Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,8,Mod(1,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, 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("531.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.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: | \(165.876448532\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} - 1493 x^{14} + 8791 x^{13} + 890490 x^{12} - 5107725 x^{11} - 269092298 x^{10} + 1488374176 x^{9} + 42885295136 x^{8} + \cdots - 23\!\cdots\!32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{5} \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(7.00808\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 531.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 7.00808 | 0.619433 | 0.309716 | − | 0.950829i | \(-0.399766\pi\) | ||||
0.309716 | + | 0.950829i | \(0.399766\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −78.8868 | −0.616303 | ||||||||
\(5\) | −449.079 | −1.60668 | −0.803338 | − | 0.595524i | \(-0.796944\pi\) | ||||
−0.803338 | + | 0.595524i | \(0.796944\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −271.717 | −0.299415 | −0.149708 | − | 0.988730i | \(-0.547833\pi\) | ||||
−0.149708 | + | 0.988730i | \(0.547833\pi\) | |||||||
\(8\) | −1449.88 | −1.00119 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3147.18 | −0.995227 | ||||||||
\(11\) | 3164.33 | 0.716816 | 0.358408 | − | 0.933565i | \(-0.383320\pi\) | ||||
0.358408 | + | 0.933565i | \(0.383320\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −9448.56 | −1.19279 | −0.596395 | − | 0.802691i | \(-0.703401\pi\) | ||||
−0.596395 | + | 0.802691i | \(0.703401\pi\) | |||||||
\(14\) | −1904.22 | −0.185468 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −63.3641 | −0.00386744 | ||||||||
\(17\) | 6793.30 | 0.335358 | 0.167679 | − | 0.985842i | \(-0.446373\pi\) | ||||
0.167679 | + | 0.985842i | \(0.446373\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 34097.6 | 1.14048 | 0.570239 | − | 0.821479i | \(-0.306851\pi\) | ||||
0.570239 | + | 0.821479i | \(0.306851\pi\) | |||||||
\(20\) | 35426.4 | 0.990199 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 22175.9 | 0.444019 | ||||||||
\(23\) | 31238.0 | 0.535348 | 0.267674 | − | 0.963510i | \(-0.413745\pi\) | ||||
0.267674 | + | 0.963510i | \(0.413745\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 123547. | 1.58141 | ||||||||
\(26\) | −66216.3 | −0.738853 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 21434.9 | 0.184531 | ||||||||
\(29\) | −82712.9 | −0.629767 | −0.314884 | − | 0.949130i | \(-0.601966\pi\) | ||||
−0.314884 | + | 0.949130i | \(0.601966\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 283828. | 1.71116 | 0.855578 | − | 0.517673i | \(-0.173202\pi\) | ||||
0.855578 | + | 0.517673i | \(0.173202\pi\) | |||||||
\(32\) | 185141. | 0.998795 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 47608.0 | 0.207732 | ||||||||
\(35\) | 122023. | 0.481063 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 26823.2 | 0.0870571 | 0.0435286 | − | 0.999052i | \(-0.486140\pi\) | ||||
0.0435286 | + | 0.999052i | \(0.486140\pi\) | |||||||
\(38\) | 238959. | 0.706449 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 651111. | 1.60859 | ||||||||
\(41\) | 19538.2 | 0.0442732 | 0.0221366 | − | 0.999755i | \(-0.492953\pi\) | ||||
0.0221366 | + | 0.999755i | \(0.492953\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −417223. | −0.800255 | −0.400128 | − | 0.916459i | \(-0.631034\pi\) | ||||
−0.400128 | + | 0.916459i | \(0.631034\pi\) | |||||||
\(44\) | −249624. | −0.441776 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 218919. | 0.331612 | ||||||||
\(47\) | 27684.6 | 0.0388952 | 0.0194476 | − | 0.999811i | \(-0.493809\pi\) | ||||
0.0194476 | + | 0.999811i | \(0.493809\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −749713. | −0.910351 | ||||||||
\(50\) | 865829. | 0.979574 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 745366. | 0.735120 | ||||||||
\(53\) | −29017.7 | −0.0267730 | −0.0133865 | − | 0.999910i | \(-0.504261\pi\) | ||||
−0.0133865 | + | 0.999910i | \(0.504261\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.42104e6 | −1.15169 | ||||||||
\(56\) | 393957. | 0.299772 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −579659. | −0.390099 | ||||||||
\(59\) | −205379. | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.53434e6 | 0.865499 | 0.432749 | − | 0.901514i | \(-0.357543\pi\) | ||||
0.432749 | + | 0.901514i | \(0.357543\pi\) | |||||||
\(62\) | 1.98909e6 | 1.05995 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.30559e6 | 0.622554 | ||||||||
\(65\) | 4.24315e6 | 1.91642 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.52949e6 | −1.02748 | −0.513738 | − | 0.857947i | \(-0.671740\pi\) | ||||
−0.513738 | + | 0.857947i | \(0.671740\pi\) | |||||||
\(68\) | −535901. | −0.206682 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 855144. | 0.297986 | ||||||||
\(71\) | 3.35724e6 | 1.11321 | 0.556606 | − | 0.830776i | \(-0.312103\pi\) | ||||
0.556606 | + | 0.830776i | \(0.312103\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.90625e6 | −0.573521 | −0.286761 | − | 0.958002i | \(-0.592578\pi\) | ||||
−0.286761 | + | 0.958002i | \(0.592578\pi\) | |||||||
\(74\) | 187979. | 0.0539260 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.68985e6 | −0.702880 | ||||||||
\(77\) | −859803. | −0.214626 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.26955e6 | 0.517899 | 0.258950 | − | 0.965891i | \(-0.416624\pi\) | ||||
0.258950 | + | 0.965891i | \(0.416624\pi\) | |||||||
\(80\) | 28455.5 | 0.00621372 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 136925. | 0.0274243 | ||||||||
\(83\) | 5.96358e6 | 1.14481 | 0.572405 | − | 0.819971i | \(-0.306011\pi\) | ||||
0.572405 | + | 0.819971i | \(0.306011\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.05073e6 | −0.538812 | ||||||||
\(86\) | −2.92393e6 | −0.495704 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.58790e6 | −0.717670 | ||||||||
\(89\) | −5.11791e6 | −0.769533 | −0.384767 | − | 0.923014i | \(-0.625718\pi\) | ||||
−0.384767 | + | 0.923014i | \(0.625718\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.56733e6 | 0.357139 | ||||||||
\(92\) | −2.46427e6 | −0.329937 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 194016. | 0.0240930 | ||||||||
\(95\) | −1.53125e7 | −1.83238 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −145042. | −0.0161359 | −0.00806793 | − | 0.999967i | \(-0.502568\pi\) | ||||
−0.00806793 | + | 0.999967i | \(0.502568\pi\) | |||||||
\(98\) | −5.25405e6 | −0.563901 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9.74625e6 | −0.974625 | ||||||||
\(101\) | −7.21193e6 | −0.696509 | −0.348254 | − | 0.937400i | \(-0.613225\pi\) | ||||
−0.348254 | + | 0.937400i | \(0.613225\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.50882e6 | 0.136052 | 0.0680262 | − | 0.997684i | \(-0.478330\pi\) | ||||
0.0680262 | + | 0.997684i | \(0.478330\pi\) | |||||||
\(104\) | 1.36993e7 | 1.19421 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −203359. | −0.0165841 | ||||||||
\(107\) | 1.20706e7 | 0.952545 | 0.476272 | − | 0.879298i | \(-0.341988\pi\) | ||||
0.476272 | + | 0.879298i | \(0.341988\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.99398e7 | −1.47479 | −0.737393 | − | 0.675464i | \(-0.763943\pi\) | ||||
−0.737393 | + | 0.675464i | \(0.763943\pi\) | |||||||
\(110\) | −9.95874e6 | −0.713395 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 17217.1 | 0.00115797 | ||||||||
\(113\) | 2.25861e7 | 1.47254 | 0.736269 | − | 0.676688i | \(-0.236586\pi\) | ||||
0.736269 | + | 0.676688i | \(0.236586\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.40284e7 | −0.860130 | ||||||||
\(116\) | 6.52495e6 | 0.388128 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.43931e6 | −0.0806433 | ||||||||
\(119\) | −1.84585e6 | −0.100411 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.47417e6 | −0.486175 | ||||||||
\(122\) | 1.07528e7 | 0.536118 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.23903e7 | −1.05459 | ||||||||
\(125\) | −2.03982e7 | −0.934129 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.83609e7 | −1.66179 | −0.830895 | − | 0.556429i | \(-0.812171\pi\) | ||||
−0.830895 | + | 0.556429i | \(0.812171\pi\) | |||||||
\(128\) | −1.45483e7 | −0.613165 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.97364e7 | 1.18710 | ||||||||
\(131\) | 2.06635e7 | 0.803070 | 0.401535 | − | 0.915844i | \(-0.368477\pi\) | ||||
0.401535 | + | 0.915844i | \(0.368477\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.26491e6 | −0.341476 | ||||||||
\(134\) | −1.77269e7 | −0.636452 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.84946e6 | −0.335758 | ||||||||
\(137\) | 2.08600e7 | 0.693095 | 0.346547 | − | 0.938033i | \(-0.387354\pi\) | ||||
0.346547 | + | 0.938033i | \(0.387354\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.87015e7 | −1.53812 | −0.769061 | − | 0.639176i | \(-0.779276\pi\) | ||||
−0.769061 | + | 0.639176i | \(0.779276\pi\) | |||||||
\(140\) | −9.62597e6 | −0.296481 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.35278e7 | 0.689560 | ||||||||
\(143\) | −2.98984e7 | −0.855011 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.71447e7 | 1.01183 | ||||||||
\(146\) | −1.33591e7 | −0.355258 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.11600e6 | −0.0536536 | ||||||||
\(149\) | −1.01955e7 | −0.252497 | −0.126249 | − | 0.991999i | \(-0.540294\pi\) | ||||
−0.126249 | + | 0.991999i | \(0.540294\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.94880e7 | 0.933354 | 0.466677 | − | 0.884428i | \(-0.345451\pi\) | ||||
0.466677 | + | 0.884428i | \(0.345451\pi\) | |||||||
\(152\) | −4.94375e7 | −1.14184 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.02557e6 | −0.132946 | ||||||||
\(155\) | −1.27461e8 | −2.74927 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.95090e7 | 1.02102 | 0.510511 | − | 0.859871i | \(-0.329456\pi\) | ||||
0.510511 | + | 0.859871i | \(0.329456\pi\) | |||||||
\(158\) | 1.59052e7 | 0.320804 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8.31428e7 | −1.60474 | ||||||||
\(161\) | −8.48791e6 | −0.160291 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.43101e7 | −1.34397 | −0.671987 | − | 0.740563i | \(-0.734559\pi\) | ||||
−0.671987 | + | 0.740563i | \(0.734559\pi\) | |||||||
\(164\) | −1.54131e6 | −0.0272857 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.17932e7 | 0.709133 | ||||||||
\(167\) | −2.90320e7 | −0.482358 | −0.241179 | − | 0.970481i | \(-0.577534\pi\) | ||||
−0.241179 | + | 0.970481i | \(0.577534\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.65267e7 | 0.422746 | ||||||||
\(170\) | −2.13798e7 | −0.333758 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.29134e7 | 0.493200 | ||||||||
\(173\) | −5.40154e7 | −0.793152 | −0.396576 | − | 0.918002i | \(-0.629802\pi\) | ||||
−0.396576 | + | 0.918002i | \(0.629802\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.35699e7 | −0.473497 | ||||||||
\(176\) | −200505. | −0.00277224 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.58667e7 | −0.476674 | ||||||||
\(179\) | 5.61319e7 | 0.731516 | 0.365758 | − | 0.930710i | \(-0.380810\pi\) | ||||
0.365758 | + | 0.930710i | \(0.380810\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.15020e7 | 0.520228 | 0.260114 | − | 0.965578i | \(-0.416240\pi\) | ||||
0.260114 | + | 0.965578i | \(0.416240\pi\) | |||||||
\(182\) | 1.79921e7 | 0.221224 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.52914e7 | −0.535986 | ||||||||
\(185\) | −1.20457e7 | −0.139873 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.14962e7 | 0.240390 | ||||||||
\(188\) | −2.18395e6 | −0.0239712 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.07312e8 | −1.13503 | ||||||||
\(191\) | 5.65111e7 | 0.586837 | 0.293418 | − | 0.955984i | \(-0.405207\pi\) | ||||
0.293418 | + | 0.955984i | \(0.405207\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.59119e8 | 1.59321 | 0.796604 | − | 0.604502i | \(-0.206628\pi\) | ||||
0.796604 | + | 0.604502i | \(0.206628\pi\) | |||||||
\(194\) | −1.01646e6 | −0.00999508 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.91424e7 | 0.561052 | ||||||||
\(197\) | −6.46721e7 | −0.602678 | −0.301339 | − | 0.953517i | \(-0.597434\pi\) | ||||
−0.301339 | + | 0.953517i | \(0.597434\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.88894e8 | −1.69915 | −0.849576 | − | 0.527467i | \(-0.823142\pi\) | ||||
−0.849576 | + | 0.527467i | \(0.823142\pi\) | |||||||
\(200\) | −1.79129e8 | −1.58329 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.05418e7 | −0.431440 | ||||||||
\(203\) | 2.24745e7 | 0.188562 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.77420e6 | −0.0711326 | ||||||||
\(206\) | 1.05739e7 | 0.0842754 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 598700. | 0.00461304 | ||||||||
\(209\) | 1.07896e8 | 0.817513 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.23127e7 | 0.603224 | 0.301612 | − | 0.953431i | \(-0.402475\pi\) | ||||
0.301612 | + | 0.953431i | \(0.402475\pi\) | |||||||
\(212\) | 2.28912e6 | 0.0165003 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.45917e7 | 0.590037 | ||||||||
\(215\) | 1.87366e8 | 1.28575 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.71210e7 | −0.512346 | ||||||||
\(218\) | −1.39740e8 | −0.913531 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.12101e8 | 0.709790 | ||||||||
\(221\) | −6.41868e7 | −0.400012 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.37252e8 | −0.828801 | −0.414400 | − | 0.910095i | \(-0.636009\pi\) | ||||
−0.414400 | + | 0.910095i | \(0.636009\pi\) | |||||||
\(224\) | −5.03058e7 | −0.299055 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.58285e8 | 0.912139 | ||||||||
\(227\) | 1.70002e8 | 0.964635 | 0.482317 | − | 0.875997i | \(-0.339795\pi\) | ||||
0.482317 | + | 0.875997i | \(0.339795\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.30825e8 | 1.27016 | 0.635082 | − | 0.772445i | \(-0.280966\pi\) | ||||
0.635082 | + | 0.772445i | \(0.280966\pi\) | |||||||
\(230\) | −9.83119e7 | −0.532793 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.19924e8 | 0.630518 | ||||||||
\(233\) | 1.24871e8 | 0.646719 | 0.323359 | − | 0.946276i | \(-0.395188\pi\) | ||||
0.323359 | + | 0.946276i | \(0.395188\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.24326e7 | −0.0624920 | ||||||||
\(236\) | 1.62017e7 | 0.0802358 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.29359e7 | −0.0621981 | ||||||||
\(239\) | 2.73260e8 | 1.29474 | 0.647371 | − | 0.762175i | \(-0.275868\pi\) | ||||
0.647371 | + | 0.762175i | \(0.275868\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.70017e8 | −1.24260 | −0.621301 | − | 0.783572i | \(-0.713396\pi\) | ||||
−0.621301 | + | 0.783572i | \(0.713396\pi\) | |||||||
\(242\) | −6.63957e7 | −0.301152 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.21039e8 | −0.533410 | ||||||||
\(245\) | 3.36681e8 | 1.46264 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.22173e8 | −1.36035 | ||||||||
\(248\) | −4.11517e8 | −1.71319 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.42952e8 | −0.578630 | ||||||||
\(251\) | −1.21031e7 | −0.0483103 | −0.0241551 | − | 0.999708i | \(-0.507690\pi\) | ||||
−0.0241551 | + | 0.999708i | \(0.507690\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.88475e7 | 0.383746 | ||||||||
\(254\) | −2.68836e8 | −1.02937 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.69071e8 | −1.00237 | ||||||||
\(257\) | −2.89004e8 | −1.06203 | −0.531017 | − | 0.847361i | \(-0.678190\pi\) | ||||
−0.531017 | + | 0.847361i | \(0.678190\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.28832e6 | −0.0260662 | ||||||||
\(260\) | −3.34729e8 | −1.18110 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.44811e8 | 0.497448 | ||||||||
\(263\) | 7.64989e6 | 0.0259304 | 0.0129652 | − | 0.999916i | \(-0.495873\pi\) | ||||
0.0129652 | + | 0.999916i | \(0.495873\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.30313e7 | 0.0430156 | ||||||||
\(266\) | −6.49293e7 | −0.211522 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.99544e8 | 0.633237 | ||||||||
\(269\) | −2.10692e8 | −0.659956 | −0.329978 | − | 0.943989i | \(-0.607041\pi\) | ||||
−0.329978 | + | 0.943989i | \(0.607041\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.98910e8 | −1.21754 | −0.608769 | − | 0.793348i | \(-0.708336\pi\) | ||||
−0.608769 | + | 0.793348i | \(0.708336\pi\) | |||||||
\(272\) | −430451. | −0.00129698 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.46189e8 | 0.429325 | ||||||||
\(275\) | 3.90945e8 | 1.13358 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.06287e8 | −1.43126 | −0.715628 | − | 0.698481i | \(-0.753859\pi\) | ||||
−0.715628 | + | 0.698481i | \(0.753859\pi\) | |||||||
\(278\) | −3.41304e8 | −0.952763 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.76918e8 | −0.481636 | ||||||||
\(281\) | 4.35455e8 | 1.17077 | 0.585384 | − | 0.810756i | \(-0.300944\pi\) | ||||
0.585384 | + | 0.810756i | \(0.300944\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.36270e7 | −0.0357394 | −0.0178697 | − | 0.999840i | \(-0.505688\pi\) | ||||
−0.0178697 | + | 0.999840i | \(0.505688\pi\) | |||||||
\(284\) | −2.64842e8 | −0.686076 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.09530e8 | −0.529622 | ||||||||
\(287\) | −5.30886e6 | −0.0132561 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.64190e8 | −0.887535 | ||||||||
\(290\) | 2.60313e8 | 0.626762 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.50378e8 | 0.353463 | ||||||||
\(293\) | 5.24778e8 | 1.21882 | 0.609409 | − | 0.792856i | \(-0.291407\pi\) | ||||
0.609409 | + | 0.792856i | \(0.291407\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.22315e7 | 0.209171 | ||||||||
\(296\) | −3.88904e7 | −0.0871608 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.14510e7 | −0.156405 | ||||||||
\(299\) | −2.95154e8 | −0.638558 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.13367e8 | 0.239609 | ||||||||
\(302\) | 2.76735e8 | 0.578150 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.16057e6 | −0.00441073 | ||||||||
\(305\) | −6.89039e8 | −1.39058 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.40106e8 | −1.06536 | −0.532678 | − | 0.846318i | \(-0.678814\pi\) | ||||
−0.532678 | + | 0.846318i | \(0.678814\pi\) | |||||||
\(308\) | 6.78271e7 | 0.132274 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.93260e8 | −1.70299 | ||||||||
\(311\) | 1.89139e8 | 0.356549 | 0.178275 | − | 0.983981i | \(-0.442948\pi\) | ||||
0.178275 | + | 0.983981i | \(0.442948\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.77137e8 | 1.06383 | 0.531917 | − | 0.846797i | \(-0.321472\pi\) | ||||
0.531917 | + | 0.846797i | \(0.321472\pi\) | |||||||
\(314\) | 3.46963e8 | 0.632454 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.79038e8 | −0.319183 | ||||||||
\(317\) | −1.18644e6 | −0.00209189 | −0.00104595 | − | 0.999999i | \(-0.500333\pi\) | ||||
−0.00104595 | + | 0.999999i | \(0.500333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.61731e8 | −0.451427 | ||||||||
\(320\) | −5.86314e8 | −1.00024 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.94840e7 | −0.0992897 | ||||||||
\(323\) | 2.31635e8 | 0.382469 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.16734e9 | −1.88628 | ||||||||
\(326\) | −5.20771e8 | −0.832502 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.83280e7 | −0.0443259 | ||||||||
\(329\) | −7.52238e6 | −0.0116458 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.08372e8 | −1.22522 | −0.612609 | − | 0.790386i | \(-0.709880\pi\) | ||||
−0.612609 | + | 0.790386i | \(0.709880\pi\) | |||||||
\(332\) | −4.70447e8 | −0.705550 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.03459e8 | −0.298788 | ||||||||
\(335\) | 1.13594e9 | 1.65082 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.85349e8 | 1.26011 | 0.630057 | − | 0.776549i | \(-0.283032\pi\) | ||||
0.630057 | + | 0.776549i | \(0.283032\pi\) | |||||||
\(338\) | 1.85901e8 | 0.261863 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.40662e8 | 0.332072 | ||||||||
\(341\) | 8.98127e8 | 1.22658 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.27481e8 | 0.571988 | ||||||||
\(344\) | 6.04923e8 | 0.801208 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.78544e8 | −0.491304 | ||||||||
\(347\) | −7.51351e8 | −0.965361 | −0.482680 | − | 0.875797i | \(-0.660337\pi\) | ||||
−0.482680 | + | 0.875797i | \(0.660337\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.06457e8 | 0.637755 | 0.318877 | − | 0.947796i | \(-0.396694\pi\) | ||||
0.318877 | + | 0.947796i | \(0.396694\pi\) | |||||||
\(350\) | −2.35261e8 | −0.293299 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.85846e8 | 0.715953 | ||||||||
\(353\) | −7.31006e8 | −0.884523 | −0.442262 | − | 0.896886i | \(-0.645824\pi\) | ||||
−0.442262 | + | 0.896886i | \(0.645824\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.50767e9 | −1.78857 | ||||||||
\(356\) | 4.03735e8 | 0.474266 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.93377e8 | 0.453125 | ||||||||
\(359\) | −1.09721e9 | −1.25158 | −0.625790 | − | 0.779992i | \(-0.715223\pi\) | ||||
−0.625790 | + | 0.779992i | \(0.715223\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.68777e8 | 0.300688 | ||||||||
\(362\) | 2.90849e8 | 0.322246 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.02529e8 | −0.220106 | ||||||||
\(365\) | 8.56057e8 | 0.921462 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.58816e8 | 0.273313 | 0.136657 | − | 0.990618i | \(-0.456364\pi\) | ||||
0.136657 | + | 0.990618i | \(0.456364\pi\) | |||||||
\(368\) | −1.97937e6 | −0.00207043 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.44175e7 | −0.0866416 | ||||||||
\(371\) | 7.88461e6 | 0.00801626 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.37810e9 | 1.37499 | 0.687497 | − | 0.726187i | \(-0.258709\pi\) | ||||
0.687497 | + | 0.726187i | \(0.258709\pi\) | |||||||
\(374\) | 1.50647e8 | 0.148906 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.01394e7 | −0.0389415 | ||||||||
\(377\) | 7.81517e8 | 0.751180 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.56880e8 | −0.148024 | −0.0740119 | − | 0.997257i | \(-0.523580\pi\) | ||||
−0.0740119 | + | 0.997257i | \(0.523580\pi\) | |||||||
\(380\) | 1.20796e9 | 1.12930 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.96035e8 | 0.363506 | ||||||||
\(383\) | 8.83458e8 | 0.803508 | 0.401754 | − | 0.915748i | \(-0.368401\pi\) | ||||
0.401754 | + | 0.915748i | \(0.368401\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.86120e8 | 0.344834 | ||||||||
\(386\) | 1.11512e9 | 0.986885 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.14419e7 | 0.00994458 | ||||||||
\(389\) | −9.53014e8 | −0.820873 | −0.410436 | − | 0.911889i | \(-0.634624\pi\) | ||||
−0.410436 | + | 0.911889i | \(0.634624\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.12209e8 | 0.179534 | ||||||||
\(392\) | 1.08699e9 | 0.911435 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.53227e8 | −0.373318 | ||||||||
\(395\) | −1.01921e9 | −0.832095 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.30889e9 | −1.85198 | −0.925992 | − | 0.377544i | \(-0.876769\pi\) | ||||
−0.925992 | + | 0.377544i | \(0.876769\pi\) | |||||||
\(398\) | −1.32378e9 | −1.05251 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.82846e6 | −0.00611599 | ||||||||
\(401\) | −1.15700e9 | −0.896039 | −0.448019 | − | 0.894024i | \(-0.647870\pi\) | ||||
−0.448019 | + | 0.894024i | \(0.647870\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.68177e9 | −2.04105 | ||||||||
\(404\) | 5.68926e8 | 0.429260 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.57503e8 | 0.116801 | ||||||||
\(407\) | 8.48775e7 | 0.0624040 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.94341e9 | 1.40454 | 0.702269 | − | 0.711911i | \(-0.252170\pi\) | ||||
0.702269 | + | 0.711911i | \(0.252170\pi\) | |||||||
\(410\) | −6.14903e7 | −0.0440619 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.19026e8 | −0.0838496 | ||||||||
\(413\) | 5.58050e7 | 0.0389805 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.67812e9 | −1.83934 | ||||||||
\(416\) | −1.74931e9 | −1.19135 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.56146e8 | 0.506394 | ||||||||
\(419\) | −2.16975e9 | −1.44099 | −0.720495 | − | 0.693460i | \(-0.756085\pi\) | ||||
−0.720495 | + | 0.693460i | \(0.756085\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.64386e8 | −0.433943 | −0.216972 | − | 0.976178i | \(-0.569618\pi\) | ||||
−0.216972 | + | 0.976178i | \(0.569618\pi\) | |||||||
\(422\) | 5.76854e8 | 0.373657 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.20722e7 | 0.0268049 | ||||||||
\(425\) | 8.39293e8 | 0.530338 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.16906e8 | −0.259144 | ||||||||
\(428\) | −9.52210e8 | −0.587056 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.31308e9 | 0.796436 | ||||||||
\(431\) | 2.35268e9 | 1.41545 | 0.707723 | − | 0.706490i | \(-0.249723\pi\) | ||||
0.707723 | + | 0.706490i | \(0.249723\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.41032e8 | 0.0834852 | 0.0417426 | − | 0.999128i | \(-0.486709\pi\) | ||||
0.0417426 | + | 0.999128i | \(0.486709\pi\) | |||||||
\(434\) | −5.40470e8 | −0.317364 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.57299e9 | 0.908915 | ||||||||
\(437\) | 1.06514e9 | 0.610552 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.83909e9 | −1.60159 | −0.800797 | − | 0.598935i | \(-0.795591\pi\) | ||||
−0.800797 | + | 0.598935i | \(0.795591\pi\) | |||||||
\(440\) | 2.06033e9 | 1.15306 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.49827e8 | −0.247781 | ||||||||
\(443\) | 3.44158e9 | 1.88081 | 0.940405 | − | 0.340058i | \(-0.110447\pi\) | ||||
0.940405 | + | 0.340058i | \(0.110447\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.29835e9 | 1.23639 | ||||||||
\(446\) | −9.61870e8 | −0.513386 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.54751e8 | −0.186402 | ||||||||
\(449\) | −8.59881e8 | −0.448308 | −0.224154 | − | 0.974554i | \(-0.571962\pi\) | ||||
−0.224154 | + | 0.974554i | \(0.571962\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.18253e7 | 0.0317357 | ||||||||
\(452\) | −1.78175e9 | −0.907530 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.19139e9 | 0.597526 | ||||||||
\(455\) | −1.15294e9 | −0.573807 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.71007e9 | −0.838124 | −0.419062 | − | 0.907958i | \(-0.637641\pi\) | ||||
−0.419062 | + | 0.907958i | \(0.637641\pi\) | |||||||
\(458\) | 1.61764e9 | 0.786781 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.10665e9 | 0.530101 | ||||||||
\(461\) | −2.48943e9 | −1.18344 | −0.591720 | − | 0.806143i | \(-0.701551\pi\) | ||||
−0.591720 | + | 0.806143i | \(0.701551\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.91198e9 | 1.36350 | 0.681749 | − | 0.731587i | \(-0.261220\pi\) | ||||
0.681749 | + | 0.731587i | \(0.261220\pi\) | |||||||
\(464\) | 5.24103e6 | 0.00243559 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.75105e8 | 0.400599 | ||||||||
\(467\) | −3.22506e9 | −1.46531 | −0.732654 | − | 0.680601i | \(-0.761719\pi\) | ||||
−0.732654 | + | 0.680601i | \(0.761719\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.87307e8 | 0.307642 | ||||||||
\(470\) | −8.71286e7 | −0.0387096 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.97775e8 | 0.130344 | ||||||||
\(473\) | −1.32023e9 | −0.573636 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.21267e9 | 1.80356 | ||||||||
\(476\) | 1.45614e8 | 0.0618839 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.91503e9 | 0.802006 | ||||||||
\(479\) | −3.79747e9 | −1.57877 | −0.789386 | − | 0.613897i | \(-0.789601\pi\) | ||||
−0.789386 | + | 0.613897i | \(0.789601\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.53440e8 | −0.103841 | ||||||||
\(482\) | −1.89230e9 | −0.769709 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.47387e8 | 0.299631 | ||||||||
\(485\) | 6.51353e7 | 0.0259251 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.70012e9 | 1.05933 | 0.529665 | − | 0.848207i | \(-0.322318\pi\) | ||||
0.529665 | + | 0.848207i | \(0.322318\pi\) | |||||||
\(488\) | −2.22460e9 | −0.866530 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.35948e9 | 0.906006 | ||||||||
\(491\) | −1.96974e9 | −0.750971 | −0.375485 | − | 0.926828i | \(-0.622524\pi\) | ||||
−0.375485 | + | 0.926828i | \(0.622524\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.61893e8 | −0.211198 | ||||||||
\(494\) | −2.25782e9 | −0.842645 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.79845e7 | −0.00661779 | ||||||||
\(497\) | −9.12219e8 | −0.333313 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.68650e8 | 0.240906 | 0.120453 | − | 0.992719i | \(-0.461565\pi\) | ||||
0.120453 | + | 0.992719i | \(0.461565\pi\) | |||||||
\(500\) | 1.60915e9 | 0.575707 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8.48197e7 | −0.0299250 | ||||||||
\(503\) | −8.13925e8 | −0.285165 | −0.142583 | − | 0.989783i | \(-0.545541\pi\) | ||||
−0.142583 | + | 0.989783i | \(0.545541\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.23873e9 | 1.11906 | ||||||||
\(506\) | 6.92732e8 | 0.237705 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.02617e9 | 1.02417 | ||||||||
\(509\) | −3.90482e9 | −1.31247 | −0.656235 | − | 0.754557i | \(-0.727852\pi\) | ||||
−0.656235 | + | 0.754557i | \(0.727852\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.17960e8 | 0.171721 | ||||||||
\(512\) | −2.34907e7 | −0.00773483 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.02537e9 | −0.657859 | ||||||||
\(515\) | −6.77579e8 | −0.218592 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.76033e7 | 0.0278807 | ||||||||
\(518\) | −5.10771e7 | −0.0161463 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.15206e9 | −1.91871 | ||||||||
\(521\) | 1.40413e9 | 0.434984 | 0.217492 | − | 0.976062i | \(-0.430212\pi\) | ||||
0.217492 | + | 0.976062i | \(0.430212\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.53390e8 | 0.169151 | 0.0845756 | − | 0.996417i | \(-0.473047\pi\) | ||||
0.0845756 | + | 0.996417i | \(0.473047\pi\) | |||||||
\(524\) | −1.63007e9 | −0.494935 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.36110e7 | 0.0160622 | ||||||||
\(527\) | 1.92813e9 | 0.573851 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.42901e9 | −0.713402 | ||||||||
\(530\) | 9.13241e7 | 0.0266453 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.30879e8 | 0.210453 | ||||||||
\(533\) | −1.84608e8 | −0.0528086 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.42065e9 | −1.53043 | ||||||||
\(536\) | 3.66746e9 | 1.02870 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.47655e9 | −0.408798 | ||||||||
\(539\) | −2.37234e9 | −0.652554 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.74177e8 | 0.0744459 | 0.0372229 | − | 0.999307i | \(-0.488149\pi\) | ||||
0.0372229 | + | 0.999307i | \(0.488149\pi\) | |||||||
\(542\) | −2.79559e9 | −0.754183 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.25771e9 | 0.334954 | ||||||||
\(545\) | 8.95457e9 | 2.36950 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.89224e8 | 0.101682 | 0.0508410 | − | 0.998707i | \(-0.483810\pi\) | ||||
0.0508410 | + | 0.998707i | \(0.483810\pi\) | |||||||
\(548\) | −1.64558e9 | −0.427156 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.73977e9 | 0.702174 | ||||||||
\(551\) | −2.82031e9 | −0.718236 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.16676e8 | −0.155067 | ||||||||
\(554\) | −3.54810e9 | −0.886567 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.84191e9 | 0.947949 | ||||||||
\(557\) | 1.89599e9 | 0.464883 | 0.232441 | − | 0.972610i | \(-0.425329\pi\) | ||||
0.232441 | + | 0.972610i | \(0.425329\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.94215e9 | 0.954536 | ||||||||
\(560\) | −7.73185e6 | −0.00186048 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.05170e9 | 0.725212 | ||||||||
\(563\) | 5.24086e9 | 1.23772 | 0.618861 | − | 0.785501i | \(-0.287594\pi\) | ||||
0.618861 | + | 0.785501i | \(0.287594\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.01430e10 | −2.36589 | ||||||||
\(566\) | −9.54991e7 | −0.0221382 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.86759e9 | −1.11454 | ||||||||
\(569\) | 6.24592e9 | 1.42136 | 0.710678 | − | 0.703517i | \(-0.248388\pi\) | ||||
0.710678 | + | 0.703517i | \(0.248388\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.35962e9 | −0.979991 | −0.489996 | − | 0.871725i | \(-0.663002\pi\) | ||||
−0.489996 | + | 0.871725i | \(0.663002\pi\) | |||||||
\(572\) | 2.35859e9 | 0.526946 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.72049e7 | −0.00821124 | ||||||||
\(575\) | 3.85937e9 | 0.846602 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.25822e9 | 0.272672 | 0.136336 | − | 0.990663i | \(-0.456467\pi\) | ||||
0.136336 | + | 0.990663i | \(0.456467\pi\) | |||||||
\(578\) | −2.55227e9 | −0.549768 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.93022e9 | −0.623595 | ||||||||
\(581\) | −1.62041e9 | −0.342773 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.18217e7 | −0.0191914 | ||||||||
\(584\) | 2.76383e9 | 0.574204 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.67768e9 | 0.754975 | ||||||||
\(587\) | 7.19197e9 | 1.46762 | 0.733812 | − | 0.679353i | \(-0.237739\pi\) | ||||
0.733812 | + | 0.679353i | \(0.237739\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.67787e9 | 1.95154 | ||||||||
\(590\) | 6.46366e8 | 0.129568 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.69963e6 | −0.000336688 0 | ||||||||
\(593\) | 8.65682e9 | 1.70477 | 0.852387 | − | 0.522911i | \(-0.175154\pi\) | ||||
0.852387 | + | 0.522911i | \(0.175154\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.28935e8 | 0.161329 | ||||||||
\(596\) | 8.04291e8 | 0.155615 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.06847e9 | −0.395543 | ||||||||
\(599\) | −5.85691e9 | −1.11346 | −0.556730 | − | 0.830693i | \(-0.687944\pi\) | ||||
−0.556730 | + | 0.830693i | \(0.687944\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.94489e9 | 1.11708 | 0.558539 | − | 0.829478i | \(-0.311362\pi\) | ||||
0.558539 | + | 0.829478i | \(0.311362\pi\) | |||||||
\(602\) | 7.94482e8 | 0.148421 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.11509e9 | −0.575229 | ||||||||
\(605\) | 4.25465e9 | 0.781125 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.31720e9 | 1.32796 | 0.663979 | − | 0.747751i | \(-0.268866\pi\) | ||||
0.663979 | + | 0.747751i | \(0.268866\pi\) | |||||||
\(608\) | 6.31285e9 | 1.13910 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.82884e9 | −0.861368 | ||||||||
\(611\) | −2.61580e8 | −0.0463938 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.17131e8 | 0.143278 | 0.0716391 | − | 0.997431i | \(-0.477177\pi\) | ||||
0.0716391 | + | 0.997431i | \(0.477177\pi\) | |||||||
\(614\) | −3.78511e9 | −0.659917 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.24661e9 | 0.214881 | ||||||||
\(617\) | 4.81332e9 | 0.824985 | 0.412493 | − | 0.910961i | \(-0.364658\pi\) | ||||
0.412493 | + | 0.910961i | \(0.364658\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.14223e8 | −0.0701968 | −0.0350984 | − | 0.999384i | \(-0.511174\pi\) | ||||
−0.0350984 | + | 0.999384i | \(0.511174\pi\) | |||||||
\(620\) | 1.00550e10 | 1.69439 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.32550e9 | 0.220858 | ||||||||
\(623\) | 1.39062e9 | 0.230410 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.91719e8 | −0.0805632 | ||||||||
\(626\) | 4.04462e9 | 0.658973 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.90560e9 | −0.629259 | ||||||||
\(629\) | 1.82218e8 | 0.0291953 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.20305e9 | −0.349078 | −0.174539 | − | 0.984650i | \(-0.555843\pi\) | ||||
−0.174539 | + | 0.984650i | \(0.555843\pi\) | |||||||
\(632\) | −3.29058e9 | −0.518516 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.31469e6 | −0.00129579 | ||||||||
\(635\) | 1.72271e10 | 2.66996 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.08370e9 | 1.08586 | ||||||||
\(638\) | −1.83423e9 | −0.279629 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.53334e9 | 0.985157 | ||||||||
\(641\) | −4.40972e9 | −0.661315 | −0.330657 | − | 0.943751i | \(-0.607270\pi\) | ||||
−0.330657 | + | 0.943751i | \(0.607270\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.75195e9 | 1.29827 | 0.649137 | − | 0.760671i | \(-0.275130\pi\) | ||||
0.649137 | + | 0.760671i | \(0.275130\pi\) | |||||||
\(644\) | 6.69584e8 | 0.0987881 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.62332e9 | 0.236914 | ||||||||
\(647\) | −4.86345e9 | −0.705959 | −0.352979 | − | 0.935631i | \(-0.614831\pi\) | ||||
−0.352979 | + | 0.935631i | \(0.614831\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.49888e8 | −0.0933215 | ||||||||
\(650\) | −8.18084e9 | −1.16843 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.86208e9 | 0.828296 | ||||||||
\(653\) | 9.35709e9 | 1.31506 | 0.657529 | − | 0.753429i | \(-0.271602\pi\) | ||||
0.657529 | + | 0.753429i | \(0.271602\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.27953e9 | −1.29027 | ||||||||
\(656\) | −1.23802e6 | −0.000171224 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.27175e7 | −0.00721380 | ||||||||
\(659\) | −5.87424e9 | −0.799562 | −0.399781 | − | 0.916611i | \(-0.630914\pi\) | ||||
−0.399781 | + | 0.916611i | \(0.630914\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.45812e8 | 0.0600408 | 0.0300204 | − | 0.999549i | \(-0.490443\pi\) | ||||
0.0300204 | + | 0.999549i | \(0.490443\pi\) | |||||||
\(662\) | −5.66514e9 | −0.758940 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.64647e9 | −1.14617 | ||||||||
\(665\) | 4.16068e9 | 0.548641 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.58379e9 | −0.337145 | ||||||||
\(668\) | 2.29024e9 | 0.297279 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.96078e9 | 1.02257 | ||||||||
\(671\) | 4.85515e9 | 0.620404 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.90168e9 | 0.366942 | 0.183471 | − | 0.983025i | \(-0.441267\pi\) | ||||
0.183471 | + | 0.983025i | \(0.441267\pi\) | |||||||
\(674\) | 6.20460e9 | 0.780556 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.09261e9 | −0.260540 | ||||||||
\(677\) | −8.77680e9 | −1.08712 | −0.543558 | − | 0.839372i | \(-0.682923\pi\) | ||||
−0.543558 | + | 0.839372i | \(0.682923\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.94103e7 | 0.00483132 | ||||||||
\(680\) | 4.42319e9 | 0.539454 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.29415e9 | 0.759787 | ||||||||
\(683\) | −6.96062e9 | −0.835940 | −0.417970 | − | 0.908461i | \(-0.637258\pi\) | ||||
−0.417970 | + | 0.908461i | \(0.637258\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.36780e9 | −1.11358 | ||||||||
\(686\) | 2.99582e9 | 0.354308 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.64370e7 | 0.00309494 | ||||||||
\(689\) | 2.74176e8 | 0.0319346 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.57378e8 | −0.0642653 | −0.0321326 | − | 0.999484i | \(-0.510230\pi\) | ||||
−0.0321326 | + | 0.999484i | \(0.510230\pi\) | |||||||
\(692\) | 4.26110e9 | 0.488822 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.26553e9 | −0.597976 | ||||||||
\(695\) | 2.18708e10 | 2.47126 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.32729e8 | 0.0148474 | ||||||||
\(698\) | 3.54929e9 | 0.395046 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.64822e9 | 0.291817 | ||||||||
\(701\) | −1.27904e10 | −1.40240 | −0.701201 | − | 0.712963i | \(-0.747353\pi\) | ||||
−0.701201 | + | 0.712963i | \(0.747353\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.14607e8 | 0.0992867 | ||||||||
\(704\) | 4.13132e9 | 0.446257 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.12295e9 | −0.547903 | ||||||||
\(707\) | 1.95960e9 | 0.208545 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.68769e10 | −1.77841 | −0.889205 | − | 0.457508i | \(-0.848742\pi\) | ||||
−0.889205 | + | 0.457508i | \(0.848742\pi\) | |||||||
\(710\) | −1.05659e10 | −1.10790 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.42035e9 | 0.770450 | ||||||||
\(713\) | 8.86624e9 | 0.916065 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.34267e10 | 1.37372 | ||||||||
\(716\) | −4.42806e9 | −0.450836 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.68933e9 | −0.775270 | ||||||||
\(719\) | −1.65145e10 | −1.65697 | −0.828484 | − | 0.560013i | \(-0.810796\pi\) | ||||
−0.828484 | + | 0.560013i | \(0.810796\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.09972e8 | −0.0407362 | ||||||||
\(722\) | 1.88361e9 | 0.186256 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.27396e9 | −0.320618 | ||||||||
\(725\) | −1.02190e10 | −0.995917 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.21987e10 | 1.17745 | 0.588727 | − | 0.808332i | \(-0.299629\pi\) | ||||
0.588727 | + | 0.808332i | \(0.299629\pi\) | |||||||
\(728\) | −3.72233e9 | −0.357565 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5.99932e9 | 0.570784 | ||||||||
\(731\) | −2.83432e9 | −0.268372 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.19756e9 | −0.862598 | −0.431299 | − | 0.902209i | \(-0.641945\pi\) | ||||
−0.431299 | + | 0.902209i | \(0.641945\pi\) | |||||||
\(734\) | 1.81381e9 | 0.169299 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.78343e9 | 0.534703 | ||||||||
\(737\) | −8.00416e9 | −0.736511 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.94615e10 | −1.77386 | −0.886932 | − | 0.461900i | \(-0.847168\pi\) | ||||
−0.886932 | + | 0.461900i | \(0.847168\pi\) | |||||||
\(740\) | 9.50250e8 | 0.0862039 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.52560e7 | 0.00496553 | ||||||||
\(743\) | −1.39586e10 | −1.24848 | −0.624238 | − | 0.781235i | \(-0.714590\pi\) | ||||
−0.624238 | + | 0.781235i | \(0.714590\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.57859e9 | 0.405681 | ||||||||
\(746\) | 9.65786e9 | 0.851717 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.69577e9 | −0.148153 | ||||||||
\(749\) | −3.27979e9 | −0.285206 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.03865e9 | −0.778688 | −0.389344 | − | 0.921092i | \(-0.627298\pi\) | ||||
−0.389344 | + | 0.921092i | \(0.627298\pi\) | |||||||
\(752\) | −1.75421e6 | −0.000150425 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.47694e9 | 0.465305 | ||||||||
\(755\) | −1.77333e10 | −1.49960 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.80250e9 | 0.402376 | 0.201188 | − | 0.979553i | \(-0.435520\pi\) | ||||
0.201188 | + | 0.979553i | \(0.435520\pi\) | |||||||
\(758\) | −1.09943e9 | −0.0916908 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.22013e10 | 1.83456 | ||||||||
\(761\) | 1.41275e10 | 1.16203 | 0.581015 | − | 0.813893i | \(-0.302656\pi\) | ||||
0.581015 | + | 0.813893i | \(0.302656\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.41800e9 | 0.441573 | ||||||||
\(764\) | −4.45798e9 | −0.361669 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.19135e9 | 0.497719 | ||||||||
\(767\) | 1.94054e9 | 0.155288 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.40261e10 | 1.11223 | 0.556113 | − | 0.831106i | \(-0.312292\pi\) | ||||
0.556113 | + | 0.831106i | \(0.312292\pi\) | |||||||
\(770\) | 2.70596e9 | 0.213601 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.25524e10 | −0.981899 | ||||||||
\(773\) | −2.02962e8 | −0.0158047 | −0.00790236 | − | 0.999969i | \(-0.502515\pi\) | ||||
−0.00790236 | + | 0.999969i | \(0.502515\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.50662e10 | 2.70603 | ||||||||
\(776\) | 2.10293e8 | 0.0161551 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.67880e9 | −0.508475 | ||||||||
\(779\) | 6.66206e8 | 0.0504926 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.06234e10 | 0.797969 | ||||||||
\(782\) | 1.48718e9 | 0.111209 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.75049e7 | 0.00352073 | ||||||||
\(785\) | −2.22335e10 | −1.64045 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.88769e9 | 0.649946 | 0.324973 | − | 0.945723i | \(-0.394645\pi\) | ||||
0.324973 | + | 0.945723i | \(0.394645\pi\) | |||||||
\(788\) | 5.10178e9 | 0.371432 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7.14270e9 | −0.515427 | ||||||||
\(791\) | −6.13703e9 | −0.440901 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.44973e10 | −1.03236 | ||||||||
\(794\) | −1.61809e10 | −1.14718 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.49012e10 | 1.04719 | ||||||||
\(797\) | 9.59859e9 | 0.671589 | 0.335794 | − | 0.941935i | \(-0.390995\pi\) | ||||
0.335794 | + | 0.941935i | \(0.390995\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.88070e8 | 0.0130438 | ||||||||
\(800\) | 2.28736e10 | 1.57950 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.10833e9 | −0.555036 | ||||||||
\(803\) | −6.03200e9 | −0.411109 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.81174e9 | 0.257536 | ||||||||
\(806\) | −1.87940e10 | −1.26429 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.04564e10 | 0.697338 | ||||||||
\(809\) | −1.06933e10 | −0.710054 | −0.355027 | − | 0.934856i | \(-0.615528\pi\) | ||||
−0.355027 | + | 0.934856i | \(0.615528\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.87262e10 | −1.23275 | −0.616376 | − | 0.787452i | \(-0.711400\pi\) | ||||
−0.616376 | + | 0.787452i | \(0.711400\pi\) | |||||||
\(812\) | −1.77294e9 | −0.116211 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.94828e8 | 0.0386551 | ||||||||
\(815\) | 3.33711e10 | 2.15933 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.42263e10 | −0.912673 | ||||||||
\(818\) | 1.36196e10 | 0.870017 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.92168e8 | 0.0438393 | ||||||||
\(821\) | 1.83953e10 | 1.16013 | 0.580065 | − | 0.814570i | \(-0.303027\pi\) | ||||
0.580065 | + | 0.814570i | \(0.303027\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.29971e9 | −0.393932 | −0.196966 | − | 0.980410i | \(-0.563109\pi\) | ||||
−0.196966 | + | 0.980410i | \(0.563109\pi\) | |||||||
\(824\) | −2.18760e9 | −0.136215 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.91086e8 | 0.0241458 | ||||||||
\(827\) | 1.00387e10 | 0.617175 | 0.308587 | − | 0.951196i | \(-0.400144\pi\) | ||||
0.308587 | + | 0.951196i | \(0.400144\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.76027e8 | 0.0168271 | 0.00841357 | − | 0.999965i | \(-0.497322\pi\) | ||||
0.00841357 | + | 0.999965i | \(0.497322\pi\) | |||||||
\(830\) | −1.87685e10 | −1.13935 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.23359e10 | −0.742576 | ||||||||
\(833\) | −5.09302e9 | −0.305294 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.30377e10 | 0.774992 | ||||||||
\(836\) | −8.51159e9 | −0.503835 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.52058e10 | −0.892597 | ||||||||
\(839\) | −2.00764e10 | −1.17360 | −0.586799 | − | 0.809733i | \(-0.699612\pi\) | ||||
−0.586799 | + | 0.809733i | \(0.699612\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.04085e10 | −0.603393 | ||||||||
\(842\) | −4.65607e9 | −0.268799 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.49339e9 | −0.371769 | ||||||||
\(845\) | −1.19126e10 | −0.679216 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.57429e9 | 0.145568 | ||||||||
\(848\) | 1.83868e6 | 0.000103543 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5.88183e9 | 0.328508 | ||||||||
\(851\) | 8.37904e8 | 0.0466059 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.43953e9 | 0.410415 | 0.205208 | − | 0.978718i | \(-0.434213\pi\) | ||||
0.205208 | + | 0.978718i | \(0.434213\pi\) | |||||||
\(854\) | −2.92171e9 | −0.160522 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.75009e10 | −0.953679 | ||||||||
\(857\) | 2.02954e10 | 1.10145 | 0.550726 | − | 0.834686i | \(-0.314351\pi\) | ||||
0.550726 | + | 0.834686i | \(0.314351\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.59155e10 | 0.856728 | 0.428364 | − | 0.903606i | \(-0.359090\pi\) | ||||
0.428364 | + | 0.903606i | \(0.359090\pi\) | |||||||
\(860\) | −1.47807e10 | −0.792412 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.64878e10 | 0.876774 | ||||||||
\(863\) | −8.64458e9 | −0.457832 | −0.228916 | − | 0.973446i | \(-0.573518\pi\) | ||||
−0.228916 | + | 0.973446i | \(0.573518\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.42572e10 | 1.27434 | ||||||||
\(866\) | 9.88363e8 | 0.0517135 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.08383e9 | 0.315761 | ||||||||
\(869\) | 7.18161e9 | 0.371238 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.39001e10 | 1.22556 | ||||||||
\(872\) | 2.89104e10 | 1.47654 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7.46461e9 | 0.378196 | ||||||||
\(875\) | 5.54254e9 | 0.279692 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.61467e10 | −1.80955 | −0.904775 | − | 0.425890i | \(-0.859961\pi\) | ||||
−0.904775 | + | 0.425890i | \(0.859961\pi\) | |||||||
\(878\) | −1.98965e10 | −0.992080 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 9.00427e7 | 0.00445409 | ||||||||
\(881\) | 2.55814e10 | 1.26040 | 0.630199 | − | 0.776433i | \(-0.282973\pi\) | ||||
0.630199 | + | 0.776433i | \(0.282973\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.64985e10 | −1.78407 | −0.892036 | − | 0.451964i | \(-0.850724\pi\) | ||||
−0.892036 | + | 0.451964i | \(0.850724\pi\) | |||||||
\(884\) | 5.06349e9 | 0.246529 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.41189e10 | 1.16503 | ||||||||
\(887\) | −1.11780e10 | −0.537812 | −0.268906 | − | 0.963166i | \(-0.586662\pi\) | ||||
−0.268906 | + | 0.963166i | \(0.586662\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.04233e10 | 0.497565 | ||||||||
\(890\) | 1.61070e10 | 0.765860 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.08273e10 | 0.510792 | ||||||||
\(893\) | 9.43980e8 | 0.0443591 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.52077e10 | −1.17531 | ||||||||
\(896\) | 3.95302e9 | 0.183591 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.02612e9 | −0.277697 | ||||||||
\(899\) | −2.34763e10 | −1.07763 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.97126e8 | −0.00897857 | ||||||||
\(902\) | 4.33277e8 | 0.0196582 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.27471e10 | −1.47429 | ||||||||
\(905\) | −1.86377e10 | −0.835837 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.45269e10 | −1.53650 | −0.768250 | − | 0.640150i | \(-0.778872\pi\) | ||||
−0.768250 | + | 0.640150i | \(0.778872\pi\) | |||||||
\(908\) | −1.34109e10 | −0.594507 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.07988e9 | −0.355435 | ||||||||
\(911\) | −1.85678e10 | −0.813665 | −0.406832 | − | 0.913503i | \(-0.633367\pi\) | ||||
−0.406832 | + | 0.913503i | \(0.633367\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.88707e10 | 0.820618 | ||||||||
\(914\) | −1.19843e10 | −0.519161 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.82091e10 | −0.782806 | ||||||||
\(917\) | −5.61462e9 | −0.240451 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.89221e10 | −1.65422 | −0.827108 | − | 0.562044i | \(-0.810015\pi\) | ||||
−0.827108 | + | 0.562044i | \(0.810015\pi\) | |||||||
\(920\) | 2.03394e10 | 0.861155 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.74461e10 | −0.733062 | ||||||||
\(923\) | −3.17211e10 | −1.32783 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.31393e9 | 0.137673 | ||||||||
\(926\) | 2.04074e10 | 0.844595 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.53135e10 | −0.629009 | ||||||||
\(929\) | 7.85450e9 | 0.321413 | 0.160707 | − | 0.987002i | \(-0.448623\pi\) | ||||
0.160707 | + | 0.987002i | \(0.448623\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.55634e10 | −1.03823 | ||||||||
\(932\) | −9.85066e9 | −0.398575 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.26015e10 | −0.907660 | ||||||||
\(935\) | −9.65352e9 | −0.386229 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.64761e10 | 0.654283 | 0.327142 | − | 0.944975i | \(-0.393915\pi\) | ||||
0.327142 | + | 0.944975i | \(0.393915\pi\) | |||||||
\(938\) | 4.81670e9 | 0.190563 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.80767e8 | 0.0385140 | ||||||||
\(941\) | −3.54317e10 | −1.38621 | −0.693105 | − | 0.720837i | \(-0.743758\pi\) | ||||
−0.693105 | + | 0.720837i | \(0.743758\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.10335e8 | 0.0237016 | ||||||||
\(944\) | 1.30137e7 | 0.000503498 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.25229e9 | −0.355329 | ||||||||
\(947\) | 1.07477e10 | 0.411237 | 0.205618 | − | 0.978632i | \(-0.434079\pi\) | ||||
0.205618 | + | 0.978632i | \(0.434079\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.80113e10 | 0.684090 | ||||||||
\(950\) | 2.95227e10 | 1.11718 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.67627e9 | 0.100531 | ||||||||
\(953\) | 4.52936e10 | 1.69516 | 0.847581 | − | 0.530666i | \(-0.178058\pi\) | ||||
0.847581 | + | 0.530666i | \(0.178058\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.53780e10 | −0.942856 | ||||||||
\(956\) | −2.15566e10 | −0.797953 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.66129e10 | −0.977943 | ||||||||
\(959\) | −5.66802e9 | −0.207523 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.30459e10 | 1.92806 | ||||||||
\(962\) | −1.77613e9 | −0.0643224 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.13008e10 | 0.765820 | ||||||||
\(965\) | −7.14572e10 | −2.55977 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.08323e10 | −1.45215 | −0.726074 | − | 0.687617i | \(-0.758657\pi\) | ||||
−0.726074 | + | 0.687617i | \(0.758657\pi\) | |||||||
\(968\) | 1.37364e10 | 0.486754 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.56473e8 | 0.0160588 | ||||||||
\(971\) | −3.91677e10 | −1.37297 | −0.686484 | − | 0.727145i | \(-0.740847\pi\) | ||||
−0.686484 | + | 0.727145i | \(0.740847\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.32330e10 | 0.460537 | ||||||||
\(974\) | 1.89226e10 | 0.656183 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.72220e7 | −0.00334726 | ||||||||
\(977\) | −4.38079e10 | −1.50287 | −0.751435 | − | 0.659808i | \(-0.770638\pi\) | ||||
−0.751435 | + | 0.659808i | \(0.770638\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.61948e10 | −0.551614 | ||||||||
\(980\) | −2.65596e10 | −0.901428 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.38041e10 | −0.465176 | ||||||||
\(983\) | −3.95635e10 | −1.32849 | −0.664244 | − | 0.747516i | \(-0.731246\pi\) | ||||
−0.664244 | + | 0.747516i | \(0.731246\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.90429e10 | 0.968308 | ||||||||
\(986\) | −3.93779e9 | −0.130823 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.54152e10 | 0.838387 | ||||||||
\(989\) | −1.30332e10 | −0.428415 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.12206e10 | −1.99820 | −0.999102 | − | 0.0423753i | \(-0.986507\pi\) | ||||
−0.999102 | + | 0.0423753i | \(0.986507\pi\) | |||||||
\(992\) | 5.25481e10 | 1.70910 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.39291e9 | −0.206465 | ||||||||
\(995\) | 8.48283e10 | 2.72998 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.27542e10 | −0.727156 | −0.363578 | − | 0.931564i | \(-0.618445\pi\) | ||||
−0.363578 | + | 0.931564i | \(0.618445\pi\) | |||||||
\(998\) | 4.68595e9 | 0.149225 | ||||||||
\(999\) | 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 | 531.8.a.b.1.11 | 16 | ||
3.2 | odd | 2 | 177.8.a.a.1.6 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.a.1.6 | ✓ | 16 | 3.2 | odd | 2 | ||
531.8.a.b.1.11 | 16 | 1.1 | even | 1 | trivial |