Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [198,8,Mod(1,198)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(198, 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("198.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 198 = 2 \cdot 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 198.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: | \(61.8522350459\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
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 | 1.2 | ||
Root | \(-60.4939\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 198.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | −104.506 | −0.373893 | −0.186946 | − | 0.982370i | \(-0.559859\pi\) | ||||
−0.186946 | + | 0.982370i | \(0.559859\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 43.0861 | 0.0474781 | 0.0237391 | − | 0.999718i | \(-0.492443\pi\) | ||||
0.0237391 | + | 0.999718i | \(0.492443\pi\) | |||||||
\(8\) | −512.000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 836.049 | 0.264382 | ||||||||
\(11\) | −1331.00 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4494.27 | 0.567359 | 0.283679 | − | 0.958919i | \(-0.408445\pi\) | ||||
0.283679 | + | 0.958919i | \(0.408445\pi\) | |||||||
\(14\) | −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 | \(0.445693\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −21063.0 | −0.704503 | −0.352252 | − | 0.935905i | \(-0.614584\pi\) | ||||
−0.352252 | + | 0.935905i | \(0.614584\pi\) | |||||||
\(20\) | −6688.39 | −0.186946 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 10648.0 | 0.213201 | ||||||||
\(23\) | 60259.0 | 1.03270 | 0.516350 | − | 0.856377i | \(-0.327290\pi\) | ||||
0.516350 | + | 0.856377i | \(0.327290\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −67203.5 | −0.860204 | ||||||||
\(26\) | −35954.2 | −0.401183 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2757.51 | 0.0237391 | ||||||||
\(29\) | 59039.5 | 0.449521 | 0.224760 | − | 0.974414i | \(-0.427840\pi\) | ||||
0.224760 | + | 0.974414i | \(0.427840\pi\) | |||||||
\(30\) | 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 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −55028.4 | −0.240110 | ||||||||
\(35\) | −4502.76 | −0.0177517 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 382131. | 1.24024 | 0.620120 | − | 0.784507i | \(-0.287084\pi\) | ||||
0.620120 | + | 0.784507i | \(0.287084\pi\) | |||||||
\(38\) | 168504. | 0.498159 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 53507.1 | 0.132191 | ||||||||
\(41\) | −550122. | −1.24657 | −0.623283 | − | 0.781996i | \(-0.714202\pi\) | ||||
−0.623283 | + | 0.781996i | \(0.714202\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 693613. | 1.33039 | 0.665193 | − | 0.746671i | \(-0.268349\pi\) | ||||
0.665193 | + | 0.746671i | \(0.268349\pi\) | |||||||
\(44\) | −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 | \(0.471737\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −821687. | −0.997746 | ||||||||
\(50\) | 537628. | 0.608256 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 287634. | 0.283679 | ||||||||
\(53\) | 1.19815e6 | 1.10546 | 0.552732 | − | 0.833359i | \(-0.313585\pi\) | ||||
0.552732 | + | 0.833359i | \(0.313585\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 139098. | 0.112733 | ||||||||
\(56\) | −22060.1 | −0.0167861 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −472316. | −0.317859 | ||||||||
\(59\) | −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 | \(0.460381\pi\) | |||||||
\(62\) | 708180. | 0.377375 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | −469679. | −0.212131 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.56366e6 | 1.44755 | 0.723777 | − | 0.690034i | \(-0.242404\pi\) | ||||
0.723777 | + | 0.690034i | \(0.242404\pi\) | |||||||
\(68\) | 440227. | 0.169784 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 36022.1 | 0.0125524 | ||||||||
\(71\) | −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 | \(0.710191\pi\) | |||||||
\(74\) | −3.05705e6 | −0.876982 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.34803e6 | −0.352252 | ||||||||
\(77\) | −57347.6 | −0.0143152 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.89723e6 | 0.432937 | 0.216468 | − | 0.976290i | \(-0.430546\pi\) | ||||
0.216468 | + | 0.976290i | \(0.430546\pi\) | |||||||
\(80\) | −428057. | −0.0934731 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.40097e6 | 0.881455 | ||||||||
\(83\) | −6.49257e6 | −1.24636 | −0.623179 | − | 0.782079i | \(-0.714159\pi\) | ||||
−0.623179 | + | 0.782079i | \(0.714159\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −718851. | −0.126962 | ||||||||
\(86\) | −5.54890e6 | −0.940725 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 681472. | 0.106600 | ||||||||
\(89\) | −9.23033e6 | −1.38788 | −0.693940 | − | 0.720032i | \(-0.744127\pi\) | ||||
−0.693940 | + | 0.720032i | \(0.744127\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 193641. | 0.0269371 | ||||||||
\(92\) | 3.85658e6 | 0.516350 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.00986e6 | −0.125405 | ||||||||
\(95\) | 2.20122e6 | 0.263409 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.38062e7 | −1.53593 | −0.767967 | − | 0.640489i | \(-0.778732\pi\) | ||||
−0.767967 | + | 0.640489i | \(0.778732\pi\) | |||||||
\(98\) | 6.57349e6 | 0.705513 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.30102e6 | −0.430102 | ||||||||
\(101\) | −6.59478e6 | −0.636906 | −0.318453 | − | 0.947939i | \(-0.603163\pi\) | ||||
−0.318453 | + | 0.947939i | \(0.603163\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.98787e7 | −1.79250 | −0.896249 | − | 0.443551i | \(-0.853718\pi\) | ||||
−0.896249 | + | 0.443551i | \(0.853718\pi\) | |||||||
\(104\) | −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 | \(0.809817\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −598244. | −0.0442472 | −0.0221236 | − | 0.999755i | \(-0.507043\pi\) | ||||
−0.0221236 | + | 0.999755i | \(0.507043\pi\) | |||||||
\(110\) | −1.11278e6 | −0.0797142 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 176481. | 0.0118695 | ||||||||
\(113\) | 1.41807e6 | 0.0924535 | 0.0462267 | − | 0.998931i | \(-0.485280\pi\) | ||||
0.0462267 | + | 0.998931i | \(0.485280\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.29744e6 | −0.386119 | ||||||||
\(116\) | 3.77853e6 | 0.224760 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.05313e7 | 0.590058 | ||||||||
\(119\) | 296370. | 0.0161220 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.77156e6 | 0.0909091 | ||||||||
\(122\) | −3.52132e6 | −0.175568 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.66544e6 | −0.266844 | ||||||||
\(125\) | 1.51877e7 | 0.695517 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.92988e7 | −0.836023 | −0.418012 | − | 0.908442i | \(-0.637273\pi\) | ||||
−0.418012 | + | 0.908442i | \(0.637273\pi\) | |||||||
\(128\) | −2.09715e6 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.75743e6 | 0.149999 | ||||||||
\(131\) | −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 | ||||||||
\(134\) | −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 | \(0.459389\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.46018e7 | −0.461164 | −0.230582 | − | 0.973053i | \(-0.574063\pi\) | ||||
−0.230582 | + | 0.973053i | \(0.574063\pi\) | |||||||
\(140\) | −288177. | −0.00887586 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.51154e7 | 0.736090 | ||||||||
\(143\) | −5.98188e6 | −0.171065 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.16999e6 | −0.168072 | ||||||||
\(146\) | 3.26198e7 | 0.867453 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.44564e7 | 0.620120 | ||||||||
\(149\) | 3.54730e7 | 0.878507 | 0.439254 | − | 0.898363i | \(-0.355243\pi\) | ||||
0.439254 | + | 0.898363i | \(0.355243\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 458780. | 0.0101224 | ||||||||
\(155\) | 9.25115e6 | 0.199542 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.66977e7 | −1.37550 | −0.687752 | − | 0.725946i | \(-0.741402\pi\) | ||||
−0.687752 | + | 0.725946i | \(0.741402\pi\) | |||||||
\(158\) | −1.51778e7 | −0.306133 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.42446e6 | 0.0660955 | ||||||||
\(161\) | 2.59632e6 | 0.0490307 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.29744e6 | 0.168154 | 0.0840769 | − | 0.996459i | \(-0.473206\pi\) | ||||
0.0840769 | + | 0.996459i | \(0.473206\pi\) | |||||||
\(164\) | −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 | \(0.335956\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.25500e7 | −0.678104 | ||||||||
\(170\) | 5.75081e6 | 0.0897754 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.43912e7 | 0.665193 | ||||||||
\(173\) | −1.19997e8 | −1.76201 | −0.881004 | − | 0.473108i | \(-0.843132\pi\) | ||||
−0.881004 | + | 0.473108i | \(0.843132\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.89553e6 | −0.0408409 | ||||||||
\(176\) | −5.45178e6 | −0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.38426e7 | 0.981380 | ||||||||
\(179\) | −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 | \(0.457045\pi\) | |||||||
\(182\) | −1.54913e6 | −0.0190474 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.08526e7 | −0.365115 | ||||||||
\(185\) | −3.99350e7 | −0.463717 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.15535e6 | −0.102383 | ||||||||
\(188\) | 8.07888e6 | 0.0886745 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.76097e7 | −0.186258 | ||||||||
\(191\) | 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 | \(0.169467\pi\) | |||||||
\(194\) | 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 | \(0.320827\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.40644e7 | −0.306418 | −0.153209 | − | 0.988194i | \(-0.548961\pi\) | ||||
−0.153209 | + | 0.988194i | \(0.548961\pi\) | |||||||
\(200\) | 3.44082e7 | 0.304128 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.27583e7 | 0.450361 | ||||||||
\(203\) | 2.54378e6 | 0.0213424 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.74911e7 | 0.466082 | ||||||||
\(206\) | 1.59030e8 | 1.26749 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.67626e8 | 1.16921 | ||||||||
\(215\) | −7.24868e7 | −0.497421 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.81409e6 | −0.0253385 | ||||||||
\(218\) | 4.78596e6 | 0.0312875 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 8.90225e6 | 0.0563664 | ||||||||
\(221\) | 3.09141e7 | 0.192656 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.45730e8 | 0.879998 | 0.439999 | − | 0.897998i | \(-0.354979\pi\) | ||||
0.439999 | + | 0.897998i | \(0.354979\pi\) | |||||||
\(224\) | −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 | \(0.382570\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.29750e8 | −0.713975 | −0.356987 | − | 0.934109i | \(-0.616196\pi\) | ||||
−0.356987 | + | 0.934109i | \(0.616196\pi\) | |||||||
\(230\) | 5.03795e7 | 0.273028 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.02282e7 | −0.158930 | ||||||||
\(233\) | 1.52210e8 | 0.788310 | 0.394155 | − | 0.919044i | \(-0.371037\pi\) | ||||
0.394155 | + | 0.919044i | \(0.371037\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.31921e7 | −0.0663095 | ||||||||
\(236\) | −8.42504e7 | −0.417234 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.37096e6 | −0.0114000 | ||||||||
\(239\) | 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 | \(0.550351\pi\) | |||||||
\(242\) | −1.41725e7 | −0.0642824 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.81705e7 | 0.124145 | ||||||||
\(245\) | 8.58713e7 | 0.373050 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.46630e7 | −0.399706 | ||||||||
\(248\) | 4.53235e7 | 0.188687 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.21502e8 | −0.491804 | ||||||||
\(251\) | −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 | ||||||||
\(254\) | 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 | \(0.749957\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.64645e7 | 0.0588843 | ||||||||
\(260\) | −3.00595e7 | −0.106066 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.37960e8 | 1.16094 | ||||||||
\(263\) | −5.09459e8 | −1.72689 | −0.863444 | − | 0.504445i | \(-0.831697\pi\) | ||||
−0.863444 | + | 0.504445i | \(0.831697\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.25214e8 | −0.413325 | ||||||||
\(266\) | 7.26018e6 | 0.0236517 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.28074e8 | 0.723777 | ||||||||
\(269\) | 5.51297e8 | 1.72684 | 0.863421 | − | 0.504484i | \(-0.168317\pi\) | ||||
0.863421 | + | 0.504484i | \(0.168317\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.12710e7 | −0.179940 | ||||||||
\(275\) | 8.94478e7 | 0.259361 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.10974e8 | −1.44451 | −0.722253 | − | 0.691629i | \(-0.756893\pi\) | ||||
−0.722253 | + | 0.691629i | \(0.756893\pi\) | |||||||
\(278\) | 1.16815e8 | 0.326092 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.30541e6 | 0.00627618 | ||||||||
\(281\) | 1.51750e7 | 0.0407998 | 0.0203999 | − | 0.999792i | \(-0.493506\pi\) | ||||
0.0203999 | + | 0.999792i | \(0.493506\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.25341e8 | −0.590999 | −0.295500 | − | 0.955343i | \(-0.595486\pi\) | ||||
−0.295500 | + | 0.955343i | \(0.595486\pi\) | |||||||
\(284\) | −2.00923e8 | −0.520494 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.78550e7 | 0.120961 | ||||||||
\(287\) | −2.37026e7 | −0.0591846 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.63024e8 | −0.884694 | ||||||||
\(290\) | 4.93599e7 | 0.118845 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.60958e8 | −0.613382 | ||||||||
\(293\) | −3.84004e8 | −0.891864 | −0.445932 | − | 0.895067i | \(-0.647128\pi\) | ||||
−0.445932 | + | 0.895067i | \(0.647128\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.37573e8 | 0.312002 | ||||||||
\(296\) | −1.95651e8 | −0.438491 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.83784e8 | −0.621199 | ||||||||
\(299\) | 2.70821e8 | 0.585912 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.98851e7 | 0.0631643 | ||||||||
\(302\) | −3.28225e8 | −0.685720 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.62741e7 | −0.176126 | ||||||||
\(305\) | −4.59999e7 | −0.0928341 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.46289e8 | 1.47205 | 0.736026 | − | 0.676954i | \(-0.236700\pi\) | ||||
0.736026 | + | 0.676954i | \(0.236700\pi\) | |||||||
\(308\) | −3.67024e6 | −0.00715760 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.40092e7 | −0.141098 | ||||||||
\(311\) | −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 | \(0.460159\pi\) | |||||||
\(314\) | 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 | \(0.527399\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.85816e7 | −0.135536 | ||||||||
\(320\) | −2.73957e7 | −0.0467366 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.07706e7 | −0.0346700 | ||||||||
\(323\) | −1.44883e8 | −0.239226 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.02031e8 | −0.488045 | ||||||||
\(326\) | −7.43795e7 | −0.118903 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 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 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.74614e8 | −0.696992 | ||||||||
\(335\) | −3.72425e8 | −0.541230 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.20870e8 | 1.02601 | 0.513006 | − | 0.858385i | \(-0.328532\pi\) | ||||
0.513006 | + | 0.858385i | \(0.328532\pi\) | |||||||
\(338\) | 3.40400e8 | 0.479492 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.60064e7 | −0.0634808 | ||||||||
\(341\) | 1.17823e8 | 0.160913 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −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 | \(0.526220\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.00379e8 | −0.126402 | −0.0632012 | − | 0.998001i | \(-0.520131\pi\) | ||||
−0.0632012 | + | 0.998001i | \(0.520131\pi\) | |||||||
\(350\) | 2.31643e7 | 0.0288789 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.36142e7 | 0.0533002 | ||||||||
\(353\) | −7.51413e8 | −0.909216 | −0.454608 | − | 0.890692i | \(-0.650221\pi\) | ||||
−0.454608 | + | 0.890692i | \(0.650221\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.28089e8 | 0.389218 | ||||||||
\(356\) | −5.90741e8 | −0.693940 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.55115e8 | 0.293864 | ||||||||
\(359\) | 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 | ||||||||
\(362\) | −1.71729e8 | −0.190267 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.23930e7 | 0.0134686 | ||||||||
\(365\) | 4.26121e8 | 0.458678 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.16435e8 | −0.967766 | −0.483883 | − | 0.875133i | \(-0.660774\pi\) | ||||
−0.483883 | + | 0.875133i | \(0.660774\pi\) | |||||||
\(368\) | 2.46821e8 | 0.258175 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.19480e8 | 0.327897 | ||||||||
\(371\) | 5.16234e7 | 0.0524854 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.56099e9 | −1.55747 | −0.778736 | − | 0.627352i | \(-0.784139\pi\) | ||||
−0.778736 | + | 0.627352i | \(0.784139\pi\) | |||||||
\(374\) | 7.32428e7 | 0.0723960 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.46311e7 | −0.0627024 | ||||||||
\(377\) | 2.65340e8 | 0.255040 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.34986e7 | 0.0410429 | 0.0205214 | − | 0.999789i | \(-0.493467\pi\) | ||||
0.0205214 | + | 0.999789i | \(0.493467\pi\) | |||||||
\(380\) | 1.40878e8 | 0.131704 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.29906e8 | −0.394595 | ||||||||
\(383\) | −1.95422e8 | −0.177737 | −0.0888685 | − | 0.996043i | \(-0.528325\pi\) | ||||
−0.0888685 | + | 0.996043i | \(0.528325\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.99317e6 | 0.00535235 | ||||||||
\(386\) | −1.37681e9 | −1.21848 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.83596e8 | −0.767967 | ||||||||
\(389\) | 1.60846e9 | 1.38543 | 0.692716 | − | 0.721210i | \(-0.256414\pi\) | ||||
0.692716 | + | 0.721210i | \(0.256414\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.14495e8 | 0.350671 | ||||||||
\(392\) | 4.20704e8 | 0.352756 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9.16205e8 | −0.754668 | ||||||||
\(395\) | −1.98272e8 | −0.161872 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.20591e9 | 0.967268 | 0.483634 | − | 0.875270i | \(-0.339317\pi\) | ||||
0.483634 | + | 0.875270i | \(0.339317\pi\) | |||||||
\(398\) | 2.72515e8 | 0.216670 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.75265e8 | −0.215051 | ||||||||
\(401\) | −7.40689e8 | −0.573628 | −0.286814 | − | 0.957986i | \(-0.592596\pi\) | ||||
−0.286814 | + | 0.957986i | \(0.592596\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.97845e8 | −0.302793 | ||||||||
\(404\) | −4.22066e8 | −0.318453 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.03502e7 | −0.0150914 | ||||||||
\(407\) | −5.08616e8 | −0.373947 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.37187e7 | 0.00991476 | 0.00495738 | − | 0.999988i | \(-0.498422\pi\) | ||||
0.00495738 | + | 0.999988i | \(0.498422\pi\) | |||||||
\(410\) | −4.59929e8 | −0.329570 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.27224e9 | −0.896249 | ||||||||
\(413\) | −5.67190e7 | −0.0396190 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.78513e8 | 0.466004 | ||||||||
\(416\) | −1.47268e8 | −0.100296 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.24279e8 | −0.150201 | ||||||||
\(419\) | −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 | \(0.772241\pi\) | |||||||
\(422\) | 1.39430e9 | 0.903156 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.13451e8 | −0.390840 | ||||||||
\(425\) | −4.62262e8 | −0.292097 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.89650e7 | 0.0117884 | ||||||||
\(428\) | −1.34101e9 | −0.826758 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.79895e8 | 0.351730 | ||||||||
\(431\) | 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 | \(0.187318\pi\) | |||||||
\(434\) | 3.05127e7 | 0.0179171 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.82876e7 | −0.0221236 | ||||||||
\(437\) | −1.26924e9 | −0.727541 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.58225e9 | 0.892587 | 0.446293 | − | 0.894887i | \(-0.352744\pi\) | ||||
0.446293 | + | 0.894887i | \(0.352744\pi\) | |||||||
\(440\) | −7.12180e7 | −0.0398571 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.47313e8 | −0.136229 | ||||||||
\(443\) | 4.88989e8 | 0.267231 | 0.133615 | − | 0.991033i | \(-0.457341\pi\) | ||||
0.133615 | + | 0.991033i | \(0.457341\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.64626e8 | 0.518918 | ||||||||
\(446\) | −1.16584e9 | −0.622253 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.12948e7 | 0.00593477 | ||||||||
\(449\) | −1.81072e9 | −0.944036 | −0.472018 | − | 0.881589i | \(-0.656474\pi\) | ||||
−0.472018 | + | 0.881589i | \(0.656474\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.32212e8 | 0.375854 | ||||||||
\(452\) | 9.07565e7 | 0.0462267 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.01682e9 | −0.509973 | ||||||||
\(455\) | −2.02366e7 | −0.0100716 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.64311e8 | −0.423607 | −0.211804 | − | 0.977312i | \(-0.567934\pi\) | ||||
−0.211804 | + | 0.977312i | \(0.567934\pi\) | |||||||
\(458\) | 1.03800e9 | 0.504857 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.03036e8 | −0.193060 | ||||||||
\(461\) | −4.85430e8 | −0.230767 | −0.115383 | − | 0.993321i | \(-0.536810\pi\) | ||||
−0.115383 | + | 0.993321i | \(0.536810\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.85376e9 | 0.867999 | 0.434000 | − | 0.900913i | \(-0.357102\pi\) | ||||
0.434000 | + | 0.900913i | \(0.357102\pi\) | |||||||
\(464\) | 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 | \(0.502286\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.53544e8 | 0.0687272 | ||||||||
\(470\) | 1.05537e8 | 0.0468879 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.74003e8 | 0.295029 | ||||||||
\(473\) | −9.23199e8 | −0.401126 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.41551e9 | 0.606017 | ||||||||
\(476\) | 1.89677e7 | 0.00806101 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.94449e9 | −0.814343 | ||||||||
\(479\) | 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 | ||||||||
\(482\) | 5.47674e8 | 0.222770 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.13380e8 | 0.0454545 | ||||||||
\(485\) | 1.44283e9 | 0.574275 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.37608e9 | −1.32453 | −0.662265 | − | 0.749270i | \(-0.730404\pi\) | ||||
−0.662265 | + | 0.749270i | \(0.730404\pi\) | |||||||
\(488\) | −2.25364e8 | −0.0877840 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.86970e8 | −0.263786 | ||||||||
\(491\) | 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 | ||||||||
\(494\) | 7.57304e8 | 0.282635 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.62588e8 | −0.133422 | ||||||||
\(497\) | −1.35266e8 | −0.0494242 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.25733e8 | −0.225443 | −0.112722 | − | 0.993627i | \(-0.535957\pi\) | ||||
−0.112722 | + | 0.993627i | \(0.535957\pi\) | |||||||
\(500\) | 9.72014e8 | 0.347758 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.33834e9 | 0.472174 | ||||||||
\(503\) | 3.43240e9 | 1.20257 | 0.601285 | − | 0.799035i | \(-0.294656\pi\) | ||||
0.601285 | + | 0.799035i | \(0.294656\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.89195e8 | 0.238135 | ||||||||
\(506\) | 6.41638e8 | 0.220173 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.23513e9 | −0.418012 | ||||||||
\(509\) | −1.36035e9 | −0.457234 | −0.228617 | − | 0.973516i | \(-0.573420\pi\) | ||||
−0.228617 | + | 0.973516i | \(0.573420\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.75682e8 | −0.0582445 | ||||||||
\(512\) | −1.34218e8 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.07831e9 | 0.999866 | ||||||||
\(515\) | 2.07745e9 | 0.670202 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.68016e8 | −0.0534727 | ||||||||
\(518\) | −1.31716e8 | −0.0416375 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.40476e8 | 0.0749997 | ||||||||
\(521\) | 2.51109e9 | 0.777912 | 0.388956 | − | 0.921256i | \(-0.372836\pi\) | ||||
0.388956 | + | 0.921256i | \(0.372836\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.25045e9 | 1.29921 | 0.649605 | − | 0.760272i | \(-0.274934\pi\) | ||||
0.649605 | + | 0.760272i | \(0.274934\pi\) | |||||||
\(524\) | −2.70368e9 | −0.820912 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.07567e9 | 1.22109 | ||||||||
\(527\) | −6.08907e8 | −0.181223 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.26323e8 | 0.0664713 | ||||||||
\(530\) | 1.00171e9 | 0.292265 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.80815e7 | −0.0167243 | ||||||||
\(533\) | −2.47240e9 | −0.707250 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.18974e9 | 0.618237 | ||||||||
\(536\) | −1.82460e9 | −0.511788 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −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 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.25396e8 | −0.0600276 | ||||||||
\(545\) | 6.25202e7 | 0.0165437 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.28564e9 | −0.858350 | −0.429175 | − | 0.903221i | \(-0.641196\pi\) | ||||
−0.429175 | + | 0.903221i | \(0.641196\pi\) | |||||||
\(548\) | 4.90168e8 | 0.127237 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.15582e8 | −0.183396 | ||||||||
\(551\) | −1.24355e9 | −0.316689 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 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 | \(0.334867\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.11729e9 | 0.754806 | ||||||||
\(560\) | −1.84433e7 | −0.00443793 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.21400e8 | −0.0288498 | ||||||||
\(563\) | 1.60197e9 | 0.378333 | 0.189167 | − | 0.981945i | \(-0.439421\pi\) | ||||
0.189167 | + | 0.981945i | \(0.439421\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.48197e8 | −0.0345677 | ||||||||
\(566\) | 1.80272e9 | 0.417899 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.60739e9 | 0.368045 | ||||||||
\(569\) | 5.94461e9 | 1.35279 | 0.676396 | − | 0.736539i | \(-0.263541\pi\) | ||||
0.676396 | + | 0.736539i | \(0.263541\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.89621e8 | 0.0418499 | ||||||||
\(575\) | −4.04961e9 | −0.888334 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.05194e8 | −0.109482 | −0.0547410 | − | 0.998501i | \(-0.517433\pi\) | ||||
−0.0547410 | + | 0.998501i | \(0.517433\pi\) | |||||||
\(578\) | 2.90419e9 | 0.625573 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.94879e8 | −0.0840362 | ||||||||
\(581\) | −2.79739e8 | −0.0591748 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −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 | \(0.519676\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.86455e9 | 0.375985 | ||||||||
\(590\) | −1.10059e9 | −0.220618 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.56521e9 | 0.310060 | ||||||||
\(593\) | 2.44359e8 | 0.0481212 | 0.0240606 | − | 0.999711i | \(-0.492341\pi\) | ||||
0.0240606 | + | 0.999711i | \(0.492341\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.09725e7 | −0.00602790 | ||||||||
\(596\) | 2.27027e9 | 0.439254 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.16656e9 | −0.414302 | ||||||||
\(599\) | −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 | \(0.631525\pi\) | |||||||
\(602\) | −2.39080e8 | −0.0446639 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.62580e9 | 0.484877 | ||||||||
\(605\) | −1.85139e8 | −0.0339902 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.40384e9 | 1.16220 | 0.581099 | − | 0.813833i | \(-0.302623\pi\) | ||||
0.581099 | + | 0.813833i | \(0.302623\pi\) | |||||||
\(608\) | 6.90193e8 | 0.124540 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.67999e8 | 0.0656436 | ||||||||
\(611\) | 5.67324e8 | 0.100621 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.98899e9 | −1.57616 | −0.788078 | − | 0.615575i | \(-0.788924\pi\) | ||||
−0.788078 | + | 0.615575i | \(0.788924\pi\) | |||||||
\(614\) | −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 | \(0.442015\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.25875e9 | −0.721713 | −0.360856 | − | 0.932621i | \(-0.617516\pi\) | ||||
−0.360856 | + | 0.932621i | \(0.617516\pi\) | |||||||
\(620\) | 5.92074e8 | 0.0997711 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.12000e9 | 0.853107 | ||||||||
\(623\) | −3.97699e8 | −0.0658940 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.66306e9 | 0.600156 | ||||||||
\(626\) | −1.08361e9 | −0.176548 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −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 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.80159e8 | 0.121582 | ||||||||
\(635\) | 2.01685e9 | 0.312583 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.69289e9 | −0.566080 | ||||||||
\(638\) | 6.28652e8 | 0.0958381 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.19165e8 | 0.0330477 | ||||||||
\(641\) | −7.93190e9 | −1.18953 | −0.594763 | − | 0.803901i | \(-0.702754\pi\) | ||||
−0.594763 | + | 0.803901i | \(0.702754\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.67790e9 | −0.545583 | −0.272792 | − | 0.962073i | \(-0.587947\pi\) | ||||
−0.272792 | + | 0.962073i | \(0.587947\pi\) | |||||||
\(644\) | 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 | \(0.422046\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.75215e9 | 0.251602 | ||||||||
\(650\) | 2.41625e9 | 0.345100 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.95036e8 | 0.0840769 | ||||||||
\(653\) | −1.23649e10 | −1.73778 | −0.868891 | − | 0.495004i | \(-0.835167\pi\) | ||||
−0.868891 | + | 0.495004i | \(0.835167\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.41487e9 | 0.613865 | ||||||||
\(656\) | −2.25330e9 | −0.311642 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.35109e7 | −0.00595398 | ||||||||
\(659\) | −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 | \(0.683385\pi\) | |||||||
\(662\) | −2.79873e9 | −0.374937 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.32419e9 | 0.440654 | ||||||||
\(665\) | 9.48417e7 | 0.0125062 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.55766e9 | 0.464220 | ||||||||
\(668\) | 3.79691e9 | 0.492848 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.97940e9 | 0.382707 | ||||||||
\(671\) | −5.85859e8 | −0.0748625 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.38929e10 | −1.75687 | −0.878436 | − | 0.477860i | \(-0.841413\pi\) | ||||
−0.878436 | + | 0.477860i | \(0.841413\pi\) | |||||||
\(674\) | −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 | \(0.628872\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.94855e8 | −0.0729233 | ||||||||
\(680\) | 3.68052e8 | 0.0448877 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9.42588e8 | −0.113783 | ||||||||
\(683\) | 7.46187e9 | 0.896139 | 0.448069 | − | 0.893999i | \(-0.352112\pi\) | ||||
0.448069 | + | 0.893999i | \(0.352112\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.00400e8 | −0.0951459 | ||||||||
\(686\) | 5.67092e8 | 0.0670686 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 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 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.02463e9 | 0.116361 | ||||||||
\(695\) | 1.52598e9 | 0.172426 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.78404e9 | −0.423293 | ||||||||
\(698\) | 8.03034e8 | 0.0893800 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.85314e8 | −0.0204205 | ||||||||
\(701\) | −1.31006e10 | −1.43641 | −0.718206 | − | 0.695831i | \(-0.755036\pi\) | ||||
−0.718206 | + | 0.695831i | \(0.755036\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.04883e9 | −0.873754 | ||||||||
\(704\) | −3.48914e8 | −0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.01130e9 | 0.642913 | ||||||||
\(707\) | −2.84143e8 | −0.0302391 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.04601e10 | −1.10223 | −0.551116 | − | 0.834429i | \(-0.685798\pi\) | ||||
−0.551116 | + | 0.834429i | \(0.685798\pi\) | |||||||
\(710\) | −2.62471e9 | −0.275219 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.72593e9 | 0.490690 | ||||||||
\(713\) | −5.33428e9 | −0.551141 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.25143e8 | 0.0639600 | ||||||||
\(716\) | −2.04092e9 | −0.207793 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.33651e9 | −0.739697 | ||||||||
\(719\) | −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 | ||||||||
\(722\) | 3.60177e9 | 0.356152 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.37383e9 | 0.134539 | ||||||||
\(725\) | −3.96766e9 | −0.386680 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.47022e9 | −0.141910 | −0.0709550 | − | 0.997480i | \(-0.522605\pi\) | ||||
−0.0709550 | + | 0.997480i | \(0.522605\pi\) | |||||||
\(728\) | −9.91440e7 | −0.00952372 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.40897e9 | −0.324334 | ||||||||
\(731\) | 4.77105e9 | 0.451755 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.30989e8 | 0.0591777 | 0.0295888 | − | 0.999562i | \(-0.490580\pi\) | ||||
0.0295888 | + | 0.999562i | \(0.490580\pi\) | |||||||
\(734\) | 7.33148e9 | 0.684314 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.97457e9 | −0.182557 | ||||||||
\(737\) | −4.74324e9 | −0.436454 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.22368e9 | 0.658420 | 0.329210 | − | 0.944257i | \(-0.393218\pi\) | ||||
0.329210 | + | 0.944257i | \(0.393218\pi\) | |||||||
\(740\) | −2.55584e9 | −0.231858 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.12987e8 | −0.0371128 | ||||||||
\(743\) | −7.72789e9 | −0.691194 | −0.345597 | − | 0.938383i | \(-0.612324\pi\) | ||||
−0.345597 | + | 0.938383i | \(0.612324\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.70714e9 | −0.328467 | ||||||||
\(746\) | 1.24880e10 | 1.10130 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −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 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.12272e9 | −0.180340 | ||||||||
\(755\) | −4.28769e9 | −0.362584 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.94159e10 | 1.62676 | 0.813378 | − | 0.581735i | \(-0.197626\pi\) | ||||
0.813378 | + | 0.581735i | \(0.197626\pi\) | |||||||
\(758\) | −3.47989e8 | −0.0290217 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.12702e9 | −0.0931290 | ||||||||
\(761\) | −5.03230e8 | −0.0413924 | −0.0206962 | − | 0.999786i | \(-0.506588\pi\) | ||||
−0.0206962 | + | 0.999786i | \(0.506588\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.57760e7 | −0.00210078 | ||||||||
\(764\) | 3.43925e9 | 0.279021 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.56338e9 | 0.125679 | ||||||||
\(767\) | −5.91632e9 | −0.473443 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.87701e10 | −1.48842 | −0.744208 | − | 0.667948i | \(-0.767173\pi\) | ||||
−0.744208 | + | 0.667948i | \(0.767173\pi\) | |||||||
\(770\) | −4.79454e7 | −0.00378468 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.10144e10 | 0.861593 | ||||||||
\(773\) | −2.39166e10 | −1.86239 | −0.931196 | − | 0.364518i | \(-0.881234\pi\) | ||||
−0.931196 | + | 0.364518i | \(0.881234\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.94902e9 | 0.459081 | ||||||||
\(776\) | 7.06877e9 | 0.543035 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.28676e10 | −0.979649 | ||||||||
\(779\) | 1.15872e10 | 0.878210 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.17858e9 | 0.313870 | ||||||||
\(782\) | −3.31596e9 | −0.247962 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.36563e9 | −0.249436 | ||||||||
\(785\) | 6.97032e9 | 0.514291 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.09777e10 | 1.53408 | 0.767038 | − | 0.641602i | \(-0.221730\pi\) | ||||
0.767038 | + | 0.641602i | \(0.221730\pi\) | |||||||
\(788\) | 7.32964e9 | 0.533631 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.58618e9 | 0.114461 | ||||||||
\(791\) | 6.10991e7 | 0.00438952 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 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 | \(0.683107\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.68297e8 | 0.0602219 | ||||||||
\(800\) | 2.20212e9 | 0.152064 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.92551e9 | 0.405617 | ||||||||
\(803\) | 5.42711e9 | 0.369883 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.71332e8 | −0.0183322 | ||||||||
\(806\) | 3.18276e9 | 0.214107 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.37653e9 | 0.225180 | ||||||||
\(809\) | 1.19959e10 | 0.796548 | 0.398274 | − | 0.917266i | \(-0.369609\pi\) | ||||
0.398274 | + | 0.917266i | \(0.369609\pi\) | |||||||
\(810\) | 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 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.06893e9 | 0.264420 | ||||||||
\(815\) | −9.71640e8 | −0.0628715 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.46096e10 | −0.937262 | ||||||||
\(818\) | −1.09750e8 | −0.00701079 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.67943e9 | 0.233041 | ||||||||
\(821\) | 1.96308e10 | 1.23805 | 0.619024 | − | 0.785372i | \(-0.287528\pi\) | ||||
0.619024 | + | 0.785372i | \(0.287528\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.67601e9 | −0.167336 | −0.0836679 | − | 0.996494i | \(-0.526663\pi\) | ||||
−0.0836679 | + | 0.996494i | \(0.526663\pi\) | |||||||
\(824\) | 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 | \(0.509069\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.94467e10 | −1.79513 | −0.897565 | − | 0.440882i | \(-0.854666\pi\) | ||||
−0.897565 | + | 0.440882i | \(0.854666\pi\) | |||||||
\(830\) | −5.42811e9 | −0.329515 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.17815e9 | 0.0709199 | ||||||||
\(833\) | −5.65201e9 | −0.338802 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.20001e9 | −0.368544 | ||||||||
\(836\) | 1.79423e9 | 0.106208 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.56477e10 | 0.918536 | ||||||||
\(839\) | 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 | ||||||||
\(842\) | 1.84888e10 | 1.06737 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.11544e10 | −0.638628 | ||||||||
\(845\) | 4.44674e9 | 0.253538 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.63296e7 | 0.00431619 | ||||||||
\(848\) | 4.90761e9 | 0.276366 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.69810e9 | 0.206544 | ||||||||
\(851\) | 2.30268e10 | 1.28080 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.71708e10 | 0.947257 | 0.473628 | − | 0.880725i | \(-0.342944\pi\) | ||||
0.473628 | + | 0.880725i | \(0.342944\pi\) | |||||||
\(854\) | −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 | \(0.432869\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.68606e10 | 0.907606 | 0.453803 | − | 0.891102i | \(-0.350067\pi\) | ||||
0.453803 | + | 0.891102i | \(0.350067\pi\) | |||||||
\(860\) | −4.63916e9 | −0.248711 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.62817e10 | −0.865813 | ||||||||
\(863\) | 2.42922e10 | 1.28656 | 0.643278 | − | 0.765633i | \(-0.277574\pi\) | ||||
0.643278 | + | 0.765633i | \(0.277574\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.25404e10 | 0.658802 | ||||||||
\(866\) | −2.24822e10 | −1.17632 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.44102e8 | −0.0126693 | ||||||||
\(869\) | −2.52521e9 | −0.130535 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.60161e10 | 0.821283 | ||||||||
\(872\) | 3.06301e8 | 0.0156438 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.01539e10 | 0.514449 | ||||||||
\(875\) | 6.54379e8 | 0.0330218 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.67740e10 | 1.34034 | 0.670169 | − | 0.742209i | \(-0.266222\pi\) | ||||
0.670169 | + | 0.742209i | \(0.266222\pi\) | |||||||
\(878\) | −1.26580e10 | −0.631154 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.69744e8 | 0.0281832 | ||||||||
\(881\) | −1.10654e10 | −0.545197 | −0.272598 | − | 0.962128i | \(-0.587883\pi\) | ||||
−0.272598 | + | 0.962128i | \(0.587883\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.06264e10 | 1.00824 | 0.504118 | − | 0.863635i | \(-0.331818\pi\) | ||||
0.504118 | + | 0.863635i | \(0.331818\pi\) | |||||||
\(884\) | 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 | \(0.441284\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.31512e8 | −0.0396928 | ||||||||
\(890\) | −7.71701e9 | −0.366931 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 9.32672e9 | 0.439999 | ||||||||
\(893\) | −2.65884e9 | −0.124943 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.33264e9 | 0.155385 | ||||||||
\(896\) | −9.03580e7 | −0.00419651 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.44857e10 | 0.667534 | ||||||||
\(899\) | −5.22633e9 | −0.239904 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.24151e9 | 0.375379 | ||||||||
\(902\) | −5.85770e9 | −0.265769 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.26052e8 | −0.0326872 | ||||||||
\(905\) | −2.24334e9 | −0.100606 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.36091e10 | −1.49566 | −0.747828 | − | 0.663893i | \(-0.768903\pi\) | ||||
−0.747828 | + | 0.663893i | \(0.768903\pi\) | |||||||
\(908\) | 8.13454e9 | 0.360606 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.61893e8 | 0.00712170 | ||||||||
\(911\) | 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 | ||||||||
\(914\) | 6.91449e9 | 0.299536 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.30400e9 | −0.356987 | ||||||||
\(917\) | −1.82017e9 | −0.0779507 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.35993e10 | 1.85300 | 0.926499 | − | 0.376296i | \(-0.122803\pi\) | ||||
0.926499 | + | 0.376296i | \(0.122803\pi\) | |||||||
\(920\) | 3.22429e9 | 0.136514 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.88344e9 | 0.163177 | ||||||||
\(923\) | −1.41094e10 | −0.590614 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.56805e10 | −1.06686 | ||||||||
\(926\) | −1.48301e10 | −0.613768 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.93461e9 | −0.0794648 | ||||||||
\(929\) | 3.06911e10 | 1.25591 | 0.627954 | − | 0.778250i | \(-0.283892\pi\) | ||||
0.627954 | + | 0.778250i | \(0.283892\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.73072e10 | 0.702915 | ||||||||
\(932\) | 9.74143e9 | 0.394155 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.52954e8 | 0.0101584 | ||||||||
\(935\) | 9.56790e8 | 0.0382804 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.51153e9 | 0.139446 | 0.0697232 | − | 0.997566i | \(-0.477788\pi\) | ||||
0.0697232 | + | 0.997566i | \(0.477788\pi\) | |||||||
\(938\) | −1.22835e9 | −0.0485975 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.44293e8 | −0.0331547 | ||||||||
\(941\) | 1.84266e10 | 0.720911 | 0.360455 | − | 0.932776i | \(-0.382621\pi\) | ||||
0.360455 | + | 0.932776i | \(0.382621\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −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 | \(0.553771\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.83253e10 | −0.696015 | ||||||||
\(950\) | −1.13241e10 | −0.428519 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.51741e8 | −0.00569999 | ||||||||
\(953\) | −1.85304e10 | −0.693521 | −0.346761 | − | 0.937954i | \(-0.612718\pi\) | ||||
−0.346761 | + | 0.937954i | \(0.612718\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.61598e9 | −0.208648 | ||||||||
\(956\) | 1.55559e10 | 0.575827 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.49470e10 | −0.916725 | ||||||||
\(959\) | 3.29991e8 | 0.0120819 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.96764e10 | −0.715176 | ||||||||
\(962\) | −1.37392e10 | −0.497564 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.38139e9 | −0.157522 | ||||||||
\(965\) | −1.79856e10 | −0.644286 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.71498e10 | 1.67682 | 0.838412 | − | 0.545037i | \(-0.183484\pi\) | ||||
0.838412 | + | 0.545037i | \(0.183484\pi\) | |||||||
\(968\) | −9.07039e8 | −0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.15427e10 | −0.406073 | ||||||||
\(971\) | 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 | ||||||||
\(974\) | 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 | \(0.465334\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.22856e10 | 0.418462 | ||||||||
\(980\) | 5.49576e9 | 0.186525 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.64035e10 | −1.22674 | ||||||||
\(983\) | −4.47312e10 | −1.50201 | −0.751006 | − | 0.660295i | \(-0.770431\pi\) | ||||
−0.751006 | + | 0.660295i | \(0.770431\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.19686e10 | −0.399041 | ||||||||
\(986\) | −3.24885e9 | −0.107934 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −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 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.08212e9 | 0.0349482 | ||||||||
\(995\) | 3.55994e9 | 0.114567 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.52392e10 | −0.487001 | −0.243501 | − | 0.969901i | \(-0.578296\pi\) | ||||
−0.243501 | + | 0.969901i | \(0.578296\pi\) | |||||||
\(998\) | 5.00587e9 | 0.159413 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 198.8.a.f.1.2 | 2 | ||
3.2 | odd | 2 | 22.8.a.d.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 176.8.a.e.1.1 | 2 | |||
15.14 | odd | 2 | 550.8.a.d.1.1 | 2 | |||
33.32 | 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 | 3.2 | odd | 2 | ||
176.8.a.e.1.1 | 2 | 12.11 | even | 2 | |||
198.8.a.f.1.2 | 2 | 1.1 | even | 1 | trivial | ||
242.8.a.h.1.2 | 2 | 33.32 | even | 2 | |||
550.8.a.d.1.1 | 2 | 15.14 | odd | 2 |