Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,22,Mod(1,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.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: | \(209.608008215\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6395796x - 2792983104 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{2}\cdot 3\cdot 5\cdot 7 \) |
Twist minimal: | no (minimal twist has level 15) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-451.072\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −719.072 | −0.496544 | −0.248272 | − | 0.968690i | \(-0.579863\pi\) | ||||
−0.248272 | + | 0.968690i | \(0.579863\pi\) | |||||||
\(3\) | −59049.0 | −0.577350 | ||||||||
\(4\) | −1.58009e6 | −0.753444 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.24605e7 | 0.286680 | ||||||||
\(7\) | 1.45023e9 | 1.94047 | 0.970234 | − | 0.242169i | \(-0.0778587\pi\) | ||||
0.970234 | + | 0.242169i | \(0.0778587\pi\) | |||||||
\(8\) | 2.64420e9 | 0.870662 | ||||||||
\(9\) | 3.48678e9 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.34415e10 | 0.621234 | 0.310617 | − | 0.950535i | \(-0.399464\pi\) | ||||
0.310617 | + | 0.950535i | \(0.399464\pi\) | |||||||
\(12\) | 9.33026e10 | 0.435001 | ||||||||
\(13\) | −6.66061e10 | −0.134001 | −0.0670006 | − | 0.997753i | \(-0.521343\pi\) | ||||
−0.0670006 | + | 0.997753i | \(0.521343\pi\) | |||||||
\(14\) | −1.04282e12 | −0.963527 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.41231e12 | 0.321123 | ||||||||
\(17\) | −6.72914e12 | −0.809554 | −0.404777 | − | 0.914415i | \(-0.632651\pi\) | ||||
−0.404777 | + | 0.914415i | \(0.632651\pi\) | |||||||
\(18\) | −2.50725e12 | −0.165515 | ||||||||
\(19\) | 5.05646e13 | 1.89206 | 0.946028 | − | 0.324084i | \(-0.105056\pi\) | ||||
0.946028 | + | 0.324084i | \(0.105056\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.56345e13 | −1.12033 | ||||||||
\(22\) | −3.84283e13 | −0.308470 | ||||||||
\(23\) | −7.33880e13 | −0.369388 | −0.184694 | − | 0.982796i | \(-0.559129\pi\) | ||||
−0.184694 | + | 0.982796i | \(0.559129\pi\) | |||||||
\(24\) | −1.56137e14 | −0.502677 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.78946e13 | 0.0665375 | ||||||||
\(27\) | −2.05891e14 | −0.192450 | ||||||||
\(28\) | −2.29149e15 | −1.46204 | ||||||||
\(29\) | −2.61187e15 | −1.15285 | −0.576425 | − | 0.817150i | \(-0.695553\pi\) | ||||
−0.576425 | + | 0.817150i | \(0.695553\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.33577e15 | −0.730968 | −0.365484 | − | 0.930818i | \(-0.619097\pi\) | ||||
−0.365484 | + | 0.930818i | \(0.619097\pi\) | |||||||
\(32\) | −6.56084e15 | −1.03011 | ||||||||
\(33\) | −3.15567e15 | −0.358670 | ||||||||
\(34\) | 4.83873e15 | 0.401979 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.50942e15 | −0.251148 | ||||||||
\(37\) | 1.04258e16 | 0.356443 | 0.178221 | − | 0.983990i | \(-0.442966\pi\) | ||||
0.178221 | + | 0.983990i | \(0.442966\pi\) | |||||||
\(38\) | −3.63596e16 | −0.939489 | ||||||||
\(39\) | 3.93302e15 | 0.0773657 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.21333e17 | −1.41171 | −0.705857 | − | 0.708354i | \(-0.749438\pi\) | ||||
−0.705857 | + | 0.708354i | \(0.749438\pi\) | |||||||
\(42\) | 6.15773e16 | 0.556293 | ||||||||
\(43\) | −1.69796e17 | −1.19815 | −0.599073 | − | 0.800695i | \(-0.704464\pi\) | ||||
−0.599073 | + | 0.800695i | \(0.704464\pi\) | |||||||
\(44\) | −8.44422e16 | −0.468066 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.27713e16 | 0.183417 | ||||||||
\(47\) | −3.98939e17 | −1.10631 | −0.553157 | − | 0.833077i | \(-0.686577\pi\) | ||||
−0.553157 | + | 0.833077i | \(0.686577\pi\) | |||||||
\(48\) | −8.33957e16 | −0.185400 | ||||||||
\(49\) | 1.54461e18 | 2.76542 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.97349e17 | 0.467396 | ||||||||
\(52\) | 1.05243e17 | 0.100963 | ||||||||
\(53\) | 2.16226e17 | 0.169829 | 0.0849146 | − | 0.996388i | \(-0.472938\pi\) | ||||
0.0849146 | + | 0.996388i | \(0.472938\pi\) | |||||||
\(54\) | 1.48051e17 | 0.0955599 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.83469e18 | 1.68949 | ||||||||
\(57\) | −2.98579e18 | −1.09238 | ||||||||
\(58\) | 1.87812e18 | 0.572440 | ||||||||
\(59\) | 4.31686e18 | 1.09957 | 0.549783 | − | 0.835307i | \(-0.314710\pi\) | ||||
0.549783 | + | 0.835307i | \(0.314710\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.13584e18 | 0.203871 | 0.101935 | − | 0.994791i | \(-0.467497\pi\) | ||||
0.101935 | + | 0.994791i | \(0.467497\pi\) | |||||||
\(62\) | 2.39866e18 | 0.362958 | ||||||||
\(63\) | 5.05663e18 | 0.646823 | ||||||||
\(64\) | 1.75588e18 | 0.190373 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.26915e18 | 0.178095 | ||||||||
\(67\) | 1.49163e18 | 0.0999711 | 0.0499855 | − | 0.998750i | \(-0.484082\pi\) | ||||
0.0499855 | + | 0.998750i | \(0.484082\pi\) | |||||||
\(68\) | 1.06326e19 | 0.609954 | ||||||||
\(69\) | 4.33349e18 | 0.213266 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.51061e19 | −0.915306 | −0.457653 | − | 0.889131i | \(-0.651310\pi\) | ||||
−0.457653 | + | 0.889131i | \(0.651310\pi\) | |||||||
\(72\) | 9.21975e18 | 0.290221 | ||||||||
\(73\) | −3.19214e19 | −0.869345 | −0.434672 | − | 0.900589i | \(-0.643136\pi\) | ||||
−0.434672 | + | 0.900589i | \(0.643136\pi\) | |||||||
\(74\) | −7.49687e18 | −0.176989 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.98966e19 | −1.42556 | ||||||||
\(77\) | 7.75023e19 | 1.20549 | ||||||||
\(78\) | −2.82813e18 | −0.0384154 | ||||||||
\(79\) | 7.75405e19 | 0.921391 | 0.460696 | − | 0.887558i | \(-0.347600\pi\) | ||||
0.460696 | + | 0.887558i | \(0.347600\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.21577e19 | 0.111111 | ||||||||
\(82\) | 8.72468e19 | 0.700978 | ||||||||
\(83\) | 2.62543e19 | 0.185729 | 0.0928646 | − | 0.995679i | \(-0.470398\pi\) | ||||
0.0928646 | + | 0.995679i | \(0.470398\pi\) | |||||||
\(84\) | 1.35310e20 | 0.844106 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.22096e20 | 0.594931 | ||||||||
\(87\) | 1.54228e20 | 0.665598 | ||||||||
\(88\) | 1.41310e20 | 0.540885 | ||||||||
\(89\) | −4.67811e20 | −1.59029 | −0.795144 | − | 0.606421i | \(-0.792605\pi\) | ||||
−0.795144 | + | 0.606421i | \(0.792605\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.65940e19 | −0.260025 | ||||||||
\(92\) | 1.15960e20 | 0.278313 | ||||||||
\(93\) | 1.96974e20 | 0.422025 | ||||||||
\(94\) | 2.86866e20 | 0.549334 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.87411e20 | 0.594736 | ||||||||
\(97\) | −8.87155e20 | −1.22151 | −0.610754 | − | 0.791820i | \(-0.709134\pi\) | ||||
−0.610754 | + | 0.791820i | \(0.709134\pi\) | |||||||
\(98\) | −1.11069e21 | −1.37315 | ||||||||
\(99\) | 1.86339e20 | 0.207078 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.60924e21 | 1.44960 | 0.724799 | − | 0.688960i | \(-0.241933\pi\) | ||||
0.724799 | + | 0.688960i | \(0.241933\pi\) | |||||||
\(102\) | −2.85722e20 | −0.232083 | ||||||||
\(103\) | 1.75803e21 | 1.28895 | 0.644475 | − | 0.764625i | \(-0.277076\pi\) | ||||
0.644475 | + | 0.764625i | \(0.277076\pi\) | |||||||
\(104\) | −1.76120e20 | −0.116670 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.55482e20 | −0.0843276 | ||||||||
\(107\) | −6.16929e20 | −0.303184 | −0.151592 | − | 0.988443i | \(-0.548440\pi\) | ||||
−0.151592 | + | 0.988443i | \(0.548440\pi\) | |||||||
\(108\) | 3.25326e20 | 0.145000 | ||||||||
\(109\) | 1.40972e21 | 0.570369 | 0.285185 | − | 0.958473i | \(-0.407945\pi\) | ||||
0.285185 | + | 0.958473i | \(0.407945\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.15631e20 | −0.205792 | ||||||||
\(112\) | 2.04818e21 | 0.623129 | ||||||||
\(113\) | −6.89762e21 | −1.91151 | −0.955753 | − | 0.294170i | \(-0.904957\pi\) | ||||
−0.955753 | + | 0.294170i | \(0.904957\pi\) | |||||||
\(114\) | 2.14700e21 | 0.542414 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.12699e21 | 0.868608 | ||||||||
\(117\) | −2.32241e20 | −0.0446671 | ||||||||
\(118\) | −3.10413e21 | −0.545983 | ||||||||
\(119\) | −9.75878e21 | −1.57091 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.54426e21 | −0.614068 | ||||||||
\(122\) | −8.16753e20 | −0.101231 | ||||||||
\(123\) | 7.16457e21 | 0.815054 | ||||||||
\(124\) | 5.27081e21 | 0.550744 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.63608e21 | −0.321176 | ||||||||
\(127\) | −1.77824e21 | −0.144561 | −0.0722807 | − | 0.997384i | \(-0.523028\pi\) | ||||
−0.0722807 | + | 0.997384i | \(0.523028\pi\) | |||||||
\(128\) | 1.24965e22 | 0.935585 | ||||||||
\(129\) | 1.00263e22 | 0.691750 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.48898e21 | 0.498318 | 0.249159 | − | 0.968463i | \(-0.419846\pi\) | ||||
0.249159 | + | 0.968463i | \(0.419846\pi\) | |||||||
\(132\) | 4.98623e21 | 0.270238 | ||||||||
\(133\) | 7.33302e22 | 3.67148 | ||||||||
\(134\) | −1.07259e21 | −0.0496400 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.77932e22 | −0.704848 | ||||||||
\(137\) | −5.12067e22 | −1.87828 | −0.939140 | − | 0.343534i | \(-0.888376\pi\) | ||||
−0.939140 | + | 0.343534i | \(0.888376\pi\) | |||||||
\(138\) | −3.11609e21 | −0.105896 | ||||||||
\(139\) | −4.53556e22 | −1.42881 | −0.714407 | − | 0.699731i | \(-0.753303\pi\) | ||||
−0.714407 | + | 0.699731i | \(0.753303\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.35569e22 | 0.638731 | ||||||||
\(142\) | 1.80531e22 | 0.454489 | ||||||||
\(143\) | −3.55953e21 | −0.0832462 | ||||||||
\(144\) | 4.92443e21 | 0.107041 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.29538e22 | 0.431668 | ||||||||
\(147\) | −9.12078e22 | −1.59661 | ||||||||
\(148\) | −1.64736e22 | −0.268560 | ||||||||
\(149\) | 8.87592e22 | 1.34821 | 0.674105 | − | 0.738635i | \(-0.264529\pi\) | ||||
0.674105 | + | 0.738635i | \(0.264529\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.20804e22 | 0.291574 | 0.145787 | − | 0.989316i | \(-0.453429\pi\) | ||||
0.145787 | + | 0.989316i | \(0.453429\pi\) | |||||||
\(152\) | 1.33703e23 | 1.64734 | ||||||||
\(153\) | −2.34631e22 | −0.269851 | ||||||||
\(154\) | −5.57297e22 | −0.598576 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −6.21452e21 | −0.0582907 | ||||||||
\(157\) | −1.24312e22 | −0.109035 | −0.0545177 | − | 0.998513i | \(-0.517362\pi\) | ||||
−0.0545177 | + | 0.998513i | \(0.517362\pi\) | |||||||
\(158\) | −5.57572e22 | −0.457511 | ||||||||
\(159\) | −1.27680e22 | −0.0980509 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.06429e23 | −0.716786 | ||||||||
\(162\) | −8.74224e21 | −0.0551715 | ||||||||
\(163\) | −1.59873e23 | −0.945815 | −0.472907 | − | 0.881112i | \(-0.656796\pi\) | ||||
−0.472907 | + | 0.881112i | \(0.656796\pi\) | |||||||
\(164\) | 1.91716e23 | 1.06365 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.88787e22 | −0.0922227 | ||||||||
\(167\) | −2.09458e23 | −0.960670 | −0.480335 | − | 0.877085i | \(-0.659485\pi\) | ||||
−0.480335 | + | 0.877085i | \(0.659485\pi\) | |||||||
\(168\) | −2.26435e23 | −0.975428 | ||||||||
\(169\) | −2.42628e23 | −0.982044 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.76308e23 | 0.630686 | ||||||||
\(172\) | 2.68293e23 | 0.902736 | ||||||||
\(173\) | 8.91449e22 | 0.282236 | 0.141118 | − | 0.989993i | \(-0.454930\pi\) | ||||
0.141118 | + | 0.989993i | \(0.454930\pi\) | |||||||
\(174\) | −1.10901e23 | −0.330499 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.54762e22 | 0.199493 | ||||||||
\(177\) | −2.54906e23 | −0.634835 | ||||||||
\(178\) | 3.36390e23 | 0.789647 | ||||||||
\(179\) | 6.46845e23 | 1.43167 | 0.715836 | − | 0.698269i | \(-0.246046\pi\) | ||||
0.715836 | + | 0.698269i | \(0.246046\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.35874e23 | −0.267615 | −0.133807 | − | 0.991007i | \(-0.542720\pi\) | ||||
−0.133807 | + | 0.991007i | \(0.542720\pi\) | |||||||
\(182\) | 6.94580e22 | 0.129114 | ||||||||
\(183\) | −6.70704e22 | −0.117705 | ||||||||
\(184\) | −1.94053e23 | −0.321612 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.41638e23 | −0.209554 | ||||||||
\(187\) | −3.59615e23 | −0.502923 | ||||||||
\(188\) | 6.30358e23 | 0.833547 | ||||||||
\(189\) | −2.98589e23 | −0.373443 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.94980e23 | −0.666273 | −0.333136 | − | 0.942879i | \(-0.608107\pi\) | ||||
−0.333136 | + | 0.942879i | \(0.608107\pi\) | |||||||
\(192\) | −1.03683e23 | −0.109912 | ||||||||
\(193\) | 3.65629e23 | 0.367019 | 0.183510 | − | 0.983018i | \(-0.441254\pi\) | ||||
0.183510 | + | 0.983018i | \(0.441254\pi\) | |||||||
\(194\) | 6.37928e23 | 0.606532 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.44062e24 | −2.08359 | ||||||||
\(197\) | 2.05182e24 | 1.66052 | 0.830259 | − | 0.557377i | \(-0.188192\pi\) | ||||
0.830259 | + | 0.557377i | \(0.188192\pi\) | |||||||
\(198\) | −1.33991e23 | −0.102823 | ||||||||
\(199\) | −1.28088e22 | −0.00932289 | −0.00466145 | − | 0.999989i | \(-0.501484\pi\) | ||||
−0.00466145 | + | 0.999989i | \(0.501484\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.80790e22 | −0.0577183 | ||||||||
\(202\) | −1.15716e24 | −0.719789 | ||||||||
\(203\) | −3.78781e24 | −2.23707 | ||||||||
\(204\) | −6.27846e23 | −0.352157 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.26415e24 | −0.640020 | ||||||||
\(207\) | −2.55888e23 | −0.123129 | ||||||||
\(208\) | −9.40687e22 | −0.0430309 | ||||||||
\(209\) | 2.70225e24 | 1.17541 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.15546e24 | −1.24193 | −0.620964 | − | 0.783839i | \(-0.713259\pi\) | ||||
−0.620964 | + | 0.783839i | \(0.713259\pi\) | |||||||
\(212\) | −3.41657e23 | −0.127957 | ||||||||
\(213\) | 1.48249e24 | 0.528452 | ||||||||
\(214\) | 4.43617e23 | 0.150544 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.44417e23 | −0.167559 | ||||||||
\(217\) | −4.83763e24 | −1.41842 | ||||||||
\(218\) | −1.01369e24 | −0.283213 | ||||||||
\(219\) | 1.88493e24 | 0.501916 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.48202e23 | 0.108481 | ||||||||
\(222\) | 4.42683e23 | 0.102185 | ||||||||
\(223\) | −6.19879e24 | −1.36492 | −0.682458 | − | 0.730925i | \(-0.739089\pi\) | ||||
−0.682458 | + | 0.730925i | \(0.739089\pi\) | |||||||
\(224\) | −9.51471e24 | −1.99890 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.95989e24 | 0.949146 | ||||||||
\(227\) | −1.08021e25 | −1.97351 | −0.986753 | − | 0.162228i | \(-0.948132\pi\) | ||||
−0.986753 | + | 0.162228i | \(0.948132\pi\) | |||||||
\(228\) | 4.71781e24 | 0.823047 | ||||||||
\(229\) | 1.04108e25 | 1.73465 | 0.867326 | − | 0.497740i | \(-0.165837\pi\) | ||||
0.867326 | + | 0.497740i | \(0.165837\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.57643e24 | −0.695987 | ||||||||
\(232\) | −6.90631e24 | −1.00374 | ||||||||
\(233\) | 2.61385e24 | 0.363114 | 0.181557 | − | 0.983380i | \(-0.441886\pi\) | ||||
0.181557 | + | 0.983380i | \(0.441886\pi\) | |||||||
\(234\) | 1.66998e23 | 0.0221792 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.82101e24 | −0.828463 | ||||||||
\(237\) | −4.57869e24 | −0.531965 | ||||||||
\(238\) | 7.01726e24 | 0.780027 | ||||||||
\(239\) | −3.17368e24 | −0.337587 | −0.168793 | − | 0.985651i | \(-0.553987\pi\) | ||||
−0.168793 | + | 0.985651i | \(0.553987\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.44859e24 | −0.433554 | −0.216777 | − | 0.976221i | \(-0.569554\pi\) | ||||
−0.216777 | + | 0.976221i | \(0.569554\pi\) | |||||||
\(242\) | 3.26765e24 | 0.304912 | ||||||||
\(243\) | −7.17898e23 | −0.0641500 | ||||||||
\(244\) | −1.79473e24 | −0.153605 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.15184e24 | −0.404710 | ||||||||
\(247\) | −3.36791e24 | −0.253538 | ||||||||
\(248\) | −8.82045e24 | −0.636426 | ||||||||
\(249\) | −1.55029e24 | −0.107231 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.43489e25 | −0.912525 | −0.456262 | − | 0.889845i | \(-0.650812\pi\) | ||||
−0.456262 | + | 0.889845i | \(0.650812\pi\) | |||||||
\(252\) | −7.98992e24 | −0.487345 | ||||||||
\(253\) | −3.92197e24 | −0.229477 | ||||||||
\(254\) | 1.27869e24 | 0.0717810 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.26682e25 | −0.654932 | ||||||||
\(257\) | 6.11572e24 | 0.303494 | 0.151747 | − | 0.988419i | \(-0.451510\pi\) | ||||
0.151747 | + | 0.988419i | \(0.451510\pi\) | |||||||
\(258\) | −7.20963e24 | −0.343484 | ||||||||
\(259\) | 1.51197e25 | 0.691666 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.10703e24 | −0.384283 | ||||||||
\(262\) | −6.10419e24 | −0.247437 | ||||||||
\(263\) | 9.31741e24 | 0.362877 | 0.181439 | − | 0.983402i | \(-0.441925\pi\) | ||||
0.181439 | + | 0.983402i | \(0.441925\pi\) | |||||||
\(264\) | −8.34421e24 | −0.312280 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5.27297e25 | −1.82305 | ||||||||
\(267\) | 2.76238e25 | 0.918153 | ||||||||
\(268\) | −2.35690e24 | −0.0753226 | ||||||||
\(269\) | 5.19103e25 | 1.59535 | 0.797673 | − | 0.603090i | \(-0.206064\pi\) | ||||
0.797673 | + | 0.603090i | \(0.206064\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.16010e24 | −0.0614181 | −0.0307090 | − | 0.999528i | \(-0.509777\pi\) | ||||
−0.0307090 | + | 0.999528i | \(0.509777\pi\) | |||||||
\(272\) | −9.50365e24 | −0.259966 | ||||||||
\(273\) | 5.70378e24 | 0.150126 | ||||||||
\(274\) | 3.68213e25 | 0.932648 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.84729e24 | −0.160684 | ||||||||
\(277\) | −7.66259e25 | −1.73116 | −0.865581 | − | 0.500769i | \(-0.833051\pi\) | ||||
−0.865581 | + | 0.500769i | \(0.833051\pi\) | |||||||
\(278\) | 3.26139e25 | 0.709468 | ||||||||
\(279\) | −1.16311e25 | −0.243656 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.52888e24 | 0.185193 | 0.0925967 | − | 0.995704i | \(-0.470483\pi\) | ||||
0.0925967 | + | 0.995704i | \(0.470483\pi\) | |||||||
\(282\) | −1.69391e25 | −0.317158 | ||||||||
\(283\) | 1.67669e25 | 0.302479 | 0.151240 | − | 0.988497i | \(-0.451674\pi\) | ||||
0.151240 | + | 0.988497i | \(0.451674\pi\) | |||||||
\(284\) | 3.96698e25 | 0.689632 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.55956e24 | 0.0413354 | ||||||||
\(287\) | −1.75960e26 | −2.73939 | ||||||||
\(288\) | −2.28762e25 | −0.343371 | ||||||||
\(289\) | −2.38106e25 | −0.344622 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.23856e25 | 0.705238 | ||||||||
\(292\) | 5.04386e25 | 0.655003 | ||||||||
\(293\) | 1.00892e26 | 1.26400 | 0.632002 | − | 0.774967i | \(-0.282233\pi\) | ||||
0.632002 | + | 0.774967i | \(0.282233\pi\) | |||||||
\(294\) | 6.55850e25 | 0.792789 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.75678e25 | 0.310341 | ||||||||
\(297\) | −1.10031e25 | −0.119557 | ||||||||
\(298\) | −6.38243e25 | −0.669445 | ||||||||
\(299\) | 4.88809e24 | 0.0494985 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.46243e26 | −2.32496 | ||||||||
\(302\) | −1.58774e25 | −0.144779 | ||||||||
\(303\) | −9.50243e25 | −0.836926 | ||||||||
\(304\) | 7.14131e25 | 0.607583 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.68716e25 | 0.133993 | ||||||||
\(307\) | −2.64734e25 | −0.203169 | −0.101584 | − | 0.994827i | \(-0.532391\pi\) | ||||
−0.101584 | + | 0.994827i | \(0.532391\pi\) | |||||||
\(308\) | −1.22460e26 | −0.908266 | ||||||||
\(309\) | −1.03810e26 | −0.744176 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.96060e26 | −1.31342 | −0.656711 | − | 0.754143i | \(-0.728053\pi\) | ||||
−0.656711 | + | 0.754143i | \(0.728053\pi\) | |||||||
\(312\) | 1.03997e25 | 0.0673593 | ||||||||
\(313\) | 1.28532e26 | 0.805000 | 0.402500 | − | 0.915420i | \(-0.368141\pi\) | ||||
0.402500 | + | 0.915420i | \(0.368141\pi\) | |||||||
\(314\) | 8.93894e24 | 0.0541408 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.22521e26 | −0.694217 | ||||||||
\(317\) | −7.55478e25 | −0.414095 | −0.207047 | − | 0.978331i | \(-0.566385\pi\) | ||||
−0.207047 | + | 0.978331i | \(0.566385\pi\) | |||||||
\(318\) | 9.18108e24 | 0.0486866 | ||||||||
\(319\) | −1.39582e26 | −0.716190 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.64291e25 | 0.175043 | ||||||||
\(322\) | 7.65303e25 | 0.355916 | ||||||||
\(323\) | −3.40256e26 | −1.53172 | ||||||||
\(324\) | −1.92102e25 | −0.0837160 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.14960e26 | 0.469638 | ||||||||
\(327\) | −8.32428e25 | −0.329303 | ||||||||
\(328\) | −3.20827e26 | −1.22913 | ||||||||
\(329\) | −5.78552e26 | −2.14677 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.16140e26 | −0.752559 | −0.376280 | − | 0.926506i | \(-0.622797\pi\) | ||||
−0.376280 | + | 0.926506i | \(0.622797\pi\) | |||||||
\(332\) | −4.14841e25 | −0.139937 | ||||||||
\(333\) | 3.63524e25 | 0.118814 | ||||||||
\(334\) | 1.50615e26 | 0.477015 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.20943e26 | −0.359764 | ||||||||
\(337\) | 2.57810e26 | 0.743337 | 0.371668 | − | 0.928366i | \(-0.378786\pi\) | ||||
0.371668 | + | 0.928366i | \(0.378786\pi\) | |||||||
\(338\) | 1.74467e26 | 0.487628 | ||||||||
\(339\) | 4.07298e26 | 1.10361 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.78269e26 | −0.454103 | ||||||||
\(342\) | −1.26778e26 | −0.313163 | ||||||||
\(343\) | 1.43002e27 | 3.42574 | ||||||||
\(344\) | −4.48975e26 | −1.04318 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.41016e25 | −0.140142 | ||||||||
\(347\) | 8.08697e25 | 0.171525 | 0.0857623 | − | 0.996316i | \(-0.472667\pi\) | ||||
0.0857623 | + | 0.996316i | \(0.472667\pi\) | |||||||
\(348\) | −2.43694e26 | −0.501491 | ||||||||
\(349\) | 3.35155e26 | 0.669235 | 0.334618 | − | 0.942354i | \(-0.391393\pi\) | ||||
0.334618 | + | 0.942354i | \(0.391393\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.37136e25 | 0.0257886 | ||||||||
\(352\) | −3.50621e26 | −0.639942 | ||||||||
\(353\) | −6.48285e26 | −1.14850 | −0.574251 | − | 0.818679i | \(-0.694707\pi\) | ||||
−0.574251 | + | 0.818679i | \(0.694707\pi\) | |||||||
\(354\) | 1.83296e26 | 0.315223 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 7.39183e26 | 1.19819 | ||||||||
\(357\) | 5.76246e26 | 0.906968 | ||||||||
\(358\) | −4.65128e26 | −0.710887 | ||||||||
\(359\) | 7.38689e26 | 1.09640 | 0.548201 | − | 0.836347i | \(-0.315313\pi\) | ||||
0.548201 | + | 0.836347i | \(0.315313\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.84257e27 | 2.57988 | ||||||||
\(362\) | 9.77029e25 | 0.132882 | ||||||||
\(363\) | 2.68334e26 | 0.354532 | ||||||||
\(364\) | 1.52627e26 | 0.195915 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.82284e25 | 0.0584456 | ||||||||
\(367\) | 1.06086e27 | 1.24929 | 0.624647 | − | 0.780907i | \(-0.285243\pi\) | ||||
0.624647 | + | 0.780907i | \(0.285243\pi\) | |||||||
\(368\) | −1.03647e26 | −0.118619 | ||||||||
\(369\) | −4.23060e26 | −0.470571 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.13578e26 | 0.329548 | ||||||||
\(372\) | −3.11236e26 | −0.317972 | ||||||||
\(373\) | −8.79522e26 | −0.873582 | −0.436791 | − | 0.899563i | \(-0.643885\pi\) | ||||
−0.436791 | + | 0.899563i | \(0.643885\pi\) | |||||||
\(374\) | 2.58589e26 | 0.249723 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.05487e27 | −0.963226 | ||||||||
\(377\) | 1.73967e26 | 0.154483 | ||||||||
\(378\) | 2.14707e26 | 0.185431 | ||||||||
\(379\) | 1.37283e27 | 1.15320 | 0.576600 | − | 0.817027i | \(-0.304379\pi\) | ||||
0.576600 | + | 0.817027i | \(0.304379\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.05003e26 | 0.0834625 | ||||||||
\(382\) | 4.27834e26 | 0.330834 | ||||||||
\(383\) | 4.70426e25 | 0.0353919 | 0.0176960 | − | 0.999843i | \(-0.494367\pi\) | ||||
0.0176960 | + | 0.999843i | \(0.494367\pi\) | |||||||
\(384\) | −7.37905e26 | −0.540160 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.62913e26 | −0.182241 | ||||||||
\(387\) | −5.92043e26 | −0.399382 | ||||||||
\(388\) | 1.40178e27 | 0.920338 | ||||||||
\(389\) | 4.91701e26 | 0.314218 | 0.157109 | − | 0.987581i | \(-0.449783\pi\) | ||||
0.157109 | + | 0.987581i | \(0.449783\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.93838e26 | 0.299040 | ||||||||
\(392\) | 4.08426e27 | 2.40774 | ||||||||
\(393\) | −5.01266e26 | −0.287704 | ||||||||
\(394\) | −1.47541e27 | −0.824520 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.94432e26 | −0.156022 | ||||||||
\(397\) | −4.75566e26 | −0.245420 | −0.122710 | − | 0.992443i | \(-0.539159\pi\) | ||||
−0.122710 | + | 0.992443i | \(0.539159\pi\) | |||||||
\(398\) | 9.21044e24 | 0.00462922 | ||||||||
\(399\) | −4.33008e27 | −2.11973 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.19241e27 | 1.48287 | 0.741434 | − | 0.671025i | \(-0.234146\pi\) | ||||
0.741434 | + | 0.671025i | \(0.234146\pi\) | |||||||
\(402\) | 6.33351e25 | 0.0286597 | ||||||||
\(403\) | 2.22183e26 | 0.0979507 | ||||||||
\(404\) | −2.54275e27 | −1.09219 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.72371e27 | 1.11080 | ||||||||
\(407\) | 5.57168e26 | 0.221434 | ||||||||
\(408\) | 1.05067e27 | 0.406944 | ||||||||
\(409\) | −5.80155e26 | −0.219003 | −0.109501 | − | 0.993987i | \(-0.534925\pi\) | ||||
−0.109501 | + | 0.993987i | \(0.534925\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.02370e27 | 1.08443 | ||||||||
\(412\) | −2.77785e27 | −0.971153 | ||||||||
\(413\) | 6.26042e27 | 2.13368 | ||||||||
\(414\) | 1.84002e26 | 0.0611391 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.36992e26 | 0.138036 | ||||||||
\(417\) | 2.67820e27 | 0.824926 | ||||||||
\(418\) | −1.94311e27 | −0.583643 | ||||||||
\(419\) | −6.91834e26 | −0.202654 | −0.101327 | − | 0.994853i | \(-0.532309\pi\) | ||||
−0.101327 | + | 0.994853i | \(0.532309\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.75790e27 | 1.60436 | 0.802181 | − | 0.597081i | \(-0.203673\pi\) | ||||
0.802181 | + | 0.597081i | \(0.203673\pi\) | |||||||
\(422\) | 2.26900e27 | 0.616672 | ||||||||
\(423\) | −1.39101e27 | −0.368772 | ||||||||
\(424\) | 5.71746e26 | 0.147864 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.06602e27 | −0.262399 | ||||||||
\(427\) | 1.64723e27 | 0.395605 | ||||||||
\(428\) | 9.74802e26 | 0.228432 | ||||||||
\(429\) | 2.10187e26 | 0.0480622 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.85181e26 | −0.0838791 | −0.0419395 | − | 0.999120i | \(-0.513354\pi\) | ||||
−0.0419395 | + | 0.999120i | \(0.513354\pi\) | |||||||
\(432\) | −2.90783e26 | −0.0618001 | ||||||||
\(433\) | 4.76715e27 | 0.988863 | 0.494432 | − | 0.869216i | \(-0.335376\pi\) | ||||
0.494432 | + | 0.869216i | \(0.335376\pi\) | |||||||
\(434\) | 3.47860e27 | 0.704308 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.22749e27 | −0.429742 | ||||||||
\(437\) | −3.71084e27 | −0.698903 | ||||||||
\(438\) | −1.35540e27 | −0.249223 | ||||||||
\(439\) | −1.30635e27 | −0.234521 | −0.117260 | − | 0.993101i | \(-0.537411\pi\) | ||||
−0.117260 | + | 0.993101i | \(0.537411\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.38573e27 | 0.921806 | ||||||||
\(442\) | −3.22289e26 | −0.0538657 | ||||||||
\(443\) | −1.05987e28 | −1.72987 | −0.864936 | − | 0.501882i | \(-0.832641\pi\) | ||||
−0.864936 | + | 0.501882i | \(0.832641\pi\) | |||||||
\(444\) | 9.72750e26 | 0.155053 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.45738e27 | 0.677741 | ||||||||
\(447\) | −5.24114e27 | −0.778390 | ||||||||
\(448\) | 2.54643e27 | 0.369413 | ||||||||
\(449\) | −2.62975e27 | −0.372673 | −0.186337 | − | 0.982486i | \(-0.559661\pi\) | ||||
−0.186337 | + | 0.982486i | \(0.559661\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.48419e27 | −0.877005 | ||||||||
\(452\) | 1.08988e28 | 1.44021 | ||||||||
\(453\) | −1.30382e27 | −0.168340 | ||||||||
\(454\) | 7.76752e27 | 0.979932 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.89503e27 | −0.951093 | ||||||||
\(457\) | 5.80657e26 | 0.0683596 | 0.0341798 | − | 0.999416i | \(-0.489118\pi\) | ||||
0.0341798 | + | 0.999416i | \(0.489118\pi\) | |||||||
\(458\) | −7.48613e27 | −0.861330 | ||||||||
\(459\) | 1.38547e27 | 0.155799 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.20734e27 | −0.989178 | −0.494589 | − | 0.869127i | \(-0.664681\pi\) | ||||
−0.494589 | + | 0.869127i | \(0.664681\pi\) | |||||||
\(462\) | 3.29079e27 | 0.345588 | ||||||||
\(463\) | 2.81089e27 | 0.288564 | 0.144282 | − | 0.989537i | \(-0.453913\pi\) | ||||
0.144282 | + | 0.989537i | \(0.453913\pi\) | |||||||
\(464\) | −3.68878e27 | −0.370207 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.87955e27 | −0.180302 | ||||||||
\(467\) | −1.43686e28 | −1.34768 | −0.673841 | − | 0.738876i | \(-0.735357\pi\) | ||||
−0.673841 | + | 0.738876i | \(0.735357\pi\) | |||||||
\(468\) | 3.66961e26 | 0.0336542 | ||||||||
\(469\) | 2.16320e27 | 0.193991 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.34051e26 | 0.0629516 | ||||||||
\(472\) | 1.14146e28 | 0.957351 | ||||||||
\(473\) | −9.07417e27 | −0.744329 | ||||||||
\(474\) | 3.29241e27 | 0.264144 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.54197e28 | 1.18360 | ||||||||
\(477\) | 7.53935e26 | 0.0566097 | ||||||||
\(478\) | 2.28211e27 | 0.167627 | ||||||||
\(479\) | −1.66001e28 | −1.19285 | −0.596426 | − | 0.802668i | \(-0.703413\pi\) | ||||
−0.596426 | + | 0.802668i | \(0.703413\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.94419e26 | −0.0477638 | ||||||||
\(482\) | 3.19885e27 | 0.215278 | ||||||||
\(483\) | 6.28454e27 | 0.413837 | ||||||||
\(484\) | 7.18032e27 | 0.462666 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 5.16220e26 | 0.0318533 | ||||||||
\(487\) | 2.39148e28 | 1.44415 | 0.722076 | − | 0.691814i | \(-0.243188\pi\) | ||||
0.722076 | + | 0.691814i | \(0.243188\pi\) | |||||||
\(488\) | 3.00340e27 | 0.177502 | ||||||||
\(489\) | 9.44036e27 | 0.546066 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.52047e28 | −1.39677 | −0.698386 | − | 0.715721i | \(-0.746098\pi\) | ||||
−0.698386 | + | 0.715721i | \(0.746098\pi\) | |||||||
\(492\) | −1.13206e28 | −0.614098 | ||||||||
\(493\) | 1.75756e28 | 0.933294 | ||||||||
\(494\) | 2.42177e27 | 0.125893 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.71116e27 | −0.234731 | ||||||||
\(497\) | −3.64095e28 | −1.77612 | ||||||||
\(498\) | 1.11477e27 | 0.0532448 | ||||||||
\(499\) | −4.60542e27 | −0.215384 | −0.107692 | − | 0.994184i | \(-0.534346\pi\) | ||||
−0.107692 | + | 0.994184i | \(0.534346\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.23683e28 | 0.554643 | ||||||||
\(502\) | 1.03179e28 | 0.453108 | ||||||||
\(503\) | −1.46909e28 | −0.631806 | −0.315903 | − | 0.948791i | \(-0.602307\pi\) | ||||
−0.315903 | + | 0.948791i | \(0.602307\pi\) | |||||||
\(504\) | 1.33707e28 | 0.563164 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.82018e27 | 0.113945 | ||||||||
\(507\) | 1.43269e28 | 0.566983 | ||||||||
\(508\) | 2.80978e27 | 0.108919 | ||||||||
\(509\) | 4.03387e27 | 0.153174 | 0.0765871 | − | 0.997063i | \(-0.475598\pi\) | ||||
0.0765871 | + | 0.997063i | \(0.475598\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.62933e28 | −1.68694 | ||||||||
\(512\) | −1.70977e28 | −0.610382 | ||||||||
\(513\) | −1.04108e28 | −0.364126 | ||||||||
\(514\) | −4.39764e27 | −0.150698 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.58424e28 | −0.521195 | ||||||||
\(517\) | −2.13199e28 | −0.687281 | ||||||||
\(518\) | −1.08722e28 | −0.343442 | ||||||||
\(519\) | −5.26392e27 | −0.162949 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.75449e28 | −1.11623 | −0.558117 | − | 0.829762i | \(-0.688476\pi\) | ||||
−0.558117 | + | 0.829762i | \(0.688476\pi\) | |||||||
\(522\) | 6.54861e27 | 0.190813 | ||||||||
\(523\) | −5.27634e28 | −1.50683 | −0.753417 | − | 0.657543i | \(-0.771596\pi\) | ||||
−0.753417 | + | 0.657543i | \(0.771596\pi\) | |||||||
\(524\) | −1.34133e28 | −0.375455 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.69989e27 | −0.180184 | ||||||||
\(527\) | 2.24469e28 | 0.591758 | ||||||||
\(528\) | −4.45679e27 | −0.115177 | ||||||||
\(529\) | −3.40858e28 | −0.863552 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.50520e28 | 0.366522 | ||||||||
\(532\) | −1.15868e29 | −2.76625 | ||||||||
\(533\) | 8.08149e27 | 0.189172 | ||||||||
\(534\) | −1.98635e28 | −0.455903 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.94416e27 | 0.0870410 | ||||||||
\(537\) | −3.81955e28 | −0.826576 | ||||||||
\(538\) | −3.73273e28 | −0.792159 | ||||||||
\(539\) | 8.25464e28 | 1.71797 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.40670e28 | 0.281598 | 0.140799 | − | 0.990038i | \(-0.455033\pi\) | ||||
0.140799 | + | 0.990038i | \(0.455033\pi\) | |||||||
\(542\) | 1.55327e27 | 0.0304968 | ||||||||
\(543\) | 8.02320e27 | 0.154508 | ||||||||
\(544\) | 4.41488e28 | 0.833932 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.10143e27 | −0.0745439 | ||||||||
\(547\) | −6.71332e28 | −1.19693 | −0.598467 | − | 0.801147i | \(-0.704223\pi\) | ||||
−0.598467 | + | 0.801147i | \(0.704223\pi\) | |||||||
\(548\) | 8.09110e28 | 1.41518 | ||||||||
\(549\) | 3.96044e27 | 0.0679569 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.32068e29 | −2.18126 | ||||||||
\(552\) | 1.14586e28 | 0.185683 | ||||||||
\(553\) | 1.12451e29 | 1.78793 | ||||||||
\(554\) | 5.50995e28 | 0.859598 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.16658e28 | 1.07653 | ||||||||
\(557\) | −4.16746e28 | −0.614316 | −0.307158 | − | 0.951658i | \(-0.599378\pi\) | ||||
−0.307158 | + | 0.951658i | \(0.599378\pi\) | |||||||
\(558\) | 8.36361e27 | 0.120986 | ||||||||
\(559\) | 1.13095e28 | 0.160553 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.12349e28 | 0.290363 | ||||||||
\(562\) | −6.85195e27 | −0.0919566 | ||||||||
\(563\) | 6.01432e27 | 0.0792225 | 0.0396112 | − | 0.999215i | \(-0.487388\pi\) | ||||
0.0396112 | + | 0.999215i | \(0.487388\pi\) | |||||||
\(564\) | −3.72220e28 | −0.481248 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.20566e28 | −0.150194 | ||||||||
\(567\) | 1.76314e28 | 0.215608 | ||||||||
\(568\) | −6.63855e28 | −0.796922 | ||||||||
\(569\) | −1.58661e28 | −0.186979 | −0.0934893 | − | 0.995620i | \(-0.529802\pi\) | ||||
−0.0934893 | + | 0.995620i | \(0.529802\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.59799e28 | 0.408677 | 0.204339 | − | 0.978900i | \(-0.434496\pi\) | ||||
0.204339 | + | 0.978900i | \(0.434496\pi\) | |||||||
\(572\) | 5.62437e27 | 0.0627214 | ||||||||
\(573\) | 3.51330e28 | 0.384673 | ||||||||
\(574\) | 1.26528e29 | 1.36023 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.12239e27 | 0.0634577 | ||||||||
\(577\) | 4.38317e28 | 0.446111 | 0.223055 | − | 0.974806i | \(-0.428397\pi\) | ||||
0.223055 | + | 0.974806i | \(0.428397\pi\) | |||||||
\(578\) | 1.71216e28 | 0.171120 | ||||||||
\(579\) | −2.15900e28 | −0.211899 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.80747e28 | 0.360402 | ||||||||
\(582\) | −3.76690e28 | −0.350181 | ||||||||
\(583\) | 1.15555e28 | 0.105504 | ||||||||
\(584\) | −8.44066e28 | −0.756905 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.25489e28 | −0.627633 | ||||||||
\(587\) | 1.20595e29 | 1.02478 | 0.512389 | − | 0.858754i | \(-0.328761\pi\) | ||||
0.512389 | + | 0.858754i | \(0.328761\pi\) | |||||||
\(588\) | 1.44116e29 | 1.20296 | ||||||||
\(589\) | −1.68672e29 | −1.38303 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.21158e29 | −0.958701 | ||||||||
\(592\) | 1.47244e28 | 0.114462 | ||||||||
\(593\) | 7.53007e27 | 0.0575075 | 0.0287538 | − | 0.999587i | \(-0.490846\pi\) | ||||
0.0287538 | + | 0.999587i | \(0.490846\pi\) | |||||||
\(594\) | 7.91204e27 | 0.0593651 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.40247e29 | −1.01580 | ||||||||
\(597\) | 7.56346e26 | 0.00538257 | ||||||||
\(598\) | −3.51489e27 | −0.0245782 | ||||||||
\(599\) | 2.68676e28 | 0.184607 | 0.0923033 | − | 0.995731i | \(-0.470577\pi\) | ||||
0.0923033 | + | 0.995731i | \(0.470577\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.40947e28 | 0.425246 | 0.212623 | − | 0.977134i | \(-0.431799\pi\) | ||||
0.212623 | + | 0.977134i | \(0.431799\pi\) | |||||||
\(602\) | 1.77067e29 | 1.15445 | ||||||||
\(603\) | 5.20098e27 | 0.0333237 | ||||||||
\(604\) | −3.48889e28 | −0.219685 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 6.83293e28 | 0.415570 | ||||||||
\(607\) | −4.48774e28 | −0.268254 | −0.134127 | − | 0.990964i | \(-0.542823\pi\) | ||||
−0.134127 | + | 0.990964i | \(0.542823\pi\) | |||||||
\(608\) | −3.31747e29 | −1.94903 | ||||||||
\(609\) | 2.23666e29 | 1.29157 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.65718e28 | 0.148248 | ||||||||
\(612\) | 3.70737e28 | 0.203318 | ||||||||
\(613\) | −1.67946e29 | −0.905390 | −0.452695 | − | 0.891665i | \(-0.649537\pi\) | ||||
−0.452695 | + | 0.891665i | \(0.649537\pi\) | |||||||
\(614\) | 1.90363e28 | 0.100882 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.04932e29 | 1.04957 | ||||||||
\(617\) | −1.45325e29 | −0.731723 | −0.365862 | − | 0.930669i | \(-0.619226\pi\) | ||||
−0.365862 | + | 0.930669i | \(0.619226\pi\) | |||||||
\(618\) | 7.46469e28 | 0.369516 | ||||||||
\(619\) | −2.90308e29 | −1.41289 | −0.706443 | − | 0.707770i | \(-0.749701\pi\) | ||||
−0.706443 | + | 0.707770i | \(0.749701\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.51099e28 | 0.0710888 | ||||||||
\(622\) | 1.40981e29 | 0.652171 | ||||||||
\(623\) | −6.78432e29 | −3.08590 | ||||||||
\(624\) | 5.55466e27 | 0.0248439 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −9.24238e28 | −0.399718 | ||||||||
\(627\) | −1.59565e29 | −0.678624 | ||||||||
\(628\) | 1.96424e28 | 0.0821521 | ||||||||
\(629\) | −7.01564e28 | −0.288559 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.05402e28 | −0.201062 | −0.100531 | − | 0.994934i | \(-0.532054\pi\) | ||||
−0.100531 | + | 0.994934i | \(0.532054\pi\) | |||||||
\(632\) | 2.05033e29 | 0.802220 | ||||||||
\(633\) | 1.86327e29 | 0.717028 | ||||||||
\(634\) | 5.43243e28 | 0.205616 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.01745e28 | 0.0738759 | ||||||||
\(637\) | −1.02881e29 | −0.370569 | ||||||||
\(638\) | 1.00370e29 | 0.355620 | ||||||||
\(639\) | −8.75395e28 | −0.305102 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.86202e29 | 1.63986 | 0.819931 | − | 0.572462i | \(-0.194012\pi\) | ||||
0.819931 | + | 0.572462i | \(0.194012\pi\) | |||||||
\(642\) | −2.61951e28 | −0.0869166 | ||||||||
\(643\) | 3.08867e29 | 1.00822 | 0.504111 | − | 0.863639i | \(-0.331820\pi\) | ||||
0.504111 | + | 0.863639i | \(0.331820\pi\) | |||||||
\(644\) | 1.68168e29 | 0.540058 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.44669e29 | 0.760567 | ||||||||
\(647\) | 4.70559e29 | 1.43919 | 0.719596 | − | 0.694393i | \(-0.244327\pi\) | ||||
0.719596 | + | 0.694393i | \(0.244327\pi\) | |||||||
\(648\) | 3.21473e28 | 0.0967402 | ||||||||
\(649\) | 2.30699e29 | 0.683089 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.85657e29 | 0.818926 | ||||||||
\(652\) | 2.52614e29 | 0.712619 | ||||||||
\(653\) | 1.04545e29 | 0.290211 | 0.145106 | − | 0.989416i | \(-0.453648\pi\) | ||||
0.145106 | + | 0.989416i | \(0.453648\pi\) | |||||||
\(654\) | 5.98576e28 | 0.163513 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.71360e29 | −0.453334 | ||||||||
\(657\) | −1.11303e29 | −0.289782 | ||||||||
\(658\) | 4.16020e29 | 1.06596 | ||||||||
\(659\) | −3.23730e29 | −0.816367 | −0.408184 | − | 0.912900i | \(-0.633838\pi\) | ||||
−0.408184 | + | 0.912900i | \(0.633838\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.98605e29 | 0.729428 | 0.364714 | − | 0.931120i | \(-0.381167\pi\) | ||||
0.364714 | + | 0.931120i | \(0.381167\pi\) | |||||||
\(662\) | 1.55420e29 | 0.373678 | ||||||||
\(663\) | −2.64659e28 | −0.0626317 | ||||||||
\(664\) | 6.94216e28 | 0.161707 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.61400e28 | −0.0589964 | ||||||||
\(667\) | 1.91680e29 | 0.425849 | ||||||||
\(668\) | 3.30962e29 | 0.723812 | ||||||||
\(669\) | 3.66033e29 | 0.788035 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.07011e28 | 0.126652 | ||||||||
\(672\) | 5.61834e29 | 1.15407 | ||||||||
\(673\) | 2.49272e29 | 0.504099 | 0.252049 | − | 0.967714i | \(-0.418895\pi\) | ||||
0.252049 | + | 0.967714i | \(0.418895\pi\) | |||||||
\(674\) | −1.85384e29 | −0.369099 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.83374e29 | 0.739915 | ||||||||
\(677\) | −6.42171e29 | −1.22031 | −0.610154 | − | 0.792283i | \(-0.708892\pi\) | ||||
−0.610154 | + | 0.792283i | \(0.708892\pi\) | |||||||
\(678\) | −2.92876e29 | −0.547990 | ||||||||
\(679\) | −1.28658e30 | −2.37030 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.37856e29 | 1.13940 | ||||||||
\(682\) | 1.28188e29 | 0.225482 | ||||||||
\(683\) | −5.44201e29 | −0.942632 | −0.471316 | − | 0.881964i | \(-0.656221\pi\) | ||||
−0.471316 | + | 0.881964i | \(0.656221\pi\) | |||||||
\(684\) | −2.78582e29 | −0.475187 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.02829e30 | −1.70103 | ||||||||
\(687\) | −6.14749e29 | −1.00150 | ||||||||
\(688\) | −2.39806e29 | −0.384752 | ||||||||
\(689\) | −1.44020e28 | −0.0227573 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.13440e30 | −1.73879 | −0.869397 | − | 0.494114i | \(-0.835492\pi\) | ||||
−0.869397 | + | 0.494114i | \(0.835492\pi\) | |||||||
\(692\) | −1.40857e29 | −0.212649 | ||||||||
\(693\) | 2.70234e29 | 0.401829 | ||||||||
\(694\) | −5.81511e28 | −0.0851694 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.07811e29 | 0.579511 | ||||||||
\(697\) | 8.16463e29 | 1.14286 | ||||||||
\(698\) | −2.41001e29 | −0.332305 | ||||||||
\(699\) | −1.54345e29 | −0.209644 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.56419e28 | 0.0601623 | 0.0300812 | − | 0.999547i | \(-0.490423\pi\) | ||||
0.0300812 | + | 0.999547i | \(0.490423\pi\) | |||||||
\(702\) | −9.86107e27 | −0.0128051 | ||||||||
\(703\) | 5.27175e29 | 0.674410 | ||||||||
\(704\) | 9.38370e28 | 0.118266 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.66164e29 | 0.570281 | ||||||||
\(707\) | 2.33377e30 | 2.81290 | ||||||||
\(708\) | 4.02774e29 | 0.478313 | ||||||||
\(709\) | 4.21173e29 | 0.492805 | 0.246403 | − | 0.969168i | \(-0.420751\pi\) | ||||
0.246403 | + | 0.969168i | \(0.420751\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.70367e29 | 0.307130 | ||||||||
\(712\) | −1.23699e30 | −1.38460 | ||||||||
\(713\) | 2.44806e29 | 0.270011 | ||||||||
\(714\) | −4.14362e29 | −0.450349 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.02207e30 | −1.07868 | ||||||||
\(717\) | 1.87403e29 | 0.194906 | ||||||||
\(718\) | −5.31171e29 | −0.544412 | ||||||||
\(719\) | 9.88968e29 | 0.998916 | 0.499458 | − | 0.866338i | \(-0.333533\pi\) | ||||
0.499458 | + | 0.866338i | \(0.333533\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.54955e30 | 2.50117 | ||||||||
\(722\) | −1.32494e30 | −1.28102 | ||||||||
\(723\) | 2.62685e29 | 0.250312 | ||||||||
\(724\) | 2.14692e29 | 0.201633 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.92951e29 | −0.176041 | ||||||||
\(727\) | −2.23750e28 | −0.0201211 | −0.0100605 | − | 0.999949i | \(-0.503202\pi\) | ||||
−0.0100605 | + | 0.999949i | \(0.503202\pi\) | |||||||
\(728\) | −2.55414e29 | −0.226394 | ||||||||
\(729\) | 4.23912e28 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.14258e30 | 0.969963 | ||||||||
\(732\) | 1.05977e29 | 0.0886841 | ||||||||
\(733\) | 4.89534e29 | 0.403823 | 0.201912 | − | 0.979404i | \(-0.435285\pi\) | ||||
0.201912 | + | 0.979404i | \(0.435285\pi\) | |||||||
\(734\) | −7.62836e29 | −0.620329 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.81487e29 | 0.380512 | ||||||||
\(737\) | 7.97147e28 | 0.0621055 | ||||||||
\(738\) | 3.04211e29 | 0.233659 | ||||||||
\(739\) | 1.30296e30 | 0.986652 | 0.493326 | − | 0.869845i | \(-0.335781\pi\) | ||||
0.493326 | + | 0.869845i | \(0.335781\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.98872e29 | 0.146380 | ||||||||
\(742\) | −2.25485e29 | −0.163635 | ||||||||
\(743\) | −1.91846e30 | −1.37268 | −0.686341 | − | 0.727280i | \(-0.740784\pi\) | ||||
−0.686341 | + | 0.727280i | \(0.740784\pi\) | |||||||
\(744\) | 5.20839e29 | 0.367441 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6.32439e29 | 0.433772 | ||||||||
\(747\) | 9.15430e28 | 0.0619097 | ||||||||
\(748\) | 5.68224e29 | 0.378924 | ||||||||
\(749\) | −8.94688e29 | −0.588318 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.65366e29 | −0.169678 | −0.0848390 | − | 0.996395i | \(-0.527038\pi\) | ||||
−0.0848390 | + | 0.996395i | \(0.527038\pi\) | |||||||
\(752\) | −5.63427e29 | −0.355263 | ||||||||
\(753\) | 8.47288e29 | 0.526846 | ||||||||
\(754\) | −1.25095e29 | −0.0767077 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.71797e29 | 0.281369 | ||||||||
\(757\) | −1.26747e30 | −0.745471 | −0.372736 | − | 0.927938i | \(-0.621580\pi\) | ||||
−0.372736 | + | 0.927938i | \(0.621580\pi\) | |||||||
\(758\) | −9.87162e29 | −0.572614 | ||||||||
\(759\) | 2.31588e29 | 0.132488 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.69492e30 | −1.49971 | −0.749854 | − | 0.661603i | \(-0.769876\pi\) | ||||
−0.749854 | + | 0.661603i | \(0.769876\pi\) | |||||||
\(762\) | −7.55051e28 | −0.0414428 | ||||||||
\(763\) | 2.04442e30 | 1.10678 | ||||||||
\(764\) | 9.40121e29 | 0.502000 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.38270e28 | −0.0175736 | ||||||||
\(767\) | −2.87529e29 | −0.147343 | ||||||||
\(768\) | 7.48046e29 | 0.378125 | ||||||||
\(769\) | 2.90682e30 | 1.44941 | 0.724707 | − | 0.689058i | \(-0.241975\pi\) | ||||
0.724707 | + | 0.689058i | \(0.241975\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.61127e29 | −0.175222 | ||||||||
\(772\) | −5.77726e29 | −0.276529 | ||||||||
\(773\) | −3.54314e30 | −1.67303 | −0.836516 | − | 0.547943i | \(-0.815411\pi\) | ||||
−0.836516 | + | 0.547943i | \(0.815411\pi\) | |||||||
\(774\) | 4.25722e29 | 0.198310 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.34582e30 | −1.06352 | ||||||||
\(777\) | −8.92804e29 | −0.399333 | ||||||||
\(778\) | −3.53569e29 | −0.156023 | ||||||||
\(779\) | −6.13514e30 | −2.67104 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.34171e30 | −0.568619 | ||||||||
\(782\) | −3.55105e29 | −0.148486 | ||||||||
\(783\) | 5.37761e29 | 0.221866 | ||||||||
\(784\) | 2.18148e30 | 0.888039 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.60446e29 | 0.142858 | ||||||||
\(787\) | 2.52723e30 | 0.988347 | 0.494174 | − | 0.869363i | \(-0.335471\pi\) | ||||
0.494174 | + | 0.869363i | \(0.335471\pi\) | |||||||
\(788\) | −3.24205e30 | −1.25111 | ||||||||
\(789\) | −5.50184e29 | −0.209507 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.00031e31 | −3.70922 | ||||||||
\(792\) | 4.92718e29 | 0.180295 | ||||||||
\(793\) | −7.56541e28 | −0.0273189 | ||||||||
\(794\) | 3.41966e29 | 0.121862 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.02390e28 | 0.00702428 | ||||||||
\(797\) | 7.95340e29 | 0.272421 | 0.136211 | − | 0.990680i | \(-0.456508\pi\) | ||||
0.136211 | + | 0.990680i | \(0.456508\pi\) | |||||||
\(798\) | 3.11364e30 | 1.05254 | ||||||||
\(799\) | 2.68451e30 | 0.895621 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.63116e30 | −0.530096 | ||||||||
\(802\) | −2.29557e30 | −0.736309 | ||||||||
\(803\) | −1.70593e30 | −0.540067 | ||||||||
\(804\) | 1.39173e29 | 0.0434876 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.59765e29 | −0.0486368 | ||||||||
\(807\) | −3.06525e30 | −0.921073 | ||||||||
\(808\) | 4.25516e30 | 1.26211 | ||||||||
\(809\) | 4.89784e29 | 0.143399 | 0.0716993 | − | 0.997426i | \(-0.477158\pi\) | ||||
0.0716993 | + | 0.997426i | \(0.477158\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.26964e30 | −0.362211 | −0.181106 | − | 0.983464i | \(-0.557968\pi\) | ||||
−0.181106 | + | 0.983464i | \(0.557968\pi\) | |||||||
\(812\) | 5.98507e30 | 1.68551 | ||||||||
\(813\) | 1.27552e29 | 0.0354598 | ||||||||
\(814\) | −4.00644e29 | −0.109952 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5.61181e29 | 0.150092 | ||||||||
\(817\) | −8.58569e30 | −2.26696 | ||||||||
\(818\) | 4.17173e29 | 0.108744 | ||||||||
\(819\) | −3.36802e29 | −0.0866751 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.19408e30 | 0.801203 | 0.400601 | − | 0.916252i | \(-0.368801\pi\) | ||||
0.400601 | + | 0.916252i | \(0.368801\pi\) | |||||||
\(822\) | −2.17426e30 | −0.538465 | ||||||||
\(823\) | 4.59957e30 | 1.12465 | 0.562327 | − | 0.826915i | \(-0.309906\pi\) | ||||
0.562327 | + | 0.826915i | \(0.309906\pi\) | |||||||
\(824\) | 4.64859e30 | 1.12224 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.50170e30 | −1.05946 | ||||||||
\(827\) | 7.96735e29 | 0.185142 | 0.0925712 | − | 0.995706i | \(-0.470491\pi\) | ||||
0.0925712 | + | 0.995706i | \(0.470491\pi\) | |||||||
\(828\) | 4.04326e29 | 0.0927712 | ||||||||
\(829\) | −5.78171e30 | −1.30989 | −0.654944 | − | 0.755678i | \(-0.727308\pi\) | ||||
−0.654944 | + | 0.755678i | \(0.727308\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.52468e30 | 0.999487 | ||||||||
\(832\) | −1.16953e29 | −0.0255103 | ||||||||
\(833\) | −1.03939e31 | −2.23875 | ||||||||
\(834\) | −1.92582e30 | −0.409612 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.26979e30 | −0.885607 | ||||||||
\(837\) | 6.86806e29 | 0.140675 | ||||||||
\(838\) | 4.97478e29 | 0.100626 | ||||||||
\(839\) | 3.18907e30 | 0.637036 | 0.318518 | − | 0.947917i | \(-0.396815\pi\) | ||||
0.318518 | + | 0.947917i | \(0.396815\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.68903e30 | 0.329063 | ||||||||
\(842\) | −4.14035e30 | −0.796636 | ||||||||
\(843\) | −5.62671e29 | −0.106922 | ||||||||
\(844\) | 4.98590e30 | 0.935724 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.00024e30 | 0.183111 | ||||||||
\(847\) | −6.59020e30 | −1.19158 | ||||||||
\(848\) | 3.05380e29 | 0.0545360 | ||||||||
\(849\) | −9.90069e29 | −0.174636 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.65126e29 | −0.131666 | ||||||||
\(852\) | −2.34246e30 | −0.398159 | ||||||||
\(853\) | −7.60896e30 | −1.27750 | −0.638750 | − | 0.769415i | \(-0.720548\pi\) | ||||
−0.638750 | + | 0.769415i | \(0.720548\pi\) | |||||||
\(854\) | −1.18448e30 | −0.196435 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.63128e30 | −0.263970 | ||||||||
\(857\) | −3.72716e30 | −0.595771 | −0.297886 | − | 0.954602i | \(-0.596281\pi\) | ||||
−0.297886 | + | 0.954602i | \(0.596281\pi\) | |||||||
\(858\) | −1.51139e29 | −0.0238650 | ||||||||
\(859\) | −7.44888e30 | −1.16188 | −0.580942 | − | 0.813945i | \(-0.697316\pi\) | ||||
−0.580942 | + | 0.813945i | \(0.697316\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.03902e31 | 1.58159 | ||||||||
\(862\) | 2.76973e29 | 0.0416496 | ||||||||
\(863\) | −2.89953e30 | −0.430740 | −0.215370 | − | 0.976533i | \(-0.569096\pi\) | ||||
−0.215370 | + | 0.976533i | \(0.569096\pi\) | |||||||
\(864\) | 1.35082e30 | 0.198245 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.42793e30 | −0.491014 | ||||||||
\(867\) | 1.40599e30 | 0.198968 | ||||||||
\(868\) | 7.64387e30 | 1.06870 | ||||||||
\(869\) | 4.14388e30 | 0.572400 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.93514e28 | −0.0133963 | ||||||||
\(872\) | 3.72759e30 | 0.496599 | ||||||||
\(873\) | −3.09332e30 | −0.407169 | ||||||||
\(874\) | 2.66836e30 | 0.347036 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.97835e30 | −0.378166 | ||||||||
\(877\) | 1.35915e31 | 1.70518 | 0.852592 | − | 0.522578i | \(-0.175030\pi\) | ||||
0.852592 | + | 0.522578i | \(0.175030\pi\) | |||||||
\(878\) | 9.39358e29 | 0.116450 | ||||||||
\(879\) | −5.95760e30 | −0.729773 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.10116e31 | −1.31705 | −0.658525 | − | 0.752559i | \(-0.728819\pi\) | ||||
−0.658525 | + | 0.752559i | \(0.728819\pi\) | |||||||
\(882\) | −3.87273e30 | −0.457717 | ||||||||
\(883\) | 4.42112e30 | 0.516351 | 0.258175 | − | 0.966098i | \(-0.416879\pi\) | ||||
0.258175 | + | 0.966098i | \(0.416879\pi\) | |||||||
\(884\) | −7.08198e29 | −0.0817346 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.62124e30 | 0.858957 | ||||||||
\(887\) | 5.76372e30 | 0.641955 | 0.320978 | − | 0.947087i | \(-0.395989\pi\) | ||||
0.320978 | + | 0.947087i | \(0.395989\pi\) | |||||||
\(888\) | −1.62785e30 | −0.179175 | ||||||||
\(889\) | −2.57886e30 | −0.280517 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.49724e29 | 0.0690260 | ||||||||
\(892\) | 9.79464e30 | 1.02839 | ||||||||
\(893\) | −2.01722e31 | −2.09321 | ||||||||
\(894\) | 3.76876e30 | 0.386505 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.81227e31 | 1.81547 | ||||||||
\(897\) | −2.88637e29 | −0.0285780 | ||||||||
\(898\) | 1.89098e30 | 0.185048 | ||||||||
\(899\) | 8.71261e30 | 0.842697 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.45502e30 | −0.137486 | ||||||||
\(902\) | 4.66260e30 | 0.435471 | ||||||||
\(903\) | 1.45404e31 | 1.34232 | ||||||||
\(904\) | −1.82387e31 | −1.66428 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 9.37543e29 | 0.0835882 | ||||||||
\(907\) | −2.23060e29 | −0.0196583 | −0.00982913 | − | 0.999952i | \(-0.503129\pi\) | ||||
−0.00982913 | + | 0.999952i | \(0.503129\pi\) | |||||||
\(908\) | 1.70683e31 | 1.48693 | ||||||||
\(909\) | 5.61109e30 | 0.483199 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.26374e31 | −1.06344 | −0.531722 | − | 0.846919i | \(-0.678455\pi\) | ||||
−0.531722 | + | 0.846919i | \(0.678455\pi\) | |||||||
\(912\) | −4.21687e30 | −0.350788 | ||||||||
\(913\) | 1.40307e30 | 0.115381 | ||||||||
\(914\) | −4.17534e29 | −0.0339435 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.64500e31 | −1.30696 | ||||||||
\(917\) | 1.23109e31 | 0.966971 | ||||||||
\(918\) | −9.96253e29 | −0.0773609 | ||||||||
\(919\) | 1.57231e31 | 1.20705 | 0.603526 | − | 0.797343i | \(-0.293762\pi\) | ||||
0.603526 | + | 0.797343i | \(0.293762\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.56323e30 | 0.117300 | ||||||||
\(922\) | 6.62074e30 | 0.491170 | ||||||||
\(923\) | 1.67222e30 | 0.122652 | ||||||||
\(924\) | 7.23117e30 | 0.524388 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.02123e30 | −0.143285 | ||||||||
\(927\) | 6.12988e30 | 0.429650 | ||||||||
\(928\) | 1.71361e31 | 1.18757 | ||||||||
\(929\) | −1.16955e31 | −0.801410 | −0.400705 | − | 0.916207i | \(-0.631235\pi\) | ||||
−0.400705 | + | 0.916207i | \(0.631235\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.81028e31 | 5.23233 | ||||||||
\(932\) | −4.13011e30 | −0.273587 | ||||||||
\(933\) | 1.15771e31 | 0.758304 | ||||||||
\(934\) | 1.03321e31 | 0.669183 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.14092e29 | −0.0388899 | ||||||||
\(937\) | −3.53331e30 | −0.221267 | −0.110633 | − | 0.993861i | \(-0.535288\pi\) | ||||
−0.110633 | + | 0.993861i | \(0.535288\pi\) | |||||||
\(938\) | −1.55549e30 | −0.0963248 | ||||||||
\(939\) | −7.58969e30 | −0.464767 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.65830e30 | −0.278956 | −0.139478 | − | 0.990225i | \(-0.544543\pi\) | ||||
−0.139478 | + | 0.990225i | \(0.544543\pi\) | |||||||
\(942\) | −5.27836e29 | −0.0312582 | ||||||||
\(943\) | 8.90436e30 | 0.521471 | ||||||||
\(944\) | 6.09676e30 | 0.353096 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.52498e30 | 0.369592 | ||||||||
\(947\) | −3.24251e30 | −0.181638 | −0.0908189 | − | 0.995867i | \(-0.528948\pi\) | ||||
−0.0908189 | + | 0.995867i | \(0.528948\pi\) | |||||||
\(948\) | 7.23473e30 | 0.400806 | ||||||||
\(949\) | 2.12616e30 | 0.116493 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.46102e30 | 0.239078 | ||||||||
\(952\) | −2.58042e31 | −1.36773 | ||||||||
\(953\) | −9.11533e30 | −0.477856 | −0.238928 | − | 0.971037i | \(-0.576796\pi\) | ||||
−0.238928 | + | 0.971037i | \(0.576796\pi\) | |||||||
\(954\) | −5.42134e29 | −0.0281092 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.01470e30 | 0.254353 | ||||||||
\(957\) | 8.24220e30 | 0.413492 | ||||||||
\(958\) | 1.19366e31 | 0.592303 | ||||||||
\(959\) | −7.42613e31 | −3.64474 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.69813e30 | −0.465685 | ||||||||
\(962\) | 4.99337e29 | 0.0237168 | ||||||||
\(963\) | −2.15110e30 | −0.101061 | ||||||||
\(964\) | 7.02915e30 | 0.326659 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.51904e30 | −0.205488 | ||||||||
\(967\) | 3.05091e31 | 1.37231 | 0.686153 | − | 0.727458i | \(-0.259298\pi\) | ||||
0.686153 | + | 0.727458i | \(0.259298\pi\) | |||||||
\(968\) | −1.20159e31 | −0.534645 | ||||||||
\(969\) | 2.00918e31 | 0.884340 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.72130e31 | 1.60285 | 0.801426 | − | 0.598094i | \(-0.204075\pi\) | ||||
0.801426 | + | 0.598094i | \(0.204075\pi\) | |||||||
\(972\) | 1.13434e30 | 0.0483335 | ||||||||
\(973\) | −6.57759e31 | −2.77257 | ||||||||
\(974\) | −1.71965e31 | −0.717084 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.60417e30 | 0.0654676 | ||||||||
\(977\) | −1.12682e31 | −0.454949 | −0.227475 | − | 0.973784i | \(-0.573047\pi\) | ||||
−0.227475 | + | 0.973784i | \(0.573047\pi\) | |||||||
\(978\) | −6.78830e30 | −0.271146 | ||||||||
\(979\) | −2.50005e31 | −0.987941 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.91541e30 | 0.190123 | ||||||||
\(982\) | 1.81240e31 | 0.693558 | ||||||||
\(983\) | −1.28263e31 | −0.485613 | −0.242807 | − | 0.970075i | \(-0.578068\pi\) | ||||
−0.242807 | + | 0.970075i | \(0.578068\pi\) | |||||||
\(984\) | 1.89445e31 | 0.709636 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.26382e31 | −0.463421 | ||||||||
\(987\) | 3.41629e31 | 1.23944 | ||||||||
\(988\) | 5.32160e30 | 0.191027 | ||||||||
\(989\) | 1.24610e31 | 0.442581 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.03312e31 | −1.05467 | −0.527334 | − | 0.849658i | \(-0.676808\pi\) | ||||
−0.527334 | + | 0.849658i | \(0.676808\pi\) | |||||||
\(992\) | 2.18855e31 | 0.752980 | ||||||||
\(993\) | 1.27628e31 | 0.434490 | ||||||||
\(994\) | 2.61811e31 | 0.881922 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.44959e30 | 0.0807925 | ||||||||
\(997\) | −5.62554e31 | −1.83597 | −0.917984 | − | 0.396618i | \(-0.870184\pi\) | ||||
−0.917984 | + | 0.396618i | \(0.870184\pi\) | |||||||
\(998\) | 3.31163e30 | 0.106948 | ||||||||
\(999\) | −2.14657e30 | −0.0685974 |
(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 | 75.22.a.e.1.2 | 3 | ||
5.2 | odd | 4 | 75.22.b.e.49.3 | 6 | |||
5.3 | odd | 4 | 75.22.b.e.49.4 | 6 | |||
5.4 | even | 2 | 15.22.a.d.1.2 | ✓ | 3 | ||
15.14 | odd | 2 | 45.22.a.b.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.22.a.d.1.2 | ✓ | 3 | 5.4 | even | 2 | ||
45.22.a.b.1.2 | 3 | 15.14 | odd | 2 | |||
75.22.a.e.1.2 | 3 | 1.1 | even | 1 | trivial | ||
75.22.b.e.49.3 | 6 | 5.2 | odd | 4 | |||
75.22.b.e.49.4 | 6 | 5.3 | odd | 4 |