\) | 5.80815e7 | 0.0167243 | ||||||||
\(533\) | −2.47240e9 | −0.707250 | ||||||||
\(534\) | 3.65476e9 | 1.03864 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.82460e9 | 0.511788 | ||||||||
\(537\) | −1.57833e9 | −0.439833 | ||||||||
\(538\) | 4.41038e9 | 1.22106 | ||||||||
\(539\) | −1.09366e9 | −0.300832 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.06279e9 | 0.288574 | 0.144287 | − | 0.989536i | \(-0.453911\pi\) | ||||
0.144287 | + | 0.989536i | \(0.453911\pi\) | |||||||
\(542\) | −2.73817e9 | −0.738690 | ||||||||
\(543\) | −1.06244e9 | −0.284778 | ||||||||
\(544\) | −2.25396e8 | −0.0600276 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 7.66722e7 | 0.0201587 | ||||||||
\(547\) | 3.28564e9 | 0.858350 | 0.429175 | − | 0.903221i | \(-0.358804\pi\) | ||||
0.429175 | + | 0.903221i | \(0.358804\pi\) | |||||||
\(548\) | 4.90168e8 | 0.127237 | ||||||||
\(549\) | 1.15605e8 | 0.0298178 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.24355e9 | 0.316689 | ||||||||
\(552\) | 1.52701e9 | 0.386417 | ||||||||
\(553\) | −8.17441e7 | −0.0205550 | ||||||||
\(554\) | −4.08779e9 | −1.02142 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.34516e8 | −0.230582 | ||||||||
\(557\) | 4.04436e9 | 0.991645 | 0.495823 | − | 0.868424i | \(-0.334867\pi\) | ||||
0.495823 | + | 0.868424i | \(0.334867\pi\) | |||||||
\(558\) | 1.85997e8 | 0.0453197 | ||||||||
\(559\) | 3.11729e9 | 0.754806 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.53133e8 | −0.108357 | ||||||||
\(562\) | 1.21400e8 | 0.0288498 | ||||||||
\(563\) | 1.60197e9 | 0.378333 | 0.189167 | − | 0.981945i | \(-0.439421\pi\) | ||||
0.189167 | + | 0.981945i | \(0.439421\pi\) | |||||||
\(564\) | −3.99855e8 | −0.0938481 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.80272e9 | −0.417899 | ||||||||
\(567\) | 2.27856e8 | 0.0524952 | ||||||||
\(568\) | −1.60739e9 | −0.368045 | ||||||||
\(569\) | −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 | \(-0.536551\pi\) | ||||
−0.114577 | + | 0.993414i | \(0.536551\pi\) | |||||||
\(572\) | −3.82840e8 | −0.0855326 | ||||||||
\(573\) | 2.65971e9 | 0.590600 | ||||||||
\(574\) | 1.89621e8 | 0.0418499 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.88499e7 | 0.0150115 | ||||||||
\(577\) | 5.05194e8 | 0.109482 | 0.0547410 | − | 0.998501i | \(-0.482567\pi\) | ||||
0.0547410 | + | 0.998501i | \(0.482567\pi\) | |||||||
\(578\) | 2.90419e9 | 0.625573 | ||||||||
\(579\) | 8.51792e9 | 1.82372 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.79739e8 | 0.0591748 | ||||||||
\(582\) | 5.46657e9 | 1.14944 | ||||||||
\(583\) | 1.59473e9 | 0.333310 | ||||||||
\(584\) | −2.08767e9 | −0.433726 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.07203e9 | 0.630643 | ||||||||
\(587\) | −6.05441e8 | −0.123549 | −0.0617744 | − | 0.998090i | \(-0.519676\pi\) | ||||
−0.0617744 | + | 0.998090i | \(0.519676\pi\) | |||||||
\(588\) | 2.60278e9 | 0.527979 | ||||||||
\(589\) | 1.86455e9 | 0.375985 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.66831e9 | −1.12953 | ||||||||
\(592\) | −1.56521e9 | −0.310060 | ||||||||
\(593\) | 2.44359e8 | 0.0481212 | 0.0240606 | − | 0.999711i | \(-0.492341\pi\) | ||||
0.0240606 | + | 0.999711i | \(0.492341\pi\) | |||||||
\(594\) | −1.01416e9 | −0.198542 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.27027e9 | −0.439254 | ||||||||
\(597\) | 1.68598e9 | 0.324296 | ||||||||
\(598\) | 2.16656e9 | 0.414302 | ||||||||
\(599\) | 4.76209e9 | 0.905324 | 0.452662 | − | 0.891682i | \(-0.350474\pi\) | ||||
0.452662 | + | 0.891682i | \(0.350474\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.27387e9 | −0.803083 | −0.401542 | − | 0.915841i | \(-0.631525\pi\) | ||||
−0.401542 | + | 0.915841i | \(0.631525\pi\) | |||||||
\(602\) | −2.39080e8 | −0.0446639 | ||||||||
\(603\) | −9.35966e8 | −0.173840 | ||||||||
\(604\) | 2.62580e9 | 0.484877 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.61121e9 | 0.476637 | ||||||||
\(607\) | −6.40384e9 | −1.16220 | −0.581099 | − | 0.813833i | \(-0.697377\pi\) | ||||
−0.581099 | + | 0.813833i | \(0.697377\pi\) | |||||||
\(608\) | 6.90193e8 | 0.124540 | ||||||||
\(609\) | −1.25901e8 | −0.0225876 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.67324e8 | −0.100621 | ||||||||
\(612\) | 1.15622e8 | 0.0203897 | ||||||||
\(613\) | 8.98899e9 | 1.57616 | 0.788078 | − | 0.615575i | \(-0.211076\pi\) | ||||
0.788078 | + | 0.615575i | \(0.211076\pi\) | |||||||
\(614\) | 5.97032e9 | 1.04090 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.93620e7 | 0.00506119 | ||||||||
\(617\) | 2.11391e9 | 0.362316 | 0.181158 | − | 0.983454i | \(-0.442015\pi\) | ||||
0.181158 | + | 0.983454i | \(0.442015\pi\) | |||||||
\(618\) | 7.87100e9 | 1.34144 | ||||||||
\(619\) | −4.25875e9 | −0.721713 | −0.360856 | − | 0.932621i | \(-0.617516\pi\) | ||||
−0.360856 | + | 0.932621i | \(0.617516\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.73930e9 | 0.961698 | ||||||||
\(622\) | −5.12000e9 | −0.853107 | ||||||||
\(623\) | −3.97699e8 | −0.0658940 | ||||||||
\(624\) | 9.11110e8 | 0.150115 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.08361e9 | 0.176548 | ||||||||
\(627\) | 1.38755e9 | 0.224809 | ||||||||
\(628\) | 4.26865e9 | 0.687752 | ||||||||
\(629\) | −2.62850e9 | −0.421145 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.55885e9 | 1.51462 | 0.757309 | − | 0.653057i | \(-0.226514\pi\) | ||||
0.757309 | + | 0.653057i | \(0.226514\pi\) | |||||||
\(632\) | −9.71380e8 | −0.153066 | ||||||||
\(633\) | 8.62617e9 | 1.35178 | ||||||||
\(634\) | 7.80159e8 | 0.121582 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.79526e9 | −0.584980 | ||||||||
\(637\) | 3.69289e9 | 0.566080 | ||||||||
\(638\) | 6.28652e8 | 0.0958381 | ||||||||
\(639\) | 8.24543e8 | 0.125015 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.93190e9 | 1.18953 | 0.594763 | − | 0.803901i | \(-0.297246\pi\) | ||||
0.594763 | + | 0.803901i | \(0.297246\pi\) | |||||||
\(642\) | −8.29646e9 | −1.23743 | ||||||||
\(643\) | 3.67790e9 | 0.545583 | 0.272792 | − | 0.962073i | \(-0.412053\pi\) | ||||
0.272792 | + | 0.962073i | \(0.412053\pi\) | |||||||
\(644\) | −1.66165e8 | −0.0245154 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.15906e9 | 0.169158 | ||||||||
\(647\) | 3.34066e9 | 0.484917 | 0.242459 | − | 0.970162i | \(-0.422046\pi\) | ||||
0.242459 | + | 0.970162i | \(0.422046\pi\) | |||||||
\(648\) | 2.70765e9 | 0.390913 | ||||||||
\(649\) | 1.75215e9 | 0.251602 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.88774e8 | −0.0268169 | ||||||||
\(652\) | −5.95036e8 | −0.0840769 | ||||||||
\(653\) | −1.23649e10 | −1.73778 | −0.868891 | − | 0.495004i | \(-0.835167\pi\) | ||||
−0.868891 | + | 0.495004i | \(0.835167\pi\) | |||||||
\(654\) | −2.36875e8 | −0.0331129 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.25330e9 | 0.311642 | ||||||||
\(657\) | 1.07091e9 | 0.147325 | ||||||||
\(658\) | 4.35109e7 | 0.00595398 | ||||||||
\(659\) | 8.58087e9 | 1.16797 | 0.583986 | − | 0.811764i | \(-0.301492\pi\) | ||||
0.583986 | + | 0.811764i | \(0.301492\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.09007e9 | −1.08955 | −0.544775 | − | 0.838582i | \(-0.683385\pi\) | ||||
−0.544775 | + | 0.838582i | \(0.683385\pi\) | |||||||
\(662\) | −2.79873e9 | −0.374937 | ||||||||
\(663\) | 1.53006e9 | 0.203897 | ||||||||
\(664\) | 3.32419e9 | 0.440654 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.02907e8 | 0.105319 | ||||||||
\(667\) | −3.55766e9 | −0.464220 | ||||||||
\(668\) | 3.79691e9 | 0.492848 | ||||||||
\(669\) | 7.21274e9 | 0.931341 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.85859e8 | 0.0748625 | ||||||||
\(672\) | −6.98776e7 | −0.00888271 | ||||||||
\(673\) | 1.38929e10 | 1.75687 | 0.878436 | − | 0.477860i | \(-0.158587\pi\) | ||||
0.878436 | + | 0.477860i | \(0.158587\pi\) | |||||||
\(674\) | 5.76696e9 | 0.725500 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.72320e9 | −0.339052 | ||||||||
\(677\) | −6.36018e9 | −0.787788 | −0.393894 | − | 0.919156i | \(-0.628872\pi\) | ||||
−0.393894 | + | 0.919156i | \(0.628872\pi\) | |||||||
\(678\) | 5.61486e8 | 0.0691887 | ||||||||
\(679\) | −5.94855e8 | −0.0729233 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.29077e9 | −0.763289 | ||||||||
\(682\) | 9.42588e8 | 0.113783 | ||||||||
\(683\) | 7.46187e9 | 0.896139 | 0.448069 | − | 0.893999i | \(-0.352112\pi\) | ||||
0.448069 | + | 0.893999i | \(0.352112\pi\) | |||||||
\(684\) | −3.54049e8 | −0.0423026 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5.67092e8 | −0.0670686 | ||||||||
\(687\) | 6.42182e9 | 0.755631 | ||||||||
\(688\) | −2.84104e9 | −0.332596 | ||||||||
\(689\) | −5.38480e9 | −0.627195 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.01338e10 | −1.16842 | −0.584212 | − | 0.811601i | \(-0.698596\pi\) | ||||
−0.584212 | + | 0.811601i | \(0.698596\pi\) | |||||||
\(692\) | −7.67979e9 | −0.881004 | ||||||||
\(693\) | −1.50618e7 | −0.00171914 | ||||||||
\(694\) | 1.02463e9 | 0.116361 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.49611e9 | −0.168202 | ||||||||
\(697\) | 3.78404e9 | 0.423293 | ||||||||
\(698\) | 8.03034e8 | 0.0893800 | ||||||||
\(699\) | −7.53345e9 | −0.834303 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.31006e10 | 1.43641 | 0.718206 | − | 0.695831i | \(-0.244964\pi\) | ||||
0.718206 | + | 0.695831i | \(0.244964\pi\) | |||||||
\(702\) | 3.42442e9 | 0.373600 | ||||||||
\(703\) | 8.04883e9 | 0.873754 | ||||||||
\(704\) | 3.48914e8 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.01130e9 | 0.642913 | ||||||||
\(707\) | −2.84143e8 | −0.0302391 | ||||||||
\(708\) | −4.16988e9 | −0.441577 | ||||||||
\(709\) | −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 | ||||||||
\(712\) | −4.72593e9 | −0.490690 | ||||||||
\(713\) | −5.33428e9 | −0.551141 | ||||||||
\(714\) | −1.17348e8 | −0.0120651 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.04092e9 | 0.207793 | ||||||||
\(717\) | 1.20300e10 | 1.21885 | ||||||||
\(718\) | 7.33651e9 | 0.739697 | ||||||||
\(719\) | 6.14452e9 | 0.616505 | 0.308253 | − | 0.951305i | \(-0.400256\pi\) | ||||
0.308253 | + | 0.951305i | \(0.400256\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.56497e8 | −0.0851045 | ||||||||
\(722\) | 3.60177e9 | 0.356152 | ||||||||
\(723\) | 3.38831e9 | 0.333426 | ||||||||
\(724\) | 1.37383e9 | 0.134539 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.01451e8 | 0.0680329 | ||||||||
\(727\) | 1.47022e9 | 0.141910 | 0.0709550 | − | 0.997480i | \(-0.477395\pi\) | ||||
0.0709550 | + | 0.997480i | \(0.477395\pi\) | |||||||
\(728\) | −9.91440e7 | −0.00952372 | ||||||||
\(729\) | 8.92054e9 | 0.852796 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.77105e9 | −0.451755 | ||||||||
\(732\) | −1.39427e9 | −0.131389 | ||||||||
\(733\) | −6.30989e8 | −0.0591777 | −0.0295888 | − | 0.999562i | \(-0.509420\pi\) | ||||
−0.0295888 | + | 0.999562i | \(0.509420\pi\) | |||||||
\(734\) | −7.33148e9 | −0.684314 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.97457e9 | −0.182557 | ||||||||
\(737\) | −4.74324e9 | −0.436454 | ||||||||
\(738\) | −1.15588e9 | −0.105856 | ||||||||
\(739\) | 7.22368e9 | 0.658420 | 0.329210 | − | 0.944257i | \(-0.393218\pi\) | ||||
0.329210 | + | 0.944257i | \(0.393218\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.68524e9 | −0.423027 | ||||||||
\(742\) | 4.12987e8 | 0.0371128 | ||||||||
\(743\) | −7.72789e9 | −0.691194 | −0.345597 | − | 0.938383i | \(-0.612324\pi\) | ||||
−0.345597 | + | 0.938383i | \(0.612324\pi\) | |||||||
\(744\) | −2.24324e9 | −0.199696 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.24880e10 | −1.10130 | ||||||||
\(747\) | −1.70522e9 | −0.149678 | ||||||||
\(748\) | 5.85942e8 | 0.0511917 | ||||||||
\(749\) | 9.02793e8 | 0.0785059 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.54417e10 | −1.33032 | −0.665158 | − | 0.746702i | \(-0.731636\pi\) | ||||
−0.665158 | + | 0.746702i | \(0.731636\pi\) | |||||||
\(752\) | 5.17048e8 | 0.0443373 | ||||||||
\(753\) | −8.27993e9 | −0.706715 | ||||||||
\(754\) | −2.12272e9 | −0.180340 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.62636e8 | −0.0221069 | ||||||||
\(757\) | −1.94159e10 | −1.62676 | −0.813378 | − | 0.581735i | \(-0.802374\pi\) | ||||
−0.813378 | + | 0.581735i | \(0.802374\pi\) | |||||||
\(758\) | −3.47989e8 | −0.0290217 | ||||||||
\(759\) | −3.96964e9 | −0.329538 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.03230e8 | 0.0413924 | 0.0206962 | − | 0.999786i | \(-0.493412\pi\) | ||||
0.0206962 | + | 0.999786i | \(0.493412\pi\) | |||||||
\(762\) | 7.64139e9 | 0.625648 | ||||||||
\(763\) | 2.57760e7 | 0.00210078 | ||||||||
\(764\) | −3.43925e9 | −0.279021 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.56338e9 | 0.125679 | ||||||||
\(767\) | −5.91632e9 | −0.473443 | ||||||||
\(768\) | −8.30369e8 | −0.0661465 | ||||||||
\(769\) | −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 | ||||||||
\(772\) | −1.10144e10 | −0.861593 | ||||||||
\(773\) | −2.39166e10 | −1.86239 | −0.931196 | − | 0.364518i | \(-0.881234\pi\) | ||||
−0.931196 | + | 0.364518i | \(0.881234\pi\) | |||||||
\(774\) | 1.45737e9 | 0.112974 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7.06877e9 | −0.543035 | ||||||||
\(777\) | −8.14892e8 | −0.0623199 | ||||||||
\(778\) | 1.28676e10 | 0.979649 | ||||||||
\(779\) | −1.15872e10 | −0.878210 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.17858e9 | 0.313870 | ||||||||
\(782\) | −3.31596e9 | −0.247962 | ||||||||
\(783\) | −5.62315e9 | −0.418614 | ||||||||
\(784\) | −3.36563e9 | −0.249436 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.67270e10 | 1.22868 | ||||||||
\(787\) | −2.09777e10 | −1.53408 | −0.767038 | − | 0.641602i | \(-0.778270\pi\) | ||||
−0.767038 | + | 0.641602i | \(0.778270\pi\) | |||||||
\(788\) | 7.32964e9 | 0.533631 | ||||||||
\(789\) | 2.52151e10 | 1.82764 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.10991e7 | −0.00438952 | ||||||||
\(792\) | −1.78983e8 | −0.0128019 | ||||||||
\(793\) | −1.97822e9 | −0.140870 | ||||||||
\(794\) | 9.64725e9 | 0.683962 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.18012e9 | −0.153209 | ||||||||
\(797\) | −1.55513e10 | −1.08809 | −0.544043 | − | 0.839057i | \(-0.683107\pi\) | ||||
−0.544043 | + | 0.839057i | \(0.683107\pi\) | |||||||
\(798\) | 3.59334e8 | 0.0250316 | ||||||||
\(799\) | 8.68297e8 | 0.0602219 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.42427e9 | 0.166673 | ||||||||
\(802\) | −5.92551e9 | −0.405617 | ||||||||
\(803\) | 5.42711e9 | 0.369883 | ||||||||
\(804\) | 1.12883e10 | 0.766005 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.18276e9 | −0.214107 | ||||||||
\(807\) | 2.72858e10 | 1.82759 | ||||||||
\(808\) | −3.37653e9 | −0.225180 | ||||||||
\(809\) | −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 | \(-0.372922\pi\) | ||||
0.388706 | + | 0.921362i | \(0.372922\pi\) | |||||||
\(812\) | 1.62802e8 | 0.0106712 | ||||||||
\(813\) | −1.69403e10 | −1.10562 | ||||||||
\(814\) | 4.06893e9 | 0.264420 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.39447e9 | −0.0898447 | ||||||||
\(817\) | 1.46096e10 | 0.937262 | ||||||||
\(818\) | −1.09750e8 | −0.00701079 | ||||||||
\(819\) | 5.08580e7 | 0.00323494 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.96308e10 | −1.23805 | −0.619024 | − | 0.785372i | \(-0.712472\pi\) | ||||
−0.619024 | + | 0.785372i | \(0.712472\pi\) | |||||||
\(822\) | 3.03254e9 | 0.190439 | ||||||||
\(823\) | 2.67601e9 | 0.167336 | 0.0836679 | − | 0.996494i | \(-0.473337\pi\) | ||||
0.0836679 | + | 0.996494i | \(0.473337\pi\) | |||||||
\(824\) | −1.01779e10 | −0.633744 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.53752e8 | 0.0280149 | ||||||||
\(827\) | −9.26722e8 | −0.0569745 | −0.0284872 | − | 0.999594i | \(-0.509069\pi\) | ||||
−0.0284872 | + | 0.999594i | \(0.509069\pi\) | |||||||
\(828\) | 1.01290e9 | 0.0620096 | ||||||||
\(829\) | −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 | ||||||||
\(832\) | −1.17815e9 | −0.0709199 | ||||||||
\(833\) | −5.65201e9 | −0.338802 | ||||||||
\(834\) | −5.78160e9 | −0.345117 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.79423e9 | −0.106208 | ||||||||
\(837\) | −8.43123e9 | −0.496995 | ||||||||
\(838\) | −1.56477e10 | −0.918536 | ||||||||
\(839\) | −8.93988e9 | −0.522595 | −0.261297 | − | 0.965258i | \(-0.584150\pi\) | ||||
−0.261297 | + | 0.965258i | \(0.584150\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.37642e10 | −0.797931 | ||||||||
\(842\) | 1.84888e10 | 1.06737 | ||||||||
\(843\) | 7.51071e8 | 0.0431802 | ||||||||
\(844\) | −1.11544e10 | −0.638628 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.65231e8 | −0.0150601 | ||||||||
\(847\) | −7.63296e7 | −0.00431619 | ||||||||
\(848\) | 4.90761e9 | 0.276366 | ||||||||
\(849\) | −1.11530e10 | −0.625480 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.30268e10 | −1.28080 | ||||||||
\(852\) | −9.94447e9 | −0.550862 | ||||||||
\(853\) | −1.71708e10 | −0.947257 | −0.473628 | − | 0.880725i | \(-0.657056\pi\) | ||||
−0.473628 | + | 0.880725i | \(0.657056\pi\) | |||||||
\(854\) | 1.51720e8 | 0.00833565 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.07281e10 | 0.584606 | ||||||||
\(857\) | 7.71458e9 | 0.418677 | 0.209339 | − | 0.977843i | \(-0.432869\pi\) | ||||
0.209339 | + | 0.977843i | \(0.432869\pi\) | |||||||
\(858\) | −2.36853e9 | −0.128019 | ||||||||
\(859\) | 1.68606e10 | 0.907606 | 0.453803 | − | 0.891102i | \(-0.350067\pi\) | ||||
0.453803 | + | 0.891102i | \(0.350067\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.17313e9 | 0.0626377 | ||||||||
\(862\) | 1.62817e10 | 0.865813 | ||||||||
\(863\) | 2.42922e10 | 1.28656 | 0.643278 | − | 0.765633i | \(-0.277574\pi\) | ||||
0.643278 | + | 0.765633i | \(0.277574\pi\) | |||||||
\(864\) | −3.12095e9 | −0.164622 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.24822e10 | 1.17632 | ||||||||
\(867\) | 1.79675e10 | 0.936311 | ||||||||
\(868\) | 2.44102e8 | 0.0126693 | ||||||||
\(869\) | 2.52521e9 | 0.130535 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.60161e10 | 0.821283 | ||||||||
\(872\) | 3.06301e8 | 0.0156438 | ||||||||
\(873\) | 3.62608e9 | 0.184454 | ||||||||
\(874\) | 1.01539e10 | 0.514449 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.29158e10 | −0.649169 | ||||||||
\(877\) | −2.67740e10 | −1.34034 | −0.670169 | − | 0.742209i | \(-0.733778\pi\) | ||||
−0.670169 | + | 0.742209i | \(0.733778\pi\) | |||||||
\(878\) | −1.26580e10 | −0.631154 | ||||||||
\(879\) | 1.90058e10 | 0.943899 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.10654e10 | 0.545197 | 0.272598 | − | 0.962128i | \(-0.412117\pi\) | ||||
0.272598 | + | 0.962128i | \(0.412117\pi\) | |||||||
\(882\) | 1.72647e9 | 0.0847265 | ||||||||
\(883\) | −2.06264e10 | −1.00824 | −0.504118 | − | 0.863635i | \(-0.668182\pi\) | ||||
−0.504118 | + | 0.863635i | \(0.668182\pi\) | |||||||
\(884\) | −1.97850e9 | −0.0963282 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.91191e9 | −0.188961 | ||||||||
\(887\) | 7.62436e9 | 0.366835 | 0.183417 | − | 0.983035i | \(-0.441284\pi\) | ||||
0.183417 | + | 0.983035i | \(0.441284\pi\) | |||||||
\(888\) | −9.68352e9 | −0.464075 | ||||||||
\(889\) | −8.31512e8 | −0.0396928 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.03884e9 | −0.333372 | ||||||||
\(892\) | −9.32672e9 | −0.439999 | ||||||||
\(893\) | −2.65884e9 | −0.124943 | ||||||||
\(894\) | −1.40455e10 | −0.657442 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 9.03580e7 | 0.00419651 | ||||||||
\(897\) | 1.34040e10 | 0.620097 | ||||||||
\(898\) | −1.44857e10 | −0.667534 | ||||||||
\(899\) | 5.22633e9 | 0.239904 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.24151e9 | 0.375379 | ||||||||
\(902\) | −5.85770e9 | −0.265769 | ||||||||
\(903\) | −1.47913e9 | −0.0668495 | ||||||||
\(904\) | −7.26052e8 | −0.0326872 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.62451e10 | 0.725728 | ||||||||
\(907\) | 3.36091e10 | 1.49566 | 0.747828 | − | 0.663893i | \(-0.231097\pi\) | ||||
0.747828 | + | 0.663893i | \(0.231097\pi\) | |||||||
\(908\) | 8.13454e9 | 0.360606 | ||||||||
\(909\) | 1.73206e9 | 0.0764874 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.89170e10 | −1.70540 | −0.852698 | − | 0.522404i | \(-0.825035\pi\) | ||||
−0.852698 | + | 0.522404i | \(0.825035\pi\) | |||||||
\(912\) | 4.27004e9 | 0.186402 | ||||||||
\(913\) | −8.64161e9 | −0.375791 | ||||||||
\(914\) | −6.91449e9 | −0.299536 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.30400e9 | −0.356987 | ||||||||
\(917\) | −1.82017e9 | −0.0779507 | ||||||||
\(918\) | −5.24112e9 | −0.223601 | ||||||||
\(919\) | 4.35993e10 | 1.85300 | 0.926499 | − | 0.376296i | \(-0.122803\pi\) | ||||
0.926499 | + | 0.376296i | \(0.122803\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.69367e10 | 1.55794 | ||||||||
\(922\) | −3.88344e9 | −0.163177 | ||||||||
\(923\) | −1.41094e10 | −0.590614 | ||||||||
\(924\) | 1.81655e8 | 0.00757520 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.48301e10 | 0.613768 | ||||||||
\(927\) | 5.22098e9 | 0.215265 | ||||||||
\(928\) | 1.93461e9 | 0.0794648 | ||||||||
\(929\) | −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 | ||||||||
\(932\) | 9.74143e9 | 0.394155 | ||||||||
\(933\) | −3.16761e10 | −1.27687 | ||||||||
\(934\) | 2.52954e8 | 0.0101584 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.04356e8 | 0.0240895 | ||||||||
\(937\) | −3.51153e9 | −0.139446 | −0.0697232 | − | 0.997566i | \(-0.522212\pi\) | ||||
−0.0697232 | + | 0.997566i | \(0.522212\pi\) | |||||||
\(938\) | −1.22835e9 | −0.0485975 | ||||||||
\(939\) | 6.70402e9 | 0.264244 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.84266e10 | −0.720911 | −0.360455 | − | 0.932776i | \(-0.617379\pi\) | ||||
−0.360455 | + | 0.932776i | \(0.617379\pi\) | |||||||
\(942\) | 2.64090e10 | 1.02938 | ||||||||
\(943\) | 3.31498e10 | 1.28733 | ||||||||
\(944\) | 5.39203e9 | 0.208617 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.38559e9 | 0.283639 | ||||||||
\(947\) | −8.78798e9 | −0.336251 | −0.168126 | − | 0.985766i | \(-0.553771\pi\) | ||||
−0.168126 | + | 0.985766i | \(0.553771\pi\) | |||||||
\(948\) | −6.00967e9 | −0.229098 | ||||||||
\(949\) | −1.83253e10 | −0.696015 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.82663e9 | 0.181975 | ||||||||
\(952\) | 1.51741e8 | 0.00569999 | ||||||||
\(953\) | −1.85304e10 | −0.693521 | −0.346761 | − | 0.937954i | \(-0.612718\pi\) | ||||
−0.346761 | + | 0.937954i | \(0.612718\pi\) | |||||||
\(954\) | −2.51746e9 | −0.0938737 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.55559e10 | −0.575827 | ||||||||
\(957\) | 3.88930e9 | 0.143443 | ||||||||
\(958\) | 2.49470e10 | 0.916725 | ||||||||
\(959\) | −3.29991e8 | −0.0120819 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.96764e10 | −0.715176 | ||||||||
\(962\) | −1.37392e10 | −0.497564 | ||||||||
\(963\) | −5.50319e9 | −0.198574 | ||||||||
\(964\) | −4.38139e9 | −0.157522 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.02802e9 | −0.0366927 | ||||||||
\(967\) | −4.71498e10 | −1.67682 | −0.838412 | − | 0.545037i | \(-0.816516\pi\) | ||||
−0.838412 | + | 0.545037i | \(0.816516\pi\) | |||||||
\(968\) | −9.07039e8 | −0.0321412 | ||||||||
\(969\) | 7.17082e9 | 0.253184 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.76215e9 | −0.307145 | −0.153572 | − | 0.988137i | \(-0.549078\pi\) | ||||
−0.153572 | + | 0.988137i | \(0.549078\pi\) | |||||||
\(972\) | 3.42042e9 | 0.119467 | ||||||||
\(973\) | 6.29135e8 | 0.0218952 | ||||||||
\(974\) | −2.70086e10 | −0.936583 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.80291e9 | 0.0620727 | ||||||||
\(977\) | 6.33661e9 | 0.217383 | 0.108692 | − | 0.994076i | \(-0.465334\pi\) | ||||
0.108692 | + | 0.994076i | \(0.465334\pi\) | |||||||
\(978\) | −3.68133e9 | −0.125840 | ||||||||
\(979\) | 1.22856e10 | 0.418462 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.57124e8 | −0.00531374 | ||||||||
\(982\) | 3.64035e10 | 1.22674 | ||||||||
\(983\) | −4.47312e10 | −1.50201 | −0.751006 | − | 0.660295i | \(-0.770431\pi\) | ||||
−0.751006 | + | 0.660295i | \(0.770431\pi\) | |||||||
\(984\) | 1.39406e10 | 0.466442 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.24885e9 | 0.107934 | ||||||||
\(987\) | 2.69190e8 | 0.00891147 | ||||||||
\(988\) | 6.05843e9 | 0.199853 | ||||||||
\(989\) | −4.17964e10 | −1.37389 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.62109e10 | 1.50830 | 0.754148 | − | 0.656705i | \(-0.228050\pi\) | ||||
0.754148 | + | 0.656705i | \(0.228050\pi\) | |||||||
\(992\) | 2.90071e9 | 0.0943437 | ||||||||
\(993\) | −1.73150e10 | −0.561178 | ||||||||
\(994\) | 1.08212e9 | 0.0349482 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.05659e10 | 0.659538 | ||||||||
\(997\) | 1.52392e10 | 0.487001 | 0.243501 | − | 0.969901i | \(-0.421704\pi\) | ||||
0.243501 | + | 0.969901i | \(0.421704\pi\) | |||||||
\(998\) | 5.00587e9 | 0.159413 | ||||||||
\(999\) | −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 | 550.8.a.d.1.1 | 2 | ||
5.4 | even | 2 | 22.8.a.d.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 198.8.a.f.1.2 | 2 | |||
20.19 | odd | 2 | 176.8.a.e.1.1 | 2 | |||
55.54 | odd | 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 | 5.4 | even | 2 | ||
176.8.a.e.1.1 | 2 | 20.19 | odd | 2 | |||
198.8.a.f.1.2 | 2 | 15.14 | odd | 2 | |||
242.8.a.h.1.2 | 2 | 55.54 | odd | 2 | |||
550.8.a.d.1.1 | 2 | 1.1 | even | 1 | trivial |