Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,10,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(5.15035836164\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −16.0000 | −0.707107 | ||||||||
\(3\) | −204.000 | −1.45407 | −0.727034 | − | 0.686602i | \(-0.759102\pi\) | ||||
−0.727034 | + | 0.686602i | \(0.759102\pi\) | |||||||
\(4\) | 256.000 | 0.500000 | ||||||||
\(5\) | 625.000 | 0.447214 | ||||||||
\(6\) | 3264.00 | 1.02818 | ||||||||
\(7\) | 5432.00 | 0.855103 | 0.427552 | − | 0.903991i | \(-0.359376\pi\) | ||||
0.427552 | + | 0.903991i | \(0.359376\pi\) | |||||||
\(8\) | −4096.00 | −0.353553 | ||||||||
\(9\) | 21933.0 | 1.11431 | ||||||||
\(10\) | −10000.0 | −0.316228 | ||||||||
\(11\) | 73932.0 | 1.52253 | 0.761264 | − | 0.648442i | \(-0.224579\pi\) | ||||
0.761264 | + | 0.648442i | \(0.224579\pi\) | |||||||
\(12\) | −52224.0 | −0.727034 | ||||||||
\(13\) | −114514. | −1.11202 | −0.556011 | − | 0.831175i | \(-0.687669\pi\) | ||||
−0.556011 | + | 0.831175i | \(0.687669\pi\) | |||||||
\(14\) | −86912.0 | −0.604649 | ||||||||
\(15\) | −127500. | −0.650279 | ||||||||
\(16\) | 65536.0 | 0.250000 | ||||||||
\(17\) | 41682.0 | 0.121040 | 0.0605199 | − | 0.998167i | \(-0.480724\pi\) | ||||
0.0605199 | + | 0.998167i | \(0.480724\pi\) | |||||||
\(18\) | −350928. | −0.787937 | ||||||||
\(19\) | 1.05746e6 | 1.86154 | 0.930771 | − | 0.365603i | \(-0.119137\pi\) | ||||
0.930771 | + | 0.365603i | \(0.119137\pi\) | |||||||
\(20\) | 160000. | 0.223607 | ||||||||
\(21\) | −1.10813e6 | −1.24338 | ||||||||
\(22\) | −1.18291e6 | −1.07659 | ||||||||
\(23\) | 1.59934e6 | 1.19169 | 0.595847 | − | 0.803098i | \(-0.296817\pi\) | ||||
0.595847 | + | 0.803098i | \(0.296817\pi\) | |||||||
\(24\) | 835584. | 0.514090 | ||||||||
\(25\) | 390625. | 0.200000 | ||||||||
\(26\) | 1.83222e6 | 0.786319 | ||||||||
\(27\) | −459000. | −0.166217 | ||||||||
\(28\) | 1.39059e6 | 0.427552 | ||||||||
\(29\) | 2.18451e6 | 0.573539 | 0.286770 | − | 0.958000i | \(-0.407419\pi\) | ||||
0.286770 | + | 0.958000i | \(0.407419\pi\) | |||||||
\(30\) | 2.04000e6 | 0.459816 | ||||||||
\(31\) | −9.61965e6 | −1.87082 | −0.935409 | − | 0.353567i | \(-0.884968\pi\) | ||||
−0.935409 | + | 0.353567i | \(0.884968\pi\) | |||||||
\(32\) | −1.04858e6 | −0.176777 | ||||||||
\(33\) | −1.50821e7 | −2.21386 | ||||||||
\(34\) | −666912. | −0.0855881 | ||||||||
\(35\) | 3.39500e6 | 0.382414 | ||||||||
\(36\) | 5.61485e6 | 0.557156 | ||||||||
\(37\) | 4.79994e6 | 0.421045 | 0.210522 | − | 0.977589i | \(-0.432484\pi\) | ||||
0.210522 | + | 0.977589i | \(0.432484\pi\) | |||||||
\(38\) | −1.69194e7 | −1.31631 | ||||||||
\(39\) | 2.33609e7 | 1.61696 | ||||||||
\(40\) | −2.56000e6 | −0.158114 | ||||||||
\(41\) | 9.53188e6 | 0.526807 | 0.263403 | − | 0.964686i | \(-0.415155\pi\) | ||||
0.263403 | + | 0.964686i | \(0.415155\pi\) | |||||||
\(42\) | 1.77300e7 | 0.879201 | ||||||||
\(43\) | −1.34645e7 | −0.600595 | −0.300297 | − | 0.953846i | \(-0.597086\pi\) | ||||
−0.300297 | + | 0.953846i | \(0.597086\pi\) | |||||||
\(44\) | 1.89266e7 | 0.761264 | ||||||||
\(45\) | 1.37081e7 | 0.498335 | ||||||||
\(46\) | −2.55894e7 | −0.842654 | ||||||||
\(47\) | 1.14420e7 | 0.342027 | 0.171013 | − | 0.985269i | \(-0.445296\pi\) | ||||
0.171013 | + | 0.985269i | \(0.445296\pi\) | |||||||
\(48\) | −1.33693e7 | −0.363517 | ||||||||
\(49\) | −1.08470e7 | −0.268798 | ||||||||
\(50\) | −6.25000e6 | −0.141421 | ||||||||
\(51\) | −8.50313e6 | −0.176000 | ||||||||
\(52\) | −2.93156e7 | −0.556011 | ||||||||
\(53\) | 5.36158e7 | 0.933364 | 0.466682 | − | 0.884425i | \(-0.345449\pi\) | ||||
0.466682 | + | 0.884425i | \(0.345449\pi\) | |||||||
\(54\) | 7.34400e6 | 0.117533 | ||||||||
\(55\) | 4.62075e7 | 0.680895 | ||||||||
\(56\) | −2.22495e7 | −0.302325 | ||||||||
\(57\) | −2.15722e8 | −2.70681 | ||||||||
\(58\) | −3.49522e7 | −0.405553 | ||||||||
\(59\) | 8.18626e7 | 0.879532 | 0.439766 | − | 0.898112i | \(-0.355061\pi\) | ||||
0.439766 | + | 0.898112i | \(0.355061\pi\) | |||||||
\(60\) | −3.26400e7 | −0.325139 | ||||||||
\(61\) | −1.04691e8 | −0.968114 | −0.484057 | − | 0.875037i | \(-0.660837\pi\) | ||||
−0.484057 | + | 0.875037i | \(0.660837\pi\) | |||||||
\(62\) | 1.53914e8 | 1.32287 | ||||||||
\(63\) | 1.19140e8 | 0.952852 | ||||||||
\(64\) | 1.67772e7 | 0.125000 | ||||||||
\(65\) | −7.15712e7 | −0.497311 | ||||||||
\(66\) | 2.41314e8 | 1.56543 | ||||||||
\(67\) | 1.40571e8 | 0.852235 | 0.426118 | − | 0.904668i | \(-0.359881\pi\) | ||||
0.426118 | + | 0.904668i | \(0.359881\pi\) | |||||||
\(68\) | 1.06706e7 | 0.0605199 | ||||||||
\(69\) | −3.26265e8 | −1.73280 | ||||||||
\(70\) | −5.43200e7 | −0.270407 | ||||||||
\(71\) | 9.70988e7 | 0.453473 | 0.226736 | − | 0.973956i | \(-0.427194\pi\) | ||||
0.226736 | + | 0.973956i | \(0.427194\pi\) | |||||||
\(72\) | −8.98376e7 | −0.393969 | ||||||||
\(73\) | 1.71849e8 | 0.708262 | 0.354131 | − | 0.935196i | \(-0.384777\pi\) | ||||
0.354131 | + | 0.935196i | \(0.384777\pi\) | |||||||
\(74\) | −7.67991e7 | −0.297724 | ||||||||
\(75\) | −7.96875e7 | −0.290813 | ||||||||
\(76\) | 2.70710e8 | 0.930771 | ||||||||
\(77\) | 4.01599e8 | 1.30192 | ||||||||
\(78\) | −3.73774e8 | −1.14336 | ||||||||
\(79\) | −1.17380e8 | −0.339057 | −0.169528 | − | 0.985525i | \(-0.554224\pi\) | ||||
−0.169528 | + | 0.985525i | \(0.554224\pi\) | |||||||
\(80\) | 4.09600e7 | 0.111803 | ||||||||
\(81\) | −3.38071e8 | −0.872621 | ||||||||
\(82\) | −1.52510e8 | −0.372509 | ||||||||
\(83\) | 3.23638e8 | 0.748527 | 0.374264 | − | 0.927322i | \(-0.377896\pi\) | ||||
0.374264 | + | 0.927322i | \(0.377896\pi\) | |||||||
\(84\) | −2.83681e8 | −0.621689 | ||||||||
\(85\) | 2.60512e7 | 0.0541307 | ||||||||
\(86\) | 2.15432e8 | 0.424685 | ||||||||
\(87\) | −4.45640e8 | −0.833965 | ||||||||
\(88\) | −3.02825e8 | −0.538295 | ||||||||
\(89\) | −8.94379e8 | −1.51101 | −0.755504 | − | 0.655144i | \(-0.772608\pi\) | ||||
−0.755504 | + | 0.655144i | \(0.772608\pi\) | |||||||
\(90\) | −2.19330e8 | −0.352376 | ||||||||
\(91\) | −6.22040e8 | −0.950894 | ||||||||
\(92\) | 4.09430e8 | 0.595847 | ||||||||
\(93\) | 1.96241e9 | 2.72030 | ||||||||
\(94\) | −1.83071e8 | −0.241849 | ||||||||
\(95\) | 6.60912e8 | 0.832507 | ||||||||
\(96\) | 2.13910e8 | 0.257045 | ||||||||
\(97\) | 2.32679e8 | 0.266860 | 0.133430 | − | 0.991058i | \(-0.457401\pi\) | ||||
0.133430 | + | 0.991058i | \(0.457401\pi\) | |||||||
\(98\) | 1.73552e8 | 0.190069 | ||||||||
\(99\) | 1.62155e9 | 1.69657 | ||||||||
\(100\) | 1.00000e8 | 0.100000 | ||||||||
\(101\) | 6.51288e8 | 0.622769 | 0.311384 | − | 0.950284i | \(-0.399207\pi\) | ||||
0.311384 | + | 0.950284i | \(0.399207\pi\) | |||||||
\(102\) | 1.36050e8 | 0.124451 | ||||||||
\(103\) | −1.71129e9 | −1.49815 | −0.749076 | − | 0.662484i | \(-0.769502\pi\) | ||||
−0.749076 | + | 0.662484i | \(0.769502\pi\) | |||||||
\(104\) | 4.69049e8 | 0.393159 | ||||||||
\(105\) | −6.92580e8 | −0.556055 | ||||||||
\(106\) | −8.57852e8 | −0.659988 | ||||||||
\(107\) | −1.31553e9 | −0.970228 | −0.485114 | − | 0.874451i | \(-0.661222\pi\) | ||||
−0.485114 | + | 0.874451i | \(0.661222\pi\) | |||||||
\(108\) | −1.17504e8 | −0.0831086 | ||||||||
\(109\) | 3.10670e8 | 0.210805 | 0.105402 | − | 0.994430i | \(-0.466387\pi\) | ||||
0.105402 | + | 0.994430i | \(0.466387\pi\) | |||||||
\(110\) | −7.39320e8 | −0.481466 | ||||||||
\(111\) | −9.79188e8 | −0.612227 | ||||||||
\(112\) | 3.55992e8 | 0.213776 | ||||||||
\(113\) | −2.74850e9 | −1.58578 | −0.792889 | − | 0.609366i | \(-0.791424\pi\) | ||||
−0.792889 | + | 0.609366i | \(0.791424\pi\) | |||||||
\(114\) | 3.45155e9 | 1.91400 | ||||||||
\(115\) | 9.99585e8 | 0.532941 | ||||||||
\(116\) | 5.59235e8 | 0.286770 | ||||||||
\(117\) | −2.51164e9 | −1.23914 | ||||||||
\(118\) | −1.30980e9 | −0.621923 | ||||||||
\(119\) | 2.26417e8 | 0.103502 | ||||||||
\(120\) | 5.22240e8 | 0.229908 | ||||||||
\(121\) | 3.10799e9 | 1.31809 | ||||||||
\(122\) | 1.67506e9 | 0.684560 | ||||||||
\(123\) | −1.94450e9 | −0.766012 | ||||||||
\(124\) | −2.46263e9 | −0.935409 | ||||||||
\(125\) | 2.44141e8 | 0.0894427 | ||||||||
\(126\) | −1.90624e9 | −0.673768 | ||||||||
\(127\) | 2.64323e9 | 0.901608 | 0.450804 | − | 0.892623i | \(-0.351137\pi\) | ||||
0.450804 | + | 0.892623i | \(0.351137\pi\) | |||||||
\(128\) | −2.68435e8 | −0.0883883 | ||||||||
\(129\) | 2.74675e9 | 0.873305 | ||||||||
\(130\) | 1.14514e9 | 0.351652 | ||||||||
\(131\) | −2.63724e9 | −0.782401 | −0.391201 | − | 0.920305i | \(-0.627940\pi\) | ||||
−0.391201 | + | 0.920305i | \(0.627940\pi\) | |||||||
\(132\) | −3.86102e9 | −1.10693 | ||||||||
\(133\) | 5.74412e9 | 1.59181 | ||||||||
\(134\) | −2.24914e9 | −0.602621 | ||||||||
\(135\) | −2.86875e8 | −0.0743346 | ||||||||
\(136\) | −1.70729e8 | −0.0427941 | ||||||||
\(137\) | 5.16539e9 | 1.25274 | 0.626370 | − | 0.779526i | \(-0.284540\pi\) | ||||
0.626370 | + | 0.779526i | \(0.284540\pi\) | |||||||
\(138\) | 5.22023e9 | 1.22528 | ||||||||
\(139\) | 2.76751e9 | 0.628815 | 0.314407 | − | 0.949288i | \(-0.398194\pi\) | ||||
0.314407 | + | 0.949288i | \(0.398194\pi\) | |||||||
\(140\) | 8.69120e8 | 0.191207 | ||||||||
\(141\) | −2.33416e9 | −0.497330 | ||||||||
\(142\) | −1.55358e9 | −0.320654 | ||||||||
\(143\) | −8.46625e9 | −1.69309 | ||||||||
\(144\) | 1.43740e9 | 0.278578 | ||||||||
\(145\) | 1.36532e9 | 0.256494 | ||||||||
\(146\) | −2.74958e9 | −0.500817 | ||||||||
\(147\) | 2.21278e9 | 0.390851 | ||||||||
\(148\) | 1.22879e9 | 0.210522 | ||||||||
\(149\) | −6.04151e9 | −1.00417 | −0.502085 | − | 0.864818i | \(-0.667434\pi\) | ||||
−0.502085 | + | 0.864818i | \(0.667434\pi\) | |||||||
\(150\) | 1.27500e9 | 0.205636 | ||||||||
\(151\) | 4.07206e8 | 0.0637408 | 0.0318704 | − | 0.999492i | \(-0.489854\pi\) | ||||
0.0318704 | + | 0.999492i | \(0.489854\pi\) | |||||||
\(152\) | −4.33136e9 | −0.658154 | ||||||||
\(153\) | 9.14211e8 | 0.134876 | ||||||||
\(154\) | −6.42558e9 | −0.920596 | ||||||||
\(155\) | −6.01228e9 | −0.836655 | ||||||||
\(156\) | 5.98038e9 | 0.808478 | ||||||||
\(157\) | 1.80938e8 | 0.0237674 | 0.0118837 | − | 0.999929i | \(-0.496217\pi\) | ||||
0.0118837 | + | 0.999929i | \(0.496217\pi\) | |||||||
\(158\) | 1.87808e9 | 0.239749 | ||||||||
\(159\) | −1.09376e10 | −1.35717 | ||||||||
\(160\) | −6.55360e8 | −0.0790569 | ||||||||
\(161\) | 8.68759e9 | 1.01902 | ||||||||
\(162\) | 5.40914e9 | 0.617036 | ||||||||
\(163\) | 5.88002e9 | 0.652432 | 0.326216 | − | 0.945295i | \(-0.394226\pi\) | ||||
0.326216 | + | 0.945295i | \(0.394226\pi\) | |||||||
\(164\) | 2.44016e9 | 0.263403 | ||||||||
\(165\) | −9.42633e9 | −0.990068 | ||||||||
\(166\) | −5.17820e9 | −0.529289 | ||||||||
\(167\) | 1.36197e9 | 0.135501 | 0.0677507 | − | 0.997702i | \(-0.478418\pi\) | ||||
0.0677507 | + | 0.997702i | \(0.478418\pi\) | |||||||
\(168\) | 4.53889e9 | 0.439600 | ||||||||
\(169\) | 2.50896e9 | 0.236594 | ||||||||
\(170\) | −4.16820e8 | −0.0382762 | ||||||||
\(171\) | 2.31933e10 | 2.07434 | ||||||||
\(172\) | −3.44691e9 | −0.300297 | ||||||||
\(173\) | −1.41778e10 | −1.20338 | −0.601688 | − | 0.798731i | \(-0.705505\pi\) | ||||
−0.601688 | + | 0.798731i | \(0.705505\pi\) | |||||||
\(174\) | 7.13024e9 | 0.589702 | ||||||||
\(175\) | 2.12188e9 | 0.171021 | ||||||||
\(176\) | 4.84521e9 | 0.380632 | ||||||||
\(177\) | −1.67000e10 | −1.27890 | ||||||||
\(178\) | 1.43101e10 | 1.06844 | ||||||||
\(179\) | 2.66456e9 | 0.193993 | 0.0969967 | − | 0.995285i | \(-0.469076\pi\) | ||||
0.0969967 | + | 0.995285i | \(0.469076\pi\) | |||||||
\(180\) | 3.50928e9 | 0.249168 | ||||||||
\(181\) | −4.05446e9 | −0.280789 | −0.140394 | − | 0.990096i | \(-0.544837\pi\) | ||||
−0.140394 | + | 0.990096i | \(0.544837\pi\) | |||||||
\(182\) | 9.95264e9 | 0.672384 | ||||||||
\(183\) | 2.13570e10 | 1.40770 | ||||||||
\(184\) | −6.55088e9 | −0.421327 | ||||||||
\(185\) | 2.99996e9 | 0.188297 | ||||||||
\(186\) | −3.13985e10 | −1.92354 | ||||||||
\(187\) | 3.08163e9 | 0.184287 | ||||||||
\(188\) | 2.92914e9 | 0.171013 | ||||||||
\(189\) | −2.49329e9 | −0.142133 | ||||||||
\(190\) | −1.05746e10 | −0.588671 | ||||||||
\(191\) | −1.01385e10 | −0.551216 | −0.275608 | − | 0.961270i | \(-0.588879\pi\) | ||||
−0.275608 | + | 0.961270i | \(0.588879\pi\) | |||||||
\(192\) | −3.42255e9 | −0.181758 | ||||||||
\(193\) | −7.57686e9 | −0.393080 | −0.196540 | − | 0.980496i | \(-0.562971\pi\) | ||||
−0.196540 | + | 0.980496i | \(0.562971\pi\) | |||||||
\(194\) | −3.72286e9 | −0.188699 | ||||||||
\(195\) | 1.46005e10 | 0.723124 | ||||||||
\(196\) | −2.77683e9 | −0.134399 | ||||||||
\(197\) | −2.20768e8 | −0.0104433 | −0.00522166 | − | 0.999986i | \(-0.501662\pi\) | ||||
−0.00522166 | + | 0.999986i | \(0.501662\pi\) | |||||||
\(198\) | −2.59448e10 | −1.19966 | ||||||||
\(199\) | −2.99296e10 | −1.35289 | −0.676445 | − | 0.736493i | \(-0.736481\pi\) | ||||
−0.676445 | + | 0.736493i | \(0.736481\pi\) | |||||||
\(200\) | −1.60000e9 | −0.0707107 | ||||||||
\(201\) | −2.86765e10 | −1.23921 | ||||||||
\(202\) | −1.04206e10 | −0.440364 | ||||||||
\(203\) | 1.18663e10 | 0.490435 | ||||||||
\(204\) | −2.17680e9 | −0.0880001 | ||||||||
\(205\) | 5.95743e9 | 0.235595 | ||||||||
\(206\) | 2.73806e10 | 1.05935 | ||||||||
\(207\) | 3.50782e10 | 1.32792 | ||||||||
\(208\) | −7.50479e9 | −0.278006 | ||||||||
\(209\) | 7.81801e10 | 2.83425 | ||||||||
\(210\) | 1.10813e10 | 0.393191 | ||||||||
\(211\) | 2.92533e10 | 1.01602 | 0.508012 | − | 0.861350i | \(-0.330381\pi\) | ||||
0.508012 | + | 0.861350i | \(0.330381\pi\) | |||||||
\(212\) | 1.37256e10 | 0.466682 | ||||||||
\(213\) | −1.98082e10 | −0.659380 | ||||||||
\(214\) | 2.10485e10 | 0.686055 | ||||||||
\(215\) | −8.41530e9 | −0.268594 | ||||||||
\(216\) | 1.88006e9 | 0.0587666 | ||||||||
\(217\) | −5.22539e10 | −1.59974 | ||||||||
\(218\) | −4.97072e9 | −0.149061 | ||||||||
\(219\) | −3.50572e10 | −1.02986 | ||||||||
\(220\) | 1.18291e10 | 0.340448 | ||||||||
\(221\) | −4.77317e9 | −0.134599 | ||||||||
\(222\) | 1.56670e10 | 0.432910 | ||||||||
\(223\) | −5.18482e10 | −1.40398 | −0.701991 | − | 0.712186i | \(-0.747705\pi\) | ||||
−0.701991 | + | 0.712186i | \(0.747705\pi\) | |||||||
\(224\) | −5.69586e9 | −0.151162 | ||||||||
\(225\) | 8.56758e9 | 0.222862 | ||||||||
\(226\) | 4.39760e10 | 1.12131 | ||||||||
\(227\) | 4.56273e10 | 1.14053 | 0.570267 | − | 0.821460i | \(-0.306840\pi\) | ||||
0.570267 | + | 0.821460i | \(0.306840\pi\) | |||||||
\(228\) | −5.52248e10 | −1.35340 | ||||||||
\(229\) | 6.21495e10 | 1.49341 | 0.746703 | − | 0.665158i | \(-0.231636\pi\) | ||||
0.746703 | + | 0.665158i | \(0.231636\pi\) | |||||||
\(230\) | −1.59934e10 | −0.376846 | ||||||||
\(231\) | −8.19261e10 | −1.89308 | ||||||||
\(232\) | −8.94775e9 | −0.202777 | ||||||||
\(233\) | −3.72165e9 | −0.0827245 | −0.0413623 | − | 0.999144i | \(-0.513170\pi\) | ||||
−0.0413623 | + | 0.999144i | \(0.513170\pi\) | |||||||
\(234\) | 4.01862e10 | 0.876204 | ||||||||
\(235\) | 7.15122e9 | 0.152959 | ||||||||
\(236\) | 2.09568e10 | 0.439766 | ||||||||
\(237\) | 2.39455e10 | 0.493011 | ||||||||
\(238\) | −3.62267e9 | −0.0731867 | ||||||||
\(239\) | 3.62221e9 | 0.0718098 | 0.0359049 | − | 0.999355i | \(-0.488569\pi\) | ||||
0.0359049 | + | 0.999355i | \(0.488569\pi\) | |||||||
\(240\) | −8.35584e9 | −0.162570 | ||||||||
\(241\) | −3.36556e10 | −0.642660 | −0.321330 | − | 0.946967i | \(-0.604130\pi\) | ||||
−0.321330 | + | 0.946967i | \(0.604130\pi\) | |||||||
\(242\) | −4.97279e10 | −0.932032 | ||||||||
\(243\) | 7.80010e10 | 1.43507 | ||||||||
\(244\) | −2.68010e10 | −0.484057 | ||||||||
\(245\) | −6.77936e9 | −0.120210 | ||||||||
\(246\) | 3.11121e10 | 0.541653 | ||||||||
\(247\) | −1.21094e11 | −2.07008 | ||||||||
\(248\) | 3.94021e10 | 0.661434 | ||||||||
\(249\) | −6.60221e10 | −1.08841 | ||||||||
\(250\) | −3.90625e9 | −0.0632456 | ||||||||
\(251\) | −5.88110e10 | −0.935248 | −0.467624 | − | 0.883928i | \(-0.654890\pi\) | ||||
−0.467624 | + | 0.883928i | \(0.654890\pi\) | |||||||
\(252\) | 3.04999e10 | 0.476426 | ||||||||
\(253\) | 1.18242e11 | 1.81439 | ||||||||
\(254\) | −4.22917e10 | −0.637533 | ||||||||
\(255\) | −5.31446e9 | −0.0787096 | ||||||||
\(256\) | 4.29497e9 | 0.0625000 | ||||||||
\(257\) | −7.52072e10 | −1.07538 | −0.537688 | − | 0.843144i | \(-0.680702\pi\) | ||||
−0.537688 | + | 0.843144i | \(0.680702\pi\) | |||||||
\(258\) | −4.39481e10 | −0.617520 | ||||||||
\(259\) | 2.60733e10 | 0.360037 | ||||||||
\(260\) | −1.83222e10 | −0.248656 | ||||||||
\(261\) | 4.79129e10 | 0.639101 | ||||||||
\(262\) | 4.21959e10 | 0.553241 | ||||||||
\(263\) | −1.16316e10 | −0.149913 | −0.0749565 | − | 0.997187i | \(-0.523882\pi\) | ||||
−0.0749565 | + | 0.997187i | \(0.523882\pi\) | |||||||
\(264\) | 6.17764e10 | 0.782717 | ||||||||
\(265\) | 3.35099e10 | 0.417413 | ||||||||
\(266\) | −9.19060e10 | −1.12558 | ||||||||
\(267\) | 1.82453e11 | 2.19711 | ||||||||
\(268\) | 3.59862e10 | 0.426118 | ||||||||
\(269\) | 2.83871e10 | 0.330549 | 0.165275 | − | 0.986248i | \(-0.447149\pi\) | ||||
0.165275 | + | 0.986248i | \(0.447149\pi\) | |||||||
\(270\) | 4.59000e9 | 0.0525625 | ||||||||
\(271\) | 1.47987e11 | 1.66672 | 0.833361 | − | 0.552729i | \(-0.186414\pi\) | ||||
0.833361 | + | 0.552729i | \(0.186414\pi\) | |||||||
\(272\) | 2.73167e9 | 0.0302600 | ||||||||
\(273\) | 1.26896e11 | 1.38266 | ||||||||
\(274\) | −8.26463e10 | −0.885820 | ||||||||
\(275\) | 2.88797e10 | 0.304506 | ||||||||
\(276\) | −8.35237e10 | −0.866401 | ||||||||
\(277\) | −7.58857e10 | −0.774464 | −0.387232 | − | 0.921982i | \(-0.626569\pi\) | ||||
−0.387232 | + | 0.921982i | \(0.626569\pi\) | |||||||
\(278\) | −4.42802e10 | −0.444639 | ||||||||
\(279\) | −2.10988e11 | −2.08467 | ||||||||
\(280\) | −1.39059e10 | −0.135204 | ||||||||
\(281\) | 1.72151e11 | 1.64714 | 0.823570 | − | 0.567215i | \(-0.191979\pi\) | ||||
0.823570 | + | 0.567215i | \(0.191979\pi\) | |||||||
\(282\) | 3.73465e10 | 0.351665 | ||||||||
\(283\) | −1.49932e11 | −1.38949 | −0.694745 | − | 0.719256i | \(-0.744483\pi\) | ||||
−0.694745 | + | 0.719256i | \(0.744483\pi\) | |||||||
\(284\) | 2.48573e10 | 0.226736 | ||||||||
\(285\) | −1.34826e11 | −1.21052 | ||||||||
\(286\) | 1.35460e11 | 1.19719 | ||||||||
\(287\) | 5.17772e10 | 0.450474 | ||||||||
\(288\) | −2.29984e10 | −0.196984 | ||||||||
\(289\) | −1.16850e11 | −0.985349 | ||||||||
\(290\) | −2.18451e10 | −0.181369 | ||||||||
\(291\) | −4.74664e10 | −0.388032 | ||||||||
\(292\) | 4.39933e10 | 0.354131 | ||||||||
\(293\) | 9.51745e9 | 0.0754426 | 0.0377213 | − | 0.999288i | \(-0.487990\pi\) | ||||
0.0377213 | + | 0.999288i | \(0.487990\pi\) | |||||||
\(294\) | −3.54046e10 | −0.276373 | ||||||||
\(295\) | 5.11641e10 | 0.393339 | ||||||||
\(296\) | −1.96606e10 | −0.148862 | ||||||||
\(297\) | −3.39348e10 | −0.253070 | ||||||||
\(298\) | 9.66642e10 | 0.710056 | ||||||||
\(299\) | −1.83146e11 | −1.32519 | ||||||||
\(300\) | −2.04000e10 | −0.145407 | ||||||||
\(301\) | −7.31391e10 | −0.513571 | ||||||||
\(302\) | −6.51529e9 | −0.0450716 | ||||||||
\(303\) | −1.32863e11 | −0.905547 | ||||||||
\(304\) | 6.93017e10 | 0.465385 | ||||||||
\(305\) | −6.54321e10 | −0.432954 | ||||||||
\(306\) | −1.46274e10 | −0.0953718 | ||||||||
\(307\) | 9.05900e10 | 0.582046 | 0.291023 | − | 0.956716i | \(-0.406004\pi\) | ||||
0.291023 | + | 0.956716i | \(0.406004\pi\) | |||||||
\(308\) | 1.02809e11 | 0.650959 | ||||||||
\(309\) | 3.49103e11 | 2.17841 | ||||||||
\(310\) | 9.61965e10 | 0.591605 | ||||||||
\(311\) | −2.81285e11 | −1.70500 | −0.852501 | − | 0.522726i | \(-0.824915\pi\) | ||||
−0.852501 | + | 0.522726i | \(0.824915\pi\) | |||||||
\(312\) | −9.56861e10 | −0.571680 | ||||||||
\(313\) | −9.11248e10 | −0.536645 | −0.268323 | − | 0.963329i | \(-0.586469\pi\) | ||||
−0.268323 | + | 0.963329i | \(0.586469\pi\) | |||||||
\(314\) | −2.89501e9 | −0.0168061 | ||||||||
\(315\) | 7.44625e10 | 0.426128 | ||||||||
\(316\) | −3.00493e10 | −0.169528 | ||||||||
\(317\) | 1.03167e11 | 0.573819 | 0.286909 | − | 0.957958i | \(-0.407372\pi\) | ||||
0.286909 | + | 0.957958i | \(0.407372\pi\) | |||||||
\(318\) | 1.75002e11 | 0.959667 | ||||||||
\(319\) | 1.61505e11 | 0.873230 | ||||||||
\(320\) | 1.04858e10 | 0.0559017 | ||||||||
\(321\) | 2.68368e11 | 1.41078 | ||||||||
\(322\) | −1.39001e11 | −0.720556 | ||||||||
\(323\) | 4.40770e10 | 0.225321 | ||||||||
\(324\) | −8.65462e10 | −0.436310 | ||||||||
\(325\) | −4.47320e10 | −0.222404 | ||||||||
\(326\) | −9.40804e10 | −0.461339 | ||||||||
\(327\) | −6.33767e10 | −0.306524 | ||||||||
\(328\) | −3.90426e10 | −0.186254 | ||||||||
\(329\) | 6.21527e10 | 0.292468 | ||||||||
\(330\) | 1.50821e11 | 0.700084 | ||||||||
\(331\) | 2.51080e11 | 1.14970 | 0.574851 | − | 0.818258i | \(-0.305060\pi\) | ||||
0.574851 | + | 0.818258i | \(0.305060\pi\) | |||||||
\(332\) | 8.28512e10 | 0.374264 | ||||||||
\(333\) | 1.05277e11 | 0.469175 | ||||||||
\(334\) | −2.17916e10 | −0.0958140 | ||||||||
\(335\) | 8.78569e10 | 0.381131 | ||||||||
\(336\) | −7.26223e10 | −0.310844 | ||||||||
\(337\) | −4.04967e11 | −1.71035 | −0.855175 | − | 0.518339i | \(-0.826550\pi\) | ||||
−0.855175 | + | 0.518339i | \(0.826550\pi\) | |||||||
\(338\) | −4.01433e10 | −0.167297 | ||||||||
\(339\) | 5.60694e11 | 2.30583 | ||||||||
\(340\) | 6.66912e9 | 0.0270653 | ||||||||
\(341\) | −7.11200e11 | −2.84837 | ||||||||
\(342\) | −3.71092e11 | −1.46678 | ||||||||
\(343\) | −2.78122e11 | −1.08495 | ||||||||
\(344\) | 5.51505e10 | 0.212342 | ||||||||
\(345\) | −2.03915e11 | −0.774933 | ||||||||
\(346\) | 2.26845e11 | 0.850916 | ||||||||
\(347\) | 4.20848e11 | 1.55827 | 0.779134 | − | 0.626857i | \(-0.215659\pi\) | ||||
0.779134 | + | 0.626857i | \(0.215659\pi\) | |||||||
\(348\) | −1.14084e11 | −0.416982 | ||||||||
\(349\) | −3.99383e11 | −1.44104 | −0.720518 | − | 0.693436i | \(-0.756096\pi\) | ||||
−0.720518 | + | 0.693436i | \(0.756096\pi\) | |||||||
\(350\) | −3.39500e10 | −0.120930 | ||||||||
\(351\) | 5.25619e10 | 0.184837 | ||||||||
\(352\) | −7.75233e10 | −0.269148 | ||||||||
\(353\) | −7.88806e10 | −0.270386 | −0.135193 | − | 0.990819i | \(-0.543165\pi\) | ||||
−0.135193 | + | 0.990819i | \(0.543165\pi\) | |||||||
\(354\) | 2.67200e11 | 0.904318 | ||||||||
\(355\) | 6.06867e10 | 0.202799 | ||||||||
\(356\) | −2.28961e11 | −0.755504 | ||||||||
\(357\) | −4.61890e10 | −0.150498 | ||||||||
\(358\) | −4.26330e10 | −0.137174 | ||||||||
\(359\) | 1.39842e11 | 0.444337 | 0.222168 | − | 0.975008i | \(-0.428686\pi\) | ||||
0.222168 | + | 0.975008i | \(0.428686\pi\) | |||||||
\(360\) | −5.61485e10 | −0.176188 | ||||||||
\(361\) | 7.95534e11 | 2.46534 | ||||||||
\(362\) | 6.48714e10 | 0.198547 | ||||||||
\(363\) | −6.34031e11 | −1.91660 | ||||||||
\(364\) | −1.59242e11 | −0.475447 | ||||||||
\(365\) | 1.07406e11 | 0.316744 | ||||||||
\(366\) | −3.41712e11 | −0.995396 | ||||||||
\(367\) | 5.08662e11 | 1.46363 | 0.731816 | − | 0.681502i | \(-0.238673\pi\) | ||||
0.731816 | + | 0.681502i | \(0.238673\pi\) | |||||||
\(368\) | 1.04814e11 | 0.297923 | ||||||||
\(369\) | 2.09063e11 | 0.587027 | ||||||||
\(370\) | −4.79994e10 | −0.133146 | ||||||||
\(371\) | 2.91241e11 | 0.798123 | ||||||||
\(372\) | 5.02376e11 | 1.36015 | ||||||||
\(373\) | −2.96761e11 | −0.793810 | −0.396905 | − | 0.917860i | \(-0.629916\pi\) | ||||
−0.396905 | + | 0.917860i | \(0.629916\pi\) | |||||||
\(374\) | −4.93061e10 | −0.130310 | ||||||||
\(375\) | −4.98047e10 | −0.130056 | ||||||||
\(376\) | −4.68662e10 | −0.120925 | ||||||||
\(377\) | −2.50157e11 | −0.637788 | ||||||||
\(378\) | 3.98926e10 | 0.100503 | ||||||||
\(379\) | −4.53918e11 | −1.13006 | −0.565030 | − | 0.825071i | \(-0.691135\pi\) | ||||
−0.565030 | + | 0.825071i | \(0.691135\pi\) | |||||||
\(380\) | 1.69194e11 | 0.416253 | ||||||||
\(381\) | −5.39219e11 | −1.31100 | ||||||||
\(382\) | 1.62215e11 | 0.389768 | ||||||||
\(383\) | 2.67567e11 | 0.635387 | 0.317694 | − | 0.948193i | \(-0.397092\pi\) | ||||
0.317694 | + | 0.948193i | \(0.397092\pi\) | |||||||
\(384\) | 5.47608e10 | 0.128523 | ||||||||
\(385\) | 2.50999e11 | 0.582236 | ||||||||
\(386\) | 1.21230e11 | 0.277950 | ||||||||
\(387\) | −2.95317e11 | −0.669250 | ||||||||
\(388\) | 5.95657e10 | 0.133430 | ||||||||
\(389\) | 3.34750e11 | 0.741221 | 0.370610 | − | 0.928788i | \(-0.379148\pi\) | ||||
0.370610 | + | 0.928788i | \(0.379148\pi\) | |||||||
\(390\) | −2.33609e11 | −0.511326 | ||||||||
\(391\) | 6.66635e10 | 0.144242 | ||||||||
\(392\) | 4.44292e10 | 0.0950346 | ||||||||
\(393\) | 5.37998e11 | 1.13766 | ||||||||
\(394\) | 3.53229e9 | 0.00738454 | ||||||||
\(395\) | −7.33626e10 | −0.151631 | ||||||||
\(396\) | 4.15117e11 | 0.848286 | ||||||||
\(397\) | −4.55573e11 | −0.920451 | −0.460226 | − | 0.887802i | \(-0.652231\pi\) | ||||
−0.460226 | + | 0.887802i | \(0.652231\pi\) | |||||||
\(398\) | 4.78874e11 | 0.956638 | ||||||||
\(399\) | −1.17180e12 | −2.31460 | ||||||||
\(400\) | 2.56000e10 | 0.0500000 | ||||||||
\(401\) | 2.18973e11 | 0.422904 | 0.211452 | − | 0.977388i | \(-0.432181\pi\) | ||||
0.211452 | + | 0.977388i | \(0.432181\pi\) | |||||||
\(402\) | 4.58824e11 | 0.876252 | ||||||||
\(403\) | 1.10158e12 | 2.08039 | ||||||||
\(404\) | 1.66730e11 | 0.311384 | ||||||||
\(405\) | −2.11295e11 | −0.390248 | ||||||||
\(406\) | −1.89860e11 | −0.346790 | ||||||||
\(407\) | 3.54869e11 | 0.641053 | ||||||||
\(408\) | 3.48288e10 | 0.0622254 | ||||||||
\(409\) | −3.63048e11 | −0.641519 | −0.320760 | − | 0.947161i | \(-0.603938\pi\) | ||||
−0.320760 | + | 0.947161i | \(0.603938\pi\) | |||||||
\(410\) | −9.53188e10 | −0.166591 | ||||||||
\(411\) | −1.05374e12 | −1.82157 | ||||||||
\(412\) | −4.38090e11 | −0.749076 | ||||||||
\(413\) | 4.44678e11 | 0.752091 | ||||||||
\(414\) | −5.61252e11 | −0.938980 | ||||||||
\(415\) | 2.02274e11 | 0.334752 | ||||||||
\(416\) | 1.20077e11 | 0.196580 | ||||||||
\(417\) | −5.64572e11 | −0.914339 | ||||||||
\(418\) | −1.25088e12 | −2.00412 | ||||||||
\(419\) | −1.14340e12 | −1.81232 | −0.906158 | − | 0.422939i | \(-0.860999\pi\) | ||||
−0.906158 | + | 0.422939i | \(0.860999\pi\) | |||||||
\(420\) | −1.77300e11 | −0.278028 | ||||||||
\(421\) | 6.58288e11 | 1.02128 | 0.510642 | − | 0.859793i | \(-0.329408\pi\) | ||||
0.510642 | + | 0.859793i | \(0.329408\pi\) | |||||||
\(422\) | −4.68053e11 | −0.718437 | ||||||||
\(423\) | 2.50956e11 | 0.381124 | ||||||||
\(424\) | −2.19610e11 | −0.329994 | ||||||||
\(425\) | 1.62820e10 | 0.0242080 | ||||||||
\(426\) | 3.16930e11 | 0.466252 | ||||||||
\(427\) | −5.68683e11 | −0.827837 | ||||||||
\(428\) | −3.36776e11 | −0.485114 | ||||||||
\(429\) | 1.72711e12 | 2.46186 | ||||||||
\(430\) | 1.34645e11 | 0.189925 | ||||||||
\(431\) | −1.27825e11 | −0.178430 | −0.0892152 | − | 0.996012i | \(-0.528436\pi\) | ||||
−0.0892152 | + | 0.996012i | \(0.528436\pi\) | |||||||
\(432\) | −3.00810e10 | −0.0415543 | ||||||||
\(433\) | −5.76786e10 | −0.0788531 | −0.0394266 | − | 0.999222i | \(-0.512553\pi\) | ||||
−0.0394266 | + | 0.999222i | \(0.512553\pi\) | |||||||
\(434\) | 8.36063e11 | 1.13119 | ||||||||
\(435\) | −2.78525e11 | −0.372960 | ||||||||
\(436\) | 7.95315e10 | 0.105402 | ||||||||
\(437\) | 1.69123e12 | 2.21839 | ||||||||
\(438\) | 5.60915e11 | 0.728221 | ||||||||
\(439\) | 4.11418e11 | 0.528681 | 0.264340 | − | 0.964429i | \(-0.414846\pi\) | ||||
0.264340 | + | 0.964429i | \(0.414846\pi\) | |||||||
\(440\) | −1.89266e11 | −0.240733 | ||||||||
\(441\) | −2.37907e11 | −0.299525 | ||||||||
\(442\) | 7.63708e10 | 0.0951759 | ||||||||
\(443\) | 1.17254e11 | 0.144647 | 0.0723237 | − | 0.997381i | \(-0.476959\pi\) | ||||
0.0723237 | + | 0.997381i | \(0.476959\pi\) | |||||||
\(444\) | −2.50672e11 | −0.306114 | ||||||||
\(445\) | −5.58987e11 | −0.675743 | ||||||||
\(446\) | 8.29571e11 | 0.992766 | ||||||||
\(447\) | 1.23247e12 | 1.46013 | ||||||||
\(448\) | 9.11338e10 | 0.106888 | ||||||||
\(449\) | 9.15676e10 | 0.106325 | 0.0531623 | − | 0.998586i | \(-0.483070\pi\) | ||||
0.0531623 | + | 0.998586i | \(0.483070\pi\) | |||||||
\(450\) | −1.37081e11 | −0.157587 | ||||||||
\(451\) | 7.04711e11 | 0.802078 | ||||||||
\(452\) | −7.03615e11 | −0.792889 | ||||||||
\(453\) | −8.30700e10 | −0.0926834 | ||||||||
\(454\) | −7.30036e11 | −0.806479 | ||||||||
\(455\) | −3.88775e11 | −0.425253 | ||||||||
\(456\) | 8.83597e11 | 0.957001 | ||||||||
\(457\) | −1.55029e12 | −1.66261 | −0.831305 | − | 0.555816i | \(-0.812406\pi\) | ||||
−0.831305 | + | 0.555816i | \(0.812406\pi\) | |||||||
\(458\) | −9.94392e11 | −1.05600 | ||||||||
\(459\) | −1.91320e10 | −0.0201189 | ||||||||
\(460\) | 2.55894e11 | 0.266471 | ||||||||
\(461\) | −1.61825e12 | −1.66875 | −0.834374 | − | 0.551198i | \(-0.814171\pi\) | ||||
−0.834374 | + | 0.551198i | \(0.814171\pi\) | |||||||
\(462\) | 1.31082e12 | 1.33861 | ||||||||
\(463\) | 9.04370e11 | 0.914601 | 0.457301 | − | 0.889312i | \(-0.348816\pi\) | ||||
0.457301 | + | 0.889312i | \(0.348816\pi\) | |||||||
\(464\) | 1.43164e11 | 0.143385 | ||||||||
\(465\) | 1.22651e12 | 1.21655 | ||||||||
\(466\) | 5.95465e10 | 0.0584951 | ||||||||
\(467\) | −1.28255e12 | −1.24781 | −0.623903 | − | 0.781502i | \(-0.714454\pi\) | ||||
−0.623903 | + | 0.781502i | \(0.714454\pi\) | |||||||
\(468\) | −6.42979e11 | −0.619570 | ||||||||
\(469\) | 7.63582e11 | 0.728749 | ||||||||
\(470\) | −1.14420e11 | −0.108158 | ||||||||
\(471\) | −3.69113e10 | −0.0345594 | ||||||||
\(472\) | −3.35309e11 | −0.310961 | ||||||||
\(473\) | −9.95456e11 | −0.914423 | ||||||||
\(474\) | −3.83129e11 | −0.348612 | ||||||||
\(475\) | 4.13070e11 | 0.372308 | ||||||||
\(476\) | 5.79627e10 | 0.0517508 | ||||||||
\(477\) | 1.17595e12 | 1.04006 | ||||||||
\(478\) | −5.79554e10 | −0.0507772 | ||||||||
\(479\) | −5.31423e11 | −0.461244 | −0.230622 | − | 0.973043i | \(-0.574076\pi\) | ||||
−0.230622 | + | 0.973043i | \(0.574076\pi\) | |||||||
\(480\) | 1.33693e11 | 0.114954 | ||||||||
\(481\) | −5.49661e11 | −0.468211 | ||||||||
\(482\) | 5.38490e11 | 0.454429 | ||||||||
\(483\) | −1.77227e12 | −1.48172 | ||||||||
\(484\) | 7.95646e11 | 0.659046 | ||||||||
\(485\) | 1.45424e11 | 0.119343 | ||||||||
\(486\) | −1.24802e12 | −1.01475 | ||||||||
\(487\) | −1.10916e12 | −0.893539 | −0.446770 | − | 0.894649i | \(-0.647426\pi\) | ||||
−0.446770 | + | 0.894649i | \(0.647426\pi\) | |||||||
\(488\) | 4.28816e11 | 0.342280 | ||||||||
\(489\) | −1.19953e12 | −0.948679 | ||||||||
\(490\) | 1.08470e11 | 0.0850015 | ||||||||
\(491\) | −9.04143e11 | −0.702054 | −0.351027 | − | 0.936365i | \(-0.614168\pi\) | ||||
−0.351027 | + | 0.936365i | \(0.614168\pi\) | |||||||
\(492\) | −4.97793e11 | −0.383006 | ||||||||
\(493\) | 9.10547e10 | 0.0694211 | ||||||||
\(494\) | 1.93750e12 | 1.46376 | ||||||||
\(495\) | 1.01347e12 | 0.758730 | ||||||||
\(496\) | −6.30433e11 | −0.467705 | ||||||||
\(497\) | 5.27441e11 | 0.387766 | ||||||||
\(498\) | 1.05635e12 | 0.769621 | ||||||||
\(499\) | 1.01146e12 | 0.730290 | 0.365145 | − | 0.930951i | \(-0.381019\pi\) | ||||
0.365145 | + | 0.930951i | \(0.381019\pi\) | |||||||
\(500\) | 6.25000e10 | 0.0447214 | ||||||||
\(501\) | −2.77842e11 | −0.197028 | ||||||||
\(502\) | 9.40975e11 | 0.661320 | ||||||||
\(503\) | 1.26417e11 | 0.0880538 | 0.0440269 | − | 0.999030i | \(-0.485981\pi\) | ||||
0.0440269 | + | 0.999030i | \(0.485981\pi\) | |||||||
\(504\) | −4.87998e11 | −0.336884 | ||||||||
\(505\) | 4.07055e11 | 0.278511 | ||||||||
\(506\) | −1.89187e12 | −1.28297 | ||||||||
\(507\) | −5.11827e11 | −0.344023 | ||||||||
\(508\) | 6.76666e11 | 0.450804 | ||||||||
\(509\) | −4.08226e11 | −0.269569 | −0.134785 | − | 0.990875i | \(-0.543034\pi\) | ||||
−0.134785 | + | 0.990875i | \(0.543034\pi\) | |||||||
\(510\) | 8.50313e10 | 0.0556561 | ||||||||
\(511\) | 9.33483e11 | 0.605637 | ||||||||
\(512\) | −6.87195e10 | −0.0441942 | ||||||||
\(513\) | −4.85374e11 | −0.309420 | ||||||||
\(514\) | 1.20332e12 | 0.760406 | ||||||||
\(515\) | −1.06956e12 | −0.669994 | ||||||||
\(516\) | 7.03169e11 | 0.436653 | ||||||||
\(517\) | 8.45926e11 | 0.520745 | ||||||||
\(518\) | −4.17173e11 | −0.254584 | ||||||||
\(519\) | 2.89227e12 | 1.74979 | ||||||||
\(520\) | 2.93156e11 | 0.175826 | ||||||||
\(521\) | 2.96958e12 | 1.76573 | 0.882867 | − | 0.469624i | \(-0.155610\pi\) | ||||
0.882867 | + | 0.469624i | \(0.155610\pi\) | |||||||
\(522\) | −7.66606e11 | −0.451913 | ||||||||
\(523\) | −4.01653e11 | −0.234743 | −0.117372 | − | 0.993088i | \(-0.537447\pi\) | ||||
−0.117372 | + | 0.993088i | \(0.537447\pi\) | |||||||
\(524\) | −6.75134e11 | −0.391201 | ||||||||
\(525\) | −4.32862e11 | −0.248676 | ||||||||
\(526\) | 1.86106e11 | 0.106004 | ||||||||
\(527\) | −4.00966e11 | −0.226444 | ||||||||
\(528\) | −9.88422e11 | −0.553465 | ||||||||
\(529\) | 7.56723e11 | 0.420133 | ||||||||
\(530\) | −5.36158e11 | −0.295156 | ||||||||
\(531\) | 1.79549e12 | 0.980073 | ||||||||
\(532\) | 1.47050e12 | 0.795905 | ||||||||
\(533\) | −1.09153e12 | −0.585821 | ||||||||
\(534\) | −2.91925e12 | −1.55359 | ||||||||
\(535\) | −8.22206e11 | −0.433899 | ||||||||
\(536\) | −5.75779e11 | −0.301311 | ||||||||
\(537\) | −5.43571e11 | −0.282080 | ||||||||
\(538\) | −4.54194e11 | −0.233734 | ||||||||
\(539\) | −8.01939e11 | −0.409253 | ||||||||
\(540\) | −7.34400e10 | −0.0371673 | ||||||||
\(541\) | −6.35088e11 | −0.318747 | −0.159374 | − | 0.987218i | \(-0.550947\pi\) | ||||
−0.159374 | + | 0.987218i | \(0.550947\pi\) | |||||||
\(542\) | −2.36780e12 | −1.17855 | ||||||||
\(543\) | 8.27110e11 | 0.408285 | ||||||||
\(544\) | −4.37067e10 | −0.0213970 | ||||||||
\(545\) | 1.94169e11 | 0.0942747 | ||||||||
\(546\) | −2.03034e12 | −0.977691 | ||||||||
\(547\) | 2.74387e12 | 1.31045 | 0.655224 | − | 0.755434i | \(-0.272574\pi\) | ||||
0.655224 | + | 0.755434i | \(0.272574\pi\) | |||||||
\(548\) | 1.32234e12 | 0.626370 | ||||||||
\(549\) | −2.29619e12 | −1.07878 | ||||||||
\(550\) | −4.62075e11 | −0.215318 | ||||||||
\(551\) | 2.31003e12 | 1.06767 | ||||||||
\(552\) | 1.33638e12 | 0.612638 | ||||||||
\(553\) | −6.37609e11 | −0.289929 | ||||||||
\(554\) | 1.21417e12 | 0.547629 | ||||||||
\(555\) | −6.11993e11 | −0.273796 | ||||||||
\(556\) | 7.08483e11 | 0.314407 | ||||||||
\(557\) | −1.31358e12 | −0.578238 | −0.289119 | − | 0.957293i | \(-0.593362\pi\) | ||||
−0.289119 | + | 0.957293i | \(0.593362\pi\) | |||||||
\(558\) | 3.37580e12 | 1.47409 | ||||||||
\(559\) | 1.54187e12 | 0.667875 | ||||||||
\(560\) | 2.22495e11 | 0.0956035 | ||||||||
\(561\) | −6.28653e11 | −0.267965 | ||||||||
\(562\) | −2.75441e12 | −1.16470 | ||||||||
\(563\) | −3.11100e12 | −1.30500 | −0.652502 | − | 0.757787i | \(-0.726281\pi\) | ||||
−0.652502 | + | 0.757787i | \(0.726281\pi\) | |||||||
\(564\) | −5.97545e11 | −0.248665 | ||||||||
\(565\) | −1.71781e12 | −0.709182 | ||||||||
\(566\) | 2.39891e12 | 0.982518 | ||||||||
\(567\) | −1.83640e12 | −0.746181 | ||||||||
\(568\) | −3.97717e11 | −0.160327 | ||||||||
\(569\) | −1.45889e12 | −0.583470 | −0.291735 | − | 0.956499i | \(-0.594233\pi\) | ||||
−0.291735 | + | 0.956499i | \(0.594233\pi\) | |||||||
\(570\) | 2.15722e12 | 0.855967 | ||||||||
\(571\) | −3.94710e12 | −1.55387 | −0.776936 | − | 0.629579i | \(-0.783227\pi\) | ||||
−0.776936 | + | 0.629579i | \(0.783227\pi\) | |||||||
\(572\) | −2.16736e12 | −0.846543 | ||||||||
\(573\) | 2.06824e12 | 0.801505 | ||||||||
\(574\) | −8.28435e11 | −0.318533 | ||||||||
\(575\) | 6.24741e11 | 0.238339 | ||||||||
\(576\) | 3.67975e11 | 0.139289 | ||||||||
\(577\) | −5.27904e11 | −0.198273 | −0.0991365 | − | 0.995074i | \(-0.531608\pi\) | ||||
−0.0991365 | + | 0.995074i | \(0.531608\pi\) | |||||||
\(578\) | 1.86961e12 | 0.696747 | ||||||||
\(579\) | 1.54568e12 | 0.571565 | ||||||||
\(580\) | 3.49522e11 | 0.128247 | ||||||||
\(581\) | 1.75800e12 | 0.640068 | ||||||||
\(582\) | 7.59463e11 | 0.274380 | ||||||||
\(583\) | 3.96392e12 | 1.42107 | ||||||||
\(584\) | −7.03893e11 | −0.250408 | ||||||||
\(585\) | −1.56977e12 | −0.554160 | ||||||||
\(586\) | −1.52279e11 | −0.0533460 | ||||||||
\(587\) | 4.56943e12 | 1.58851 | 0.794255 | − | 0.607584i | \(-0.207861\pi\) | ||||
0.794255 | + | 0.607584i | \(0.207861\pi\) | |||||||
\(588\) | 5.66473e11 | 0.195425 | ||||||||
\(589\) | −1.01724e13 | −3.48261 | ||||||||
\(590\) | −8.18626e11 | −0.278132 | ||||||||
\(591\) | 4.50367e10 | 0.0151853 | ||||||||
\(592\) | 3.14569e11 | 0.105261 | ||||||||
\(593\) | 3.19168e12 | 1.05992 | 0.529960 | − | 0.848022i | \(-0.322207\pi\) | ||||
0.529960 | + | 0.848022i | \(0.322207\pi\) | |||||||
\(594\) | 5.42957e11 | 0.178948 | ||||||||
\(595\) | 1.41510e11 | 0.0462873 | ||||||||
\(596\) | −1.54663e12 | −0.502085 | ||||||||
\(597\) | 6.10565e12 | 1.96719 | ||||||||
\(598\) | 2.93034e12 | 0.937050 | ||||||||
\(599\) | 2.72611e12 | 0.865211 | 0.432605 | − | 0.901583i | \(-0.357594\pi\) | ||||
0.432605 | + | 0.901583i | \(0.357594\pi\) | |||||||
\(600\) | 3.26400e11 | 0.102818 | ||||||||
\(601\) | 1.16094e11 | 0.0362974 | 0.0181487 | − | 0.999835i | \(-0.494223\pi\) | ||||
0.0181487 | + | 0.999835i | \(0.494223\pi\) | |||||||
\(602\) | 1.17023e12 | 0.363149 | ||||||||
\(603\) | 3.08315e12 | 0.949656 | ||||||||
\(604\) | 1.04245e11 | 0.0318704 | ||||||||
\(605\) | 1.94250e12 | 0.589469 | ||||||||
\(606\) | 2.12580e12 | 0.640319 | ||||||||
\(607\) | −3.81951e12 | −1.14198 | −0.570990 | − | 0.820957i | \(-0.693441\pi\) | ||||
−0.570990 | + | 0.820957i | \(0.693441\pi\) | |||||||
\(608\) | −1.10883e12 | −0.329077 | ||||||||
\(609\) | −2.42072e12 | −0.713126 | ||||||||
\(610\) | 1.04691e12 | 0.306144 | ||||||||
\(611\) | −1.31026e12 | −0.380341 | ||||||||
\(612\) | 2.34038e11 | 0.0674381 | ||||||||
\(613\) | −3.74021e12 | −1.06985 | −0.534926 | − | 0.844899i | \(-0.679660\pi\) | ||||
−0.534926 | + | 0.844899i | \(0.679660\pi\) | |||||||
\(614\) | −1.44944e12 | −0.411569 | ||||||||
\(615\) | −1.21531e12 | −0.342571 | ||||||||
\(616\) | −1.64495e12 | −0.460298 | ||||||||
\(617\) | 6.24435e12 | 1.73462 | 0.867310 | − | 0.497769i | \(-0.165847\pi\) | ||||
0.867310 | + | 0.497769i | \(0.165847\pi\) | |||||||
\(618\) | −5.58565e12 | −1.54037 | ||||||||
\(619\) | 4.46634e12 | 1.22277 | 0.611383 | − | 0.791335i | \(-0.290613\pi\) | ||||
0.611383 | + | 0.791335i | \(0.290613\pi\) | |||||||
\(620\) | −1.53914e12 | −0.418328 | ||||||||
\(621\) | −7.34095e11 | −0.198080 | ||||||||
\(622\) | 4.50056e12 | 1.20562 | ||||||||
\(623\) | −4.85827e12 | −1.29207 | ||||||||
\(624\) | 1.53098e12 | 0.404239 | ||||||||
\(625\) | 1.52588e11 | 0.0400000 | ||||||||
\(626\) | 1.45800e12 | 0.379465 | ||||||||
\(627\) | −1.59487e13 | −4.12119 | ||||||||
\(628\) | 4.63201e10 | 0.0118837 | ||||||||
\(629\) | 2.00071e11 | 0.0509632 | ||||||||
\(630\) | −1.19140e12 | −0.301318 | ||||||||
\(631\) | −3.08003e12 | −0.773434 | −0.386717 | − | 0.922198i | \(-0.626391\pi\) | ||||
−0.386717 | + | 0.922198i | \(0.626391\pi\) | |||||||
\(632\) | 4.80789e11 | 0.119875 | ||||||||
\(633\) | −5.96767e12 | −1.47737 | ||||||||
\(634\) | −1.65067e12 | −0.405751 | ||||||||
\(635\) | 1.65202e12 | 0.403212 | ||||||||
\(636\) | −2.80003e12 | −0.678587 | ||||||||
\(637\) | 1.24213e12 | 0.298910 | ||||||||
\(638\) | −2.58408e12 | −0.617467 | ||||||||
\(639\) | 2.12967e12 | 0.505310 | ||||||||
\(640\) | −1.67772e11 | −0.0395285 | ||||||||
\(641\) | 7.87684e12 | 1.84285 | 0.921427 | − | 0.388552i | \(-0.127025\pi\) | ||||
0.921427 | + | 0.388552i | \(0.127025\pi\) | |||||||
\(642\) | −4.29389e12 | −0.997570 | ||||||||
\(643\) | −2.80833e12 | −0.647886 | −0.323943 | − | 0.946077i | \(-0.605009\pi\) | ||||
−0.323943 | + | 0.946077i | \(0.605009\pi\) | |||||||
\(644\) | 2.22402e12 | 0.509510 | ||||||||
\(645\) | 1.71672e12 | 0.390554 | ||||||||
\(646\) | −7.05233e11 | −0.159326 | ||||||||
\(647\) | 2.03365e12 | 0.456254 | 0.228127 | − | 0.973631i | \(-0.426740\pi\) | ||||
0.228127 | + | 0.973631i | \(0.426740\pi\) | |||||||
\(648\) | 1.38474e12 | 0.308518 | ||||||||
\(649\) | 6.05227e12 | 1.33911 | ||||||||
\(650\) | 7.15712e11 | 0.157264 | ||||||||
\(651\) | 1.06598e13 | 2.32613 | ||||||||
\(652\) | 1.50529e12 | 0.326216 | ||||||||
\(653\) | 5.29056e12 | 1.13865 | 0.569327 | − | 0.822111i | \(-0.307204\pi\) | ||||
0.569327 | + | 0.822111i | \(0.307204\pi\) | |||||||
\(654\) | 1.01403e12 | 0.216745 | ||||||||
\(655\) | −1.64828e12 | −0.349900 | ||||||||
\(656\) | 6.24681e11 | 0.131702 | ||||||||
\(657\) | 3.76916e12 | 0.789225 | ||||||||
\(658\) | −9.94443e11 | −0.206806 | ||||||||
\(659\) | −5.06766e12 | −1.04670 | −0.523351 | − | 0.852117i | \(-0.675318\pi\) | ||||
−0.523351 | + | 0.852117i | \(0.675318\pi\) | |||||||
\(660\) | −2.41314e12 | −0.495034 | ||||||||
\(661\) | −6.05804e12 | −1.23431 | −0.617157 | − | 0.786840i | \(-0.711716\pi\) | ||||
−0.617157 | + | 0.786840i | \(0.711716\pi\) | |||||||
\(662\) | −4.01728e12 | −0.812963 | ||||||||
\(663\) | 9.73727e11 | 0.195716 | ||||||||
\(664\) | −1.32562e12 | −0.264644 | ||||||||
\(665\) | 3.59008e12 | 0.711879 | ||||||||
\(666\) | −1.68443e12 | −0.331757 | ||||||||
\(667\) | 3.49377e12 | 0.683483 | ||||||||
\(668\) | 3.48665e11 | 0.0677507 | ||||||||
\(669\) | 1.05770e13 | 2.04149 | ||||||||
\(670\) | −1.40571e12 | −0.269500 | ||||||||
\(671\) | −7.74004e12 | −1.47398 | ||||||||
\(672\) | 1.16196e12 | 0.219800 | ||||||||
\(673\) | 5.03218e12 | 0.945559 | 0.472779 | − | 0.881181i | \(-0.343251\pi\) | ||||
0.472779 | + | 0.881181i | \(0.343251\pi\) | |||||||
\(674\) | 6.47947e12 | 1.20940 | ||||||||
\(675\) | −1.79297e11 | −0.0332434 | ||||||||
\(676\) | 6.42293e11 | 0.118297 | ||||||||
\(677\) | −8.61276e12 | −1.57577 | −0.787886 | − | 0.615821i | \(-0.788824\pi\) | ||||
−0.787886 | + | 0.615821i | \(0.788824\pi\) | |||||||
\(678\) | −8.97110e12 | −1.63047 | ||||||||
\(679\) | 1.26391e12 | 0.228193 | ||||||||
\(680\) | −1.06706e11 | −0.0191381 | ||||||||
\(681\) | −9.30796e12 | −1.65841 | ||||||||
\(682\) | 1.13792e13 | 2.01410 | ||||||||
\(683\) | −3.37706e11 | −0.0593807 | −0.0296903 | − | 0.999559i | \(-0.509452\pi\) | ||||
−0.0296903 | + | 0.999559i | \(0.509452\pi\) | |||||||
\(684\) | 5.93748e12 | 1.03717 | ||||||||
\(685\) | 3.22837e12 | 0.560242 | ||||||||
\(686\) | 4.44995e12 | 0.767178 | ||||||||
\(687\) | −1.26785e13 | −2.17151 | ||||||||
\(688\) | −8.82408e11 | −0.150149 | ||||||||
\(689\) | −6.13976e12 | −1.03792 | ||||||||
\(690\) | 3.26265e12 | 0.547960 | ||||||||
\(691\) | 1.74896e11 | 0.0291830 | 0.0145915 | − | 0.999894i | \(-0.495355\pi\) | ||||
0.0145915 | + | 0.999894i | \(0.495355\pi\) | |||||||
\(692\) | −3.62952e12 | −0.601688 | ||||||||
\(693\) | 8.80826e12 | 1.45074 | ||||||||
\(694\) | −6.73356e12 | −1.10186 | ||||||||
\(695\) | 1.72969e12 | 0.281214 | ||||||||
\(696\) | 1.82534e12 | 0.294851 | ||||||||
\(697\) | 3.97308e11 | 0.0637646 | ||||||||
\(698\) | 6.39012e12 | 1.01897 | ||||||||
\(699\) | 7.59217e11 | 0.120287 | ||||||||
\(700\) | 5.43200e11 | 0.0855103 | ||||||||
\(701\) | −5.36577e12 | −0.839269 | −0.419634 | − | 0.907693i | \(-0.637842\pi\) | ||||
−0.419634 | + | 0.907693i | \(0.637842\pi\) | |||||||
\(702\) | −8.40991e11 | −0.130700 | ||||||||
\(703\) | 5.07575e12 | 0.783792 | ||||||||
\(704\) | 1.24037e12 | 0.190316 | ||||||||
\(705\) | −1.45885e12 | −0.222413 | ||||||||
\(706\) | 1.26209e12 | 0.191192 | ||||||||
\(707\) | 3.53779e12 | 0.532531 | ||||||||
\(708\) | −4.27519e12 | −0.639449 | ||||||||
\(709\) | 5.45452e12 | 0.810679 | 0.405339 | − | 0.914166i | \(-0.367153\pi\) | ||||
0.405339 | + | 0.914166i | \(0.367153\pi\) | |||||||
\(710\) | −9.70988e11 | −0.143401 | ||||||||
\(711\) | −2.57450e12 | −0.377815 | ||||||||
\(712\) | 3.66338e12 | 0.534222 | ||||||||
\(713\) | −1.53850e13 | −2.22944 | ||||||||
\(714\) | 7.39024e11 | 0.106418 | ||||||||
\(715\) | −5.29141e12 | −0.757171 | ||||||||
\(716\) | 6.82128e11 | 0.0969967 | ||||||||
\(717\) | −7.38932e11 | −0.104416 | ||||||||
\(718\) | −2.23747e12 | −0.314194 | ||||||||
\(719\) | −6.60953e12 | −0.922339 | −0.461169 | − | 0.887312i | \(-0.652570\pi\) | ||||
−0.461169 | + | 0.887312i | \(0.652570\pi\) | |||||||
\(720\) | 8.98376e11 | 0.124584 | ||||||||
\(721\) | −9.29572e12 | −1.28107 | ||||||||
\(722\) | −1.27285e13 | −1.74326 | ||||||||
\(723\) | 6.86575e12 | 0.934471 | ||||||||
\(724\) | −1.03794e12 | −0.140394 | ||||||||
\(725\) | 8.53324e11 | 0.114708 | ||||||||
\(726\) | 1.01445e13 | 1.35524 | ||||||||
\(727\) | 1.12652e13 | 1.49566 | 0.747832 | − | 0.663888i | \(-0.231095\pi\) | ||||
0.747832 | + | 0.663888i | \(0.231095\pi\) | |||||||
\(728\) | 2.54788e12 | 0.336192 | ||||||||
\(729\) | −9.25795e12 | −1.21406 | ||||||||
\(730\) | −1.71849e12 | −0.223972 | ||||||||
\(731\) | −5.61227e11 | −0.0726959 | ||||||||
\(732\) | 5.46740e12 | 0.703851 | ||||||||
\(733\) | −1.55010e13 | −1.98332 | −0.991659 | − | 0.128890i | \(-0.958859\pi\) | ||||
−0.991659 | + | 0.128890i | \(0.958859\pi\) | |||||||
\(734\) | −8.13859e12 | −1.03494 | ||||||||
\(735\) | 1.38299e12 | 0.174794 | ||||||||
\(736\) | −1.67703e12 | −0.210664 | ||||||||
\(737\) | 1.03927e13 | 1.29755 | ||||||||
\(738\) | −3.34500e12 | −0.415091 | ||||||||
\(739\) | 8.86702e12 | 1.09365 | 0.546824 | − | 0.837247i | \(-0.315837\pi\) | ||||
0.546824 | + | 0.837247i | \(0.315837\pi\) | |||||||
\(740\) | 7.67991e11 | 0.0941485 | ||||||||
\(741\) | 2.47032e13 | 3.01003 | ||||||||
\(742\) | −4.65985e12 | −0.564358 | ||||||||
\(743\) | 1.04586e13 | 1.25900 | 0.629500 | − | 0.777001i | \(-0.283260\pi\) | ||||
0.629500 | + | 0.777001i | \(0.283260\pi\) | |||||||
\(744\) | −8.03802e12 | −0.961770 | ||||||||
\(745\) | −3.77595e12 | −0.449079 | ||||||||
\(746\) | 4.74817e12 | 0.561309 | ||||||||
\(747\) | 7.09834e12 | 0.834093 | ||||||||
\(748\) | 7.88898e11 | 0.0921433 | ||||||||
\(749\) | −7.14596e12 | −0.829645 | ||||||||
\(750\) | 7.96875e11 | 0.0919633 | ||||||||
\(751\) | 3.37332e11 | 0.0386971 | 0.0193485 | − | 0.999813i | \(-0.493841\pi\) | ||||
0.0193485 | + | 0.999813i | \(0.493841\pi\) | |||||||
\(752\) | 7.49860e11 | 0.0855066 | ||||||||
\(753\) | 1.19974e13 | 1.35991 | ||||||||
\(754\) | 4.00251e12 | 0.450984 | ||||||||
\(755\) | 2.54504e11 | 0.0285058 | ||||||||
\(756\) | −6.38282e11 | −0.0710664 | ||||||||
\(757\) | 1.61864e12 | 0.179151 | 0.0895756 | − | 0.995980i | \(-0.471449\pi\) | ||||
0.0895756 | + | 0.995980i | \(0.471449\pi\) | |||||||
\(758\) | 7.26269e12 | 0.799073 | ||||||||
\(759\) | −2.41214e13 | −2.63824 | ||||||||
\(760\) | −2.70710e12 | −0.294336 | ||||||||
\(761\) | −3.16676e12 | −0.342282 | −0.171141 | − | 0.985247i | \(-0.554745\pi\) | ||||
−0.171141 | + | 0.985247i | \(0.554745\pi\) | |||||||
\(762\) | 8.62750e12 | 0.927016 | ||||||||
\(763\) | 1.68756e12 | 0.180260 | ||||||||
\(764\) | −2.59544e12 | −0.275608 | ||||||||
\(765\) | 5.71382e11 | 0.0603184 | ||||||||
\(766\) | −4.28108e12 | −0.449287 | ||||||||
\(767\) | −9.37442e12 | −0.978059 | ||||||||
\(768\) | −8.76173e11 | −0.0908792 | ||||||||
\(769\) | 9.41136e12 | 0.970474 | 0.485237 | − | 0.874383i | \(-0.338733\pi\) | ||||
0.485237 | + | 0.874383i | \(0.338733\pi\) | |||||||
\(770\) | −4.01599e12 | −0.411703 | ||||||||
\(771\) | 1.53423e13 | 1.56367 | ||||||||
\(772\) | −1.93967e12 | −0.196540 | ||||||||
\(773\) | −3.00421e12 | −0.302638 | −0.151319 | − | 0.988485i | \(-0.548352\pi\) | ||||
−0.151319 | + | 0.988485i | \(0.548352\pi\) | |||||||
\(774\) | 4.72506e12 | 0.473231 | ||||||||
\(775\) | −3.75768e12 | −0.374164 | ||||||||
\(776\) | −9.53051e11 | −0.0943493 | ||||||||
\(777\) | −5.31895e12 | −0.523518 | ||||||||
\(778\) | −5.35600e12 | −0.524122 | ||||||||
\(779\) | 1.00796e13 | 0.980673 | ||||||||
\(780\) | 3.73774e12 | 0.361562 | ||||||||
\(781\) | 7.17871e12 | 0.690425 | ||||||||
\(782\) | −1.06662e12 | −0.101995 | ||||||||
\(783\) | −1.00269e12 | −0.0953320 | ||||||||
\(784\) | −7.10868e11 | −0.0671996 | ||||||||
\(785\) | 1.13086e11 | 0.0106291 | ||||||||
\(786\) | −8.60796e12 | −0.804450 | ||||||||
\(787\) | 4.78765e12 | 0.444873 | 0.222436 | − | 0.974947i | \(-0.428599\pi\) | ||||
0.222436 | + | 0.974947i | \(0.428599\pi\) | |||||||
\(788\) | −5.65167e10 | −0.00522166 | ||||||||
\(789\) | 2.37285e12 | 0.217983 | ||||||||
\(790\) | 1.17380e12 | 0.107219 | ||||||||
\(791\) | −1.49298e13 | −1.35600 | ||||||||
\(792\) | −6.64187e12 | −0.599829 | ||||||||
\(793\) | 1.19886e13 | 1.07656 | ||||||||
\(794\) | 7.28917e12 | 0.650857 | ||||||||
\(795\) | −6.83601e12 | −0.606947 | ||||||||
\(796\) | −7.66199e12 | −0.676445 | ||||||||
\(797\) | −8.82657e12 | −0.774871 | −0.387436 | − | 0.921897i | \(-0.626639\pi\) | ||||
−0.387436 | + | 0.921897i | \(0.626639\pi\) | |||||||
\(798\) | 1.87488e13 | 1.63667 | ||||||||
\(799\) | 4.76923e11 | 0.0413988 | ||||||||
\(800\) | −4.09600e11 | −0.0353553 | ||||||||
\(801\) | −1.96164e13 | −1.68373 | ||||||||
\(802\) | −3.50358e12 | −0.299038 | ||||||||
\(803\) | 1.27051e13 | 1.07835 | ||||||||
\(804\) | −7.34118e12 | −0.619604 | ||||||||
\(805\) | 5.42975e12 | 0.455720 | ||||||||
\(806\) | −1.76253e13 | −1.47106 | ||||||||
\(807\) | −5.79097e12 | −0.480641 | ||||||||
\(808\) | −2.66767e12 | −0.220182 | ||||||||
\(809\) | −4.75875e12 | −0.390593 | −0.195296 | − | 0.980744i | \(-0.562567\pi\) | ||||
−0.195296 | + | 0.980744i | \(0.562567\pi\) | |||||||
\(810\) | 3.38071e12 | 0.275947 | ||||||||
\(811\) | 1.32270e13 | 1.07366 | 0.536831 | − | 0.843690i | \(-0.319621\pi\) | ||||
0.536831 | + | 0.843690i | \(0.319621\pi\) | |||||||
\(812\) | 3.03776e12 | 0.245218 | ||||||||
\(813\) | −3.01894e13 | −2.42353 | ||||||||
\(814\) | −5.67791e12 | −0.453293 | ||||||||
\(815\) | 3.67502e12 | 0.291776 | ||||||||
\(816\) | −5.57261e11 | −0.0440000 | ||||||||
\(817\) | −1.42382e13 | −1.11803 | ||||||||
\(818\) | 5.80877e12 | 0.453623 | ||||||||
\(819\) | −1.36432e13 | −1.05959 | ||||||||
\(820\) | 1.52510e12 | 0.117798 | ||||||||
\(821\) | 1.96204e13 | 1.50717 | 0.753587 | − | 0.657348i | \(-0.228322\pi\) | ||||
0.753587 | + | 0.657348i | \(0.228322\pi\) | |||||||
\(822\) | 1.68598e13 | 1.28804 | ||||||||
\(823\) | 1.44369e12 | 0.109692 | 0.0548461 | − | 0.998495i | \(-0.482533\pi\) | ||||
0.0548461 | + | 0.998495i | \(0.482533\pi\) | |||||||
\(824\) | 7.00944e12 | 0.529677 | ||||||||
\(825\) | −5.89146e12 | −0.442772 | ||||||||
\(826\) | −7.11484e12 | −0.531808 | ||||||||
\(827\) | −6.15968e12 | −0.457913 | −0.228957 | − | 0.973437i | \(-0.573531\pi\) | ||||
−0.228957 | + | 0.973437i | \(0.573531\pi\) | |||||||
\(828\) | 8.98003e12 | 0.663959 | ||||||||
\(829\) | −7.89482e12 | −0.580560 | −0.290280 | − | 0.956942i | \(-0.593748\pi\) | ||||
−0.290280 | + | 0.956942i | \(0.593748\pi\) | |||||||
\(830\) | −3.23638e12 | −0.236705 | ||||||||
\(831\) | 1.54807e13 | 1.12612 | ||||||||
\(832\) | −1.92123e12 | −0.139003 | ||||||||
\(833\) | −4.52124e11 | −0.0325353 | ||||||||
\(834\) | 9.03315e12 | 0.646535 | ||||||||
\(835\) | 8.51232e11 | 0.0605981 | ||||||||
\(836\) | 2.00141e13 | 1.41712 | ||||||||
\(837\) | 4.41542e12 | 0.310962 | ||||||||
\(838\) | 1.82944e13 | 1.28150 | ||||||||
\(839\) | 1.39455e13 | 0.971642 | 0.485821 | − | 0.874058i | \(-0.338521\pi\) | ||||
0.485821 | + | 0.874058i | \(0.338521\pi\) | |||||||
\(840\) | 2.83681e12 | 0.196595 | ||||||||
\(841\) | −9.73506e12 | −0.671053 | ||||||||
\(842\) | −1.05326e13 | −0.722157 | ||||||||
\(843\) | −3.51188e13 | −2.39505 | ||||||||
\(844\) | 7.48884e12 | 0.508012 | ||||||||
\(845\) | 1.56810e12 | 0.105808 | ||||||||
\(846\) | −4.01530e12 | −0.269495 | ||||||||
\(847\) | 1.68826e13 | 1.12711 | ||||||||
\(848\) | 3.51376e12 | 0.233341 | ||||||||
\(849\) | 3.05861e13 | 2.02041 | ||||||||
\(850\) | −2.60512e11 | −0.0171176 | ||||||||
\(851\) | 7.67672e12 | 0.501756 | ||||||||
\(852\) | −5.07089e12 | −0.329690 | ||||||||
\(853\) | 2.06868e12 | 0.133789 | 0.0668947 | − | 0.997760i | \(-0.478691\pi\) | ||||
0.0668947 | + | 0.997760i | \(0.478691\pi\) | |||||||
\(854\) | 9.09893e12 | 0.585369 | ||||||||
\(855\) | 1.44958e13 | 0.927672 | ||||||||
\(856\) | 5.38841e12 | 0.343027 | ||||||||
\(857\) | 1.27749e13 | 0.808989 | 0.404494 | − | 0.914540i | \(-0.367447\pi\) | ||||
0.404494 | + | 0.914540i | \(0.367447\pi\) | |||||||
\(858\) | −2.76338e13 | −1.74080 | ||||||||
\(859\) | 2.44751e13 | 1.53376 | 0.766878 | − | 0.641793i | \(-0.221809\pi\) | ||||
0.766878 | + | 0.641793i | \(0.221809\pi\) | |||||||
\(860\) | −2.15432e12 | −0.134297 | ||||||||
\(861\) | −1.05625e13 | −0.655020 | ||||||||
\(862\) | 2.04520e12 | 0.126169 | ||||||||
\(863\) | −3.04987e13 | −1.87169 | −0.935843 | − | 0.352417i | \(-0.885360\pi\) | ||||
−0.935843 | + | 0.352417i | \(0.885360\pi\) | |||||||
\(864\) | 4.81296e11 | 0.0293833 | ||||||||
\(865\) | −8.86113e12 | −0.538167 | ||||||||
\(866\) | 9.22857e11 | 0.0557576 | ||||||||
\(867\) | 2.38375e13 | 1.43276 | ||||||||
\(868\) | −1.33770e13 | −0.799871 | ||||||||
\(869\) | −8.67814e12 | −0.516224 | ||||||||
\(870\) | 4.45640e12 | 0.263723 | ||||||||
\(871\) | −1.60974e13 | −0.947704 | ||||||||
\(872\) | −1.27250e12 | −0.0745307 | ||||||||
\(873\) | 5.10334e12 | 0.297365 | ||||||||
\(874\) | −2.70597e13 | −1.56864 | ||||||||
\(875\) | 1.32617e12 | 0.0764828 | ||||||||
\(876\) | −8.97464e12 | −0.514930 | ||||||||
\(877\) | −3.32305e13 | −1.89688 | −0.948439 | − | 0.316960i | \(-0.897338\pi\) | ||||
−0.948439 | + | 0.316960i | \(0.897338\pi\) | |||||||
\(878\) | −6.58270e12 | −0.373834 | ||||||||
\(879\) | −1.94156e12 | −0.109699 | ||||||||
\(880\) | 3.02825e12 | 0.170224 | ||||||||
\(881\) | 1.65219e13 | 0.923995 | 0.461998 | − | 0.886881i | \(-0.347133\pi\) | ||||
0.461998 | + | 0.886881i | \(0.347133\pi\) | |||||||
\(882\) | 3.80651e12 | 0.211796 | ||||||||
\(883\) | −2.19061e13 | −1.21267 | −0.606333 | − | 0.795211i | \(-0.707360\pi\) | ||||
−0.606333 | + | 0.795211i | \(0.707360\pi\) | |||||||
\(884\) | −1.22193e12 | −0.0672995 | ||||||||
\(885\) | −1.04375e13 | −0.571941 | ||||||||
\(886\) | −1.87606e12 | −0.102281 | ||||||||
\(887\) | 1.63192e13 | 0.885203 | 0.442601 | − | 0.896718i | \(-0.354056\pi\) | ||||
0.442601 | + | 0.896718i | \(0.354056\pi\) | |||||||
\(888\) | 4.01075e12 | 0.216455 | ||||||||
\(889\) | 1.43580e13 | 0.770968 | ||||||||
\(890\) | 8.94379e12 | 0.477823 | ||||||||
\(891\) | −2.49943e13 | −1.32859 | ||||||||
\(892\) | −1.32731e13 | −0.701991 | ||||||||
\(893\) | 1.20994e13 | 0.636697 | ||||||||
\(894\) | −1.97195e13 | −1.03247 | ||||||||
\(895\) | 1.66535e12 | 0.0867565 | ||||||||
\(896\) | −1.45814e12 | −0.0755812 | ||||||||
\(897\) | 3.73619e13 | 1.92691 | ||||||||
\(898\) | −1.46508e12 | −0.0751828 | ||||||||
\(899\) | −2.10142e13 | −1.07299 | ||||||||
\(900\) | 2.19330e12 | 0.111431 | ||||||||
\(901\) | 2.23481e12 | 0.112974 | ||||||||
\(902\) | −1.12754e13 | −0.567155 | ||||||||
\(903\) | 1.49204e13 | 0.746766 | ||||||||
\(904\) | 1.12578e13 | 0.560657 | ||||||||
\(905\) | −2.53404e12 | −0.125572 | ||||||||
\(906\) | 1.32912e12 | 0.0655371 | ||||||||
\(907\) | −1.98103e12 | −0.0971980 | −0.0485990 | − | 0.998818i | \(-0.515476\pi\) | ||||
−0.0485990 | + | 0.998818i | \(0.515476\pi\) | |||||||
\(908\) | 1.16806e13 | 0.570267 | ||||||||
\(909\) | 1.42847e13 | 0.693958 | ||||||||
\(910\) | 6.22040e12 | 0.300699 | ||||||||
\(911\) | −1.60376e12 | −0.0771446 | −0.0385723 | − | 0.999256i | \(-0.512281\pi\) | ||||
−0.0385723 | + | 0.999256i | \(0.512281\pi\) | |||||||
\(912\) | −1.41375e13 | −0.676702 | ||||||||
\(913\) | 2.39272e13 | 1.13965 | ||||||||
\(914\) | 2.48047e13 | 1.17564 | ||||||||
\(915\) | 1.33481e13 | 0.629544 | ||||||||
\(916\) | 1.59103e13 | 0.746703 | ||||||||
\(917\) | −1.43255e13 | −0.669034 | ||||||||
\(918\) | 3.06113e11 | 0.0142262 | ||||||||
\(919\) | −2.81428e13 | −1.30151 | −0.650755 | − | 0.759288i | \(-0.725548\pi\) | ||||
−0.650755 | + | 0.759288i | \(0.725548\pi\) | |||||||
\(920\) | −4.09430e12 | −0.188423 | ||||||||
\(921\) | −1.84804e13 | −0.846335 | ||||||||
\(922\) | 2.58920e13 | 1.17998 | ||||||||
\(923\) | −1.11192e13 | −0.504272 | ||||||||
\(924\) | −2.09731e13 | −0.946539 | ||||||||
\(925\) | 1.87498e12 | 0.0842089 | ||||||||
\(926\) | −1.44699e13 | −0.646721 | ||||||||
\(927\) | −3.75337e13 | −1.66941 | ||||||||
\(928\) | −2.29062e12 | −0.101388 | ||||||||
\(929\) | −5.39418e12 | −0.237605 | −0.118802 | − | 0.992918i | \(-0.537905\pi\) | ||||
−0.118802 | + | 0.992918i | \(0.537905\pi\) | |||||||
\(930\) | −1.96241e13 | −0.860233 | ||||||||
\(931\) | −1.14703e13 | −0.500379 | ||||||||
\(932\) | −9.52743e11 | −0.0413623 | ||||||||
\(933\) | 5.73821e13 | 2.47919 | ||||||||
\(934\) | 2.05208e13 | 0.882333 | ||||||||
\(935\) | 1.92602e12 | 0.0824155 | ||||||||
\(936\) | 1.02877e13 | 0.438102 | ||||||||
\(937\) | −1.25051e13 | −0.529978 | −0.264989 | − | 0.964251i | \(-0.585368\pi\) | ||||
−0.264989 | + | 0.964251i | \(0.585368\pi\) | |||||||
\(938\) | −1.22173e13 | −0.515303 | ||||||||
\(939\) | 1.85895e13 | 0.780318 | ||||||||
\(940\) | 1.83071e12 | 0.0764795 | ||||||||
\(941\) | 9.23095e12 | 0.383789 | 0.191895 | − | 0.981416i | \(-0.438537\pi\) | ||||
0.191895 | + | 0.981416i | \(0.438537\pi\) | |||||||
\(942\) | 5.90582e11 | 0.0244372 | ||||||||
\(943\) | 1.52447e13 | 0.627792 | ||||||||
\(944\) | 5.36495e12 | 0.219883 | ||||||||
\(945\) | −1.55830e12 | −0.0635637 | ||||||||
\(946\) | 1.59273e13 | 0.646595 | ||||||||
\(947\) | 4.13417e13 | 1.67037 | 0.835186 | − | 0.549967i | \(-0.185360\pi\) | ||||
0.835186 | + | 0.549967i | \(0.185360\pi\) | |||||||
\(948\) | 6.13006e12 | 0.246506 | ||||||||
\(949\) | −1.96791e13 | −0.787603 | ||||||||
\(950\) | −6.60912e12 | −0.263262 | ||||||||
\(951\) | −2.10461e13 | −0.834371 | ||||||||
\(952\) | −9.27402e11 | −0.0365933 | ||||||||
\(953\) | 1.05715e13 | 0.415162 | 0.207581 | − | 0.978218i | \(-0.433441\pi\) | ||||
0.207581 | + | 0.978218i | \(0.433441\pi\) | |||||||
\(954\) | −1.88153e13 | −0.735433 | ||||||||
\(955\) | −6.33653e12 | −0.246511 | ||||||||
\(956\) | 9.27287e11 | 0.0359049 | ||||||||
\(957\) | −3.29471e13 | −1.26973 | ||||||||
\(958\) | 8.50277e12 | 0.326149 | ||||||||
\(959\) | 2.80584e13 | 1.07122 | ||||||||
\(960\) | −2.13910e12 | −0.0812848 | ||||||||
\(961\) | 6.60980e13 | 2.49996 | ||||||||
\(962\) | 8.79457e12 | 0.331075 | ||||||||
\(963\) | −2.88535e13 | −1.08114 | ||||||||
\(964\) | −8.61585e12 | −0.321330 | ||||||||
\(965\) | −4.73553e12 | −0.175791 | ||||||||
\(966\) | 2.83563e13 | 1.04774 | ||||||||
\(967\) | −4.28128e13 | −1.57454 | −0.787271 | − | 0.616607i | \(-0.788507\pi\) | ||||
−0.787271 | + | 0.616607i | \(0.788507\pi\) | |||||||
\(968\) | −1.27303e13 | −0.466016 | ||||||||
\(969\) | −8.99172e12 | −0.327632 | ||||||||
\(970\) | −2.32679e12 | −0.0843886 | ||||||||
\(971\) | 5.22930e12 | 0.188780 | 0.0943902 | − | 0.995535i | \(-0.469910\pi\) | ||||
0.0943902 | + | 0.995535i | \(0.469910\pi\) | |||||||
\(972\) | 1.99683e13 | 0.717533 | ||||||||
\(973\) | 1.50331e13 | 0.537702 | ||||||||
\(974\) | 1.77466e13 | 0.631828 | ||||||||
\(975\) | 9.12533e12 | 0.323391 | ||||||||
\(976\) | −6.86105e12 | −0.242028 | ||||||||
\(977\) | 3.56421e12 | 0.125152 | 0.0625760 | − | 0.998040i | \(-0.480068\pi\) | ||||
0.0625760 | + | 0.998040i | \(0.480068\pi\) | |||||||
\(978\) | 1.91924e13 | 0.670818 | ||||||||
\(979\) | −6.61232e13 | −2.30055 | ||||||||
\(980\) | −1.73552e12 | −0.0601051 | ||||||||
\(981\) | 6.81393e12 | 0.234902 | ||||||||
\(982\) | 1.44663e13 | 0.496427 | ||||||||
\(983\) | 1.92286e13 | 0.656837 | 0.328418 | − | 0.944532i | \(-0.393484\pi\) | ||||
0.328418 | + | 0.944532i | \(0.393484\pi\) | |||||||
\(984\) | 7.96469e12 | 0.270826 | ||||||||
\(985\) | −1.37980e11 | −0.00467039 | ||||||||
\(986\) | −1.45688e12 | −0.0490881 | ||||||||
\(987\) | −1.26791e13 | −0.425268 | ||||||||
\(988\) | −3.10001e13 | −1.03504 | ||||||||
\(989\) | −2.15342e13 | −0.715725 | ||||||||
\(990\) | −1.62155e13 | −0.536503 | ||||||||
\(991\) | −3.28794e13 | −1.08291 | −0.541454 | − | 0.840730i | \(-0.682126\pi\) | ||||
−0.541454 | + | 0.840730i | \(0.682126\pi\) | |||||||
\(992\) | 1.00869e13 | 0.330717 | ||||||||
\(993\) | −5.12203e13 | −1.67175 | ||||||||
\(994\) | −8.43905e12 | −0.274192 | ||||||||
\(995\) | −1.87060e13 | −0.605031 | ||||||||
\(996\) | −1.69017e13 | −0.544205 | ||||||||
\(997\) | 1.66280e13 | 0.532982 | 0.266491 | − | 0.963837i | \(-0.414136\pi\) | ||||
0.266491 | + | 0.963837i | \(0.414136\pi\) | |||||||
\(998\) | −1.61833e13 | −0.516393 | ||||||||
\(999\) | −2.20317e12 | −0.0699848 |
(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 | 10.10.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 90.10.a.g.1.1 | 1 | |||
4.3 | odd | 2 | 80.10.a.e.1.1 | 1 | |||
5.2 | odd | 4 | 50.10.b.e.49.1 | 2 | |||
5.3 | odd | 4 | 50.10.b.e.49.2 | 2 | |||
5.4 | even | 2 | 50.10.a.f.1.1 | 1 | |||
8.3 | odd | 2 | 320.10.a.a.1.1 | 1 | |||
8.5 | even | 2 | 320.10.a.j.1.1 | 1 | |||
20.3 | even | 4 | 400.10.c.b.49.2 | 2 | |||
20.7 | even | 4 | 400.10.c.b.49.1 | 2 | |||
20.19 | odd | 2 | 400.10.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.10.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
50.10.a.f.1.1 | 1 | 5.4 | even | 2 | |||
50.10.b.e.49.1 | 2 | 5.2 | odd | 4 | |||
50.10.b.e.49.2 | 2 | 5.3 | odd | 4 | |||
80.10.a.e.1.1 | 1 | 4.3 | odd | 2 | |||
90.10.a.g.1.1 | 1 | 3.2 | odd | 2 | |||
320.10.a.a.1.1 | 1 | 8.3 | odd | 2 | |||
320.10.a.j.1.1 | 1 | 8.5 | even | 2 | |||
400.10.a.a.1.1 | 1 | 20.19 | odd | 2 | |||
400.10.c.b.49.1 | 2 | 20.7 | even | 4 | |||
400.10.c.b.49.2 | 2 | 20.3 | even | 4 |