Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,62,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 62, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 62);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 62 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(23.5656183265\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 180363795469121x^{2} + 166129321978984507920x + 2785609847439483545242446300 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{28}\cdot 3^{8}\cdot 5^{2}\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(4.76281e6\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −6.27881e8 | −0.413487 | −0.206744 | − | 0.978395i | \(-0.566287\pi\) | ||||
−0.206744 | + | 0.978395i | \(0.566287\pi\) | |||||||
\(3\) | −6.22194e14 | −1.74473 | −0.872364 | − | 0.488857i | \(-0.837414\pi\) | ||||
−0.872364 | + | 0.488857i | \(0.837414\pi\) | |||||||
\(4\) | −1.91161e18 | −0.829028 | ||||||||
\(5\) | 2.33985e20 | 0.112358 | 0.0561789 | − | 0.998421i | \(-0.482108\pi\) | ||||
0.0561789 | + | 0.998421i | \(0.482108\pi\) | |||||||
\(6\) | 3.90664e23 | 0.721423 | ||||||||
\(7\) | 6.25792e25 | 1.04940 | 0.524699 | − | 0.851288i | \(-0.324178\pi\) | ||||
0.524699 | + | 0.851288i | \(0.324178\pi\) | |||||||
\(8\) | 2.64806e27 | 0.756280 | ||||||||
\(9\) | 2.59952e29 | 2.04408 | ||||||||
\(10\) | −1.46915e29 | −0.0464585 | ||||||||
\(11\) | −9.05394e31 | −1.56445 | −0.782223 | − | 0.622998i | \(-0.785914\pi\) | ||||
−0.782223 | + | 0.622998i | \(0.785914\pi\) | |||||||
\(12\) | 1.18939e33 | 1.44643 | ||||||||
\(13\) | 7.79086e33 | 0.824732 | 0.412366 | − | 0.911018i | \(-0.364702\pi\) | ||||
0.412366 | + | 0.911018i | \(0.364702\pi\) | |||||||
\(14\) | −3.92923e34 | −0.433913 | ||||||||
\(15\) | −1.45584e35 | −0.196034 | ||||||||
\(16\) | 2.74521e36 | 0.516316 | ||||||||
\(17\) | −1.64134e37 | −0.485855 | −0.242927 | − | 0.970044i | \(-0.578108\pi\) | ||||
−0.242927 | + | 0.970044i | \(0.578108\pi\) | |||||||
\(18\) | −1.63219e38 | −0.845200 | ||||||||
\(19\) | 1.45265e39 | 1.44603 | 0.723014 | − | 0.690834i | \(-0.242756\pi\) | ||||
0.723014 | + | 0.690834i | \(0.242756\pi\) | |||||||
\(20\) | −4.47288e38 | −0.0931477 | ||||||||
\(21\) | −3.89364e40 | −1.83091 | ||||||||
\(22\) | 5.68480e40 | 0.646879 | ||||||||
\(23\) | −1.28631e41 | −0.377266 | −0.188633 | − | 0.982048i | \(-0.560406\pi\) | ||||
−0.188633 | + | 0.982048i | \(0.560406\pi\) | |||||||
\(24\) | −1.64761e42 | −1.31950 | ||||||||
\(25\) | −4.28206e42 | −0.987376 | ||||||||
\(26\) | −4.89173e42 | −0.341016 | ||||||||
\(27\) | −8.26143e43 | −1.82163 | ||||||||
\(28\) | −1.19627e44 | −0.869980 | ||||||||
\(29\) | 1.23922e44 | 0.309036 | 0.154518 | − | 0.987990i | \(-0.450618\pi\) | ||||
0.154518 | + | 0.987990i | \(0.450618\pi\) | |||||||
\(30\) | 9.14095e43 | 0.0810575 | ||||||||
\(31\) | 2.17946e45 | 0.710915 | 0.355457 | − | 0.934692i | \(-0.384325\pi\) | ||||
0.355457 | + | 0.934692i | \(0.384325\pi\) | |||||||
\(32\) | −7.82966e45 | −0.969770 | ||||||||
\(33\) | 5.63331e46 | 2.72953 | ||||||||
\(34\) | 1.03057e46 | 0.200895 | ||||||||
\(35\) | 1.46426e46 | 0.117908 | ||||||||
\(36\) | −4.96927e47 | −1.69460 | ||||||||
\(37\) | 5.13297e47 | 0.758955 | 0.379478 | − | 0.925201i | \(-0.376104\pi\) | ||||
0.379478 | + | 0.925201i | \(0.376104\pi\) | |||||||
\(38\) | −9.12091e47 | −0.597914 | ||||||||
\(39\) | −4.84743e48 | −1.43893 | ||||||||
\(40\) | 6.19606e47 | 0.0849739 | ||||||||
\(41\) | 1.44082e49 | 0.930469 | 0.465234 | − | 0.885188i | \(-0.345970\pi\) | ||||
0.465234 | + | 0.885188i | \(0.345970\pi\) | |||||||
\(42\) | 2.44474e49 | 0.757059 | ||||||||
\(43\) | −4.68902e49 | −0.708425 | −0.354213 | − | 0.935165i | \(-0.615251\pi\) | ||||
−0.354213 | + | 0.935165i | \(0.615251\pi\) | |||||||
\(44\) | 1.73076e50 | 1.29697 | ||||||||
\(45\) | 6.08250e49 | 0.229668 | ||||||||
\(46\) | 8.07652e49 | 0.155995 | ||||||||
\(47\) | −1.55786e51 | −1.56150 | −0.780751 | − | 0.624842i | \(-0.785163\pi\) | ||||
−0.780751 | + | 0.624842i | \(0.785163\pi\) | |||||||
\(48\) | −1.70805e51 | −0.900831 | ||||||||
\(49\) | 3.60006e50 | 0.101235 | ||||||||
\(50\) | 2.68862e51 | 0.408267 | ||||||||
\(51\) | 1.02123e52 | 0.847685 | ||||||||
\(52\) | −1.48931e52 | −0.683726 | ||||||||
\(53\) | 2.61505e52 | 0.671531 | 0.335765 | − | 0.941946i | \(-0.391005\pi\) | ||||
0.335765 | + | 0.941946i | \(0.391005\pi\) | |||||||
\(54\) | 5.18719e52 | 0.753221 | ||||||||
\(55\) | −2.11849e52 | −0.175778 | ||||||||
\(56\) | 1.65713e53 | 0.793638 | ||||||||
\(57\) | −9.03831e53 | −2.52292 | ||||||||
\(58\) | −7.78081e52 | −0.127782 | ||||||||
\(59\) | 5.85447e53 | 0.570823 | 0.285411 | − | 0.958405i | \(-0.407870\pi\) | ||||
0.285411 | + | 0.958405i | \(0.407870\pi\) | |||||||
\(60\) | 2.78300e53 | 0.162517 | ||||||||
\(61\) | −6.99841e53 | −0.246854 | −0.123427 | − | 0.992354i | \(-0.539388\pi\) | ||||
−0.123427 | + | 0.992354i | \(0.539388\pi\) | |||||||
\(62\) | −1.36844e54 | −0.293954 | ||||||||
\(63\) | 1.62676e55 | 2.14505 | ||||||||
\(64\) | −1.41392e54 | −0.115328 | ||||||||
\(65\) | 1.82294e54 | 0.0926650 | ||||||||
\(66\) | −3.53705e55 | −1.12863 | ||||||||
\(67\) | −5.65118e55 | −1.13988 | −0.569938 | − | 0.821688i | \(-0.693033\pi\) | ||||
−0.569938 | + | 0.821688i | \(0.693033\pi\) | |||||||
\(68\) | 3.13760e55 | 0.402787 | ||||||||
\(69\) | 8.00337e55 | 0.658227 | ||||||||
\(70\) | −9.19381e54 | −0.0487534 | ||||||||
\(71\) | −4.76482e56 | −1.63933 | −0.819667 | − | 0.572841i | \(-0.805841\pi\) | ||||
−0.819667 | + | 0.572841i | \(0.805841\pi\) | |||||||
\(72\) | 6.88368e56 | 1.54589 | ||||||||
\(73\) | 4.87633e56 | 0.719028 | 0.359514 | − | 0.933140i | \(-0.382942\pi\) | ||||
0.359514 | + | 0.933140i | \(0.382942\pi\) | |||||||
\(74\) | −3.22289e56 | −0.313818 | ||||||||
\(75\) | 2.66427e57 | 1.72270 | ||||||||
\(76\) | −2.77690e57 | −1.19880 | ||||||||
\(77\) | −5.66589e57 | −1.64173 | ||||||||
\(78\) | 3.04361e57 | 0.594981 | ||||||||
\(79\) | −6.21907e57 | −0.824326 | −0.412163 | − | 0.911110i | \(-0.635227\pi\) | ||||
−0.412163 | + | 0.911110i | \(0.635227\pi\) | |||||||
\(80\) | 6.42337e56 | 0.0580121 | ||||||||
\(81\) | 1.83431e58 | 1.13417 | ||||||||
\(82\) | −9.04662e57 | −0.384737 | ||||||||
\(83\) | −1.18158e58 | −0.347202 | −0.173601 | − | 0.984816i | \(-0.555540\pi\) | ||||
−0.173601 | + | 0.984816i | \(0.555540\pi\) | |||||||
\(84\) | 7.44312e58 | 1.51788 | ||||||||
\(85\) | −3.84049e57 | −0.0545895 | ||||||||
\(86\) | 2.94414e58 | 0.292925 | ||||||||
\(87\) | −7.71034e58 | −0.539183 | ||||||||
\(88\) | −2.39753e59 | −1.18316 | ||||||||
\(89\) | −8.44939e58 | −0.295414 | −0.147707 | − | 0.989031i | \(-0.547189\pi\) | ||||
−0.147707 | + | 0.989031i | \(0.547189\pi\) | |||||||
\(90\) | −3.81908e58 | −0.0949647 | ||||||||
\(91\) | 4.87546e59 | 0.865472 | ||||||||
\(92\) | 2.45893e59 | 0.312764 | ||||||||
\(93\) | −1.35605e60 | −1.24035 | ||||||||
\(94\) | 9.78147e59 | 0.645661 | ||||||||
\(95\) | 3.39899e59 | 0.162472 | ||||||||
\(96\) | 4.87157e60 | 1.69199 | ||||||||
\(97\) | 8.57527e59 | 0.217125 | 0.108563 | − | 0.994090i | \(-0.465375\pi\) | ||||
0.108563 | + | 0.994090i | \(0.465375\pi\) | |||||||
\(98\) | −2.26041e59 | −0.0418593 | ||||||||
\(99\) | −2.35359e61 | −3.19785 | ||||||||
\(100\) | 8.18562e60 | 0.818562 | ||||||||
\(101\) | −4.46035e59 | −0.0329281 | −0.0164641 | − | 0.999864i | \(-0.505241\pi\) | ||||
−0.0164641 | + | 0.999864i | \(0.505241\pi\) | |||||||
\(102\) | −6.41212e60 | −0.350507 | ||||||||
\(103\) | 1.96351e61 | 0.797074 | 0.398537 | − | 0.917152i | \(-0.369518\pi\) | ||||
0.398537 | + | 0.917152i | \(0.369518\pi\) | |||||||
\(104\) | 2.06306e61 | 0.623728 | ||||||||
\(105\) | −9.11055e60 | −0.205717 | ||||||||
\(106\) | −1.64194e61 | −0.277670 | ||||||||
\(107\) | 1.32237e61 | 0.167937 | 0.0839687 | − | 0.996468i | \(-0.473240\pi\) | ||||
0.0839687 | + | 0.996468i | \(0.473240\pi\) | |||||||
\(108\) | 1.57926e62 | 1.51018 | ||||||||
\(109\) | −1.12679e62 | −0.813455 | −0.406728 | − | 0.913549i | \(-0.633330\pi\) | ||||
−0.406728 | + | 0.913549i | \(0.633330\pi\) | |||||||
\(110\) | 1.33016e61 | 0.0726819 | ||||||||
\(111\) | −3.19371e62 | −1.32417 | ||||||||
\(112\) | 1.71793e62 | 0.541821 | ||||||||
\(113\) | −6.52796e62 | −1.56995 | −0.784973 | − | 0.619530i | \(-0.787323\pi\) | ||||
−0.784973 | + | 0.619530i | \(0.787323\pi\) | |||||||
\(114\) | 5.67498e62 | 1.04320 | ||||||||
\(115\) | −3.00978e61 | −0.0423888 | ||||||||
\(116\) | −2.36890e62 | −0.256199 | ||||||||
\(117\) | 2.02525e63 | 1.68582 | ||||||||
\(118\) | −3.67591e62 | −0.236028 | ||||||||
\(119\) | −1.02714e63 | −0.509855 | ||||||||
\(120\) | −3.85515e62 | −0.148256 | ||||||||
\(121\) | 4.84809e63 | 1.44749 | ||||||||
\(122\) | 4.39417e62 | 0.102071 | ||||||||
\(123\) | −8.96469e63 | −1.62341 | ||||||||
\(124\) | −4.16628e63 | −0.589369 | ||||||||
\(125\) | −2.01669e63 | −0.223297 | ||||||||
\(126\) | −1.02141e64 | −0.886950 | ||||||||
\(127\) | 9.36757e63 | 0.639166 | 0.319583 | − | 0.947558i | \(-0.396457\pi\) | ||||
0.319583 | + | 0.947558i | \(0.396457\pi\) | |||||||
\(128\) | 1.89418e64 | 1.01746 | ||||||||
\(129\) | 2.91748e64 | 1.23601 | ||||||||
\(130\) | −1.14459e63 | −0.0383158 | ||||||||
\(131\) | 2.23839e63 | 0.0593144 | 0.0296572 | − | 0.999560i | \(-0.490558\pi\) | ||||
0.0296572 | + | 0.999560i | \(0.490558\pi\) | |||||||
\(132\) | −1.07687e65 | −2.26286 | ||||||||
\(133\) | 9.09058e64 | 1.51746 | ||||||||
\(134\) | 3.54827e64 | 0.471324 | ||||||||
\(135\) | −1.93305e64 | −0.204674 | ||||||||
\(136\) | −4.34636e64 | −0.367442 | ||||||||
\(137\) | −3.22204e64 | −0.217848 | −0.108924 | − | 0.994050i | \(-0.534741\pi\) | ||||
−0.108924 | + | 0.994050i | \(0.534741\pi\) | |||||||
\(138\) | −5.02516e64 | −0.272169 | ||||||||
\(139\) | −4.43557e65 | −1.92752 | −0.963758 | − | 0.266776i | \(-0.914042\pi\) | ||||
−0.963758 | + | 0.266776i | \(0.914042\pi\) | |||||||
\(140\) | −2.79909e64 | −0.0977490 | ||||||||
\(141\) | 9.69289e65 | 2.72440 | ||||||||
\(142\) | 2.99174e65 | 0.677843 | ||||||||
\(143\) | −7.05380e65 | −1.29025 | ||||||||
\(144\) | 7.13623e65 | 1.05539 | ||||||||
\(145\) | 2.89958e64 | 0.0347226 | ||||||||
\(146\) | −3.06175e65 | −0.297309 | ||||||||
\(147\) | −2.23994e65 | −0.176627 | ||||||||
\(148\) | −9.81223e65 | −0.629195 | ||||||||
\(149\) | 1.19782e66 | 0.625478 | 0.312739 | − | 0.949839i | \(-0.398754\pi\) | ||||
0.312739 | + | 0.949839i | \(0.398754\pi\) | |||||||
\(150\) | −1.67285e66 | −0.712316 | ||||||||
\(151\) | −3.40521e66 | −1.18399 | −0.591994 | − | 0.805943i | \(-0.701659\pi\) | ||||
−0.591994 | + | 0.805943i | \(0.701659\pi\) | |||||||
\(152\) | 3.84670e66 | 1.09360 | ||||||||
\(153\) | −4.26670e66 | −0.993125 | ||||||||
\(154\) | 3.55750e66 | 0.678833 | ||||||||
\(155\) | 5.09962e65 | 0.0798768 | ||||||||
\(156\) | 9.26638e66 | 1.19292 | ||||||||
\(157\) | 6.21574e66 | 0.658496 | 0.329248 | − | 0.944243i | \(-0.393205\pi\) | ||||
0.329248 | + | 0.944243i | \(0.393205\pi\) | |||||||
\(158\) | 3.90483e66 | 0.340849 | ||||||||
\(159\) | −1.62707e67 | −1.17164 | ||||||||
\(160\) | −1.83202e66 | −0.108961 | ||||||||
\(161\) | −8.04965e66 | −0.395902 | ||||||||
\(162\) | −1.15173e67 | −0.468966 | ||||||||
\(163\) | 1.73234e67 | 0.584670 | 0.292335 | − | 0.956316i | \(-0.405568\pi\) | ||||
0.292335 | + | 0.956316i | \(0.405568\pi\) | |||||||
\(164\) | −2.75428e67 | −0.771385 | ||||||||
\(165\) | 1.31811e67 | 0.306684 | ||||||||
\(166\) | 7.41893e66 | 0.143564 | ||||||||
\(167\) | 3.54014e67 | 0.570385 | 0.285193 | − | 0.958470i | \(-0.407942\pi\) | ||||
0.285193 | + | 0.958470i | \(0.407942\pi\) | |||||||
\(168\) | −1.03106e68 | −1.38468 | ||||||||
\(169\) | −2.85395e67 | −0.319817 | ||||||||
\(170\) | 2.41137e66 | 0.0225721 | ||||||||
\(171\) | 3.77620e68 | 2.95579 | ||||||||
\(172\) | 8.96357e67 | 0.587304 | ||||||||
\(173\) | −1.75625e68 | −0.964231 | −0.482116 | − | 0.876108i | \(-0.660131\pi\) | ||||
−0.482116 | + | 0.876108i | \(0.660131\pi\) | |||||||
\(174\) | 4.84118e67 | 0.222946 | ||||||||
\(175\) | −2.67968e68 | −1.03615 | ||||||||
\(176\) | −2.48549e68 | −0.807749 | ||||||||
\(177\) | −3.64262e68 | −0.995931 | ||||||||
\(178\) | 5.30521e67 | 0.122150 | ||||||||
\(179\) | 4.59004e68 | 0.890839 | 0.445419 | − | 0.895322i | \(-0.353055\pi\) | ||||
0.445419 | + | 0.895322i | \(0.353055\pi\) | |||||||
\(180\) | −1.16274e68 | −0.190401 | ||||||||
\(181\) | 4.08776e68 | 0.565312 | 0.282656 | − | 0.959221i | \(-0.408784\pi\) | ||||
0.282656 | + | 0.959221i | \(0.408784\pi\) | |||||||
\(182\) | −3.06121e68 | −0.357862 | ||||||||
\(183\) | 4.35437e68 | 0.430692 | ||||||||
\(184\) | −3.40623e68 | −0.285319 | ||||||||
\(185\) | 1.20104e68 | 0.0852745 | ||||||||
\(186\) | 8.51437e68 | 0.512870 | ||||||||
\(187\) | 1.48606e69 | 0.760094 | ||||||||
\(188\) | 2.97801e69 | 1.29453 | ||||||||
\(189\) | −5.16994e69 | −1.91161 | ||||||||
\(190\) | −2.13416e68 | −0.0671803 | ||||||||
\(191\) | −6.52737e69 | −1.75074 | −0.875368 | − | 0.483457i | \(-0.839381\pi\) | ||||
−0.875368 | + | 0.483457i | \(0.839381\pi\) | |||||||
\(192\) | 8.79734e68 | 0.201217 | ||||||||
\(193\) | 3.40957e69 | 0.665582 | 0.332791 | − | 0.943001i | \(-0.392010\pi\) | ||||
0.332791 | + | 0.943001i | \(0.392010\pi\) | |||||||
\(194\) | −5.38425e68 | −0.0897785 | ||||||||
\(195\) | −1.13423e69 | −0.161675 | ||||||||
\(196\) | −6.88191e68 | −0.0839264 | ||||||||
\(197\) | 5.81412e69 | 0.607105 | 0.303552 | − | 0.952815i | \(-0.401827\pi\) | ||||
0.303552 | + | 0.952815i | \(0.401827\pi\) | |||||||
\(198\) | 1.47778e70 | 1.32227 | ||||||||
\(199\) | −1.86375e70 | −1.43011 | −0.715055 | − | 0.699068i | \(-0.753599\pi\) | ||||
−0.715055 | + | 0.699068i | \(0.753599\pi\) | |||||||
\(200\) | −1.13391e70 | −0.746733 | ||||||||
\(201\) | 3.51613e70 | 1.98877 | ||||||||
\(202\) | 2.80057e68 | 0.0136154 | ||||||||
\(203\) | 7.75493e69 | 0.324301 | ||||||||
\(204\) | −1.95220e70 | −0.702754 | ||||||||
\(205\) | 3.37130e69 | 0.104545 | ||||||||
\(206\) | −1.23285e70 | −0.329580 | ||||||||
\(207\) | −3.34380e70 | −0.771161 | ||||||||
\(208\) | 2.13875e70 | 0.425822 | ||||||||
\(209\) | −1.31522e71 | −2.26223 | ||||||||
\(210\) | 5.72033e69 | 0.0850615 | ||||||||
\(211\) | 1.02222e71 | 1.31501 | 0.657506 | − | 0.753449i | \(-0.271611\pi\) | ||||
0.657506 | + | 0.753449i | \(0.271611\pi\) | |||||||
\(212\) | −4.99895e70 | −0.556718 | ||||||||
\(213\) | 2.96465e71 | 2.86019 | ||||||||
\(214\) | −8.30290e69 | −0.0694400 | ||||||||
\(215\) | −1.09716e70 | −0.0795971 | ||||||||
\(216\) | −2.18767e71 | −1.37766 | ||||||||
\(217\) | 1.36389e71 | 0.746032 | ||||||||
\(218\) | 7.07488e70 | 0.336353 | ||||||||
\(219\) | −3.03403e71 | −1.25451 | ||||||||
\(220\) | 4.04972e70 | 0.145725 | ||||||||
\(221\) | −1.27874e71 | −0.400700 | ||||||||
\(222\) | 2.00527e71 | 0.547528 | ||||||||
\(223\) | 4.66041e71 | 1.10950 | 0.554748 | − | 0.832019i | \(-0.312815\pi\) | ||||
0.554748 | + | 0.832019i | \(0.312815\pi\) | |||||||
\(224\) | −4.89974e71 | −1.01767 | ||||||||
\(225\) | −1.11313e72 | −2.01827 | ||||||||
\(226\) | 4.09878e71 | 0.649153 | ||||||||
\(227\) | −4.66130e71 | −0.645236 | −0.322618 | − | 0.946529i | \(-0.604563\pi\) | ||||
−0.322618 | + | 0.946529i | \(0.604563\pi\) | |||||||
\(228\) | 1.72777e72 | 2.09158 | ||||||||
\(229\) | −8.29575e71 | −0.878767 | −0.439383 | − | 0.898300i | \(-0.644803\pi\) | ||||
−0.439383 | + | 0.898300i | \(0.644803\pi\) | |||||||
\(230\) | 1.88978e70 | 0.0175272 | ||||||||
\(231\) | 3.52528e72 | 2.86437 | ||||||||
\(232\) | 3.28152e71 | 0.233718 | ||||||||
\(233\) | −2.87441e72 | −1.79553 | −0.897767 | − | 0.440471i | \(-0.854812\pi\) | ||||
−0.897767 | + | 0.440471i | \(0.854812\pi\) | |||||||
\(234\) | −1.27162e72 | −0.697064 | ||||||||
\(235\) | −3.64515e71 | −0.175447 | ||||||||
\(236\) | −1.11915e72 | −0.473228 | ||||||||
\(237\) | 3.86947e72 | 1.43823 | ||||||||
\(238\) | 6.44920e71 | 0.210818 | ||||||||
\(239\) | −5.74905e72 | −1.65371 | −0.826857 | − | 0.562412i | \(-0.809873\pi\) | ||||
−0.826857 | + | 0.562412i | \(0.809873\pi\) | |||||||
\(240\) | −3.99659e71 | −0.101215 | ||||||||
\(241\) | 1.60687e72 | 0.358476 | 0.179238 | − | 0.983806i | \(-0.442637\pi\) | ||||
0.179238 | + | 0.983806i | \(0.442637\pi\) | |||||||
\(242\) | −3.04402e72 | −0.598520 | ||||||||
\(243\) | −9.06622e71 | −0.157194 | ||||||||
\(244\) | 1.33782e72 | 0.204649 | ||||||||
\(245\) | 8.42361e70 | 0.0113745 | ||||||||
\(246\) | 5.62876e72 | 0.671261 | ||||||||
\(247\) | 1.13174e73 | 1.19258 | ||||||||
\(248\) | 5.77134e72 | 0.537651 | ||||||||
\(249\) | 7.35174e72 | 0.605773 | ||||||||
\(250\) | 1.26624e72 | 0.0923305 | ||||||||
\(251\) | −2.02500e73 | −1.30730 | −0.653651 | − | 0.756796i | \(-0.726764\pi\) | ||||
−0.653651 | + | 0.756796i | \(0.726764\pi\) | |||||||
\(252\) | −3.10973e73 | −1.77831 | ||||||||
\(253\) | 1.16462e73 | 0.590213 | ||||||||
\(254\) | −5.88172e72 | −0.264287 | ||||||||
\(255\) | 2.38953e72 | 0.0952439 | ||||||||
\(256\) | −8.63288e72 | −0.305377 | ||||||||
\(257\) | 1.08823e73 | 0.341790 | 0.170895 | − | 0.985289i | \(-0.445334\pi\) | ||||
0.170895 | + | 0.985289i | \(0.445334\pi\) | |||||||
\(258\) | −1.83183e73 | −0.511074 | ||||||||
\(259\) | 3.21217e73 | 0.796446 | ||||||||
\(260\) | −3.48476e72 | −0.0768219 | ||||||||
\(261\) | 3.22138e73 | 0.631693 | ||||||||
\(262\) | −1.40544e72 | −0.0245258 | ||||||||
\(263\) | −1.14768e74 | −1.78307 | −0.891536 | − | 0.452950i | \(-0.850372\pi\) | ||||
−0.891536 | + | 0.452950i | \(0.850372\pi\) | |||||||
\(264\) | 1.49173e74 | 2.06429 | ||||||||
\(265\) | 6.11883e72 | 0.0754517 | ||||||||
\(266\) | −5.70780e73 | −0.627449 | ||||||||
\(267\) | 5.25717e73 | 0.515416 | ||||||||
\(268\) | 1.08028e74 | 0.944989 | ||||||||
\(269\) | 1.34285e72 | 0.0104853 | 0.00524267 | − | 0.999986i | \(-0.498331\pi\) | ||||
0.00524267 | + | 0.999986i | \(0.498331\pi\) | |||||||
\(270\) | 1.21372e73 | 0.0846302 | ||||||||
\(271\) | −3.00222e74 | −1.87016 | −0.935080 | − | 0.354437i | \(-0.884673\pi\) | ||||
−0.935080 | + | 0.354437i | \(0.884673\pi\) | |||||||
\(272\) | −4.50582e73 | −0.250855 | ||||||||
\(273\) | −3.03348e74 | −1.51001 | ||||||||
\(274\) | 2.02306e73 | 0.0900775 | ||||||||
\(275\) | 3.87695e74 | 1.54470 | ||||||||
\(276\) | −1.52993e74 | −0.545689 | ||||||||
\(277\) | −8.70383e73 | −0.278021 | −0.139011 | − | 0.990291i | \(-0.544392\pi\) | ||||
−0.139011 | + | 0.990291i | \(0.544392\pi\) | |||||||
\(278\) | 2.78501e74 | 0.797004 | ||||||||
\(279\) | 5.66556e74 | 1.45316 | ||||||||
\(280\) | 3.87744e73 | 0.0891714 | ||||||||
\(281\) | −1.17276e74 | −0.241917 | −0.120959 | − | 0.992658i | \(-0.538597\pi\) | ||||
−0.120959 | + | 0.992658i | \(0.538597\pi\) | |||||||
\(282\) | −6.08598e74 | −1.12650 | ||||||||
\(283\) | −1.34561e74 | −0.223580 | −0.111790 | − | 0.993732i | \(-0.535658\pi\) | ||||
−0.111790 | + | 0.993732i | \(0.535658\pi\) | |||||||
\(284\) | 9.10848e74 | 1.35905 | ||||||||
\(285\) | −2.11483e74 | −0.283470 | ||||||||
\(286\) | 4.42894e74 | 0.533502 | ||||||||
\(287\) | 9.01653e74 | 0.976431 | ||||||||
\(288\) | −2.03534e75 | −1.98228 | ||||||||
\(289\) | −8.71859e74 | −0.763945 | ||||||||
\(290\) | −1.82059e73 | −0.0143573 | ||||||||
\(291\) | −5.33549e74 | −0.378824 | ||||||||
\(292\) | −9.32164e74 | −0.596095 | ||||||||
\(293\) | 3.33052e74 | 0.191889 | 0.0959445 | − | 0.995387i | \(-0.469413\pi\) | ||||
0.0959445 | + | 0.995387i | \(0.469413\pi\) | |||||||
\(294\) | 1.40641e74 | 0.0730331 | ||||||||
\(295\) | 1.36986e74 | 0.0641364 | ||||||||
\(296\) | 1.35924e75 | 0.573983 | ||||||||
\(297\) | 7.47985e75 | 2.84984 | ||||||||
\(298\) | −7.52090e74 | −0.258627 | ||||||||
\(299\) | −1.00215e75 | −0.311144 | ||||||||
\(300\) | −5.09305e75 | −1.42817 | ||||||||
\(301\) | −2.93435e75 | −0.743419 | ||||||||
\(302\) | 2.13807e75 | 0.489564 | ||||||||
\(303\) | 2.77520e74 | 0.0574506 | ||||||||
\(304\) | 3.98783e75 | 0.746607 | ||||||||
\(305\) | −1.63752e74 | −0.0277359 | ||||||||
\(306\) | 2.67898e75 | 0.410644 | ||||||||
\(307\) | −1.19531e76 | −1.65868 | −0.829338 | − | 0.558748i | \(-0.811282\pi\) | ||||
−0.829338 | + | 0.558748i | \(0.811282\pi\) | |||||||
\(308\) | 1.08310e76 | 1.36104 | ||||||||
\(309\) | −1.22169e76 | −1.39068 | ||||||||
\(310\) | −3.20195e74 | −0.0330280 | ||||||||
\(311\) | −3.79842e75 | −0.355150 | −0.177575 | − | 0.984107i | \(-0.556825\pi\) | ||||
−0.177575 | + | 0.984107i | \(0.556825\pi\) | |||||||
\(312\) | −1.28363e76 | −1.08824 | ||||||||
\(313\) | 1.65384e76 | 1.27172 | 0.635861 | − | 0.771804i | \(-0.280645\pi\) | ||||
0.635861 | + | 0.771804i | \(0.280645\pi\) | |||||||
\(314\) | −3.90274e75 | −0.272280 | ||||||||
\(315\) | 3.80638e75 | 0.241013 | ||||||||
\(316\) | 1.18884e76 | 0.683390 | ||||||||
\(317\) | 2.82467e76 | 1.47455 | 0.737275 | − | 0.675592i | \(-0.236112\pi\) | ||||
0.737275 | + | 0.675592i | \(0.236112\pi\) | |||||||
\(318\) | 1.02161e76 | 0.484458 | ||||||||
\(319\) | −1.12198e76 | −0.483470 | ||||||||
\(320\) | −3.30836e74 | −0.0129580 | ||||||||
\(321\) | −8.22770e75 | −0.293005 | ||||||||
\(322\) | 5.05422e75 | 0.163701 | ||||||||
\(323\) | −2.38429e76 | −0.702559 | ||||||||
\(324\) | −3.50648e76 | −0.940261 | ||||||||
\(325\) | −3.33609e76 | −0.814321 | ||||||||
\(326\) | −1.08770e76 | −0.241754 | ||||||||
\(327\) | 7.01081e76 | 1.41926 | ||||||||
\(328\) | 3.81537e76 | 0.703695 | ||||||||
\(329\) | −9.74894e76 | −1.63864 | ||||||||
\(330\) | −8.27616e75 | −0.126810 | ||||||||
\(331\) | 1.56426e75 | 0.0218553 | 0.0109276 | − | 0.999940i | \(-0.496522\pi\) | ||||
0.0109276 | + | 0.999940i | \(0.496522\pi\) | |||||||
\(332\) | 2.25872e76 | 0.287840 | ||||||||
\(333\) | 1.33433e77 | 1.55136 | ||||||||
\(334\) | −2.22279e76 | −0.235847 | ||||||||
\(335\) | −1.32229e76 | −0.128074 | ||||||||
\(336\) | −1.06889e77 | −0.945330 | ||||||||
\(337\) | 4.48909e76 | 0.362615 | 0.181308 | − | 0.983426i | \(-0.441967\pi\) | ||||
0.181308 | + | 0.983426i | \(0.441967\pi\) | |||||||
\(338\) | 1.79194e76 | 0.132240 | ||||||||
\(339\) | 4.06166e77 | 2.73913 | ||||||||
\(340\) | 7.34152e75 | 0.0452563 | ||||||||
\(341\) | −1.97327e77 | −1.11219 | ||||||||
\(342\) | −2.37100e77 | −1.22218 | ||||||||
\(343\) | −2.00012e77 | −0.943162 | ||||||||
\(344\) | −1.24168e77 | −0.535768 | ||||||||
\(345\) | 1.87267e76 | 0.0739569 | ||||||||
\(346\) | 1.10272e77 | 0.398697 | ||||||||
\(347\) | −2.97382e77 | −0.984615 | −0.492307 | − | 0.870421i | \(-0.663846\pi\) | ||||
−0.492307 | + | 0.870421i | \(0.663846\pi\) | |||||||
\(348\) | 1.47392e77 | 0.446998 | ||||||||
\(349\) | 5.36967e77 | 1.49201 | 0.746005 | − | 0.665940i | \(-0.231969\pi\) | ||||
0.746005 | + | 0.665940i | \(0.231969\pi\) | |||||||
\(350\) | 1.68252e77 | 0.428435 | ||||||||
\(351\) | −6.43636e77 | −1.50236 | ||||||||
\(352\) | 7.08893e77 | 1.51715 | ||||||||
\(353\) | −7.22267e77 | −1.41765 | −0.708825 | − | 0.705384i | \(-0.750774\pi\) | ||||
−0.708825 | + | 0.705384i | \(0.750774\pi\) | |||||||
\(354\) | 2.28713e77 | 0.411805 | ||||||||
\(355\) | −1.11490e77 | −0.184192 | ||||||||
\(356\) | 1.61519e77 | 0.244906 | ||||||||
\(357\) | 6.39079e77 | 0.889558 | ||||||||
\(358\) | −2.88200e77 | −0.368351 | ||||||||
\(359\) | 7.97496e77 | 0.936155 | 0.468078 | − | 0.883687i | \(-0.344947\pi\) | ||||
0.468078 | + | 0.883687i | \(0.344947\pi\) | |||||||
\(360\) | 1.61068e77 | 0.173693 | ||||||||
\(361\) | 1.10101e78 | 1.09099 | ||||||||
\(362\) | −2.56662e77 | −0.233750 | ||||||||
\(363\) | −3.01645e78 | −2.52548 | ||||||||
\(364\) | −9.31997e77 | −0.717500 | ||||||||
\(365\) | 1.14099e77 | 0.0807884 | ||||||||
\(366\) | −2.73402e77 | −0.178086 | ||||||||
\(367\) | −2.30364e78 | −1.38070 | −0.690350 | − | 0.723476i | \(-0.742543\pi\) | ||||
−0.690350 | + | 0.723476i | \(0.742543\pi\) | |||||||
\(368\) | −3.53120e77 | −0.194789 | ||||||||
\(369\) | 3.74544e78 | 1.90195 | ||||||||
\(370\) | −7.54109e76 | −0.0352599 | ||||||||
\(371\) | 1.63648e78 | 0.704703 | ||||||||
\(372\) | 2.59224e78 | 1.02829 | ||||||||
\(373\) | 3.65569e77 | 0.133613 | 0.0668067 | − | 0.997766i | \(-0.478719\pi\) | ||||
0.0668067 | + | 0.997766i | \(0.478719\pi\) | |||||||
\(374\) | −9.33068e77 | −0.314289 | ||||||||
\(375\) | 1.25477e78 | 0.389593 | ||||||||
\(376\) | −4.12529e78 | −1.18093 | ||||||||
\(377\) | 9.65457e77 | 0.254872 | ||||||||
\(378\) | 3.24610e78 | 0.790428 | ||||||||
\(379\) | −1.75228e78 | −0.393647 | −0.196823 | − | 0.980439i | \(-0.563063\pi\) | ||||
−0.196823 | + | 0.980439i | \(0.563063\pi\) | |||||||
\(380\) | −6.49753e77 | −0.134694 | ||||||||
\(381\) | −5.82845e78 | −1.11517 | ||||||||
\(382\) | 4.09841e78 | 0.723907 | ||||||||
\(383\) | 1.06584e79 | 1.73832 | 0.869158 | − | 0.494534i | \(-0.164661\pi\) | ||||
0.869158 | + | 0.494534i | \(0.164661\pi\) | |||||||
\(384\) | −1.17855e79 | −1.77519 | ||||||||
\(385\) | −1.32573e78 | −0.184461 | ||||||||
\(386\) | −2.14080e78 | −0.275210 | ||||||||
\(387\) | −1.21892e79 | −1.44808 | ||||||||
\(388\) | −1.63926e78 | −0.180003 | ||||||||
\(389\) | 1.40497e79 | 1.42628 | 0.713140 | − | 0.701021i | \(-0.247272\pi\) | ||||
0.713140 | + | 0.701021i | \(0.247272\pi\) | |||||||
\(390\) | 7.12158e77 | 0.0668507 | ||||||||
\(391\) | 2.11128e78 | 0.183297 | ||||||||
\(392\) | 9.53317e77 | 0.0765618 | ||||||||
\(393\) | −1.39271e78 | −0.103488 | ||||||||
\(394\) | −3.65057e78 | −0.251030 | ||||||||
\(395\) | −1.45517e78 | −0.0926194 | ||||||||
\(396\) | 4.49915e79 | 2.65111 | ||||||||
\(397\) | 5.99515e78 | 0.327107 | 0.163553 | − | 0.986534i | \(-0.447704\pi\) | ||||
0.163553 | + | 0.986534i | \(0.447704\pi\) | |||||||
\(398\) | 1.17021e79 | 0.591333 | ||||||||
\(399\) | −5.65611e79 | −2.64755 | ||||||||
\(400\) | −1.17551e79 | −0.509798 | ||||||||
\(401\) | 1.50995e79 | 0.606818 | 0.303409 | − | 0.952860i | \(-0.401875\pi\) | ||||
0.303409 | + | 0.952860i | \(0.401875\pi\) | |||||||
\(402\) | −2.20771e79 | −0.822333 | ||||||||
\(403\) | 1.69799e79 | 0.586314 | ||||||||
\(404\) | 8.52644e77 | 0.0272983 | ||||||||
\(405\) | 4.29201e78 | 0.127433 | ||||||||
\(406\) | −4.86917e78 | −0.134094 | ||||||||
\(407\) | −4.64736e79 | −1.18735 | ||||||||
\(408\) | 2.70428e79 | 0.641087 | ||||||||
\(409\) | −2.38844e79 | −0.525476 | −0.262738 | − | 0.964867i | \(-0.584626\pi\) | ||||
−0.262738 | + | 0.964867i | \(0.584626\pi\) | |||||||
\(410\) | −2.11677e78 | −0.0432282 | ||||||||
\(411\) | 2.00474e79 | 0.380086 | ||||||||
\(412\) | −3.75347e79 | −0.660796 | ||||||||
\(413\) | 3.66368e79 | 0.599020 | ||||||||
\(414\) | 2.09951e79 | 0.318865 | ||||||||
\(415\) | −2.76473e78 | −0.0390108 | ||||||||
\(416\) | −6.09998e79 | −0.799801 | ||||||||
\(417\) | 2.75979e80 | 3.36299 | ||||||||
\(418\) | 8.25802e79 | 0.935405 | ||||||||
\(419\) | −1.50267e80 | −1.58247 | −0.791233 | − | 0.611514i | \(-0.790561\pi\) | ||||
−0.791233 | + | 0.611514i | \(0.790561\pi\) | |||||||
\(420\) | 1.74158e79 | 0.170545 | ||||||||
\(421\) | 6.15744e79 | 0.560785 | 0.280392 | − | 0.959885i | \(-0.409535\pi\) | ||||
0.280392 | + | 0.959885i | \(0.409535\pi\) | |||||||
\(422\) | −6.41833e79 | −0.543741 | ||||||||
\(423\) | −4.04968e80 | −3.19183 | ||||||||
\(424\) | 6.92480e79 | 0.507865 | ||||||||
\(425\) | 7.02832e79 | 0.479721 | ||||||||
\(426\) | −1.86144e80 | −1.18265 | ||||||||
\(427\) | −4.37955e79 | −0.259047 | ||||||||
\(428\) | −2.52785e79 | −0.139225 | ||||||||
\(429\) | 4.38883e80 | 2.25113 | ||||||||
\(430\) | 6.88886e78 | 0.0329124 | ||||||||
\(431\) | 2.96244e80 | 1.31854 | 0.659269 | − | 0.751907i | \(-0.270866\pi\) | ||||
0.659269 | + | 0.751907i | \(0.270866\pi\) | |||||||
\(432\) | −2.26793e80 | −0.940537 | ||||||||
\(433\) | −2.82927e80 | −1.09344 | −0.546719 | − | 0.837316i | \(-0.684123\pi\) | ||||
−0.546719 | + | 0.837316i | \(0.684123\pi\) | |||||||
\(434\) | −8.56360e79 | −0.308475 | ||||||||
\(435\) | −1.80411e79 | −0.0605814 | ||||||||
\(436\) | 2.15398e80 | 0.674377 | ||||||||
\(437\) | −1.86857e80 | −0.545537 | ||||||||
\(438\) | 1.90501e80 | 0.518723 | ||||||||
\(439\) | 6.24335e80 | 1.58580 | 0.792902 | − | 0.609349i | \(-0.208569\pi\) | ||||
0.792902 | + | 0.609349i | \(0.208569\pi\) | |||||||
\(440\) | −5.60987e79 | −0.132937 | ||||||||
\(441\) | 9.35845e79 | 0.206932 | ||||||||
\(442\) | 8.02899e79 | 0.165684 | ||||||||
\(443\) | −7.11121e80 | −1.36971 | −0.684857 | − | 0.728678i | \(-0.740135\pi\) | ||||
−0.684857 | + | 0.728678i | \(0.740135\pi\) | |||||||
\(444\) | 6.10512e80 | 1.09778 | ||||||||
\(445\) | −1.97703e79 | −0.0331920 | ||||||||
\(446\) | −2.92618e80 | −0.458762 | ||||||||
\(447\) | −7.45279e80 | −1.09129 | ||||||||
\(448\) | −8.84821e79 | −0.121025 | ||||||||
\(449\) | −1.48296e81 | −1.89503 | −0.947514 | − | 0.319714i | \(-0.896413\pi\) | ||||
−0.947514 | + | 0.319714i | \(0.896413\pi\) | |||||||
\(450\) | 6.98914e80 | 0.834530 | ||||||||
\(451\) | −1.30451e81 | −1.45567 | ||||||||
\(452\) | 1.24789e81 | 1.30153 | ||||||||
\(453\) | 2.11870e81 | 2.06574 | ||||||||
\(454\) | 2.92674e80 | 0.266797 | ||||||||
\(455\) | 1.14078e80 | 0.0972424 | ||||||||
\(456\) | −2.39340e81 | −1.90804 | ||||||||
\(457\) | 8.32281e80 | 0.620620 | 0.310310 | − | 0.950635i | \(-0.399567\pi\) | ||||
0.310310 | + | 0.950635i | \(0.399567\pi\) | |||||||
\(458\) | 5.20874e80 | 0.363359 | ||||||||
\(459\) | 1.35598e81 | 0.885048 | ||||||||
\(460\) | 5.75353e79 | 0.0351415 | ||||||||
\(461\) | 1.90621e81 | 1.08966 | 0.544832 | − | 0.838545i | \(-0.316594\pi\) | ||||
0.544832 | + | 0.838545i | \(0.316594\pi\) | |||||||
\(462\) | −2.21346e81 | −1.18438 | ||||||||
\(463\) | −7.11693e80 | −0.356511 | −0.178255 | − | 0.983984i | \(-0.557045\pi\) | ||||
−0.178255 | + | 0.983984i | \(0.557045\pi\) | |||||||
\(464\) | 3.40191e80 | 0.159560 | ||||||||
\(465\) | −3.17295e80 | −0.139363 | ||||||||
\(466\) | 1.80479e81 | 0.742431 | ||||||||
\(467\) | 1.96641e81 | 0.757721 | 0.378860 | − | 0.925454i | \(-0.376316\pi\) | ||||
0.378860 | + | 0.925454i | \(0.376316\pi\) | |||||||
\(468\) | −3.87149e81 | −1.39759 | ||||||||
\(469\) | −3.53646e81 | −1.19618 | ||||||||
\(470\) | 2.28872e80 | 0.0725451 | ||||||||
\(471\) | −3.86740e81 | −1.14890 | ||||||||
\(472\) | 1.55030e81 | 0.431702 | ||||||||
\(473\) | 4.24541e81 | 1.10829 | ||||||||
\(474\) | −2.42957e81 | −0.594688 | ||||||||
\(475\) | −6.22034e81 | −1.42777 | ||||||||
\(476\) | 1.96349e81 | 0.422684 | ||||||||
\(477\) | 6.79788e81 | 1.37266 | ||||||||
\(478\) | 3.60972e81 | 0.683790 | ||||||||
\(479\) | 2.12205e81 | 0.377158 | 0.188579 | − | 0.982058i | \(-0.439612\pi\) | ||||
0.188579 | + | 0.982058i | \(0.439612\pi\) | |||||||
\(480\) | 1.13988e81 | 0.190108 | ||||||||
\(481\) | 3.99902e81 | 0.625935 | ||||||||
\(482\) | −1.00892e81 | −0.148225 | ||||||||
\(483\) | 5.00845e81 | 0.690742 | ||||||||
\(484\) | −9.26765e81 | −1.20001 | ||||||||
\(485\) | 2.00649e80 | 0.0243957 | ||||||||
\(486\) | 5.69250e80 | 0.0649976 | ||||||||
\(487\) | −6.70124e81 | −0.718658 | −0.359329 | − | 0.933211i | \(-0.616994\pi\) | ||||
−0.359329 | + | 0.933211i | \(0.616994\pi\) | |||||||
\(488\) | −1.85322e81 | −0.186690 | ||||||||
\(489\) | −1.07785e82 | −1.02009 | ||||||||
\(490\) | −5.28902e79 | −0.00470321 | ||||||||
\(491\) | 8.10525e81 | 0.677300 | 0.338650 | − | 0.940912i | \(-0.390030\pi\) | ||||
0.338650 | + | 0.940912i | \(0.390030\pi\) | |||||||
\(492\) | 1.71370e82 | 1.34586 | ||||||||
\(493\) | −2.03398e81 | −0.150147 | ||||||||
\(494\) | −7.10597e81 | −0.493119 | ||||||||
\(495\) | −5.50706e81 | −0.359303 | ||||||||
\(496\) | 5.98307e81 | 0.367057 | ||||||||
\(497\) | −2.98179e82 | −1.72031 | ||||||||
\(498\) | −4.61602e81 | −0.250480 | ||||||||
\(499\) | 6.93437e81 | 0.353949 | 0.176974 | − | 0.984215i | \(-0.443369\pi\) | ||||
0.176974 | + | 0.984215i | \(0.443369\pi\) | |||||||
\(500\) | 3.85512e81 | 0.185120 | ||||||||
\(501\) | −2.20266e82 | −0.995167 | ||||||||
\(502\) | 1.27146e82 | 0.540553 | ||||||||
\(503\) | 4.44563e82 | 1.77873 | 0.889364 | − | 0.457200i | \(-0.151147\pi\) | ||||
0.889364 | + | 0.457200i | \(0.151147\pi\) | |||||||
\(504\) | 4.30776e82 | 1.62226 | ||||||||
\(505\) | −1.04366e80 | −0.00369973 | ||||||||
\(506\) | −7.31243e81 | −0.244046 | ||||||||
\(507\) | 1.77571e82 | 0.557994 | ||||||||
\(508\) | −1.79071e82 | −0.529886 | ||||||||
\(509\) | −1.53808e82 | −0.428635 | −0.214317 | − | 0.976764i | \(-0.568753\pi\) | ||||
−0.214317 | + | 0.976764i | \(0.568753\pi\) | |||||||
\(510\) | −1.50034e81 | −0.0393822 | ||||||||
\(511\) | 3.05157e82 | 0.754546 | ||||||||
\(512\) | −3.82563e82 | −0.891187 | ||||||||
\(513\) | −1.20010e83 | −2.63413 | ||||||||
\(514\) | −6.83276e81 | −0.141326 | ||||||||
\(515\) | 4.59433e81 | 0.0895574 | ||||||||
\(516\) | −5.57708e82 | −1.02469 | ||||||||
\(517\) | 1.41047e83 | 2.44289 | ||||||||
\(518\) | −2.01686e82 | −0.329320 | ||||||||
\(519\) | 1.09273e83 | 1.68232 | ||||||||
\(520\) | 4.82726e81 | 0.0700807 | ||||||||
\(521\) | −1.18328e83 | −1.62009 | −0.810044 | − | 0.586369i | \(-0.800557\pi\) | ||||
−0.810044 | + | 0.586369i | \(0.800557\pi\) | |||||||
\(522\) | −2.02264e82 | −0.261197 | ||||||||
\(523\) | −9.45207e82 | −1.15140 | −0.575699 | − | 0.817662i | \(-0.695270\pi\) | ||||
−0.575699 | + | 0.817662i | \(0.695270\pi\) | |||||||
\(524\) | −4.27892e81 | −0.0491733 | ||||||||
\(525\) | 1.66728e83 | 1.80780 | ||||||||
\(526\) | 7.20603e82 | 0.737278 | ||||||||
\(527\) | −3.57724e82 | −0.345401 | ||||||||
\(528\) | 1.54646e83 | 1.40930 | ||||||||
\(529\) | −9.97053e82 | −0.857670 | ||||||||
\(530\) | −3.84189e81 | −0.0311983 | ||||||||
\(531\) | 1.52188e83 | 1.16681 | ||||||||
\(532\) | −1.73776e83 | −1.25801 | ||||||||
\(533\) | 1.12252e83 | 0.767387 | ||||||||
\(534\) | −3.30087e82 | −0.213118 | ||||||||
\(535\) | 3.09415e81 | 0.0188691 | ||||||||
\(536\) | −1.49646e83 | −0.862065 | ||||||||
\(537\) | −2.85590e83 | −1.55427 | ||||||||
\(538\) | −8.43148e80 | −0.00433555 | ||||||||
\(539\) | −3.25948e82 | −0.158376 | ||||||||
\(540\) | 3.69524e82 | 0.169681 | ||||||||
\(541\) | 1.48411e82 | 0.0644093 | 0.0322046 | − | 0.999481i | \(-0.489747\pi\) | ||||
0.0322046 | + | 0.999481i | \(0.489747\pi\) | |||||||
\(542\) | 1.88503e83 | 0.773287 | ||||||||
\(543\) | −2.54338e83 | −0.986316 | ||||||||
\(544\) | 1.28511e83 | 0.471167 | ||||||||
\(545\) | −2.63651e82 | −0.0913980 | ||||||||
\(546\) | 1.90466e83 | 0.624371 | ||||||||
\(547\) | 3.24255e83 | 1.00525 | 0.502624 | − | 0.864505i | \(-0.332368\pi\) | ||||
0.502624 | + | 0.864505i | \(0.332368\pi\) | |||||||
\(548\) | 6.15929e82 | 0.180602 | ||||||||
\(549\) | −1.81925e83 | −0.504588 | ||||||||
\(550\) | −2.43426e83 | −0.638713 | ||||||||
\(551\) | 1.80015e83 | 0.446874 | ||||||||
\(552\) | 2.11934e83 | 0.497804 | ||||||||
\(553\) | −3.89185e83 | −0.865046 | ||||||||
\(554\) | 5.46497e82 | 0.114958 | ||||||||
\(555\) | −7.47279e82 | −0.148781 | ||||||||
\(556\) | 8.47908e83 | 1.59797 | ||||||||
\(557\) | 4.33577e83 | 0.773540 | 0.386770 | − | 0.922176i | \(-0.373591\pi\) | ||||
0.386770 | + | 0.922176i | \(0.373591\pi\) | |||||||
\(558\) | −3.55730e83 | −0.600865 | ||||||||
\(559\) | −3.65315e83 | −0.584261 | ||||||||
\(560\) | 4.01970e82 | 0.0608777 | ||||||||
\(561\) | −9.24618e83 | −1.32616 | ||||||||
\(562\) | 7.36355e82 | 0.100030 | ||||||||
\(563\) | 8.30382e83 | 1.06849 | 0.534247 | − | 0.845328i | \(-0.320595\pi\) | ||||
0.534247 | + | 0.845328i | \(0.320595\pi\) | |||||||
\(564\) | −1.85290e84 | −2.25860 | ||||||||
\(565\) | −1.52744e83 | −0.176396 | ||||||||
\(566\) | 8.44882e82 | 0.0924474 | ||||||||
\(567\) | 1.14790e84 | 1.19020 | ||||||||
\(568\) | −1.26175e84 | −1.23979 | ||||||||
\(569\) | −1.27745e84 | −1.18965 | −0.594826 | − | 0.803854i | \(-0.702779\pi\) | ||||
−0.594826 | + | 0.803854i | \(0.702779\pi\) | |||||||
\(570\) | 1.32786e83 | 0.117211 | ||||||||
\(571\) | 8.91829e83 | 0.746243 | 0.373121 | − | 0.927783i | \(-0.378288\pi\) | ||||
0.373121 | + | 0.927783i | \(0.378288\pi\) | |||||||
\(572\) | 1.34841e84 | 1.06965 | ||||||||
\(573\) | 4.06129e84 | 3.05456 | ||||||||
\(574\) | −5.66131e83 | −0.403742 | ||||||||
\(575\) | 5.50807e83 | 0.372504 | ||||||||
\(576\) | −3.67552e83 | −0.235740 | ||||||||
\(577\) | −1.15402e84 | −0.702023 | −0.351012 | − | 0.936371i | \(-0.614162\pi\) | ||||
−0.351012 | + | 0.936371i | \(0.614162\pi\) | |||||||
\(578\) | 5.47424e83 | 0.315882 | ||||||||
\(579\) | −2.12142e84 | −1.16126 | ||||||||
\(580\) | −5.54287e82 | −0.0287860 | ||||||||
\(581\) | −7.39425e83 | −0.364353 | ||||||||
\(582\) | 3.35005e83 | 0.156639 | ||||||||
\(583\) | −2.36765e84 | −1.05057 | ||||||||
\(584\) | 1.29128e84 | 0.543787 | ||||||||
\(585\) | 4.73879e83 | 0.189414 | ||||||||
\(586\) | −2.09117e83 | −0.0793437 | ||||||||
\(587\) | −1.26376e84 | −0.455200 | −0.227600 | − | 0.973755i | \(-0.573088\pi\) | ||||
−0.227600 | + | 0.973755i | \(0.573088\pi\) | |||||||
\(588\) | 4.28189e83 | 0.146429 | ||||||||
\(589\) | 3.16600e84 | 1.02800 | ||||||||
\(590\) | −8.60108e82 | −0.0265196 | ||||||||
\(591\) | −3.61751e84 | −1.05923 | ||||||||
\(592\) | 1.40911e84 | 0.391861 | ||||||||
\(593\) | −2.81980e84 | −0.744818 | −0.372409 | − | 0.928069i | \(-0.621468\pi\) | ||||
−0.372409 | + | 0.928069i | \(0.621468\pi\) | |||||||
\(594\) | −4.69645e84 | −1.17837 | ||||||||
\(595\) | −2.40335e83 | −0.0572861 | ||||||||
\(596\) | −2.28977e84 | −0.518539 | ||||||||
\(597\) | 1.15962e85 | 2.49515 | ||||||||
\(598\) | 6.29230e83 | 0.128654 | ||||||||
\(599\) | 2.57638e84 | 0.500602 | 0.250301 | − | 0.968168i | \(-0.419470\pi\) | ||||
0.250301 | + | 0.968168i | \(0.419470\pi\) | |||||||
\(600\) | 7.05515e84 | 1.30285 | ||||||||
\(601\) | 1.93837e84 | 0.340224 | 0.170112 | − | 0.985425i | \(-0.445587\pi\) | ||||
0.170112 | + | 0.985425i | \(0.445587\pi\) | |||||||
\(602\) | 1.84242e84 | 0.307395 | ||||||||
\(603\) | −1.46904e85 | −2.32999 | ||||||||
\(604\) | 6.50943e84 | 0.981559 | ||||||||
\(605\) | 1.13438e84 | 0.162637 | ||||||||
\(606\) | −1.74250e83 | −0.0237551 | ||||||||
\(607\) | 9.64610e83 | 0.125054 | 0.0625269 | − | 0.998043i | \(-0.480084\pi\) | ||||
0.0625269 | + | 0.998043i | \(0.480084\pi\) | |||||||
\(608\) | −1.13738e85 | −1.40231 | ||||||||
\(609\) | −4.82507e84 | −0.565818 | ||||||||
\(610\) | 1.02817e83 | 0.0114684 | ||||||||
\(611\) | −1.21370e85 | −1.28782 | ||||||||
\(612\) | 8.15627e84 | 0.823328 | ||||||||
\(613\) | 1.07878e85 | 1.03607 | 0.518034 | − | 0.855360i | \(-0.326664\pi\) | ||||
0.518034 | + | 0.855360i | \(0.326664\pi\) | |||||||
\(614\) | 7.50514e84 | 0.685841 | ||||||||
\(615\) | −2.09760e84 | −0.182403 | ||||||||
\(616\) | −1.50036e85 | −1.24160 | ||||||||
\(617\) | −3.73172e84 | −0.293908 | −0.146954 | − | 0.989143i | \(-0.546947\pi\) | ||||
−0.146954 | + | 0.989143i | \(0.546947\pi\) | |||||||
\(618\) | 7.67073e84 | 0.575027 | ||||||||
\(619\) | −8.80827e84 | −0.628529 | −0.314265 | − | 0.949335i | \(-0.601758\pi\) | ||||
−0.314265 | + | 0.949335i | \(0.601758\pi\) | |||||||
\(620\) | −9.74847e83 | −0.0662201 | ||||||||
\(621\) | 1.06268e85 | 0.687240 | ||||||||
\(622\) | 2.38496e84 | 0.146850 | ||||||||
\(623\) | −5.28757e84 | −0.310006 | ||||||||
\(624\) | −1.33072e85 | −0.742944 | ||||||||
\(625\) | 1.80986e85 | 0.962287 | ||||||||
\(626\) | −1.03842e85 | −0.525841 | ||||||||
\(627\) | 8.18324e85 | 3.94698 | ||||||||
\(628\) | −1.18821e85 | −0.545912 | ||||||||
\(629\) | −8.42495e84 | −0.368742 | ||||||||
\(630\) | −2.38995e84 | −0.0996558 | ||||||||
\(631\) | 1.68356e85 | 0.668856 | 0.334428 | − | 0.942421i | \(-0.391457\pi\) | ||||
0.334428 | + | 0.942421i | \(0.391457\pi\) | |||||||
\(632\) | −1.64684e85 | −0.623422 | ||||||||
\(633\) | −6.36020e85 | −2.29434 | ||||||||
\(634\) | −1.77355e85 | −0.609708 | ||||||||
\(635\) | 2.19187e84 | 0.0718152 | ||||||||
\(636\) | 3.11032e85 | 0.971322 | ||||||||
\(637\) | 2.80476e84 | 0.0834915 | ||||||||
\(638\) | 7.04470e84 | 0.199909 | ||||||||
\(639\) | −1.23863e86 | −3.35092 | ||||||||
\(640\) | 4.43209e84 | 0.114319 | ||||||||
\(641\) | 6.42250e85 | 1.57955 | 0.789777 | − | 0.613394i | \(-0.210196\pi\) | ||||
0.789777 | + | 0.613394i | \(0.210196\pi\) | |||||||
\(642\) | 5.16602e84 | 0.121154 | ||||||||
\(643\) | −3.55027e84 | −0.0794011 | −0.0397005 | − | 0.999212i | \(-0.512640\pi\) | ||||
−0.0397005 | + | 0.999212i | \(0.512640\pi\) | |||||||
\(644\) | 1.53878e85 | 0.328214 | ||||||||
\(645\) | 6.82647e84 | 0.138875 | ||||||||
\(646\) | 1.49705e85 | 0.290499 | ||||||||
\(647\) | 8.24068e85 | 1.52539 | 0.762697 | − | 0.646755i | \(-0.223875\pi\) | ||||
0.762697 | + | 0.646755i | \(0.223875\pi\) | |||||||
\(648\) | 4.85735e85 | 0.857752 | ||||||||
\(649\) | −5.30061e85 | −0.893022 | ||||||||
\(650\) | 2.09467e85 | 0.336711 | ||||||||
\(651\) | −8.48605e85 | −1.30162 | ||||||||
\(652\) | −3.31155e85 | −0.484708 | ||||||||
\(653\) | 3.96464e85 | 0.553799 | 0.276899 | − | 0.960899i | \(-0.410693\pi\) | ||||
0.276899 | + | 0.960899i | \(0.410693\pi\) | |||||||
\(654\) | −4.40195e85 | −0.586845 | ||||||||
\(655\) | 5.23749e83 | 0.00666443 | ||||||||
\(656\) | 3.95534e85 | 0.480416 | ||||||||
\(657\) | 1.26761e86 | 1.46975 | ||||||||
\(658\) | 6.12117e85 | 0.677555 | ||||||||
\(659\) | −8.56515e85 | −0.905169 | −0.452585 | − | 0.891721i | \(-0.649498\pi\) | ||||
−0.452585 | + | 0.891721i | \(0.649498\pi\) | |||||||
\(660\) | −2.51971e85 | −0.254250 | ||||||||
\(661\) | −1.49484e86 | −1.44029 | −0.720144 | − | 0.693825i | \(-0.755924\pi\) | ||||
−0.720144 | + | 0.693825i | \(0.755924\pi\) | |||||||
\(662\) | −9.82171e83 | −0.00903688 | ||||||||
\(663\) | 7.95628e85 | 0.699113 | ||||||||
\(664\) | −3.12890e85 | −0.262582 | ||||||||
\(665\) | 2.12706e85 | 0.170498 | ||||||||
\(666\) | −8.37799e85 | −0.641469 | ||||||||
\(667\) | −1.59402e85 | −0.116589 | ||||||||
\(668\) | −6.76737e85 | −0.472865 | ||||||||
\(669\) | −2.89968e86 | −1.93577 | ||||||||
\(670\) | 8.30241e84 | 0.0529569 | ||||||||
\(671\) | 6.33632e85 | 0.386189 | ||||||||
\(672\) | 3.04859e86 | 1.77556 | ||||||||
\(673\) | 9.30605e85 | 0.517972 | 0.258986 | − | 0.965881i | \(-0.416612\pi\) | ||||
0.258986 | + | 0.965881i | \(0.416612\pi\) | |||||||
\(674\) | −2.81861e85 | −0.149937 | ||||||||
\(675\) | 3.53759e86 | 1.79863 | ||||||||
\(676\) | 5.45563e85 | 0.265137 | ||||||||
\(677\) | 1.12642e85 | 0.0523293 | 0.0261646 | − | 0.999658i | \(-0.491671\pi\) | ||||
0.0261646 | + | 0.999658i | \(0.491671\pi\) | |||||||
\(678\) | −2.55024e86 | −1.13260 | ||||||||
\(679\) | 5.36634e85 | 0.227851 | ||||||||
\(680\) | −1.01698e85 | −0.0412850 | ||||||||
\(681\) | 2.90023e86 | 1.12576 | ||||||||
\(682\) | 1.23898e86 | 0.459876 | ||||||||
\(683\) | −3.40704e86 | −1.20933 | −0.604666 | − | 0.796479i | \(-0.706693\pi\) | ||||
−0.604666 | + | 0.796479i | \(0.706693\pi\) | |||||||
\(684\) | −7.21862e86 | −2.45043 | ||||||||
\(685\) | −7.53910e84 | −0.0244769 | ||||||||
\(686\) | 1.25584e86 | 0.389986 | ||||||||
\(687\) | 5.16157e86 | 1.53321 | ||||||||
\(688\) | −1.28723e86 | −0.365771 | ||||||||
\(689\) | 2.03735e86 | 0.553833 | ||||||||
\(690\) | −1.17581e85 | −0.0305803 | ||||||||
\(691\) | −4.85715e85 | −0.120865 | −0.0604326 | − | 0.998172i | \(-0.519248\pi\) | ||||
−0.0604326 | + | 0.998172i | \(0.519248\pi\) | |||||||
\(692\) | 3.35727e86 | 0.799375 | ||||||||
\(693\) | −1.47286e87 | −3.35581 | ||||||||
\(694\) | 1.86721e86 | 0.407126 | ||||||||
\(695\) | −1.03786e86 | −0.216571 | ||||||||
\(696\) | −2.04174e86 | −0.407774 | ||||||||
\(697\) | −2.36487e86 | −0.452073 | ||||||||
\(698\) | −3.37151e86 | −0.616927 | ||||||||
\(699\) | 1.78844e87 | 3.13272 | ||||||||
\(700\) | 5.12250e86 | 0.858997 | ||||||||
\(701\) | −9.30644e86 | −1.49411 | −0.747057 | − | 0.664759i | \(-0.768534\pi\) | ||||
−0.747057 | + | 0.664759i | \(0.768534\pi\) | |||||||
\(702\) | 4.04126e86 | 0.621206 | ||||||||
\(703\) | 7.45642e86 | 1.09747 | ||||||||
\(704\) | 1.28016e86 | 0.180425 | ||||||||
\(705\) | 2.26799e86 | 0.306107 | ||||||||
\(706\) | 4.53497e86 | 0.586180 | ||||||||
\(707\) | −2.79125e85 | −0.0345547 | ||||||||
\(708\) | 6.96326e86 | 0.825655 | ||||||||
\(709\) | −1.39697e87 | −1.58663 | −0.793316 | − | 0.608810i | \(-0.791647\pi\) | ||||
−0.793316 | + | 0.608810i | \(0.791647\pi\) | |||||||
\(710\) | 7.00023e85 | 0.0761610 | ||||||||
\(711\) | −1.61666e87 | −1.68499 | ||||||||
\(712\) | −2.23745e86 | −0.223415 | ||||||||
\(713\) | −2.80347e86 | −0.268204 | ||||||||
\(714\) | −4.01266e86 | −0.367821 | ||||||||
\(715\) | −1.65048e86 | −0.144970 | ||||||||
\(716\) | −8.77436e86 | −0.738530 | ||||||||
\(717\) | 3.57703e87 | 2.88528 | ||||||||
\(718\) | −5.00732e86 | −0.387088 | ||||||||
\(719\) | −1.38529e87 | −1.02639 | −0.513193 | − | 0.858273i | \(-0.671537\pi\) | ||||
−0.513193 | + | 0.858273i | \(0.671537\pi\) | |||||||
\(720\) | 1.66977e86 | 0.118581 | ||||||||
\(721\) | 1.22875e87 | 0.836447 | ||||||||
\(722\) | −6.91304e86 | −0.451112 | ||||||||
\(723\) | −9.99784e86 | −0.625444 | ||||||||
\(724\) | −7.81419e86 | −0.468660 | ||||||||
\(725\) | −5.30641e86 | −0.305134 | ||||||||
\(726\) | 1.89397e87 | 1.04426 | ||||||||
\(727\) | 3.07878e85 | 0.0162772 | 0.00813860 | − | 0.999967i | \(-0.497409\pi\) | ||||
0.00813860 | + | 0.999967i | \(0.497409\pi\) | |||||||
\(728\) | 1.29105e87 | 0.654539 | ||||||||
\(729\) | −1.76866e87 | −0.859913 | ||||||||
\(730\) | −7.16405e85 | −0.0334050 | ||||||||
\(731\) | 7.69627e86 | 0.344192 | ||||||||
\(732\) | −8.32385e86 | −0.357056 | ||||||||
\(733\) | 2.95619e87 | 1.21636 | 0.608178 | − | 0.793801i | \(-0.291901\pi\) | ||||
0.608178 | + | 0.793801i | \(0.291901\pi\) | |||||||
\(734\) | 1.44641e87 | 0.570902 | ||||||||
\(735\) | −5.24112e85 | −0.0198454 | ||||||||
\(736\) | 1.00714e87 | 0.365862 | ||||||||
\(737\) | 5.11654e87 | 1.78328 | ||||||||
\(738\) | −2.35169e87 | −0.786432 | ||||||||
\(739\) | −2.83483e87 | −0.909646 | −0.454823 | − | 0.890582i | \(-0.650297\pi\) | ||||
−0.454823 | + | 0.890582i | \(0.650297\pi\) | |||||||
\(740\) | −2.29592e86 | −0.0706950 | ||||||||
\(741\) | −7.04162e87 | −2.08074 | ||||||||
\(742\) | −1.02751e87 | −0.291386 | ||||||||
\(743\) | 4.13337e87 | 1.12498 | 0.562491 | − | 0.826804i | \(-0.309843\pi\) | ||||
0.562491 | + | 0.826804i | \(0.309843\pi\) | |||||||
\(744\) | −3.59089e87 | −0.938054 | ||||||||
\(745\) | 2.80273e86 | 0.0702773 | ||||||||
\(746\) | −2.29534e86 | −0.0552475 | ||||||||
\(747\) | −3.07155e87 | −0.709708 | ||||||||
\(748\) | −2.84077e87 | −0.630139 | ||||||||
\(749\) | 8.27528e86 | 0.176233 | ||||||||
\(750\) | −7.87846e86 | −0.161092 | ||||||||
\(751\) | 3.63538e87 | 0.713727 | 0.356863 | − | 0.934157i | \(-0.383846\pi\) | ||||
0.356863 | + | 0.934157i | \(0.383846\pi\) | |||||||
\(752\) | −4.27664e87 | −0.806229 | ||||||||
\(753\) | 1.25994e88 | 2.28089 | ||||||||
\(754\) | −6.06192e86 | −0.105386 | ||||||||
\(755\) | −7.96768e86 | −0.133030 | ||||||||
\(756\) | 9.88290e87 | 1.58478 | ||||||||
\(757\) | −1.27239e87 | −0.195972 | −0.0979861 | − | 0.995188i | \(-0.531240\pi\) | ||||
−0.0979861 | + | 0.995188i | \(0.531240\pi\) | |||||||
\(758\) | 1.10022e87 | 0.162768 | ||||||||
\(759\) | −7.24621e87 | −1.02976 | ||||||||
\(760\) | 9.00071e86 | 0.122875 | ||||||||
\(761\) | −4.01227e87 | −0.526209 | −0.263104 | − | 0.964767i | \(-0.584746\pi\) | ||||
−0.263104 | + | 0.964767i | \(0.584746\pi\) | |||||||
\(762\) | 3.65957e87 | 0.461109 | ||||||||
\(763\) | −7.05135e87 | −0.853638 | ||||||||
\(764\) | 1.24778e88 | 1.45141 | ||||||||
\(765\) | −9.98345e86 | −0.111585 | ||||||||
\(766\) | −6.69219e87 | −0.718772 | ||||||||
\(767\) | 4.56113e87 | 0.470776 | ||||||||
\(768\) | 5.37133e87 | 0.532800 | ||||||||
\(769\) | −1.06276e87 | −0.101317 | −0.0506584 | − | 0.998716i | \(-0.516132\pi\) | ||||
−0.0506584 | + | 0.998716i | \(0.516132\pi\) | |||||||
\(770\) | 8.32402e86 | 0.0762721 | ||||||||
\(771\) | −6.77088e87 | −0.596330 | ||||||||
\(772\) | −6.51777e87 | −0.551787 | ||||||||
\(773\) | −1.73425e88 | −1.41136 | −0.705679 | − | 0.708532i | \(-0.749358\pi\) | ||||
−0.705679 | + | 0.708532i | \(0.749358\pi\) | |||||||
\(774\) | 7.65337e87 | 0.598761 | ||||||||
\(775\) | −9.33259e87 | −0.701940 | ||||||||
\(776\) | 2.27078e87 | 0.164207 | ||||||||
\(777\) | −1.99860e88 | −1.38958 | ||||||||
\(778\) | −8.82155e87 | −0.589749 | ||||||||
\(779\) | 2.09301e88 | 1.34548 | ||||||||
\(780\) | 2.16820e87 | 0.134033 | ||||||||
\(781\) | 4.31404e88 | 2.56465 | ||||||||
\(782\) | −1.32563e87 | −0.0757909 | ||||||||
\(783\) | −1.02377e88 | −0.562949 | ||||||||
\(784\) | 9.88291e86 | 0.0522691 | ||||||||
\(785\) | 1.45439e87 | 0.0739871 | ||||||||
\(786\) | 8.74456e86 | 0.0427908 | ||||||||
\(787\) | 7.10492e87 | 0.334449 | 0.167224 | − | 0.985919i | \(-0.446520\pi\) | ||||
0.167224 | + | 0.985919i | \(0.446520\pi\) | |||||||
\(788\) | −1.11143e88 | −0.503307 | ||||||||
\(789\) | 7.14077e88 | 3.11098 | ||||||||
\(790\) | 9.13673e86 | 0.0382970 | ||||||||
\(791\) | −4.08514e88 | −1.64750 | ||||||||
\(792\) | −6.23245e88 | −2.41847 | ||||||||
\(793\) | −5.45236e87 | −0.203588 | ||||||||
\(794\) | −3.76424e87 | −0.135255 | ||||||||
\(795\) | −3.80710e87 | −0.131643 | ||||||||
\(796\) | 3.56277e88 | 1.18560 | ||||||||
\(797\) | −2.01224e88 | −0.644467 | −0.322233 | − | 0.946660i | \(-0.604434\pi\) | ||||
−0.322233 | + | 0.946660i | \(0.604434\pi\) | |||||||
\(798\) | 3.55136e88 | 1.09473 | ||||||||
\(799\) | 2.55697e88 | 0.758663 | ||||||||
\(800\) | 3.35271e88 | 0.957528 | ||||||||
\(801\) | −2.19644e88 | −0.603848 | ||||||||
\(802\) | −9.48066e87 | −0.250911 | ||||||||
\(803\) | −4.41500e88 | −1.12488 | ||||||||
\(804\) | −6.72147e88 | −1.64875 | ||||||||
\(805\) | −1.88350e87 | −0.0444827 | ||||||||
\(806\) | −1.06613e88 | −0.242434 | ||||||||
\(807\) | −8.35512e86 | −0.0182941 | ||||||||
\(808\) | −1.18113e87 | −0.0249029 | ||||||||
\(809\) | −1.07349e88 | −0.217957 | −0.108978 | − | 0.994044i | \(-0.534758\pi\) | ||||
−0.108978 | + | 0.994044i | \(0.534758\pi\) | |||||||
\(810\) | −2.69487e87 | −0.0526920 | ||||||||
\(811\) | −7.32258e87 | −0.137888 | −0.0689442 | − | 0.997621i | \(-0.521963\pi\) | ||||
−0.0689442 | + | 0.997621i | \(0.521963\pi\) | |||||||
\(812\) | −1.48244e88 | −0.268855 | ||||||||
\(813\) | 1.86796e89 | 3.26292 | ||||||||
\(814\) | 2.91799e88 | 0.490952 | ||||||||
\(815\) | 4.05341e87 | 0.0656922 | ||||||||
\(816\) | 2.80349e88 | 0.437673 | ||||||||
\(817\) | −6.81151e88 | −1.02440 | ||||||||
\(818\) | 1.49965e88 | 0.217278 | ||||||||
\(819\) | 1.26739e89 | 1.76909 | ||||||||
\(820\) | −6.44461e87 | −0.0866710 | ||||||||
\(821\) | −8.61776e88 | −1.11668 | −0.558339 | − | 0.829613i | \(-0.688561\pi\) | ||||
−0.558339 | + | 0.829613i | \(0.688561\pi\) | |||||||
\(822\) | −1.25874e88 | −0.157161 | ||||||||
\(823\) | −8.68150e87 | −0.104448 | −0.0522240 | − | 0.998635i | \(-0.516631\pi\) | ||||
−0.0522240 | + | 0.998635i | \(0.516631\pi\) | |||||||
\(824\) | 5.19949e88 | 0.602811 | ||||||||
\(825\) | −2.41222e89 | −2.69508 | ||||||||
\(826\) | −2.30036e88 | −0.247687 | ||||||||
\(827\) | −2.76062e88 | −0.286476 | −0.143238 | − | 0.989688i | \(-0.545751\pi\) | ||||
−0.143238 | + | 0.989688i | \(0.545751\pi\) | |||||||
\(828\) | 6.39205e88 | 0.639315 | ||||||||
\(829\) | −1.28246e88 | −0.123632 | −0.0618162 | − | 0.998088i | \(-0.519689\pi\) | ||||
−0.0618162 | + | 0.998088i | \(0.519689\pi\) | |||||||
\(830\) | 1.73592e87 | 0.0161305 | ||||||||
\(831\) | 5.41548e88 | 0.485071 | ||||||||
\(832\) | −1.10157e88 | −0.0951149 | ||||||||
\(833\) | −5.90893e87 | −0.0491854 | ||||||||
\(834\) | −1.73282e89 | −1.39056 | ||||||||
\(835\) | 8.28340e87 | 0.0640872 | ||||||||
\(836\) | 2.51419e89 | 1.87545 | ||||||||
\(837\) | −1.80055e89 | −1.29502 | ||||||||
\(838\) | 9.43495e88 | 0.654330 | ||||||||
\(839\) | 1.98229e89 | 1.32565 | 0.662824 | − | 0.748776i | \(-0.269358\pi\) | ||||
0.662824 | + | 0.748776i | \(0.269358\pi\) | |||||||
\(840\) | −2.41252e88 | −0.155580 | ||||||||
\(841\) | −1.45440e89 | −0.904497 | ||||||||
\(842\) | −3.86614e88 | −0.231878 | ||||||||
\(843\) | 7.29686e88 | 0.422080 | ||||||||
\(844\) | −1.95409e89 | −1.09018 | ||||||||
\(845\) | −6.67781e87 | −0.0359339 | ||||||||
\(846\) | 2.54272e89 | 1.31978 | ||||||||
\(847\) | 3.03390e89 | 1.51900 | ||||||||
\(848\) | 7.17885e88 | 0.346722 | ||||||||
\(849\) | 8.37230e88 | 0.390086 | ||||||||
\(850\) | −4.41294e88 | −0.198359 | ||||||||
\(851\) | −6.60261e88 | −0.286328 | ||||||||
\(852\) | −5.66724e89 | −2.37118 | ||||||||
\(853\) | 1.96594e89 | 0.793641 | 0.396821 | − | 0.917896i | \(-0.370114\pi\) | ||||
0.396821 | + | 0.917896i | \(0.370114\pi\) | |||||||
\(854\) | 2.74983e88 | 0.107113 | ||||||||
\(855\) | 8.83574e88 | 0.332106 | ||||||||
\(856\) | 3.50171e88 | 0.127008 | ||||||||
\(857\) | 1.54952e89 | 0.542353 | 0.271177 | − | 0.962530i | \(-0.412587\pi\) | ||||
0.271177 | + | 0.962530i | \(0.412587\pi\) | |||||||
\(858\) | −2.75566e89 | −0.930816 | ||||||||
\(859\) | −2.29205e89 | −0.747192 | −0.373596 | − | 0.927592i | \(-0.621875\pi\) | ||||
−0.373596 | + | 0.927592i | \(0.621875\pi\) | |||||||
\(860\) | 2.09734e88 | 0.0659882 | ||||||||
\(861\) | −5.61003e89 | −1.70361 | ||||||||
\(862\) | −1.86006e89 | −0.545199 | ||||||||
\(863\) | −2.50671e89 | −0.709211 | −0.354606 | − | 0.935016i | \(-0.615385\pi\) | ||||
−0.354606 | + | 0.935016i | \(0.615385\pi\) | |||||||
\(864\) | 6.46842e89 | 1.76656 | ||||||||
\(865\) | −4.10937e88 | −0.108339 | ||||||||
\(866\) | 1.77645e89 | 0.452123 | ||||||||
\(867\) | 5.42466e89 | 1.33288 | ||||||||
\(868\) | −2.60722e89 | −0.618482 | ||||||||
\(869\) | 5.63071e89 | 1.28961 | ||||||||
\(870\) | 1.13276e88 | 0.0250497 | ||||||||
\(871\) | −4.40275e89 | −0.940092 | ||||||||
\(872\) | −2.98380e89 | −0.615200 | ||||||||
\(873\) | 2.22916e89 | 0.443820 | ||||||||
\(874\) | 1.17324e89 | 0.225573 | ||||||||
\(875\) | −1.26203e89 | −0.234327 | ||||||||
\(876\) | 5.79987e89 | 1.04002 | ||||||||
\(877\) | 2.61925e89 | 0.453617 | 0.226809 | − | 0.973939i | \(-0.427171\pi\) | ||||
0.226809 | + | 0.973939i | \(0.427171\pi\) | |||||||
\(878\) | −3.92008e89 | −0.655710 | ||||||||
\(879\) | −2.07223e89 | −0.334794 | ||||||||
\(880\) | −5.81569e88 | −0.0907568 | ||||||||
\(881\) | −7.15408e87 | −0.0107842 | −0.00539211 | − | 0.999985i | \(-0.501716\pi\) | ||||
−0.00539211 | + | 0.999985i | \(0.501716\pi\) | |||||||
\(882\) | −5.87599e88 | −0.0855636 | ||||||||
\(883\) | 8.44585e89 | 1.18807 | 0.594035 | − | 0.804439i | \(-0.297534\pi\) | ||||
0.594035 | + | 0.804439i | \(0.297534\pi\) | |||||||
\(884\) | 2.44446e89 | 0.332192 | ||||||||
\(885\) | −8.52319e88 | −0.111901 | ||||||||
\(886\) | 4.46499e89 | 0.566359 | ||||||||
\(887\) | −6.84839e89 | −0.839302 | −0.419651 | − | 0.907686i | \(-0.637847\pi\) | ||||
−0.419651 | + | 0.907686i | \(0.637847\pi\) | |||||||
\(888\) | −8.45711e89 | −1.00144 | ||||||||
\(889\) | 5.86215e89 | 0.670739 | ||||||||
\(890\) | 1.24134e88 | 0.0137245 | ||||||||
\(891\) | −1.66077e90 | −1.77435 | ||||||||
\(892\) | −8.90887e89 | −0.919803 | ||||||||
\(893\) | −2.26302e90 | −2.25797 | ||||||||
\(894\) | 4.67946e89 | 0.451234 | ||||||||
\(895\) | 1.07400e89 | 0.100093 | ||||||||
\(896\) | 1.18536e90 | 1.06772 | ||||||||
\(897\) | 6.23531e89 | 0.542861 | ||||||||
\(898\) | 9.31121e89 | 0.783570 | ||||||||
\(899\) | 2.70083e89 | 0.219698 | ||||||||
\(900\) | 2.12787e90 | 1.67320 | ||||||||
\(901\) | −4.29219e89 | −0.326267 | ||||||||
\(902\) | 8.19076e89 | 0.601901 | ||||||||
\(903\) | 1.82574e90 | 1.29706 | ||||||||
\(904\) | −1.72864e90 | −1.18732 | ||||||||
\(905\) | 9.56474e88 | 0.0635172 | ||||||||
\(906\) | −1.33029e90 | −0.854156 | ||||||||
\(907\) | 1.40576e90 | 0.872748 | 0.436374 | − | 0.899765i | \(-0.356262\pi\) | ||||
0.436374 | + | 0.899765i | \(0.356262\pi\) | |||||||
\(908\) | 8.91058e89 | 0.534919 | ||||||||
\(909\) | −1.15948e89 | −0.0673076 | ||||||||
\(910\) | −7.16276e88 | −0.0402085 | ||||||||
\(911\) | −2.64352e90 | −1.43507 | −0.717534 | − | 0.696523i | \(-0.754729\pi\) | ||||
−0.717534 | + | 0.696523i | \(0.754729\pi\) | |||||||
\(912\) | −2.48120e90 | −1.30263 | ||||||||
\(913\) | 1.06980e90 | 0.543179 | ||||||||
\(914\) | −5.22573e89 | −0.256618 | ||||||||
\(915\) | 1.01886e89 | 0.0483916 | ||||||||
\(916\) | 1.58582e90 | 0.728522 | ||||||||
\(917\) | 1.40076e89 | 0.0622444 | ||||||||
\(918\) | −8.51394e89 | −0.365956 | ||||||||
\(919\) | −4.96356e89 | −0.206381 | −0.103191 | − | 0.994662i | \(-0.532905\pi\) | ||||
−0.103191 | + | 0.994662i | \(0.532905\pi\) | |||||||
\(920\) | −7.97008e88 | −0.0320578 | ||||||||
\(921\) | 7.43717e90 | 2.89394 | ||||||||
\(922\) | −1.19687e90 | −0.450562 | ||||||||
\(923\) | −3.71221e90 | −1.35201 | ||||||||
\(924\) | −6.73896e90 | −2.37464 | ||||||||
\(925\) | −2.19797e90 | −0.749374 | ||||||||
\(926\) | 4.46858e89 | 0.147413 | ||||||||
\(927\) | 5.10420e90 | 1.62928 | ||||||||
\(928\) | −9.70266e89 | −0.299694 | ||||||||
\(929\) | −3.32635e90 | −0.994234 | −0.497117 | − | 0.867684i | \(-0.665608\pi\) | ||||
−0.497117 | + | 0.867684i | \(0.665608\pi\) | |||||||
\(930\) | 1.99223e89 | 0.0576250 | ||||||||
\(931\) | 5.22963e89 | 0.146388 | ||||||||
\(932\) | 5.49475e90 | 1.48855 | ||||||||
\(933\) | 2.36336e90 | 0.619640 | ||||||||
\(934\) | −1.23467e90 | −0.313308 | ||||||||
\(935\) | 3.47716e89 | 0.0854024 | ||||||||
\(936\) | 5.36298e90 | 1.27495 | ||||||||
\(937\) | 5.45798e90 | 1.25596 | 0.627978 | − | 0.778231i | \(-0.283883\pi\) | ||||
0.627978 | + | 0.778231i | \(0.283883\pi\) | |||||||
\(938\) | 2.22048e90 | 0.494606 | ||||||||
\(939\) | −1.02901e91 | −2.21881 | ||||||||
\(940\) | 6.96810e89 | 0.145450 | ||||||||
\(941\) | −2.34364e90 | −0.473595 | −0.236797 | − | 0.971559i | \(-0.576098\pi\) | ||||
−0.236797 | + | 0.971559i | \(0.576098\pi\) | |||||||
\(942\) | 2.42826e90 | 0.475054 | ||||||||
\(943\) | −1.85335e90 | −0.351034 | ||||||||
\(944\) | 1.60717e90 | 0.294725 | ||||||||
\(945\) | −1.20969e90 | −0.214785 | ||||||||
\(946\) | −2.66561e90 | −0.458265 | ||||||||
\(947\) | 4.24224e90 | 0.706190 | 0.353095 | − | 0.935588i | \(-0.385129\pi\) | ||||
0.353095 | + | 0.935588i | \(0.385129\pi\) | |||||||
\(948\) | −7.39691e90 | −1.19233 | ||||||||
\(949\) | 3.79908e90 | 0.593006 | ||||||||
\(950\) | 3.90563e90 | 0.590366 | ||||||||
\(951\) | −1.75749e91 | −2.57269 | ||||||||
\(952\) | −2.71992e90 | −0.385593 | ||||||||
\(953\) | 4.76356e90 | 0.654031 | 0.327015 | − | 0.945019i | \(-0.393957\pi\) | ||||
0.327015 | + | 0.945019i | \(0.393957\pi\) | |||||||
\(954\) | −4.26826e90 | −0.567578 | ||||||||
\(955\) | −1.52731e90 | −0.196709 | ||||||||
\(956\) | 1.09899e91 | 1.37098 | ||||||||
\(957\) | 6.98090e90 | 0.843524 | ||||||||
\(958\) | −1.33240e90 | −0.155950 | ||||||||
\(959\) | −2.01633e90 | −0.228609 | ||||||||
\(960\) | 2.05844e89 | 0.0226082 | ||||||||
\(961\) | −4.64855e90 | −0.494600 | ||||||||
\(962\) | −2.51091e90 | −0.258816 | ||||||||
\(963\) | 3.43753e90 | 0.343277 | ||||||||
\(964\) | −3.07170e90 | −0.297187 | ||||||||
\(965\) | 7.97789e89 | 0.0747833 | ||||||||
\(966\) | −3.14471e90 | −0.285613 | ||||||||
\(967\) | 1.00304e91 | 0.882699 | 0.441350 | − | 0.897335i | \(-0.354500\pi\) | ||||
0.441350 | + | 0.897335i | \(0.354500\pi\) | |||||||
\(968\) | 1.28380e91 | 1.09471 | ||||||||
\(969\) | 1.48349e91 | 1.22577 | ||||||||
\(970\) | −1.25983e89 | −0.0100873 | ||||||||
\(971\) | 3.02928e90 | 0.235046 | 0.117523 | − | 0.993070i | \(-0.462505\pi\) | ||||
0.117523 | + | 0.993070i | \(0.462505\pi\) | |||||||
\(972\) | 1.73311e90 | 0.130318 | ||||||||
\(973\) | −2.77575e91 | −2.02273 | ||||||||
\(974\) | 4.20758e90 | 0.297156 | ||||||||
\(975\) | 2.07570e91 | 1.42077 | ||||||||
\(976\) | −1.92121e90 | −0.127454 | ||||||||
\(977\) | −2.66487e91 | −1.71353 | −0.856764 | − | 0.515709i | \(-0.827529\pi\) | ||||
−0.856764 | + | 0.515709i | \(0.827529\pi\) | |||||||
\(978\) | 6.76762e90 | 0.421794 | ||||||||
\(979\) | 7.65003e90 | 0.462159 | ||||||||
\(980\) | −1.61026e89 | −0.00942979 | ||||||||
\(981\) | −2.92911e91 | −1.66277 | ||||||||
\(982\) | −5.08913e90 | −0.280055 | ||||||||
\(983\) | −2.34161e91 | −1.24920 | −0.624601 | − | 0.780944i | \(-0.714739\pi\) | ||||
−0.624601 | + | 0.780944i | \(0.714739\pi\) | |||||||
\(984\) | −2.37390e91 | −1.22776 | ||||||||
\(985\) | 1.36042e90 | 0.0682129 | ||||||||
\(986\) | 1.27710e90 | 0.0620837 | ||||||||
\(987\) | 6.06574e91 | 2.85897 | ||||||||
\(988\) | −2.16344e91 | −0.988687 | ||||||||
\(989\) | 6.03155e90 | 0.267265 | ||||||||
\(990\) | 3.45777e90 | 0.148567 | ||||||||
\(991\) | 3.94657e91 | 1.64427 | 0.822135 | − | 0.569292i | \(-0.192783\pi\) | ||||
0.822135 | + | 0.569292i | \(0.192783\pi\) | |||||||
\(992\) | −1.70645e91 | −0.689424 | ||||||||
\(993\) | −9.73276e89 | −0.0381315 | ||||||||
\(994\) | 1.87221e91 | 0.711327 | ||||||||
\(995\) | −4.36090e90 | −0.160684 | ||||||||
\(996\) | −1.40537e91 | −0.502203 | ||||||||
\(997\) | 5.53684e91 | 1.91893 | 0.959466 | − | 0.281823i | \(-0.0909390\pi\) | ||||
0.959466 | + | 0.281823i | \(0.0909390\pi\) | |||||||
\(998\) | −4.35396e90 | −0.146353 | ||||||||
\(999\) | −4.24057e91 | −1.38254 |
(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 | 1.62.a.a.1.2 | ✓ | 4 | |
3.2 | odd | 2 | 9.62.a.a.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.62.a.a.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
9.62.a.a.1.3 | 4 | 3.2 | odd | 2 |