Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,12,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(135.996742959\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.21206 | −0.115171 | −0.0575857 | − | 0.998341i | \(-0.518340\pi\) | ||||
−0.0575857 | + | 0.998341i | \(0.518340\pi\) | |||||||
\(3\) | 243.000 | 0.577350 | ||||||||
\(4\) | −2020.83 | −0.986736 | ||||||||
\(5\) | −8551.43 | −1.22378 | −0.611891 | − | 0.790942i | \(-0.709591\pi\) | ||||
−0.611891 | + | 0.790942i | \(0.709591\pi\) | |||||||
\(6\) | −1266.53 | −0.0664943 | ||||||||
\(7\) | −16524.4 | −0.371608 | −0.185804 | − | 0.982587i | \(-0.559489\pi\) | ||||
−0.185804 | + | 0.982587i | \(0.559489\pi\) | |||||||
\(8\) | 21207.0 | 0.228815 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | 44570.6 | 0.140945 | ||||||||
\(11\) | −89297.0 | −0.167177 | −0.0835886 | − | 0.996500i | \(-0.526638\pi\) | ||||
−0.0835886 | + | 0.996500i | \(0.526638\pi\) | |||||||
\(12\) | −491063. | −0.569692 | ||||||||
\(13\) | −114841. | −0.0857843 | −0.0428922 | − | 0.999080i | \(-0.513657\pi\) | ||||
−0.0428922 | + | 0.999080i | \(0.513657\pi\) | |||||||
\(14\) | 86126.0 | 0.0427987 | ||||||||
\(15\) | −2.07800e6 | −0.706551 | ||||||||
\(16\) | 4.02814e6 | 0.960383 | ||||||||
\(17\) | −2.27567e6 | −0.388723 | −0.194361 | − | 0.980930i | \(-0.562263\pi\) | ||||
−0.194361 | + | 0.980930i | \(0.562263\pi\) | |||||||
\(18\) | −307767. | −0.0383905 | ||||||||
\(19\) | −1.31943e7 | −1.22248 | −0.611240 | − | 0.791445i | \(-0.709329\pi\) | ||||
−0.611240 | + | 0.791445i | \(0.709329\pi\) | |||||||
\(20\) | 1.72810e7 | 1.20755 | ||||||||
\(21\) | −4.01542e6 | −0.214548 | ||||||||
\(22\) | 465421. | 0.0192540 | ||||||||
\(23\) | −2.62891e7 | −0.851671 | −0.425836 | − | 0.904801i | \(-0.640020\pi\) | ||||
−0.425836 | + | 0.904801i | \(0.640020\pi\) | |||||||
\(24\) | 5.15331e6 | 0.132107 | ||||||||
\(25\) | 2.42989e7 | 0.497641 | ||||||||
\(26\) | 598558. | 0.00987990 | ||||||||
\(27\) | 1.43489e7 | 0.192450 | ||||||||
\(28\) | 3.33930e7 | 0.366679 | ||||||||
\(29\) | −1.02740e8 | −0.930142 | −0.465071 | − | 0.885273i | \(-0.653971\pi\) | ||||
−0.465071 | + | 0.885273i | \(0.653971\pi\) | |||||||
\(30\) | 1.08307e7 | 0.0813745 | ||||||||
\(31\) | −2.81409e8 | −1.76542 | −0.882710 | − | 0.469918i | \(-0.844284\pi\) | ||||
−0.882710 | + | 0.469918i | \(0.844284\pi\) | |||||||
\(32\) | −6.44269e7 | −0.339424 | ||||||||
\(33\) | −2.16992e7 | −0.0965198 | ||||||||
\(34\) | 1.18609e7 | 0.0447698 | ||||||||
\(35\) | 1.41307e8 | 0.454767 | ||||||||
\(36\) | −1.19328e8 | −0.328912 | ||||||||
\(37\) | −9.42260e7 | −0.223389 | −0.111694 | − | 0.993743i | \(-0.535628\pi\) | ||||
−0.111694 | + | 0.993743i | \(0.535628\pi\) | |||||||
\(38\) | 6.87696e7 | 0.140795 | ||||||||
\(39\) | −2.79063e7 | −0.0495276 | ||||||||
\(40\) | −1.81350e8 | −0.280020 | ||||||||
\(41\) | −1.20015e9 | −1.61780 | −0.808901 | − | 0.587945i | \(-0.799937\pi\) | ||||
−0.808901 | + | 0.587945i | \(0.799937\pi\) | |||||||
\(42\) | 2.09286e7 | 0.0247098 | ||||||||
\(43\) | −6.09679e8 | −0.632448 | −0.316224 | − | 0.948685i | \(-0.602415\pi\) | ||||
−0.316224 | + | 0.948685i | \(0.602415\pi\) | |||||||
\(44\) | 1.80454e8 | 0.164960 | ||||||||
\(45\) | −5.04954e8 | −0.407927 | ||||||||
\(46\) | 1.37020e8 | 0.0980882 | ||||||||
\(47\) | −2.59230e9 | −1.64872 | −0.824362 | − | 0.566064i | \(-0.808466\pi\) | ||||
−0.824362 | + | 0.566064i | \(0.808466\pi\) | |||||||
\(48\) | 9.78837e8 | 0.554477 | ||||||||
\(49\) | −1.70427e9 | −0.861907 | ||||||||
\(50\) | −1.26647e8 | −0.0573141 | ||||||||
\(51\) | −5.52988e8 | −0.224429 | ||||||||
\(52\) | 2.32074e8 | 0.0846464 | ||||||||
\(53\) | 5.94524e9 | 1.95277 | 0.976387 | − | 0.216031i | \(-0.0693112\pi\) | ||||
0.976387 | + | 0.216031i | \(0.0693112\pi\) | |||||||
\(54\) | −7.47874e7 | −0.0221648 | ||||||||
\(55\) | 7.63617e8 | 0.204588 | ||||||||
\(56\) | −3.50433e8 | −0.0850296 | ||||||||
\(57\) | −3.20622e9 | −0.705799 | ||||||||
\(58\) | 5.35486e8 | 0.107126 | ||||||||
\(59\) | 7.14924e8 | 0.130189 | ||||||||
\(60\) | 4.19929e9 | 0.697179 | ||||||||
\(61\) | 4.54803e9 | 0.689460 | 0.344730 | − | 0.938702i | \(-0.387970\pi\) | ||||
0.344730 | + | 0.938702i | \(0.387970\pi\) | |||||||
\(62\) | 1.46672e9 | 0.203326 | ||||||||
\(63\) | −9.75747e8 | −0.123869 | ||||||||
\(64\) | −7.91383e9 | −0.921291 | ||||||||
\(65\) | 9.82054e8 | 0.104981 | ||||||||
\(66\) | 1.13097e8 | 0.0111163 | ||||||||
\(67\) | 9.68563e9 | 0.876428 | 0.438214 | − | 0.898871i | \(-0.355611\pi\) | ||||
0.438214 | + | 0.898871i | \(0.355611\pi\) | |||||||
\(68\) | 4.59875e9 | 0.383567 | ||||||||
\(69\) | −6.38824e9 | −0.491713 | ||||||||
\(70\) | −7.36501e8 | −0.0523762 | ||||||||
\(71\) | 1.70954e10 | 1.12450 | 0.562248 | − | 0.826968i | \(-0.309937\pi\) | ||||
0.562248 | + | 0.826968i | \(0.309937\pi\) | |||||||
\(72\) | 1.25225e9 | 0.0762717 | ||||||||
\(73\) | −8.07569e9 | −0.455936 | −0.227968 | − | 0.973669i | \(-0.573208\pi\) | ||||
−0.227968 | + | 0.973669i | \(0.573208\pi\) | |||||||
\(74\) | 4.91112e8 | 0.0257280 | ||||||||
\(75\) | 5.90463e9 | 0.287313 | ||||||||
\(76\) | 2.66635e10 | 1.20626 | ||||||||
\(77\) | 1.47557e9 | 0.0621244 | ||||||||
\(78\) | 1.45450e8 | 0.00570416 | ||||||||
\(79\) | 3.36701e10 | 1.23111 | 0.615554 | − | 0.788095i | \(-0.288932\pi\) | ||||
0.615554 | + | 0.788095i | \(0.288932\pi\) | |||||||
\(80\) | −3.44463e10 | −1.17530 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | 6.25527e9 | 0.186325 | ||||||||
\(83\) | −2.87180e10 | −0.800247 | −0.400123 | − | 0.916461i | \(-0.631033\pi\) | ||||
−0.400123 | + | 0.916461i | \(0.631033\pi\) | |||||||
\(84\) | 8.11450e9 | 0.211702 | ||||||||
\(85\) | 1.94602e10 | 0.475712 | ||||||||
\(86\) | 3.17769e9 | 0.0728400 | ||||||||
\(87\) | −2.49657e10 | −0.537018 | ||||||||
\(88\) | −1.89372e9 | −0.0382527 | ||||||||
\(89\) | −2.72935e9 | −0.0518102 | −0.0259051 | − | 0.999664i | \(-0.508247\pi\) | ||||
−0.0259051 | + | 0.999664i | \(0.508247\pi\) | |||||||
\(90\) | 2.63185e9 | 0.0469816 | ||||||||
\(91\) | 1.89767e9 | 0.0318782 | ||||||||
\(92\) | 5.31258e10 | 0.840374 | ||||||||
\(93\) | −6.83823e10 | −1.01927 | ||||||||
\(94\) | 1.35113e10 | 0.189886 | ||||||||
\(95\) | 1.12830e11 | 1.49605 | ||||||||
\(96\) | −1.56557e10 | −0.195966 | ||||||||
\(97\) | 1.22050e11 | 1.44309 | 0.721545 | − | 0.692368i | \(-0.243432\pi\) | ||||
0.721545 | + | 0.692368i | \(0.243432\pi\) | |||||||
\(98\) | 8.88278e9 | 0.0992671 | ||||||||
\(99\) | −5.27290e9 | −0.0557257 | ||||||||
\(100\) | −4.91041e10 | −0.491041 | ||||||||
\(101\) | 9.32657e10 | 0.882987 | 0.441493 | − | 0.897265i | \(-0.354449\pi\) | ||||
0.441493 | + | 0.897265i | \(0.354449\pi\) | |||||||
\(102\) | 2.88221e9 | 0.0258478 | ||||||||
\(103\) | −1.62092e11 | −1.37770 | −0.688852 | − | 0.724902i | \(-0.741885\pi\) | ||||
−0.688852 | + | 0.724902i | \(0.741885\pi\) | |||||||
\(104\) | −2.43543e9 | −0.0196288 | ||||||||
\(105\) | 3.43376e10 | 0.262560 | ||||||||
\(106\) | −3.09869e10 | −0.224904 | ||||||||
\(107\) | 1.14640e10 | 0.0790180 | 0.0395090 | − | 0.999219i | \(-0.487421\pi\) | ||||
0.0395090 | + | 0.999219i | \(0.487421\pi\) | |||||||
\(108\) | −2.89968e10 | −0.189897 | ||||||||
\(109\) | −1.94706e11 | −1.21208 | −0.606042 | − | 0.795433i | \(-0.707244\pi\) | ||||
−0.606042 | + | 0.795433i | \(0.707244\pi\) | |||||||
\(110\) | −3.98002e9 | −0.0235627 | ||||||||
\(111\) | −2.28969e10 | −0.128974 | ||||||||
\(112\) | −6.65624e10 | −0.356886 | ||||||||
\(113\) | −3.50109e11 | −1.78761 | −0.893804 | − | 0.448458i | \(-0.851973\pi\) | ||||
−0.893804 | + | 0.448458i | \(0.851973\pi\) | |||||||
\(114\) | 1.67110e10 | 0.0812879 | ||||||||
\(115\) | 2.24809e11 | 1.04226 | ||||||||
\(116\) | 2.07620e11 | 0.917804 | ||||||||
\(117\) | −6.78124e9 | −0.0285948 | ||||||||
\(118\) | −3.72623e9 | −0.0149940 | ||||||||
\(119\) | 3.76040e10 | 0.144453 | ||||||||
\(120\) | −4.40682e10 | −0.161670 | ||||||||
\(121\) | −2.77338e11 | −0.972052 | ||||||||
\(122\) | −2.37046e10 | −0.0794061 | ||||||||
\(123\) | −2.91637e11 | −0.934038 | ||||||||
\(124\) | 5.68680e11 | 1.74200 | ||||||||
\(125\) | 2.09760e11 | 0.614777 | ||||||||
\(126\) | 5.08566e9 | 0.0142662 | ||||||||
\(127\) | −4.12670e11 | −1.10836 | −0.554182 | − | 0.832396i | \(-0.686969\pi\) | ||||
−0.554182 | + | 0.832396i | \(0.686969\pi\) | |||||||
\(128\) | 1.73194e11 | 0.445530 | ||||||||
\(129\) | −1.48152e11 | −0.365144 | ||||||||
\(130\) | −5.11853e9 | −0.0120908 | ||||||||
\(131\) | −1.90011e11 | −0.430316 | −0.215158 | − | 0.976579i | \(-0.569027\pi\) | ||||
−0.215158 | + | 0.976579i | \(0.569027\pi\) | |||||||
\(132\) | 4.38504e10 | 0.0952395 | ||||||||
\(133\) | 2.18027e11 | 0.454284 | ||||||||
\(134\) | −5.04821e10 | −0.100940 | ||||||||
\(135\) | −1.22704e11 | −0.235517 | ||||||||
\(136\) | −4.82602e10 | −0.0889457 | ||||||||
\(137\) | 3.59136e11 | 0.635764 | 0.317882 | − | 0.948130i | \(-0.397028\pi\) | ||||
0.317882 | + | 0.948130i | \(0.397028\pi\) | |||||||
\(138\) | 3.32959e10 | 0.0566312 | ||||||||
\(139\) | 8.45010e11 | 1.38128 | 0.690638 | − | 0.723201i | \(-0.257330\pi\) | ||||
0.690638 | + | 0.723201i | \(0.257330\pi\) | |||||||
\(140\) | −2.85558e11 | −0.448735 | ||||||||
\(141\) | −6.29930e11 | −0.951891 | ||||||||
\(142\) | −8.91023e10 | −0.129510 | ||||||||
\(143\) | 1.02549e10 | 0.0143412 | ||||||||
\(144\) | 2.37857e11 | 0.320128 | ||||||||
\(145\) | 8.78572e11 | 1.13829 | ||||||||
\(146\) | 4.20910e10 | 0.0525108 | ||||||||
\(147\) | −4.14138e11 | −0.497622 | ||||||||
\(148\) | 1.90415e11 | 0.220426 | ||||||||
\(149\) | −6.07518e11 | −0.677695 | −0.338848 | − | 0.940841i | \(-0.610037\pi\) | ||||
−0.338848 | + | 0.940841i | \(0.610037\pi\) | |||||||
\(150\) | −3.07753e10 | −0.0330903 | ||||||||
\(151\) | 5.39506e11 | 0.559272 | 0.279636 | − | 0.960106i | \(-0.409786\pi\) | ||||
0.279636 | + | 0.960106i | \(0.409786\pi\) | |||||||
\(152\) | −2.79812e11 | −0.279722 | ||||||||
\(153\) | −1.34376e11 | −0.129574 | ||||||||
\(154\) | −7.69079e9 | −0.00715496 | ||||||||
\(155\) | 2.40645e12 | 2.16049 | ||||||||
\(156\) | 5.63940e10 | 0.0488706 | ||||||||
\(157\) | −4.28284e11 | −0.358331 | −0.179165 | − | 0.983819i | \(-0.557340\pi\) | ||||
−0.179165 | + | 0.983819i | \(0.557340\pi\) | |||||||
\(158\) | −1.75491e11 | −0.141788 | ||||||||
\(159\) | 1.44469e12 | 1.12743 | ||||||||
\(160\) | 5.50942e11 | 0.415381 | ||||||||
\(161\) | 4.34410e11 | 0.316488 | ||||||||
\(162\) | −1.81733e10 | −0.0127968 | ||||||||
\(163\) | 1.99661e12 | 1.35913 | 0.679567 | − | 0.733613i | \(-0.262168\pi\) | ||||
0.679567 | + | 0.733613i | \(0.262168\pi\) | |||||||
\(164\) | 2.42531e12 | 1.59634 | ||||||||
\(165\) | 1.85559e11 | 0.118119 | ||||||||
\(166\) | 1.49680e11 | 0.0921656 | ||||||||
\(167\) | 2.56504e12 | 1.52810 | 0.764052 | − | 0.645155i | \(-0.223207\pi\) | ||||
0.764052 | + | 0.645155i | \(0.223207\pi\) | |||||||
\(168\) | −8.51551e10 | −0.0490919 | ||||||||
\(169\) | −1.77897e12 | −0.992641 | ||||||||
\(170\) | −1.01428e11 | −0.0547884 | ||||||||
\(171\) | −7.79110e11 | −0.407493 | ||||||||
\(172\) | 1.23206e12 | 0.624059 | ||||||||
\(173\) | −2.30931e12 | −1.13300 | −0.566500 | − | 0.824062i | \(-0.691703\pi\) | ||||
−0.566500 | + | 0.824062i | \(0.691703\pi\) | |||||||
\(174\) | 1.30123e11 | 0.0618491 | ||||||||
\(175\) | −4.01524e11 | −0.184928 | ||||||||
\(176\) | −3.59700e11 | −0.160554 | ||||||||
\(177\) | 1.73727e11 | 0.0751646 | ||||||||
\(178\) | 1.42256e10 | 0.00596705 | ||||||||
\(179\) | 1.60705e12 | 0.653638 | 0.326819 | − | 0.945087i | \(-0.394023\pi\) | ||||
0.326819 | + | 0.945087i | \(0.394023\pi\) | |||||||
\(180\) | 1.02043e12 | 0.402516 | ||||||||
\(181\) | 3.40265e12 | 1.30192 | 0.650961 | − | 0.759111i | \(-0.274366\pi\) | ||||
0.650961 | + | 0.759111i | \(0.274366\pi\) | |||||||
\(182\) | −9.89078e9 | −0.00367145 | ||||||||
\(183\) | 1.10517e12 | 0.398060 | ||||||||
\(184\) | −5.57513e11 | −0.194875 | ||||||||
\(185\) | 8.05767e11 | 0.273379 | ||||||||
\(186\) | 3.56413e11 | 0.117390 | ||||||||
\(187\) | 2.03210e11 | 0.0649856 | ||||||||
\(188\) | 5.23862e12 | 1.62685 | ||||||||
\(189\) | −2.37107e11 | −0.0715161 | ||||||||
\(190\) | −5.88078e11 | −0.172302 | ||||||||
\(191\) | −5.66849e12 | −1.61355 | −0.806777 | − | 0.590856i | \(-0.798790\pi\) | ||||
−0.806777 | + | 0.590856i | \(0.798790\pi\) | |||||||
\(192\) | −1.92306e12 | −0.531907 | ||||||||
\(193\) | 1.68647e12 | 0.453330 | 0.226665 | − | 0.973973i | \(-0.427218\pi\) | ||||
0.226665 | + | 0.973973i | \(0.427218\pi\) | |||||||
\(194\) | −6.36132e11 | −0.166203 | ||||||||
\(195\) | 2.38639e11 | 0.0606110 | ||||||||
\(196\) | 3.44405e12 | 0.850475 | ||||||||
\(197\) | −5.21431e11 | −0.125208 | −0.0626041 | − | 0.998038i | \(-0.519941\pi\) | ||||
−0.0626041 | + | 0.998038i | \(0.519941\pi\) | |||||||
\(198\) | 2.74827e10 | 0.00641801 | ||||||||
\(199\) | −9.64663e11 | −0.219121 | −0.109560 | − | 0.993980i | \(-0.534944\pi\) | ||||
−0.109560 | + | 0.993980i | \(0.534944\pi\) | |||||||
\(200\) | 5.15307e11 | 0.113868 | ||||||||
\(201\) | 2.35361e12 | 0.506006 | ||||||||
\(202\) | −4.86107e11 | −0.101695 | ||||||||
\(203\) | 1.69771e12 | 0.345649 | ||||||||
\(204\) | 1.11750e12 | 0.221452 | ||||||||
\(205\) | 1.02630e13 | 1.97984 | ||||||||
\(206\) | 8.44832e11 | 0.158672 | ||||||||
\(207\) | −1.55234e12 | −0.283890 | ||||||||
\(208\) | −4.62594e11 | −0.0823858 | ||||||||
\(209\) | 1.17821e12 | 0.204371 | ||||||||
\(210\) | −1.78970e11 | −0.0302394 | ||||||||
\(211\) | 1.06069e13 | 1.74595 | 0.872977 | − | 0.487760i | \(-0.162186\pi\) | ||||
0.872977 | + | 0.487760i | \(0.162186\pi\) | |||||||
\(212\) | −1.20143e13 | −1.92687 | ||||||||
\(213\) | 4.15418e12 | 0.649228 | ||||||||
\(214\) | −5.97512e10 | −0.00910061 | ||||||||
\(215\) | 5.21363e12 | 0.773978 | ||||||||
\(216\) | 3.04298e11 | 0.0440355 | ||||||||
\(217\) | 4.65010e12 | 0.656045 | ||||||||
\(218\) | 1.01482e12 | 0.139597 | ||||||||
\(219\) | −1.96239e12 | −0.263235 | ||||||||
\(220\) | −1.54314e12 | −0.201875 | ||||||||
\(221\) | 2.61340e11 | 0.0333463 | ||||||||
\(222\) | 1.19340e11 | 0.0148541 | ||||||||
\(223\) | −4.74343e12 | −0.575991 | −0.287995 | − | 0.957632i | \(-0.592989\pi\) | ||||
−0.287995 | + | 0.957632i | \(0.592989\pi\) | |||||||
\(224\) | 1.06461e12 | 0.126133 | ||||||||
\(225\) | 1.43483e12 | 0.165880 | ||||||||
\(226\) | 1.82479e12 | 0.205881 | ||||||||
\(227\) | −1.00024e13 | −1.10144 | −0.550719 | − | 0.834691i | \(-0.685646\pi\) | ||||
−0.550719 | + | 0.834691i | \(0.685646\pi\) | |||||||
\(228\) | 6.47923e12 | 0.696437 | ||||||||
\(229\) | −1.55990e13 | −1.63682 | −0.818412 | − | 0.574632i | \(-0.805145\pi\) | ||||
−0.818412 | + | 0.574632i | \(0.805145\pi\) | |||||||
\(230\) | −1.17172e12 | −0.120039 | ||||||||
\(231\) | 3.58565e11 | 0.0358675 | ||||||||
\(232\) | −2.17880e12 | −0.212831 | ||||||||
\(233\) | −3.16513e12 | −0.301949 | −0.150975 | − | 0.988538i | \(-0.548241\pi\) | ||||
−0.150975 | + | 0.988538i | \(0.548241\pi\) | |||||||
\(234\) | 3.53442e10 | 0.00329330 | ||||||||
\(235\) | 2.21679e13 | 2.01768 | ||||||||
\(236\) | −1.44474e12 | −0.128462 | ||||||||
\(237\) | 8.18184e12 | 0.710780 | ||||||||
\(238\) | −1.95994e11 | −0.0166368 | ||||||||
\(239\) | −4.40436e12 | −0.365337 | −0.182669 | − | 0.983175i | \(-0.558474\pi\) | ||||
−0.182669 | + | 0.983175i | \(0.558474\pi\) | |||||||
\(240\) | −8.37046e12 | −0.678559 | ||||||||
\(241\) | −1.99297e12 | −0.157909 | −0.0789545 | − | 0.996878i | \(-0.525158\pi\) | ||||
−0.0789545 | + | 0.996878i | \(0.525158\pi\) | |||||||
\(242\) | 1.44550e12 | 0.111953 | ||||||||
\(243\) | 8.47289e11 | 0.0641500 | ||||||||
\(244\) | −9.19081e12 | −0.680315 | ||||||||
\(245\) | 1.45740e13 | 1.05479 | ||||||||
\(246\) | 1.52003e12 | 0.107575 | ||||||||
\(247\) | 1.51524e12 | 0.104870 | ||||||||
\(248\) | −5.96784e12 | −0.403955 | ||||||||
\(249\) | −6.97846e12 | −0.462023 | ||||||||
\(250\) | −1.09328e12 | −0.0708048 | ||||||||
\(251\) | 1.99837e13 | 1.26611 | 0.633053 | − | 0.774108i | \(-0.281801\pi\) | ||||
0.633053 | + | 0.774108i | \(0.281801\pi\) | |||||||
\(252\) | 1.97182e12 | 0.122226 | ||||||||
\(253\) | 2.34753e12 | 0.142380 | ||||||||
\(254\) | 2.15086e12 | 0.127652 | ||||||||
\(255\) | 4.72884e12 | 0.274652 | ||||||||
\(256\) | 1.53048e13 | 0.869978 | ||||||||
\(257\) | 3.10791e13 | 1.72917 | 0.864583 | − | 0.502491i | \(-0.167583\pi\) | ||||
0.864583 | + | 0.502491i | \(0.167583\pi\) | |||||||
\(258\) | 7.72178e11 | 0.0420542 | ||||||||
\(259\) | 1.55702e12 | 0.0830131 | ||||||||
\(260\) | −1.98457e12 | −0.103589 | ||||||||
\(261\) | −6.06668e12 | −0.310047 | ||||||||
\(262\) | 9.90352e11 | 0.0495601 | ||||||||
\(263\) | 1.67030e12 | 0.0818535 | 0.0409268 | − | 0.999162i | \(-0.486969\pi\) | ||||
0.0409268 | + | 0.999162i | \(0.486969\pi\) | |||||||
\(264\) | −4.60175e11 | −0.0220852 | ||||||||
\(265\) | −5.08403e13 | −2.38977 | ||||||||
\(266\) | −1.13637e12 | −0.0523205 | ||||||||
\(267\) | −6.63233e11 | −0.0299126 | ||||||||
\(268\) | −1.95731e13 | −0.864803 | ||||||||
\(269\) | 4.16327e13 | 1.80217 | 0.901087 | − | 0.433638i | \(-0.142770\pi\) | ||||
0.901087 | + | 0.433638i | \(0.142770\pi\) | |||||||
\(270\) | 6.39540e11 | 0.0271248 | ||||||||
\(271\) | −2.71374e13 | −1.12782 | −0.563908 | − | 0.825838i | \(-0.690703\pi\) | ||||
−0.563908 | + | 0.825838i | \(0.690703\pi\) | |||||||
\(272\) | −9.16671e12 | −0.373323 | ||||||||
\(273\) | 4.61134e11 | 0.0184049 | ||||||||
\(274\) | −1.87184e12 | −0.0732219 | ||||||||
\(275\) | −2.16982e12 | −0.0831943 | ||||||||
\(276\) | 1.29096e13 | 0.485190 | ||||||||
\(277\) | −2.19871e13 | −0.810082 | −0.405041 | − | 0.914299i | \(-0.632743\pi\) | ||||
−0.405041 | + | 0.914299i | \(0.632743\pi\) | |||||||
\(278\) | −4.40425e12 | −0.159083 | ||||||||
\(279\) | −1.66169e13 | −0.588474 | ||||||||
\(280\) | 2.99670e12 | 0.104058 | ||||||||
\(281\) | −2.21421e13 | −0.753934 | −0.376967 | − | 0.926227i | \(-0.623033\pi\) | ||||
−0.376967 | + | 0.926227i | \(0.623033\pi\) | |||||||
\(282\) | 3.28324e12 | 0.109631 | ||||||||
\(283\) | 3.42500e11 | 0.0112159 | 0.00560796 | − | 0.999984i | \(-0.498215\pi\) | ||||
0.00560796 | + | 0.999984i | \(0.498215\pi\) | |||||||
\(284\) | −3.45470e13 | −1.10958 | ||||||||
\(285\) | 2.74177e13 | 0.863744 | ||||||||
\(286\) | −5.34494e10 | −0.00165169 | ||||||||
\(287\) | 1.98318e13 | 0.601189 | ||||||||
\(288\) | −3.80434e12 | −0.113141 | ||||||||
\(289\) | −2.90932e13 | −0.848894 | ||||||||
\(290\) | −4.57917e12 | −0.131099 | ||||||||
\(291\) | 2.96581e13 | 0.833168 | ||||||||
\(292\) | 1.63196e13 | 0.449888 | ||||||||
\(293\) | 4.84850e13 | 1.31170 | 0.655851 | − | 0.754890i | \(-0.272310\pi\) | ||||
0.655851 | + | 0.754890i | \(0.272310\pi\) | |||||||
\(294\) | 2.15851e12 | 0.0573119 | ||||||||
\(295\) | −6.11363e12 | −0.159323 | ||||||||
\(296\) | −1.99825e12 | −0.0511147 | ||||||||
\(297\) | −1.28131e12 | −0.0321733 | ||||||||
\(298\) | 3.16642e12 | 0.0780511 | ||||||||
\(299\) | 3.01906e12 | 0.0730600 | ||||||||
\(300\) | −1.19323e13 | −0.283502 | ||||||||
\(301\) | 1.00746e13 | 0.235023 | ||||||||
\(302\) | −2.81194e12 | −0.0644121 | ||||||||
\(303\) | 2.26636e13 | 0.509793 | ||||||||
\(304\) | −5.31485e13 | −1.17405 | ||||||||
\(305\) | −3.88922e13 | −0.843748 | ||||||||
\(306\) | 7.00376e11 | 0.0149233 | ||||||||
\(307\) | 7.50703e13 | 1.57111 | 0.785556 | − | 0.618791i | \(-0.212377\pi\) | ||||
0.785556 | + | 0.618791i | \(0.212377\pi\) | |||||||
\(308\) | −2.98189e12 | −0.0613004 | ||||||||
\(309\) | −3.93883e13 | −0.795418 | ||||||||
\(310\) | −1.25426e13 | −0.248827 | ||||||||
\(311\) | −2.70953e13 | −0.528094 | −0.264047 | − | 0.964510i | \(-0.585057\pi\) | ||||
−0.264047 | + | 0.964510i | \(0.585057\pi\) | |||||||
\(312\) | −5.91810e11 | −0.0113327 | ||||||||
\(313\) | 5.44038e13 | 1.02361 | 0.511806 | − | 0.859101i | \(-0.328977\pi\) | ||||
0.511806 | + | 0.859101i | \(0.328977\pi\) | |||||||
\(314\) | 2.23225e12 | 0.0412695 | ||||||||
\(315\) | 8.34404e12 | 0.151589 | ||||||||
\(316\) | −6.80418e13 | −1.21478 | ||||||||
\(317\) | 6.63376e13 | 1.16395 | 0.581974 | − | 0.813207i | \(-0.302280\pi\) | ||||
0.581974 | + | 0.813207i | \(0.302280\pi\) | |||||||
\(318\) | −7.52983e12 | −0.129848 | ||||||||
\(319\) | 9.17434e12 | 0.155498 | ||||||||
\(320\) | 6.76746e13 | 1.12746 | ||||||||
\(321\) | 2.78575e12 | 0.0456210 | ||||||||
\(322\) | −2.26417e12 | −0.0364504 | ||||||||
\(323\) | 3.00259e13 | 0.475206 | ||||||||
\(324\) | −7.04621e12 | −0.109637 | ||||||||
\(325\) | −2.79051e12 | −0.0426898 | ||||||||
\(326\) | −1.04065e13 | −0.156533 | ||||||||
\(327\) | −4.73135e13 | −0.699797 | ||||||||
\(328\) | −2.54517e13 | −0.370178 | ||||||||
\(329\) | 4.28362e13 | 0.612679 | ||||||||
\(330\) | −9.67145e11 | −0.0136039 | ||||||||
\(331\) | 7.23224e13 | 1.00050 | 0.500252 | − | 0.865880i | \(-0.333241\pi\) | ||||
0.500252 | + | 0.865880i | \(0.333241\pi\) | |||||||
\(332\) | 5.80342e13 | 0.789632 | ||||||||
\(333\) | −5.56395e12 | −0.0744629 | ||||||||
\(334\) | −1.33691e13 | −0.175994 | ||||||||
\(335\) | −8.28260e13 | −1.07256 | ||||||||
\(336\) | −1.61747e13 | −0.206048 | ||||||||
\(337\) | −1.52367e14 | −1.90954 | −0.954768 | − | 0.297353i | \(-0.903896\pi\) | ||||
−0.954768 | + | 0.297353i | \(0.903896\pi\) | |||||||
\(338\) | 9.27212e12 | 0.114324 | ||||||||
\(339\) | −8.50766e13 | −1.03208 | ||||||||
\(340\) | −3.93259e13 | −0.469402 | ||||||||
\(341\) | 2.51289e13 | 0.295138 | ||||||||
\(342\) | 4.06077e12 | 0.0469316 | ||||||||
\(343\) | 6.08361e13 | 0.691900 | ||||||||
\(344\) | −1.29295e13 | −0.144714 | ||||||||
\(345\) | 5.46286e13 | 0.601749 | ||||||||
\(346\) | 1.20363e13 | 0.130489 | ||||||||
\(347\) | −1.14214e14 | −1.21873 | −0.609363 | − | 0.792891i | \(-0.708575\pi\) | ||||
−0.609363 | + | 0.792891i | \(0.708575\pi\) | |||||||
\(348\) | 5.04516e13 | 0.529895 | ||||||||
\(349\) | −6.78528e13 | −0.701500 | −0.350750 | − | 0.936469i | \(-0.614073\pi\) | ||||
−0.350750 | + | 0.936469i | \(0.614073\pi\) | |||||||
\(350\) | 2.09277e12 | 0.0212984 | ||||||||
\(351\) | −1.64784e12 | −0.0165092 | ||||||||
\(352\) | 5.75313e12 | 0.0567439 | ||||||||
\(353\) | −7.72969e13 | −0.750588 | −0.375294 | − | 0.926906i | \(-0.622458\pi\) | ||||
−0.375294 | + | 0.926906i | \(0.622458\pi\) | |||||||
\(354\) | −9.05474e11 | −0.00865682 | ||||||||
\(355\) | −1.46190e14 | −1.37614 | ||||||||
\(356\) | 5.51557e12 | 0.0511229 | ||||||||
\(357\) | 9.13777e12 | 0.0833998 | ||||||||
\(358\) | −8.37603e12 | −0.0752804 | ||||||||
\(359\) | 1.37432e14 | 1.21638 | 0.608190 | − | 0.793792i | \(-0.291896\pi\) | ||||
0.608190 | + | 0.793792i | \(0.291896\pi\) | |||||||
\(360\) | −1.07086e13 | −0.0933399 | ||||||||
\(361\) | 5.75994e13 | 0.494457 | ||||||||
\(362\) | −1.77348e13 | −0.149944 | ||||||||
\(363\) | −6.73931e13 | −0.561214 | ||||||||
\(364\) | −3.83488e12 | −0.0314553 | ||||||||
\(365\) | 6.90587e13 | 0.557966 | ||||||||
\(366\) | −5.76022e12 | −0.0458451 | ||||||||
\(367\) | −1.97753e14 | −1.55045 | −0.775227 | − | 0.631683i | \(-0.782364\pi\) | ||||
−0.775227 | + | 0.631683i | \(0.782364\pi\) | |||||||
\(368\) | −1.05896e14 | −0.817930 | ||||||||
\(369\) | −7.08678e13 | −0.539267 | ||||||||
\(370\) | −4.19971e12 | −0.0314855 | ||||||||
\(371\) | −9.82412e13 | −0.725667 | ||||||||
\(372\) | 1.38189e14 | 1.00575 | ||||||||
\(373\) | −1.38885e14 | −0.995997 | −0.497998 | − | 0.867178i | \(-0.665931\pi\) | ||||
−0.497998 | + | 0.867178i | \(0.665931\pi\) | |||||||
\(374\) | −1.05915e12 | −0.00748448 | ||||||||
\(375\) | 5.09717e13 | 0.354942 | ||||||||
\(376\) | −5.49751e13 | −0.377253 | ||||||||
\(377\) | 1.17987e13 | 0.0797916 | ||||||||
\(378\) | 1.23581e12 | 0.00823661 | ||||||||
\(379\) | −6.00439e13 | −0.394415 | −0.197207 | − | 0.980362i | \(-0.563187\pi\) | ||||
−0.197207 | + | 0.980362i | \(0.563187\pi\) | |||||||
\(380\) | −2.28011e14 | −1.47620 | ||||||||
\(381\) | −1.00279e14 | −0.639914 | ||||||||
\(382\) | 2.95445e13 | 0.185835 | ||||||||
\(383\) | 1.50750e14 | 0.934684 | 0.467342 | − | 0.884077i | \(-0.345212\pi\) | ||||
0.467342 | + | 0.884077i | \(0.345212\pi\) | |||||||
\(384\) | 4.20861e13 | 0.257227 | ||||||||
\(385\) | −1.26183e13 | −0.0760267 | ||||||||
\(386\) | −8.79001e12 | −0.0522106 | ||||||||
\(387\) | −3.60010e13 | −0.210816 | ||||||||
\(388\) | −2.46643e14 | −1.42395 | ||||||||
\(389\) | 1.37224e14 | 0.781098 | 0.390549 | − | 0.920582i | \(-0.372285\pi\) | ||||
0.390549 | + | 0.920582i | \(0.372285\pi\) | |||||||
\(390\) | −1.24380e12 | −0.00698065 | ||||||||
\(391\) | 5.98252e13 | 0.331064 | ||||||||
\(392\) | −3.61425e13 | −0.197217 | ||||||||
\(393\) | −4.61728e13 | −0.248443 | ||||||||
\(394\) | 2.71773e12 | 0.0144204 | ||||||||
\(395\) | −2.87928e14 | −1.50661 | ||||||||
\(396\) | 1.06556e13 | 0.0549865 | ||||||||
\(397\) | 1.01916e14 | 0.518674 | 0.259337 | − | 0.965787i | \(-0.416496\pi\) | ||||
0.259337 | + | 0.965787i | \(0.416496\pi\) | |||||||
\(398\) | 5.02789e12 | 0.0252365 | ||||||||
\(399\) | 5.29807e13 | 0.262281 | ||||||||
\(400\) | 9.78793e13 | 0.477926 | ||||||||
\(401\) | −3.55470e14 | −1.71202 | −0.856009 | − | 0.516960i | \(-0.827063\pi\) | ||||
−0.856009 | + | 0.516960i | \(0.827063\pi\) | |||||||
\(402\) | −1.22672e13 | −0.0582775 | ||||||||
\(403\) | 3.23172e13 | 0.151445 | ||||||||
\(404\) | −1.88474e14 | −0.871274 | ||||||||
\(405\) | −2.98170e13 | −0.135976 | ||||||||
\(406\) | −8.84856e12 | −0.0398088 | ||||||||
\(407\) | 8.41409e12 | 0.0373455 | ||||||||
\(408\) | −1.17272e13 | −0.0513528 | ||||||||
\(409\) | 1.58196e14 | 0.683469 | 0.341734 | − | 0.939797i | \(-0.388986\pi\) | ||||
0.341734 | + | 0.939797i | \(0.388986\pi\) | |||||||
\(410\) | −5.34916e13 | −0.228021 | ||||||||
\(411\) | 8.72701e13 | 0.367059 | ||||||||
\(412\) | 3.27560e14 | 1.35943 | ||||||||
\(413\) | −1.18137e13 | −0.0483793 | ||||||||
\(414\) | 8.09091e12 | 0.0326961 | ||||||||
\(415\) | 2.45580e14 | 0.979327 | ||||||||
\(416\) | 7.39884e12 | 0.0291172 | ||||||||
\(417\) | 2.05337e14 | 0.797480 | ||||||||
\(418\) | −6.14091e12 | −0.0235377 | ||||||||
\(419\) | −4.16354e14 | −1.57502 | −0.787510 | − | 0.616302i | \(-0.788630\pi\) | ||||
−0.787510 | + | 0.616302i | \(0.788630\pi\) | |||||||
\(420\) | −6.93906e13 | −0.259077 | ||||||||
\(421\) | −4.53385e14 | −1.67077 | −0.835383 | − | 0.549668i | \(-0.814754\pi\) | ||||
−0.835383 | + | 0.549668i | \(0.814754\pi\) | |||||||
\(422\) | −5.52836e13 | −0.201084 | ||||||||
\(423\) | −1.53073e14 | −0.549574 | ||||||||
\(424\) | 1.26081e14 | 0.446824 | ||||||||
\(425\) | −5.52963e13 | −0.193445 | ||||||||
\(426\) | −2.16519e13 | −0.0747726 | ||||||||
\(427\) | −7.51533e13 | −0.256209 | ||||||||
\(428\) | −2.31669e13 | −0.0779698 | ||||||||
\(429\) | 2.49195e12 | 0.00827988 | ||||||||
\(430\) | −2.71738e13 | −0.0891402 | ||||||||
\(431\) | 5.47784e14 | 1.77412 | 0.887062 | − | 0.461650i | \(-0.152742\pi\) | ||||
0.887062 | + | 0.461650i | \(0.152742\pi\) | |||||||
\(432\) | 5.77994e13 | 0.184826 | ||||||||
\(433\) | −3.13894e14 | −0.991059 | −0.495530 | − | 0.868591i | \(-0.665026\pi\) | ||||
−0.495530 | + | 0.868591i | \(0.665026\pi\) | |||||||
\(434\) | −2.42366e13 | −0.0755576 | ||||||||
\(435\) | 2.13493e14 | 0.657192 | ||||||||
\(436\) | 3.93468e14 | 1.19601 | ||||||||
\(437\) | 3.46866e14 | 1.04115 | ||||||||
\(438\) | 1.02281e13 | 0.0303171 | ||||||||
\(439\) | 7.60946e13 | 0.222740 | 0.111370 | − | 0.993779i | \(-0.464476\pi\) | ||||
0.111370 | + | 0.993779i | \(0.464476\pi\) | |||||||
\(440\) | 1.61940e13 | 0.0468129 | ||||||||
\(441\) | −1.00636e14 | −0.287302 | ||||||||
\(442\) | −1.36212e12 | −0.00384054 | ||||||||
\(443\) | −1.57927e14 | −0.439780 | −0.219890 | − | 0.975525i | \(-0.570570\pi\) | ||||
−0.219890 | + | 0.975525i | \(0.570570\pi\) | |||||||
\(444\) | 4.62709e13 | 0.127263 | ||||||||
\(445\) | 2.33399e13 | 0.0634043 | ||||||||
\(446\) | 2.47230e13 | 0.0663377 | ||||||||
\(447\) | −1.47627e14 | −0.391268 | ||||||||
\(448\) | 1.30771e14 | 0.342359 | ||||||||
\(449\) | 5.86221e13 | 0.151602 | 0.0758012 | − | 0.997123i | \(-0.475849\pi\) | ||||
0.0758012 | + | 0.997123i | \(0.475849\pi\) | |||||||
\(450\) | −7.47840e12 | −0.0191047 | ||||||||
\(451\) | 1.07170e14 | 0.270460 | ||||||||
\(452\) | 7.07513e14 | 1.76390 | ||||||||
\(453\) | 1.31100e14 | 0.322896 | ||||||||
\(454\) | 5.21329e13 | 0.126854 | ||||||||
\(455\) | −1.62278e13 | −0.0390119 | ||||||||
\(456\) | −6.79943e13 | −0.161498 | ||||||||
\(457\) | −2.69689e13 | −0.0632883 | −0.0316441 | − | 0.999499i | \(-0.510074\pi\) | ||||
−0.0316441 | + | 0.999499i | \(0.510074\pi\) | |||||||
\(458\) | 8.13031e13 | 0.188515 | ||||||||
\(459\) | −3.26534e13 | −0.0748098 | ||||||||
\(460\) | −4.54302e14 | −1.02843 | ||||||||
\(461\) | 7.62958e14 | 1.70665 | 0.853327 | − | 0.521376i | \(-0.174581\pi\) | ||||
0.853327 | + | 0.521376i | \(0.174581\pi\) | |||||||
\(462\) | −1.86886e12 | −0.00413092 | ||||||||
\(463\) | −1.72470e14 | −0.376720 | −0.188360 | − | 0.982100i | \(-0.560317\pi\) | ||||
−0.188360 | + | 0.982100i | \(0.560317\pi\) | |||||||
\(464\) | −4.13849e14 | −0.893292 | ||||||||
\(465\) | 5.84767e14 | 1.24736 | ||||||||
\(466\) | 1.64969e13 | 0.0347759 | ||||||||
\(467\) | 4.90313e14 | 1.02148 | 0.510741 | − | 0.859735i | \(-0.329371\pi\) | ||||
0.510741 | + | 0.859735i | \(0.329371\pi\) | |||||||
\(468\) | 1.37038e13 | 0.0282155 | ||||||||
\(469\) | −1.60049e14 | −0.325688 | ||||||||
\(470\) | −1.15541e14 | −0.232379 | ||||||||
\(471\) | −1.04073e14 | −0.206882 | ||||||||
\(472\) | 1.51614e13 | 0.0297892 | ||||||||
\(473\) | 5.44425e13 | 0.105731 | ||||||||
\(474\) | −4.26443e13 | −0.0818616 | ||||||||
\(475\) | −3.20607e14 | −0.608357 | ||||||||
\(476\) | −7.59914e13 | −0.142537 | ||||||||
\(477\) | 3.51060e14 | 0.650924 | ||||||||
\(478\) | 2.29558e13 | 0.0420764 | ||||||||
\(479\) | 7.87631e14 | 1.42718 | 0.713588 | − | 0.700566i | \(-0.247069\pi\) | ||||
0.713588 | + | 0.700566i | \(0.247069\pi\) | |||||||
\(480\) | 1.33879e14 | 0.239820 | ||||||||
\(481\) | 1.08210e13 | 0.0191632 | ||||||||
\(482\) | 1.03875e13 | 0.0181866 | ||||||||
\(483\) | 1.05562e14 | 0.182724 | ||||||||
\(484\) | 5.60454e14 | 0.959158 | ||||||||
\(485\) | −1.04370e15 | −1.76603 | ||||||||
\(486\) | −4.41612e12 | −0.00738825 | ||||||||
\(487\) | −6.23331e14 | −1.03112 | −0.515560 | − | 0.856853i | \(-0.672416\pi\) | ||||
−0.515560 | + | 0.856853i | \(0.672416\pi\) | |||||||
\(488\) | 9.64502e13 | 0.157759 | ||||||||
\(489\) | 4.85177e14 | 0.784696 | ||||||||
\(490\) | −7.59605e13 | −0.121481 | ||||||||
\(491\) | 3.47269e13 | 0.0549184 | 0.0274592 | − | 0.999623i | \(-0.491258\pi\) | ||||
0.0274592 | + | 0.999623i | \(0.491258\pi\) | |||||||
\(492\) | 5.89350e14 | 0.921649 | ||||||||
\(493\) | 2.33802e14 | 0.361568 | ||||||||
\(494\) | −7.89755e12 | −0.0120780 | ||||||||
\(495\) | 4.50908e13 | 0.0681961 | ||||||||
\(496\) | −1.13355e15 | −1.69548 | ||||||||
\(497\) | −2.82490e14 | −0.417872 | ||||||||
\(498\) | 3.63722e13 | 0.0532118 | ||||||||
\(499\) | −1.72369e14 | −0.249405 | −0.124703 | − | 0.992194i | \(-0.539798\pi\) | ||||
−0.124703 | + | 0.992194i | \(0.539798\pi\) | |||||||
\(500\) | −4.23890e14 | −0.606622 | ||||||||
\(501\) | 6.23304e14 | 0.882251 | ||||||||
\(502\) | −1.04156e14 | −0.145819 | ||||||||
\(503\) | −1.52985e14 | −0.211848 | −0.105924 | − | 0.994374i | \(-0.533780\pi\) | ||||
−0.105924 | + | 0.994374i | \(0.533780\pi\) | |||||||
\(504\) | −2.06927e13 | −0.0283432 | ||||||||
\(505\) | −7.97555e14 | −1.08058 | ||||||||
\(506\) | −1.22355e13 | −0.0163981 | ||||||||
\(507\) | −4.32290e14 | −0.573102 | ||||||||
\(508\) | 8.33937e14 | 1.09366 | ||||||||
\(509\) | 3.75714e14 | 0.487427 | 0.243714 | − | 0.969847i | \(-0.421634\pi\) | ||||
0.243714 | + | 0.969847i | \(0.421634\pi\) | |||||||
\(510\) | −2.46470e13 | −0.0316321 | ||||||||
\(511\) | 1.33446e14 | 0.169430 | ||||||||
\(512\) | −4.34470e14 | −0.545727 | ||||||||
\(513\) | −1.89324e14 | −0.235266 | ||||||||
\(514\) | −1.61986e14 | −0.199150 | ||||||||
\(515\) | 1.38612e15 | 1.68601 | ||||||||
\(516\) | 2.99391e14 | 0.360301 | ||||||||
\(517\) | 2.31485e14 | 0.275629 | ||||||||
\(518\) | −8.11531e12 | −0.00956074 | ||||||||
\(519\) | −5.61163e14 | −0.654137 | ||||||||
\(520\) | 2.08264e13 | 0.0240213 | ||||||||
\(521\) | 1.37663e13 | 0.0157112 | 0.00785560 | − | 0.999969i | \(-0.497499\pi\) | ||||
0.00785560 | + | 0.999969i | \(0.497499\pi\) | |||||||
\(522\) | 3.16199e13 | 0.0357086 | ||||||||
\(523\) | −4.65180e14 | −0.519831 | −0.259915 | − | 0.965631i | \(-0.583695\pi\) | ||||
−0.259915 | + | 0.965631i | \(0.583695\pi\) | |||||||
\(524\) | 3.83982e14 | 0.424608 | ||||||||
\(525\) | −9.75703e13 | −0.106768 | ||||||||
\(526\) | −8.70570e12 | −0.00942719 | ||||||||
\(527\) | 6.40393e14 | 0.686260 | ||||||||
\(528\) | −8.74072e13 | −0.0926959 | ||||||||
\(529\) | −2.61695e14 | −0.274656 | ||||||||
\(530\) | 2.64983e14 | 0.275233 | ||||||||
\(531\) | 4.22156e13 | 0.0433963 | ||||||||
\(532\) | −4.40597e14 | −0.448258 | ||||||||
\(533\) | 1.37827e14 | 0.138782 | ||||||||
\(534\) | 3.45681e12 | 0.00344508 | ||||||||
\(535\) | −9.80337e13 | −0.0967007 | ||||||||
\(536\) | 2.05403e14 | 0.200540 | ||||||||
\(537\) | 3.90512e14 | 0.377378 | ||||||||
\(538\) | −2.16992e14 | −0.207559 | ||||||||
\(539\) | 1.52186e14 | 0.144091 | ||||||||
\(540\) | 2.47964e14 | 0.232393 | ||||||||
\(541\) | −8.31910e14 | −0.771776 | −0.385888 | − | 0.922546i | \(-0.626105\pi\) | ||||
−0.385888 | + | 0.922546i | \(0.626105\pi\) | |||||||
\(542\) | 1.41442e14 | 0.129892 | ||||||||
\(543\) | 8.26843e14 | 0.751665 | ||||||||
\(544\) | 1.46614e14 | 0.131942 | ||||||||
\(545\) | 1.66501e15 | 1.48333 | ||||||||
\(546\) | −2.40346e12 | −0.00211971 | ||||||||
\(547\) | −1.37546e15 | −1.20093 | −0.600466 | − | 0.799651i | \(-0.705018\pi\) | ||||
−0.600466 | + | 0.799651i | \(0.705018\pi\) | |||||||
\(548\) | −7.25755e14 | −0.627331 | ||||||||
\(549\) | 2.68557e14 | 0.229820 | ||||||||
\(550\) | 1.13092e13 | 0.00958160 | ||||||||
\(551\) | 1.35558e15 | 1.13708 | ||||||||
\(552\) | −1.35476e14 | −0.112511 | ||||||||
\(553\) | −5.56378e14 | −0.457490 | ||||||||
\(554\) | 1.14598e14 | 0.0932983 | ||||||||
\(555\) | 1.95801e14 | 0.157835 | ||||||||
\(556\) | −1.70762e15 | −1.36295 | ||||||||
\(557\) | 1.83778e15 | 1.45241 | 0.726206 | − | 0.687477i | \(-0.241282\pi\) | ||||
0.726206 | + | 0.687477i | \(0.241282\pi\) | |||||||
\(558\) | 8.66084e13 | 0.0677753 | ||||||||
\(559\) | 7.00161e13 | 0.0542541 | ||||||||
\(560\) | 5.69204e14 | 0.436751 | ||||||||
\(561\) | 4.93801e13 | 0.0375194 | ||||||||
\(562\) | 1.15406e14 | 0.0868316 | ||||||||
\(563\) | 1.22975e15 | 0.916262 | 0.458131 | − | 0.888885i | \(-0.348519\pi\) | ||||
0.458131 | + | 0.888885i | \(0.348519\pi\) | |||||||
\(564\) | 1.27298e15 | 0.939264 | ||||||||
\(565\) | 2.99394e15 | 2.18764 | ||||||||
\(566\) | −1.78513e12 | −0.00129175 | ||||||||
\(567\) | −5.76169e13 | −0.0412898 | ||||||||
\(568\) | 3.62542e14 | 0.257302 | ||||||||
\(569\) | −7.10444e14 | −0.499358 | −0.249679 | − | 0.968329i | \(-0.580325\pi\) | ||||
−0.249679 | + | 0.968329i | \(0.580325\pi\) | |||||||
\(570\) | −1.42903e14 | −0.0994786 | ||||||||
\(571\) | −2.86714e15 | −1.97675 | −0.988373 | − | 0.152048i | \(-0.951413\pi\) | ||||
−0.988373 | + | 0.152048i | \(0.951413\pi\) | |||||||
\(572\) | −2.07235e13 | −0.0141509 | ||||||||
\(573\) | −1.37744e15 | −0.931586 | ||||||||
\(574\) | −1.03364e14 | −0.0692398 | ||||||||
\(575\) | −6.38795e14 | −0.423827 | ||||||||
\(576\) | −4.67304e14 | −0.307097 | ||||||||
\(577\) | 1.78351e15 | 1.16094 | 0.580468 | − | 0.814283i | \(-0.302869\pi\) | ||||
0.580468 | + | 0.814283i | \(0.302869\pi\) | |||||||
\(578\) | 1.51636e14 | 0.0977684 | ||||||||
\(579\) | 4.09813e14 | 0.261730 | ||||||||
\(580\) | −1.77545e15 | −1.12319 | ||||||||
\(581\) | 4.74546e14 | 0.297378 | ||||||||
\(582\) | −1.54580e14 | −0.0959572 | ||||||||
\(583\) | −5.30891e14 | −0.326459 | ||||||||
\(584\) | −1.71261e14 | −0.104325 | ||||||||
\(585\) | 5.79893e13 | 0.0349938 | ||||||||
\(586\) | −2.52707e14 | −0.151071 | ||||||||
\(587\) | −9.89640e14 | −0.586095 | −0.293047 | − | 0.956098i | \(-0.594669\pi\) | ||||
−0.293047 | + | 0.956098i | \(0.594669\pi\) | |||||||
\(588\) | 8.36905e14 | 0.491022 | ||||||||
\(589\) | 3.71299e15 | 2.15819 | ||||||||
\(590\) | 3.18646e13 | 0.0183494 | ||||||||
\(591\) | −1.26708e14 | −0.0722890 | ||||||||
\(592\) | −3.79555e14 | −0.214539 | ||||||||
\(593\) | 3.41739e15 | 1.91379 | 0.956894 | − | 0.290437i | \(-0.0938008\pi\) | ||||
0.956894 | + | 0.290437i | \(0.0938008\pi\) | |||||||
\(594\) | 6.67829e12 | 0.00370544 | ||||||||
\(595\) | −3.21568e14 | −0.176779 | ||||||||
\(596\) | 1.22769e15 | 0.668706 | ||||||||
\(597\) | −2.34413e14 | −0.126509 | ||||||||
\(598\) | −1.57355e13 | −0.00841443 | ||||||||
\(599\) | −1.53010e15 | −0.810725 | −0.405362 | − | 0.914156i | \(-0.632855\pi\) | ||||
−0.405362 | + | 0.914156i | \(0.632855\pi\) | |||||||
\(600\) | 1.25220e14 | 0.0657417 | ||||||||
\(601\) | 7.71695e14 | 0.401454 | 0.200727 | − | 0.979647i | \(-0.435670\pi\) | ||||
0.200727 | + | 0.979647i | \(0.435670\pi\) | |||||||
\(602\) | −5.25093e13 | −0.0270679 | ||||||||
\(603\) | 5.71927e14 | 0.292143 | ||||||||
\(604\) | −1.09025e15 | −0.551853 | ||||||||
\(605\) | 2.37164e15 | 1.18958 | ||||||||
\(606\) | −1.18124e14 | −0.0587136 | ||||||||
\(607\) | −1.94990e15 | −0.960451 | −0.480225 | − | 0.877145i | \(-0.659445\pi\) | ||||
−0.480225 | + | 0.877145i | \(0.659445\pi\) | |||||||
\(608\) | 8.50068e14 | 0.414939 | ||||||||
\(609\) | 4.12543e14 | 0.199560 | ||||||||
\(610\) | 2.02708e14 | 0.0971757 | ||||||||
\(611\) | 2.97702e14 | 0.141435 | ||||||||
\(612\) | 2.71552e14 | 0.127856 | ||||||||
\(613\) | −2.81617e15 | −1.31409 | −0.657047 | − | 0.753850i | \(-0.728195\pi\) | ||||
−0.657047 | + | 0.753850i | \(0.728195\pi\) | |||||||
\(614\) | −3.91271e14 | −0.180947 | ||||||||
\(615\) | 2.49392e15 | 1.14306 | ||||||||
\(616\) | 3.12926e13 | 0.0142150 | ||||||||
\(617\) | 3.74732e15 | 1.68715 | 0.843573 | − | 0.537014i | \(-0.180448\pi\) | ||||
0.843573 | + | 0.537014i | \(0.180448\pi\) | |||||||
\(618\) | 2.05294e14 | 0.0916094 | ||||||||
\(619\) | 9.40230e14 | 0.415849 | 0.207924 | − | 0.978145i | \(-0.433329\pi\) | ||||
0.207924 | + | 0.978145i | \(0.433329\pi\) | |||||||
\(620\) | −4.86303e15 | −2.13183 | ||||||||
\(621\) | −3.77219e14 | −0.163904 | ||||||||
\(622\) | 1.41222e14 | 0.0608213 | ||||||||
\(623\) | 4.51008e13 | 0.0192531 | ||||||||
\(624\) | −1.12410e14 | −0.0475654 | ||||||||
\(625\) | −2.98022e15 | −1.24999 | ||||||||
\(626\) | −2.83556e14 | −0.117891 | ||||||||
\(627\) | 2.86305e14 | 0.117993 | ||||||||
\(628\) | 8.65492e14 | 0.353578 | ||||||||
\(629\) | 2.14427e14 | 0.0868363 | ||||||||
\(630\) | −4.34897e13 | −0.0174587 | ||||||||
\(631\) | 4.12374e15 | 1.64108 | 0.820540 | − | 0.571589i | \(-0.193673\pi\) | ||||
0.820540 | + | 0.571589i | \(0.193673\pi\) | |||||||
\(632\) | 7.14044e14 | 0.281696 | ||||||||
\(633\) | 2.57747e15 | 1.00803 | ||||||||
\(634\) | −3.45756e14 | −0.134054 | ||||||||
\(635\) | 3.52892e15 | 1.35639 | ||||||||
\(636\) | −2.91948e15 | −1.11248 | ||||||||
\(637\) | 1.95720e14 | 0.0739381 | ||||||||
\(638\) | −4.78173e13 | −0.0179090 | ||||||||
\(639\) | 1.00947e15 | 0.374832 | ||||||||
\(640\) | −1.48105e15 | −0.545232 | ||||||||
\(641\) | −7.38983e14 | −0.269721 | −0.134861 | − | 0.990865i | \(-0.543059\pi\) | ||||
−0.134861 | + | 0.990865i | \(0.543059\pi\) | |||||||
\(642\) | −1.45195e13 | −0.00525424 | ||||||||
\(643\) | −5.39380e15 | −1.93524 | −0.967620 | − | 0.252412i | \(-0.918776\pi\) | ||||
−0.967620 | + | 0.252412i | \(0.918776\pi\) | |||||||
\(644\) | −8.77870e14 | −0.312290 | ||||||||
\(645\) | 1.26691e15 | 0.446857 | ||||||||
\(646\) | −1.56497e14 | −0.0547302 | ||||||||
\(647\) | −2.67699e14 | −0.0928268 | −0.0464134 | − | 0.998922i | \(-0.514779\pi\) | ||||
−0.0464134 | + | 0.998922i | \(0.514779\pi\) | |||||||
\(648\) | 7.39443e13 | 0.0254239 | ||||||||
\(649\) | −6.38406e13 | −0.0217646 | ||||||||
\(650\) | 1.45443e13 | 0.00491665 | ||||||||
\(651\) | 1.12997e15 | 0.378768 | ||||||||
\(652\) | −4.03483e15 | −1.34111 | ||||||||
\(653\) | 4.11687e14 | 0.135689 | 0.0678445 | − | 0.997696i | \(-0.478388\pi\) | ||||
0.0678445 | + | 0.997696i | \(0.478388\pi\) | |||||||
\(654\) | 2.46601e14 | 0.0805966 | ||||||||
\(655\) | 1.62487e15 | 0.526613 | ||||||||
\(656\) | −4.83438e15 | −1.55371 | ||||||||
\(657\) | −4.76861e14 | −0.151979 | ||||||||
\(658\) | −2.23265e14 | −0.0705631 | ||||||||
\(659\) | −1.67225e15 | −0.524121 | −0.262061 | − | 0.965051i | \(-0.584402\pi\) | ||||
−0.262061 | + | 0.965051i | \(0.584402\pi\) | |||||||
\(660\) | −3.74984e14 | −0.116552 | ||||||||
\(661\) | −7.32781e14 | −0.225874 | −0.112937 | − | 0.993602i | \(-0.536026\pi\) | ||||
−0.112937 | + | 0.993602i | \(0.536026\pi\) | |||||||
\(662\) | −3.76949e14 | −0.115229 | ||||||||
\(663\) | 6.35056e13 | 0.0192525 | ||||||||
\(664\) | −6.09022e14 | −0.183109 | ||||||||
\(665\) | −1.86445e15 | −0.555944 | ||||||||
\(666\) | 2.89997e13 | 0.00857600 | ||||||||
\(667\) | 2.70093e15 | 0.792175 | ||||||||
\(668\) | −5.18351e15 | −1.50783 | ||||||||
\(669\) | −1.15265e15 | −0.332548 | ||||||||
\(670\) | 4.31695e14 | 0.123528 | ||||||||
\(671\) | −4.06125e14 | −0.115262 | ||||||||
\(672\) | 2.58701e14 | 0.0728228 | ||||||||
\(673\) | −5.90906e15 | −1.64982 | −0.824908 | − | 0.565267i | \(-0.808773\pi\) | ||||
−0.824908 | + | 0.565267i | \(0.808773\pi\) | |||||||
\(674\) | 7.94149e14 | 0.219924 | ||||||||
\(675\) | 3.48663e14 | 0.0957711 | ||||||||
\(676\) | 3.59501e15 | 0.979474 | ||||||||
\(677\) | −2.93415e15 | −0.792949 | −0.396474 | − | 0.918046i | \(-0.629766\pi\) | ||||
−0.396474 | + | 0.918046i | \(0.629766\pi\) | |||||||
\(678\) | 4.43425e14 | 0.118866 | ||||||||
\(679\) | −2.01680e15 | −0.536264 | ||||||||
\(680\) | 4.12694e14 | 0.108850 | ||||||||
\(681\) | −2.43057e15 | −0.635915 | ||||||||
\(682\) | −1.30974e14 | −0.0339915 | ||||||||
\(683\) | −2.31821e15 | −0.596815 | −0.298407 | − | 0.954439i | \(-0.596455\pi\) | ||||
−0.298407 | + | 0.954439i | \(0.596455\pi\) | |||||||
\(684\) | 1.57445e15 | 0.402088 | ||||||||
\(685\) | −3.07113e15 | −0.778037 | ||||||||
\(686\) | −3.17082e14 | −0.0796871 | ||||||||
\(687\) | −3.79056e15 | −0.945021 | ||||||||
\(688\) | −2.45587e15 | −0.607392 | ||||||||
\(689\) | −6.82756e14 | −0.167517 | ||||||||
\(690\) | −2.84728e14 | −0.0693043 | ||||||||
\(691\) | 5.28556e15 | 1.27633 | 0.638163 | − | 0.769901i | \(-0.279695\pi\) | ||||
0.638163 | + | 0.769901i | \(0.279695\pi\) | |||||||
\(692\) | 4.66674e15 | 1.11797 | ||||||||
\(693\) | 8.71312e13 | 0.0207081 | ||||||||
\(694\) | 5.95289e14 | 0.140362 | ||||||||
\(695\) | −7.22605e15 | −1.69038 | ||||||||
\(696\) | −5.29449e14 | −0.122878 | ||||||||
\(697\) | 2.73115e15 | 0.628877 | ||||||||
\(698\) | 3.53653e14 | 0.0807928 | ||||||||
\(699\) | −7.69127e14 | −0.174331 | ||||||||
\(700\) | 8.11413e14 | 0.182475 | ||||||||
\(701\) | 5.74005e15 | 1.28076 | 0.640378 | − | 0.768060i | \(-0.278778\pi\) | ||||
0.640378 | + | 0.768060i | \(0.278778\pi\) | |||||||
\(702\) | 8.58865e12 | 0.00190139 | ||||||||
\(703\) | 1.24325e15 | 0.273088 | ||||||||
\(704\) | 7.06681e14 | 0.154019 | ||||||||
\(705\) | 5.38680e15 | 1.16491 | ||||||||
\(706\) | 4.02877e14 | 0.0864462 | ||||||||
\(707\) | −1.54116e15 | −0.328125 | ||||||||
\(708\) | −3.51073e14 | −0.0741676 | ||||||||
\(709\) | −7.44495e14 | −0.156066 | −0.0780328 | − | 0.996951i | \(-0.524864\pi\) | ||||
−0.0780328 | + | 0.996951i | \(0.524864\pi\) | |||||||
\(710\) | 7.61952e14 | 0.158492 | ||||||||
\(711\) | 1.98819e15 | 0.410369 | ||||||||
\(712\) | −5.78815e13 | −0.0118550 | ||||||||
\(713\) | 7.39797e15 | 1.50356 | ||||||||
\(714\) | −4.76266e13 | −0.00960527 | ||||||||
\(715\) | −8.76944e13 | −0.0175505 | ||||||||
\(716\) | −3.24758e15 | −0.644967 | ||||||||
\(717\) | −1.07026e15 | −0.210928 | ||||||||
\(718\) | −7.16306e14 | −0.140092 | ||||||||
\(719\) | −6.85041e15 | −1.32956 | −0.664779 | − | 0.747040i | \(-0.731474\pi\) | ||||
−0.664779 | + | 0.747040i | \(0.731474\pi\) | |||||||
\(720\) | −2.03402e15 | −0.391766 | ||||||||
\(721\) | 2.67846e15 | 0.511966 | ||||||||
\(722\) | −3.00212e14 | −0.0569473 | ||||||||
\(723\) | −4.84291e14 | −0.0911688 | ||||||||
\(724\) | −6.87619e15 | −1.28465 | ||||||||
\(725\) | −2.49646e15 | −0.462877 | ||||||||
\(726\) | 3.51257e14 | 0.0646359 | ||||||||
\(727\) | −5.98546e15 | −1.09310 | −0.546548 | − | 0.837428i | \(-0.684058\pi\) | ||||
−0.546548 | + | 0.837428i | \(0.684058\pi\) | |||||||
\(728\) | 4.02440e13 | 0.00729421 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | −3.59939e14 | −0.0642618 | ||||||||
\(731\) | 1.38743e15 | 0.245847 | ||||||||
\(732\) | −2.23337e15 | −0.392780 | ||||||||
\(733\) | −6.65829e15 | −1.16223 | −0.581113 | − | 0.813823i | \(-0.697383\pi\) | ||||
−0.581113 | + | 0.813823i | \(0.697383\pi\) | |||||||
\(734\) | 1.03070e15 | 0.178568 | ||||||||
\(735\) | 3.54148e15 | 0.608981 | ||||||||
\(736\) | 1.69372e15 | 0.289077 | ||||||||
\(737\) | −8.64897e14 | −0.146519 | ||||||||
\(738\) | 3.69368e14 | 0.0621082 | ||||||||
\(739\) | −8.08499e15 | −1.34938 | −0.674692 | − | 0.738100i | \(-0.735723\pi\) | ||||
−0.674692 | + | 0.738100i | \(0.735723\pi\) | |||||||
\(740\) | −1.62832e15 | −0.269753 | ||||||||
\(741\) | 3.68204e14 | 0.0605465 | ||||||||
\(742\) | 5.12040e14 | 0.0835761 | ||||||||
\(743\) | −8.56884e15 | −1.38830 | −0.694150 | − | 0.719830i | \(-0.744220\pi\) | ||||
−0.694150 | + | 0.719830i | \(0.744220\pi\) | |||||||
\(744\) | −1.45019e15 | −0.233224 | ||||||||
\(745\) | 5.19515e15 | 0.829351 | ||||||||
\(746\) | 7.23879e14 | 0.114710 | ||||||||
\(747\) | −1.69577e15 | −0.266749 | ||||||||
\(748\) | −4.10655e14 | −0.0641236 | ||||||||
\(749\) | −1.89435e14 | −0.0293637 | ||||||||
\(750\) | −2.65668e14 | −0.0408792 | ||||||||
\(751\) | −4.53331e15 | −0.692462 | −0.346231 | − | 0.938149i | \(-0.612539\pi\) | ||||
−0.346231 | + | 0.938149i | \(0.612539\pi\) | |||||||
\(752\) | −1.04422e16 | −1.58340 | ||||||||
\(753\) | 4.85604e15 | 0.730987 | ||||||||
\(754\) | −6.14956e13 | −0.00918971 | ||||||||
\(755\) | −4.61355e15 | −0.684426 | ||||||||
\(756\) | 4.79153e14 | 0.0705674 | ||||||||
\(757\) | 2.66059e15 | 0.389001 | 0.194501 | − | 0.980902i | \(-0.437691\pi\) | ||||
0.194501 | + | 0.980902i | \(0.437691\pi\) | |||||||
\(758\) | 3.12953e14 | 0.0454253 | ||||||||
\(759\) | 5.70450e14 | 0.0822031 | ||||||||
\(760\) | 2.39279e15 | 0.342319 | ||||||||
\(761\) | 5.68425e15 | 0.807342 | 0.403671 | − | 0.914904i | \(-0.367734\pi\) | ||||
0.403671 | + | 0.914904i | \(0.367734\pi\) | |||||||
\(762\) | 5.22659e14 | 0.0736998 | ||||||||
\(763\) | 3.21739e15 | 0.450420 | ||||||||
\(764\) | 1.14551e16 | 1.59215 | ||||||||
\(765\) | 1.14911e15 | 0.158571 | ||||||||
\(766\) | −7.85720e14 | −0.107649 | ||||||||
\(767\) | −8.21025e13 | −0.0111682 | ||||||||
\(768\) | 3.71907e15 | 0.502282 | ||||||||
\(769\) | 1.54022e15 | 0.206532 | 0.103266 | − | 0.994654i | \(-0.467071\pi\) | ||||
0.103266 | + | 0.994654i | \(0.467071\pi\) | |||||||
\(770\) | 6.57673e13 | 0.00875611 | ||||||||
\(771\) | 7.55223e15 | 0.998334 | ||||||||
\(772\) | −3.40808e15 | −0.447317 | ||||||||
\(773\) | −7.67995e14 | −0.100086 | −0.0500428 | − | 0.998747i | \(-0.515936\pi\) | ||||
−0.0500428 | + | 0.998747i | \(0.515936\pi\) | |||||||
\(774\) | 1.87639e14 | 0.0242800 | ||||||||
\(775\) | −6.83792e15 | −0.878547 | ||||||||
\(776\) | 2.58832e15 | 0.330201 | ||||||||
\(777\) | 3.78357e14 | 0.0479276 | ||||||||
\(778\) | −7.15218e14 | −0.0899602 | ||||||||
\(779\) | 1.58352e16 | 1.97773 | ||||||||
\(780\) | −4.82250e14 | −0.0598070 | ||||||||
\(781\) | −1.52657e15 | −0.187990 | ||||||||
\(782\) | −3.11813e14 | −0.0381291 | ||||||||
\(783\) | −1.47420e15 | −0.179006 | ||||||||
\(784\) | −6.86504e15 | −0.827761 | ||||||||
\(785\) | 3.66245e15 | 0.438519 | ||||||||
\(786\) | 2.40656e14 | 0.0286136 | ||||||||
\(787\) | 5.07026e15 | 0.598645 | 0.299322 | − | 0.954152i | \(-0.403239\pi\) | ||||
0.299322 | + | 0.954152i | \(0.403239\pi\) | |||||||
\(788\) | 1.05373e15 | 0.123547 | ||||||||
\(789\) | 4.05883e14 | 0.0472582 | ||||||||
\(790\) | 1.50070e15 | 0.173518 | ||||||||
\(791\) | 5.78533e15 | 0.664290 | ||||||||
\(792\) | −1.11822e14 | −0.0127509 | ||||||||
\(793\) | −5.22299e14 | −0.0591448 | ||||||||
\(794\) | −5.31193e14 | −0.0597364 | ||||||||
\(795\) | −1.23542e16 | −1.37973 | ||||||||
\(796\) | 1.94942e15 | 0.216214 | ||||||||
\(797\) | 7.88311e15 | 0.868314 | 0.434157 | − | 0.900837i | \(-0.357046\pi\) | ||||
0.434157 | + | 0.900837i | \(0.357046\pi\) | |||||||
\(798\) | −2.76139e14 | −0.0302073 | ||||||||
\(799\) | 5.89923e15 | 0.640896 | ||||||||
\(800\) | −1.56550e15 | −0.168911 | ||||||||
\(801\) | −1.61166e14 | −0.0172701 | ||||||||
\(802\) | 1.85273e15 | 0.197176 | ||||||||
\(803\) | 7.21134e14 | 0.0762221 | ||||||||
\(804\) | −4.75625e15 | −0.499294 | ||||||||
\(805\) | −3.71483e15 | −0.387312 | ||||||||
\(806\) | −1.68439e14 | −0.0174422 | ||||||||
\(807\) | 1.01167e16 | 1.04049 | ||||||||
\(808\) | 1.97789e15 | 0.202041 | ||||||||
\(809\) | −9.15896e15 | −0.929243 | −0.464622 | − | 0.885509i | \(-0.653810\pi\) | ||||
−0.464622 | + | 0.885509i | \(0.653810\pi\) | |||||||
\(810\) | 1.55408e14 | 0.0156605 | ||||||||
\(811\) | 1.35494e16 | 1.35615 | 0.678073 | − | 0.734994i | \(-0.262815\pi\) | ||||
0.678073 | + | 0.734994i | \(0.262815\pi\) | |||||||
\(812\) | −3.43079e15 | −0.341064 | ||||||||
\(813\) | −6.59440e15 | −0.651144 | ||||||||
\(814\) | −4.38548e13 | −0.00430113 | ||||||||
\(815\) | −1.70739e16 | −1.66328 | ||||||||
\(816\) | −2.22751e15 | −0.215538 | ||||||||
\(817\) | 8.04429e15 | 0.773155 | ||||||||
\(818\) | −8.24530e14 | −0.0787161 | ||||||||
\(819\) | 1.12056e14 | 0.0106261 | ||||||||
\(820\) | −2.07399e16 | −1.95358 | ||||||||
\(821\) | −1.53313e15 | −0.143447 | −0.0717237 | − | 0.997425i | \(-0.522850\pi\) | ||||
−0.0717237 | + | 0.997425i | \(0.522850\pi\) | |||||||
\(822\) | −4.54858e14 | −0.0422747 | ||||||||
\(823\) | −1.19210e16 | −1.10056 | −0.550279 | − | 0.834981i | \(-0.685479\pi\) | ||||
−0.550279 | + | 0.834981i | \(0.685479\pi\) | |||||||
\(824\) | −3.43748e15 | −0.315240 | ||||||||
\(825\) | −5.27266e14 | −0.0480322 | ||||||||
\(826\) | 6.15736e13 | 0.00557191 | ||||||||
\(827\) | −4.09891e15 | −0.368459 | −0.184229 | − | 0.982883i | \(-0.558979\pi\) | ||||
−0.184229 | + | 0.982883i | \(0.558979\pi\) | |||||||
\(828\) | 3.13703e15 | 0.280125 | ||||||||
\(829\) | −3.92677e15 | −0.348326 | −0.174163 | − | 0.984717i | \(-0.555722\pi\) | ||||
−0.174163 | + | 0.984717i | \(0.555722\pi\) | |||||||
\(830\) | −1.27998e15 | −0.112791 | ||||||||
\(831\) | −5.34286e15 | −0.467701 | ||||||||
\(832\) | 9.08830e14 | 0.0790323 | ||||||||
\(833\) | 3.87836e15 | 0.335043 | ||||||||
\(834\) | −1.07023e15 | −0.0918469 | ||||||||
\(835\) | −2.19347e16 | −1.87006 | ||||||||
\(836\) | −2.38097e15 | −0.201660 | ||||||||
\(837\) | −4.03791e15 | −0.339755 | ||||||||
\(838\) | 2.17007e15 | 0.181397 | ||||||||
\(839\) | 6.60581e15 | 0.548574 | 0.274287 | − | 0.961648i | \(-0.411558\pi\) | ||||
0.274287 | + | 0.961648i | \(0.411558\pi\) | |||||||
\(840\) | 7.28198e14 | 0.0600777 | ||||||||
\(841\) | −1.64507e15 | −0.134836 | ||||||||
\(842\) | 2.36307e15 | 0.192425 | ||||||||
\(843\) | −5.38052e15 | −0.435284 | ||||||||
\(844\) | −2.14347e16 | −1.72280 | ||||||||
\(845\) | 1.52128e16 | 1.21478 | ||||||||
\(846\) | 7.97826e14 | 0.0632953 | ||||||||
\(847\) | 4.58283e15 | 0.361223 | ||||||||
\(848\) | 2.39482e16 | 1.87541 | ||||||||
\(849\) | 8.32275e13 | 0.00647552 | ||||||||
\(850\) | 2.88208e14 | 0.0222793 | ||||||||
\(851\) | 2.47711e15 | 0.190254 | ||||||||
\(852\) | −8.39491e15 | −0.640617 | ||||||||
\(853\) | 1.19891e16 | 0.909007 | 0.454503 | − | 0.890745i | \(-0.349817\pi\) | ||||
0.454503 | + | 0.890745i | \(0.349817\pi\) | |||||||
\(854\) | 3.91704e14 | 0.0295080 | ||||||||
\(855\) | 6.66251e15 | 0.498683 | ||||||||
\(856\) | 2.43118e14 | 0.0180805 | ||||||||
\(857\) | −9.30733e15 | −0.687750 | −0.343875 | − | 0.939015i | \(-0.611740\pi\) | ||||
−0.343875 | + | 0.939015i | \(0.611740\pi\) | |||||||
\(858\) | −1.29882e13 | −0.000953606 0 | ||||||||
\(859\) | 2.79249e15 | 0.203718 | 0.101859 | − | 0.994799i | \(-0.467521\pi\) | ||||
0.101859 | + | 0.994799i | \(0.467521\pi\) | |||||||
\(860\) | −1.05359e16 | −0.763712 | ||||||||
\(861\) | 4.81912e15 | 0.347096 | ||||||||
\(862\) | −2.85508e15 | −0.204328 | ||||||||
\(863\) | 4.56386e15 | 0.324544 | 0.162272 | − | 0.986746i | \(-0.448118\pi\) | ||||
0.162272 | + | 0.986746i | \(0.448118\pi\) | |||||||
\(864\) | −9.24456e14 | −0.0653221 | ||||||||
\(865\) | 1.97480e16 | 1.38654 | ||||||||
\(866\) | 1.63604e15 | 0.114142 | ||||||||
\(867\) | −7.06965e15 | −0.490109 | ||||||||
\(868\) | −9.39708e15 | −0.647343 | ||||||||
\(869\) | −3.00664e15 | −0.205813 | ||||||||
\(870\) | −1.11274e15 | −0.0756898 | ||||||||
\(871\) | −1.11231e15 | −0.0751838 | ||||||||
\(872\) | −4.12913e15 | −0.277343 | ||||||||
\(873\) | 7.20693e15 | 0.481030 | ||||||||
\(874\) | −1.80789e15 | −0.119911 | ||||||||
\(875\) | −3.46615e15 | −0.228456 | ||||||||
\(876\) | 3.96567e15 | 0.259743 | ||||||||
\(877\) | 3.01027e16 | 1.95933 | 0.979667 | − | 0.200633i | \(-0.0642997\pi\) | ||||
0.979667 | + | 0.200633i | \(0.0642997\pi\) | |||||||
\(878\) | −3.96610e14 | −0.0256533 | ||||||||
\(879\) | 1.17818e16 | 0.757311 | ||||||||
\(880\) | 3.07595e15 | 0.196483 | ||||||||
\(881\) | 1.13358e15 | 0.0719592 | 0.0359796 | − | 0.999353i | \(-0.488545\pi\) | ||||
0.0359796 | + | 0.999353i | \(0.488545\pi\) | |||||||
\(882\) | 5.24519e14 | 0.0330890 | ||||||||
\(883\) | −1.68216e16 | −1.05459 | −0.527295 | − | 0.849682i | \(-0.676794\pi\) | ||||
−0.527295 | + | 0.849682i | \(0.676794\pi\) | |||||||
\(884\) | −5.28124e14 | −0.0329040 | ||||||||
\(885\) | −1.48561e15 | −0.0919851 | ||||||||
\(886\) | 8.23125e14 | 0.0506501 | ||||||||
\(887\) | 2.54107e16 | 1.55395 | 0.776974 | − | 0.629533i | \(-0.216754\pi\) | ||||
0.776974 | + | 0.629533i | \(0.216754\pi\) | |||||||
\(888\) | −4.85575e14 | −0.0295111 | ||||||||
\(889\) | 6.81910e15 | 0.411877 | ||||||||
\(890\) | −1.21649e14 | −0.00730237 | ||||||||
\(891\) | −3.11359e14 | −0.0185752 | ||||||||
\(892\) | 9.58568e15 | 0.568350 | ||||||||
\(893\) | 3.42036e16 | 2.01553 | ||||||||
\(894\) | 7.69440e14 | 0.0450628 | ||||||||
\(895\) | −1.37426e16 | −0.799910 | ||||||||
\(896\) | −2.86191e15 | −0.165563 | ||||||||
\(897\) | 7.33631e14 | 0.0421812 | ||||||||
\(898\) | −3.05542e14 | −0.0174603 | ||||||||
\(899\) | 2.89118e16 | 1.64209 | ||||||||
\(900\) | −2.89955e15 | −0.163680 | ||||||||
\(901\) | −1.35294e16 | −0.759088 | ||||||||
\(902\) | −5.58577e14 | −0.0311492 | ||||||||
\(903\) | 2.44812e15 | 0.135691 | ||||||||
\(904\) | −7.42478e15 | −0.409032 | ||||||||
\(905\) | −2.90975e16 | −1.59327 | ||||||||
\(906\) | −6.83301e14 | −0.0371884 | ||||||||
\(907\) | −8.67146e15 | −0.469086 | −0.234543 | − | 0.972106i | \(-0.575359\pi\) | ||||
−0.234543 | + | 0.972106i | \(0.575359\pi\) | |||||||
\(908\) | 2.02131e16 | 1.08683 | ||||||||
\(909\) | 5.50724e15 | 0.294329 | ||||||||
\(910\) | 8.45804e13 | 0.00449306 | ||||||||
\(911\) | 1.89333e14 | 0.00999713 | 0.00499856 | − | 0.999988i | \(-0.498409\pi\) | ||||
0.00499856 | + | 0.999988i | \(0.498409\pi\) | |||||||
\(912\) | −1.29151e16 | −0.677837 | ||||||||
\(913\) | 2.56443e15 | 0.133783 | ||||||||
\(914\) | 1.40563e14 | 0.00728900 | ||||||||
\(915\) | −9.45080e15 | −0.487138 | ||||||||
\(916\) | 3.15230e16 | 1.61511 | ||||||||
\(917\) | 3.13982e15 | 0.159909 | ||||||||
\(918\) | 1.70191e14 | 0.00861595 | ||||||||
\(919\) | 2.69305e16 | 1.35522 | 0.677610 | − | 0.735421i | \(-0.263016\pi\) | ||||
0.677610 | + | 0.735421i | \(0.263016\pi\) | |||||||
\(920\) | 4.76753e15 | 0.238485 | ||||||||
\(921\) | 1.82421e16 | 0.907081 | ||||||||
\(922\) | −3.97659e15 | −0.196558 | ||||||||
\(923\) | −1.96325e15 | −0.0964642 | ||||||||
\(924\) | −7.24600e14 | −0.0353918 | ||||||||
\(925\) | −2.28959e15 | −0.111167 | ||||||||
\(926\) | 8.98925e14 | 0.0433874 | ||||||||
\(927\) | −9.57135e15 | −0.459235 | ||||||||
\(928\) | 6.61920e15 | 0.315712 | ||||||||
\(929\) | 2.50400e14 | 0.0118727 | 0.00593633 | − | 0.999982i | \(-0.498110\pi\) | ||||
0.00593633 | + | 0.999982i | \(0.498110\pi\) | |||||||
\(930\) | −3.04784e15 | −0.143660 | ||||||||
\(931\) | 2.24867e16 | 1.05366 | ||||||||
\(932\) | 6.39620e15 | 0.297944 | ||||||||
\(933\) | −6.58415e15 | −0.304895 | ||||||||
\(934\) | −2.55554e15 | −0.117646 | ||||||||
\(935\) | −1.73774e15 | −0.0795282 | ||||||||
\(936\) | −1.43810e14 | −0.00654292 | ||||||||
\(937\) | 1.27295e16 | 0.575764 | 0.287882 | − | 0.957666i | \(-0.407049\pi\) | ||||
0.287882 | + | 0.957666i | \(0.407049\pi\) | |||||||
\(938\) | 8.34185e14 | 0.0375100 | ||||||||
\(939\) | 1.32201e16 | 0.590982 | ||||||||
\(940\) | −4.47977e16 | −1.99091 | ||||||||
\(941\) | 4.30849e15 | 0.190363 | 0.0951815 | − | 0.995460i | \(-0.469657\pi\) | ||||
0.0951815 | + | 0.995460i | \(0.469657\pi\) | |||||||
\(942\) | 5.42436e14 | 0.0238269 | ||||||||
\(943\) | 3.15509e16 | 1.37784 | ||||||||
\(944\) | 2.87981e15 | 0.125031 | ||||||||
\(945\) | 2.02760e15 | 0.0875200 | ||||||||
\(946\) | −2.83758e14 | −0.0121772 | ||||||||
\(947\) | −8.23320e15 | −0.351272 | −0.175636 | − | 0.984455i | \(-0.556198\pi\) | ||||
−0.175636 | + | 0.984455i | \(0.556198\pi\) | |||||||
\(948\) | −1.65342e16 | −0.701352 | ||||||||
\(949\) | 9.27419e14 | 0.0391122 | ||||||||
\(950\) | 1.67102e15 | 0.0700653 | ||||||||
\(951\) | 1.61200e16 | 0.672006 | ||||||||
\(952\) | 7.97469e14 | 0.0330530 | ||||||||
\(953\) | −1.84384e15 | −0.0759821 | −0.0379911 | − | 0.999278i | \(-0.512096\pi\) | ||||
−0.0379911 | + | 0.999278i | \(0.512096\pi\) | |||||||
\(954\) | −1.82975e15 | −0.0749679 | ||||||||
\(955\) | 4.84737e16 | 1.97464 | ||||||||
\(956\) | 8.90047e15 | 0.360491 | ||||||||
\(957\) | 2.22936e15 | 0.0897771 | ||||||||
\(958\) | −4.10518e15 | −0.164370 | ||||||||
\(959\) | −5.93450e15 | −0.236255 | ||||||||
\(960\) | 1.64449e16 | 0.650938 | ||||||||
\(961\) | 5.37824e16 | 2.11671 | ||||||||
\(962\) | −5.63997e13 | −0.00220706 | ||||||||
\(963\) | 6.76938e14 | 0.0263393 | ||||||||
\(964\) | 4.02746e15 | 0.155814 | ||||||||
\(965\) | −1.44218e16 | −0.554777 | ||||||||
\(966\) | −5.50194e14 | −0.0210446 | ||||||||
\(967\) | 3.36559e16 | 1.28002 | 0.640009 | − | 0.768368i | \(-0.278931\pi\) | ||||
0.640009 | + | 0.768368i | \(0.278931\pi\) | |||||||
\(968\) | −5.88151e15 | −0.222420 | ||||||||
\(969\) | 7.29629e15 | 0.274360 | ||||||||
\(970\) | 5.43984e15 | 0.203396 | ||||||||
\(971\) | −2.08661e15 | −0.0775775 | −0.0387888 | − | 0.999247i | \(-0.512350\pi\) | ||||
−0.0387888 | + | 0.999247i | \(0.512350\pi\) | |||||||
\(972\) | −1.71223e15 | −0.0632991 | ||||||||
\(973\) | −1.39632e16 | −0.513293 | ||||||||
\(974\) | 3.24884e15 | 0.118756 | ||||||||
\(975\) | −6.78093e14 | −0.0246470 | ||||||||
\(976\) | 1.83201e16 | 0.662145 | ||||||||
\(977\) | −4.70144e15 | −0.168970 | −0.0844851 | − | 0.996425i | \(-0.526925\pi\) | ||||
−0.0844851 | + | 0.996425i | \(0.526925\pi\) | |||||||
\(978\) | −2.52877e15 | −0.0903746 | ||||||||
\(979\) | 2.43723e14 | 0.00866147 | ||||||||
\(980\) | −2.94516e16 | −1.04080 | ||||||||
\(981\) | −1.14972e16 | −0.404028 | ||||||||
\(982\) | −1.80999e14 | −0.00632503 | ||||||||
\(983\) | 2.49311e16 | 0.866358 | 0.433179 | − | 0.901308i | \(-0.357392\pi\) | ||||
0.433179 | + | 0.901308i | \(0.357392\pi\) | |||||||
\(984\) | −6.18476e15 | −0.213722 | ||||||||
\(985\) | 4.45899e15 | 0.153228 | ||||||||
\(986\) | −1.21859e15 | −0.0416423 | ||||||||
\(987\) | 1.04092e16 | 0.353731 | ||||||||
\(988\) | −3.06206e15 | −0.103479 | ||||||||
\(989\) | 1.60279e16 | 0.538638 | ||||||||
\(990\) | −2.35016e14 | −0.00785424 | ||||||||
\(991\) | 1.15949e16 | 0.385357 | 0.192678 | − | 0.981262i | \(-0.438283\pi\) | ||||
0.192678 | + | 0.981262i | \(0.438283\pi\) | |||||||
\(992\) | 1.81303e16 | 0.599226 | ||||||||
\(993\) | 1.75743e16 | 0.577641 | ||||||||
\(994\) | 1.47236e15 | 0.0481270 | ||||||||
\(995\) | 8.24925e15 | 0.268156 | ||||||||
\(996\) | 1.41023e16 | 0.455894 | ||||||||
\(997\) | 6.17929e16 | 1.98662 | 0.993311 | − | 0.115467i | \(-0.0368366\pi\) | ||||
0.993311 | + | 0.115467i | \(0.0368366\pi\) | |||||||
\(998\) | 8.98397e14 | 0.0287244 | ||||||||
\(999\) | −1.35204e15 | −0.0429912 |
(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 | 177.12.a.d.1.14 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.d.1.14 | ✓ | 28 | 1.1 | even | 1 | trivial |