Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,16,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, 16, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 16);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 16 \) |
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: | \(14.2693505100\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{239569}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 59892 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(245.229\) of defining polynomial | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 128.000 | 0.707107 | ||||||||
\(3\) | −5816.58 | −1.53553 | −0.767765 | − | 0.640732i | \(-0.778631\pi\) | ||||
−0.767765 | + | 0.640732i | \(0.778631\pi\) | |||||||
\(4\) | 16384.0 | 0.500000 | ||||||||
\(5\) | 78125.0 | 0.447214 | ||||||||
\(6\) | −744522. | −1.08578 | ||||||||
\(7\) | −2.56287e6 | −1.17623 | −0.588114 | − | 0.808778i | \(-0.700129\pi\) | ||||
−0.588114 | + | 0.808778i | \(0.700129\pi\) | |||||||
\(8\) | 2.09715e6 | 0.353553 | ||||||||
\(9\) | 1.94837e7 | 1.35785 | ||||||||
\(10\) | 1.00000e7 | 0.316228 | ||||||||
\(11\) | 1.14540e8 | 1.77220 | 0.886102 | − | 0.463491i | \(-0.153403\pi\) | ||||
0.886102 | + | 0.463491i | \(0.153403\pi\) | |||||||
\(12\) | −9.52988e7 | −0.767765 | ||||||||
\(13\) | 2.84387e8 | 1.25700 | 0.628500 | − | 0.777810i | \(-0.283669\pi\) | ||||
0.628500 | + | 0.777810i | \(0.283669\pi\) | |||||||
\(14\) | −3.28048e8 | −0.831719 | ||||||||
\(15\) | −4.54420e8 | −0.686710 | ||||||||
\(16\) | 2.68435e8 | 0.250000 | ||||||||
\(17\) | 7.76594e8 | 0.459015 | 0.229508 | − | 0.973307i | \(-0.426288\pi\) | ||||
0.229508 | + | 0.973307i | \(0.426288\pi\) | |||||||
\(18\) | 2.49391e9 | 0.960146 | ||||||||
\(19\) | 3.74029e9 | 0.959962 | 0.479981 | − | 0.877279i | \(-0.340644\pi\) | ||||
0.479981 | + | 0.877279i | \(0.340644\pi\) | |||||||
\(20\) | 1.28000e9 | 0.223607 | ||||||||
\(21\) | 1.49072e10 | 1.80613 | ||||||||
\(22\) | 1.46612e10 | 1.25314 | ||||||||
\(23\) | −2.76376e10 | −1.69255 | −0.846277 | − | 0.532744i | \(-0.821161\pi\) | ||||
−0.846277 | + | 0.532744i | \(0.821161\pi\) | |||||||
\(24\) | −1.21982e10 | −0.542892 | ||||||||
\(25\) | 6.10352e9 | 0.200000 | ||||||||
\(26\) | 3.64016e10 | 0.888833 | ||||||||
\(27\) | −2.98668e10 | −0.549491 | ||||||||
\(28\) | −4.19901e10 | −0.588114 | ||||||||
\(29\) | 1.59731e10 | 0.171951 | 0.0859754 | − | 0.996297i | \(-0.472599\pi\) | ||||
0.0859754 | + | 0.996297i | \(0.472599\pi\) | |||||||
\(30\) | −5.81658e10 | −0.485577 | ||||||||
\(31\) | 2.79408e9 | 0.0182400 | 0.00912002 | − | 0.999958i | \(-0.497097\pi\) | ||||
0.00912002 | + | 0.999958i | \(0.497097\pi\) | |||||||
\(32\) | 3.43597e10 | 0.176777 | ||||||||
\(33\) | −6.66233e11 | −2.72127 | ||||||||
\(34\) | 9.94040e10 | 0.324573 | ||||||||
\(35\) | −2.00224e11 | −0.526025 | ||||||||
\(36\) | 3.19221e11 | 0.678926 | ||||||||
\(37\) | 6.85921e11 | 1.18785 | 0.593924 | − | 0.804521i | \(-0.297578\pi\) | ||||
0.593924 | + | 0.804521i | \(0.297578\pi\) | |||||||
\(38\) | 4.78758e11 | 0.678795 | ||||||||
\(39\) | −1.65416e12 | −1.93016 | ||||||||
\(40\) | 1.63840e11 | 0.158114 | ||||||||
\(41\) | 9.09210e11 | 0.729097 | 0.364549 | − | 0.931184i | \(-0.381223\pi\) | ||||
0.364549 | + | 0.931184i | \(0.381223\pi\) | |||||||
\(42\) | 1.90812e12 | 1.27713 | ||||||||
\(43\) | −4.11856e11 | −0.231064 | −0.115532 | − | 0.993304i | \(-0.536857\pi\) | ||||
−0.115532 | + | 0.993304i | \(0.536857\pi\) | |||||||
\(44\) | 1.87663e12 | 0.886102 | ||||||||
\(45\) | 1.52216e12 | 0.607249 | ||||||||
\(46\) | −3.53762e12 | −1.19682 | ||||||||
\(47\) | −4.29904e11 | −0.123776 | −0.0618881 | − | 0.998083i | \(-0.519712\pi\) | ||||
−0.0618881 | + | 0.998083i | \(0.519712\pi\) | |||||||
\(48\) | −1.56138e12 | −0.383882 | ||||||||
\(49\) | 1.82076e12 | 0.383514 | ||||||||
\(50\) | 7.81250e11 | 0.141421 | ||||||||
\(51\) | −4.51712e12 | −0.704832 | ||||||||
\(52\) | 4.65940e12 | 0.628500 | ||||||||
\(53\) | 1.11312e13 | 1.30159 | 0.650793 | − | 0.759255i | \(-0.274437\pi\) | ||||
0.650793 | + | 0.759255i | \(0.274437\pi\) | |||||||
\(54\) | −3.82295e12 | −0.388549 | ||||||||
\(55\) | 8.94847e12 | 0.792553 | ||||||||
\(56\) | −5.37473e12 | −0.415860 | ||||||||
\(57\) | −2.17557e13 | −1.47405 | ||||||||
\(58\) | 2.04456e12 | 0.121588 | ||||||||
\(59\) | −2.98542e13 | −1.56177 | −0.780883 | − | 0.624678i | \(-0.785230\pi\) | ||||
−0.780883 | + | 0.624678i | \(0.785230\pi\) | |||||||
\(60\) | −7.44522e12 | −0.343355 | ||||||||
\(61\) | 1.56049e13 | 0.635750 | 0.317875 | − | 0.948133i | \(-0.397031\pi\) | ||||
0.317875 | + | 0.948133i | \(0.397031\pi\) | |||||||
\(62\) | 3.57642e11 | 0.0128977 | ||||||||
\(63\) | −4.99342e13 | −1.59714 | ||||||||
\(64\) | 4.39805e12 | 0.125000 | ||||||||
\(65\) | 2.22178e13 | 0.562147 | ||||||||
\(66\) | −8.52778e13 | −1.92423 | ||||||||
\(67\) | 6.47436e13 | 1.30508 | 0.652538 | − | 0.757756i | \(-0.273704\pi\) | ||||
0.652538 | + | 0.757756i | \(0.273704\pi\) | |||||||
\(68\) | 1.27237e13 | 0.229508 | ||||||||
\(69\) | 1.60757e14 | 2.59897 | ||||||||
\(70\) | −2.56287e13 | −0.371956 | ||||||||
\(71\) | 1.38360e14 | 1.80540 | 0.902700 | − | 0.430270i | \(-0.141582\pi\) | ||||
0.902700 | + | 0.430270i | \(0.141582\pi\) | |||||||
\(72\) | 4.08602e13 | 0.480073 | ||||||||
\(73\) | −5.76496e13 | −0.610766 | −0.305383 | − | 0.952230i | \(-0.598784\pi\) | ||||
−0.305383 | + | 0.952230i | \(0.598784\pi\) | |||||||
\(74\) | 8.77978e13 | 0.839935 | ||||||||
\(75\) | −3.55016e13 | −0.307106 | ||||||||
\(76\) | 6.12810e13 | 0.479981 | ||||||||
\(77\) | −2.93552e14 | −2.08452 | ||||||||
\(78\) | −2.11733e14 | −1.36483 | ||||||||
\(79\) | 1.85835e14 | 1.08874 | 0.544370 | − | 0.838846i | \(-0.316769\pi\) | ||||
0.544370 | + | 0.838846i | \(0.316769\pi\) | |||||||
\(80\) | 2.09715e13 | 0.111803 | ||||||||
\(81\) | −1.05847e14 | −0.514091 | ||||||||
\(82\) | 1.16379e14 | 0.515550 | ||||||||
\(83\) | −3.07642e14 | −1.24440 | −0.622200 | − | 0.782859i | \(-0.713761\pi\) | ||||
−0.622200 | + | 0.782859i | \(0.713761\pi\) | |||||||
\(84\) | 2.44239e14 | 0.903067 | ||||||||
\(85\) | 6.06714e13 | 0.205278 | ||||||||
\(86\) | −5.27175e13 | −0.163387 | ||||||||
\(87\) | −9.29088e13 | −0.264036 | ||||||||
\(88\) | 2.40209e14 | 0.626568 | ||||||||
\(89\) | −1.81716e14 | −0.435480 | −0.217740 | − | 0.976007i | \(-0.569868\pi\) | ||||
−0.217740 | + | 0.976007i | \(0.569868\pi\) | |||||||
\(90\) | 1.94837e14 | 0.429390 | ||||||||
\(91\) | −7.28848e14 | −1.47852 | ||||||||
\(92\) | −4.52815e14 | −0.846277 | ||||||||
\(93\) | −1.62520e13 | −0.0280081 | ||||||||
\(94\) | −5.50277e13 | −0.0875230 | ||||||||
\(95\) | 2.92211e14 | 0.429308 | ||||||||
\(96\) | −1.99856e14 | −0.271446 | ||||||||
\(97\) | −1.82237e14 | −0.229006 | −0.114503 | − | 0.993423i | \(-0.536528\pi\) | ||||
−0.114503 | + | 0.993423i | \(0.536528\pi\) | |||||||
\(98\) | 2.33057e14 | 0.271185 | ||||||||
\(99\) | 2.23167e15 | 2.40639 | ||||||||
\(100\) | 1.00000e14 | 0.100000 | ||||||||
\(101\) | −6.88940e14 | −0.639398 | −0.319699 | − | 0.947519i | \(-0.603582\pi\) | ||||
−0.319699 | + | 0.947519i | \(0.603582\pi\) | |||||||
\(102\) | −5.78191e14 | −0.498391 | ||||||||
\(103\) | −1.74084e15 | −1.39470 | −0.697350 | − | 0.716731i | \(-0.745637\pi\) | ||||
−0.697350 | + | 0.716731i | \(0.745637\pi\) | |||||||
\(104\) | 5.96403e14 | 0.444416 | ||||||||
\(105\) | 1.16462e15 | 0.807728 | ||||||||
\(106\) | 1.42479e15 | 0.920360 | ||||||||
\(107\) | 2.39193e15 | 1.44002 | 0.720012 | − | 0.693962i | \(-0.244136\pi\) | ||||
0.720012 | + | 0.693962i | \(0.244136\pi\) | |||||||
\(108\) | −4.89338e14 | −0.274746 | ||||||||
\(109\) | 2.24908e15 | 1.17844 | 0.589218 | − | 0.807974i | \(-0.299436\pi\) | ||||
0.589218 | + | 0.807974i | \(0.299436\pi\) | |||||||
\(110\) | 1.14540e15 | 0.560420 | ||||||||
\(111\) | −3.98971e15 | −1.82398 | ||||||||
\(112\) | −6.87966e14 | −0.294057 | ||||||||
\(113\) | −4.98952e14 | −0.199513 | −0.0997564 | − | 0.995012i | \(-0.531806\pi\) | ||||
−0.0997564 | + | 0.995012i | \(0.531806\pi\) | |||||||
\(114\) | −2.78473e15 | −1.04231 | ||||||||
\(115\) | −2.15919e15 | −0.756933 | ||||||||
\(116\) | 2.61703e14 | 0.0859754 | ||||||||
\(117\) | 5.54091e15 | 1.70682 | ||||||||
\(118\) | −3.82134e15 | −1.10433 | ||||||||
\(119\) | −1.99031e15 | −0.539907 | ||||||||
\(120\) | −9.52988e14 | −0.242789 | ||||||||
\(121\) | 8.94225e15 | 2.14070 | ||||||||
\(122\) | 1.99742e15 | 0.449543 | ||||||||
\(123\) | −5.28849e15 | −1.11955 | ||||||||
\(124\) | 4.57782e13 | 0.00912002 | ||||||||
\(125\) | 4.76837e14 | 0.0894427 | ||||||||
\(126\) | −6.39158e15 | −1.12935 | ||||||||
\(127\) | −8.49486e15 | −1.41458 | −0.707291 | − | 0.706922i | \(-0.750083\pi\) | ||||
−0.707291 | + | 0.706922i | \(0.750083\pi\) | |||||||
\(128\) | 5.62950e14 | 0.0883883 | ||||||||
\(129\) | 2.39559e15 | 0.354805 | ||||||||
\(130\) | 2.84387e15 | 0.397498 | ||||||||
\(131\) | 3.46115e15 | 0.456758 | 0.228379 | − | 0.973572i | \(-0.426657\pi\) | ||||
0.228379 | + | 0.973572i | \(0.426657\pi\) | |||||||
\(132\) | −1.09156e16 | −1.36064 | ||||||||
\(133\) | −9.58590e15 | −1.12913 | ||||||||
\(134\) | 8.28718e15 | 0.922828 | ||||||||
\(135\) | −2.33334e15 | −0.245740 | ||||||||
\(136\) | 1.62864e15 | 0.162286 | ||||||||
\(137\) | 8.45917e14 | 0.0797854 | 0.0398927 | − | 0.999204i | \(-0.487298\pi\) | ||||
0.0398927 | + | 0.999204i | \(0.487298\pi\) | |||||||
\(138\) | 2.05768e16 | 1.83775 | ||||||||
\(139\) | −1.00576e16 | −0.850912 | −0.425456 | − | 0.904979i | \(-0.639886\pi\) | ||||
−0.425456 | + | 0.904979i | \(0.639886\pi\) | |||||||
\(140\) | −3.28048e15 | −0.263013 | ||||||||
\(141\) | 2.50057e15 | 0.190062 | ||||||||
\(142\) | 1.77101e16 | 1.27661 | ||||||||
\(143\) | 3.25738e16 | 2.22766 | ||||||||
\(144\) | 5.23011e15 | 0.339463 | ||||||||
\(145\) | 1.24790e15 | 0.0768987 | ||||||||
\(146\) | −7.37914e15 | −0.431876 | ||||||||
\(147\) | −1.05906e16 | −0.588897 | ||||||||
\(148\) | 1.12381e16 | 0.593924 | ||||||||
\(149\) | 1.57171e15 | 0.0789726 | 0.0394863 | − | 0.999220i | \(-0.487428\pi\) | ||||
0.0394863 | + | 0.999220i | \(0.487428\pi\) | |||||||
\(150\) | −4.54420e15 | −0.217157 | ||||||||
\(151\) | −6.62626e15 | −0.301260 | −0.150630 | − | 0.988590i | \(-0.548130\pi\) | ||||
−0.150630 | + | 0.988590i | \(0.548130\pi\) | |||||||
\(152\) | 7.84397e15 | 0.339398 | ||||||||
\(153\) | 1.51309e16 | 0.623274 | ||||||||
\(154\) | −3.75747e16 | −1.47398 | ||||||||
\(155\) | 2.18287e14 | 0.00815719 | ||||||||
\(156\) | −2.71018e16 | −0.965080 | ||||||||
\(157\) | −3.43384e16 | −1.16555 | −0.582777 | − | 0.812632i | \(-0.698034\pi\) | ||||
−0.582777 | + | 0.812632i | \(0.698034\pi\) | |||||||
\(158\) | 2.37869e16 | 0.769855 | ||||||||
\(159\) | −6.47455e16 | −1.99862 | ||||||||
\(160\) | 2.68435e15 | 0.0790569 | ||||||||
\(161\) | 7.08318e16 | 1.99083 | ||||||||
\(162\) | −1.35484e16 | −0.363518 | ||||||||
\(163\) | −5.08560e16 | −1.30297 | −0.651486 | − | 0.758661i | \(-0.725854\pi\) | ||||
−0.651486 | + | 0.758661i | \(0.725854\pi\) | |||||||
\(164\) | 1.48965e16 | 0.364549 | ||||||||
\(165\) | −5.20495e16 | −1.21699 | ||||||||
\(166\) | −3.93782e16 | −0.879923 | ||||||||
\(167\) | 3.23520e16 | 0.691078 | 0.345539 | − | 0.938404i | \(-0.387696\pi\) | ||||
0.345539 | + | 0.938404i | \(0.387696\pi\) | |||||||
\(168\) | 3.12626e16 | 0.638565 | ||||||||
\(169\) | 2.96902e16 | 0.580047 | ||||||||
\(170\) | 7.76594e15 | 0.145153 | ||||||||
\(171\) | 7.28747e16 | 1.30348 | ||||||||
\(172\) | −6.74785e15 | −0.115532 | ||||||||
\(173\) | −1.02507e16 | −0.168039 | −0.0840193 | − | 0.996464i | \(-0.526776\pi\) | ||||
−0.0840193 | + | 0.996464i | \(0.526776\pi\) | |||||||
\(174\) | −1.18923e16 | −0.186701 | ||||||||
\(175\) | −1.56425e16 | −0.235246 | ||||||||
\(176\) | 3.07467e16 | 0.443051 | ||||||||
\(177\) | 1.73649e17 | 2.39814 | ||||||||
\(178\) | −2.32596e16 | −0.307931 | ||||||||
\(179\) | −1.04290e17 | −1.32387 | −0.661933 | − | 0.749563i | \(-0.730264\pi\) | ||||
−0.661933 | + | 0.749563i | \(0.730264\pi\) | |||||||
\(180\) | 2.49391e16 | 0.303625 | ||||||||
\(181\) | −1.35448e16 | −0.158192 | −0.0790959 | − | 0.996867i | \(-0.525203\pi\) | ||||
−0.0790959 | + | 0.996867i | \(0.525203\pi\) | |||||||
\(182\) | −9.32926e16 | −1.04547 | ||||||||
\(183\) | −9.07669e16 | −0.976213 | ||||||||
\(184\) | −5.79604e16 | −0.598408 | ||||||||
\(185\) | 5.35875e16 | 0.531222 | ||||||||
\(186\) | −2.08025e15 | −0.0198047 | ||||||||
\(187\) | 8.89514e16 | 0.813468 | ||||||||
\(188\) | −7.04354e15 | −0.0618881 | ||||||||
\(189\) | 7.65448e16 | 0.646327 | ||||||||
\(190\) | 3.74029e16 | 0.303567 | ||||||||
\(191\) | 1.60733e17 | 1.25417 | 0.627084 | − | 0.778952i | \(-0.284248\pi\) | ||||
0.627084 | + | 0.778952i | \(0.284248\pi\) | |||||||
\(192\) | −2.55816e16 | −0.191941 | ||||||||
\(193\) | 6.73174e16 | 0.485789 | 0.242895 | − | 0.970053i | \(-0.421903\pi\) | ||||
0.242895 | + | 0.970053i | \(0.421903\pi\) | |||||||
\(194\) | −2.33263e16 | −0.161932 | ||||||||
\(195\) | −1.29231e17 | −0.863193 | ||||||||
\(196\) | 2.98313e16 | 0.191757 | ||||||||
\(197\) | 9.46393e16 | 0.585565 | 0.292782 | − | 0.956179i | \(-0.405419\pi\) | ||||
0.292782 | + | 0.956179i | \(0.405419\pi\) | |||||||
\(198\) | 2.85654e17 | 1.70157 | ||||||||
\(199\) | 2.16580e16 | 0.124228 | 0.0621141 | − | 0.998069i | \(-0.480216\pi\) | ||||
0.0621141 | + | 0.998069i | \(0.480216\pi\) | |||||||
\(200\) | 1.28000e16 | 0.0707107 | ||||||||
\(201\) | −3.76586e17 | −2.00398 | ||||||||
\(202\) | −8.81843e16 | −0.452123 | ||||||||
\(203\) | −4.09370e16 | −0.202253 | ||||||||
\(204\) | −7.40085e16 | −0.352416 | ||||||||
\(205\) | 7.10321e16 | 0.326062 | ||||||||
\(206\) | −2.22828e17 | −0.986201 | ||||||||
\(207\) | −5.38483e17 | −2.29824 | ||||||||
\(208\) | 7.63396e16 | 0.314250 | ||||||||
\(209\) | 4.28415e17 | 1.70125 | ||||||||
\(210\) | 1.49072e17 | 0.571150 | ||||||||
\(211\) | −3.78004e17 | −1.39758 | −0.698792 | − | 0.715325i | \(-0.746279\pi\) | ||||
−0.698792 | + | 0.715325i | \(0.746279\pi\) | |||||||
\(212\) | 1.82374e17 | 0.650793 | ||||||||
\(213\) | −8.04783e17 | −2.77225 | ||||||||
\(214\) | 3.06167e17 | 1.01825 | ||||||||
\(215\) | −3.21762e16 | −0.103335 | ||||||||
\(216\) | −6.26352e16 | −0.194274 | ||||||||
\(217\) | −7.16086e15 | −0.0214545 | ||||||||
\(218\) | 2.87882e17 | 0.833280 | ||||||||
\(219\) | 3.35323e17 | 0.937849 | ||||||||
\(220\) | 1.46612e17 | 0.396277 | ||||||||
\(221\) | 2.20853e17 | 0.576982 | ||||||||
\(222\) | −5.10683e17 | −1.28975 | ||||||||
\(223\) | 7.06105e16 | 0.172418 | 0.0862090 | − | 0.996277i | \(-0.472525\pi\) | ||||
0.0862090 | + | 0.996277i | \(0.472525\pi\) | |||||||
\(224\) | −8.80596e16 | −0.207930 | ||||||||
\(225\) | 1.18919e17 | 0.271570 | ||||||||
\(226\) | −6.38659e16 | −0.141077 | ||||||||
\(227\) | 6.99664e17 | 1.49519 | 0.747594 | − | 0.664156i | \(-0.231209\pi\) | ||||
0.747594 | + | 0.664156i | \(0.231209\pi\) | |||||||
\(228\) | −3.56446e17 | −0.737025 | ||||||||
\(229\) | 7.68134e16 | 0.153699 | 0.0768495 | − | 0.997043i | \(-0.475514\pi\) | ||||
0.0768495 | + | 0.997043i | \(0.475514\pi\) | |||||||
\(230\) | −2.76376e17 | −0.535232 | ||||||||
\(231\) | 1.70747e18 | 3.20084 | ||||||||
\(232\) | 3.34980e16 | 0.0607938 | ||||||||
\(233\) | −7.01643e17 | −1.23295 | −0.616477 | − | 0.787373i | \(-0.711441\pi\) | ||||
−0.616477 | + | 0.787373i | \(0.711441\pi\) | |||||||
\(234\) | 7.09236e17 | 1.20690 | ||||||||
\(235\) | −3.35862e16 | −0.0553544 | ||||||||
\(236\) | −4.89132e17 | −0.780883 | ||||||||
\(237\) | −1.08092e18 | −1.67179 | ||||||||
\(238\) | −2.54760e17 | −0.381772 | ||||||||
\(239\) | −4.82159e17 | −0.700174 | −0.350087 | − | 0.936717i | \(-0.613848\pi\) | ||||
−0.350087 | + | 0.936717i | \(0.613848\pi\) | |||||||
\(240\) | −1.21982e17 | −0.171677 | ||||||||
\(241\) | 1.37391e17 | 0.187426 | 0.0937129 | − | 0.995599i | \(-0.470126\pi\) | ||||
0.0937129 | + | 0.995599i | \(0.470126\pi\) | |||||||
\(242\) | 1.14461e18 | 1.51371 | ||||||||
\(243\) | 1.04422e18 | 1.33889 | ||||||||
\(244\) | 2.55670e17 | 0.317875 | ||||||||
\(245\) | 1.42247e17 | 0.171513 | ||||||||
\(246\) | −6.76927e17 | −0.791642 | ||||||||
\(247\) | 1.06369e18 | 1.20667 | ||||||||
\(248\) | 5.85960e15 | 0.00644883 | ||||||||
\(249\) | 1.78942e18 | 1.91081 | ||||||||
\(250\) | 6.10352e16 | 0.0632456 | ||||||||
\(251\) | −6.45195e17 | −0.648840 | −0.324420 | − | 0.945913i | \(-0.605169\pi\) | ||||
−0.324420 | + | 0.945913i | \(0.605169\pi\) | |||||||
\(252\) | −8.18122e17 | −0.798572 | ||||||||
\(253\) | −3.16563e18 | −2.99955 | ||||||||
\(254\) | −1.08734e18 | −1.00026 | ||||||||
\(255\) | −3.52900e17 | −0.315210 | ||||||||
\(256\) | 7.20576e16 | 0.0625000 | ||||||||
\(257\) | −1.22215e18 | −1.02950 | −0.514751 | − | 0.857339i | \(-0.672116\pi\) | ||||
−0.514751 | + | 0.857339i | \(0.672116\pi\) | |||||||
\(258\) | 3.06636e17 | 0.250885 | ||||||||
\(259\) | −1.75793e18 | −1.39718 | ||||||||
\(260\) | 3.64016e17 | 0.281074 | ||||||||
\(261\) | 3.11215e17 | 0.233484 | ||||||||
\(262\) | 4.43028e17 | 0.322977 | ||||||||
\(263\) | 1.57962e18 | 1.11914 | 0.559571 | − | 0.828783i | \(-0.310966\pi\) | ||||
0.559571 | + | 0.828783i | \(0.310966\pi\) | |||||||
\(264\) | −1.39719e18 | −0.962114 | ||||||||
\(265\) | 8.69625e17 | 0.582087 | ||||||||
\(266\) | −1.22700e18 | −0.798419 | ||||||||
\(267\) | 1.05696e18 | 0.668692 | ||||||||
\(268\) | 1.06076e18 | 0.652538 | ||||||||
\(269\) | −1.84403e18 | −1.10313 | −0.551563 | − | 0.834134i | \(-0.685968\pi\) | ||||
−0.551563 | + | 0.834134i | \(0.685968\pi\) | |||||||
\(270\) | −2.98668e17 | −0.173764 | ||||||||
\(271\) | −1.85427e18 | −1.04931 | −0.524655 | − | 0.851315i | \(-0.675806\pi\) | ||||
−0.524655 | + | 0.851315i | \(0.675806\pi\) | |||||||
\(272\) | 2.08465e17 | 0.114754 | ||||||||
\(273\) | 4.23940e18 | 2.27031 | ||||||||
\(274\) | 1.08277e17 | 0.0564168 | ||||||||
\(275\) | 6.99099e17 | 0.354441 | ||||||||
\(276\) | 2.63384e18 | 1.29948 | ||||||||
\(277\) | 2.28133e18 | 1.09544 | 0.547721 | − | 0.836661i | \(-0.315496\pi\) | ||||
0.547721 | + | 0.836661i | \(0.315496\pi\) | |||||||
\(278\) | −1.28738e18 | −0.601685 | ||||||||
\(279\) | 5.44389e16 | 0.0247673 | ||||||||
\(280\) | −4.19901e17 | −0.185978 | ||||||||
\(281\) | −2.36990e18 | −1.02196 | −0.510979 | − | 0.859593i | \(-0.670717\pi\) | ||||
−0.510979 | + | 0.859593i | \(0.670717\pi\) | |||||||
\(282\) | 3.20073e17 | 0.134394 | ||||||||
\(283\) | 2.74133e18 | 1.12089 | 0.560445 | − | 0.828192i | \(-0.310630\pi\) | ||||
0.560445 | + | 0.828192i | \(0.310630\pi\) | |||||||
\(284\) | 2.26689e18 | 0.902700 | ||||||||
\(285\) | −1.69967e18 | −0.659215 | ||||||||
\(286\) | 4.16945e18 | 1.57519 | ||||||||
\(287\) | −2.33019e18 | −0.857585 | ||||||||
\(288\) | 6.69454e17 | 0.240036 | ||||||||
\(289\) | −2.25932e18 | −0.789305 | ||||||||
\(290\) | 1.59731e17 | 0.0543756 | ||||||||
\(291\) | 1.05999e18 | 0.351646 | ||||||||
\(292\) | −9.44530e17 | −0.305383 | ||||||||
\(293\) | 7.10128e17 | 0.223784 | 0.111892 | − | 0.993720i | \(-0.464309\pi\) | ||||
0.111892 | + | 0.993720i | \(0.464309\pi\) | |||||||
\(294\) | −1.35559e18 | −0.416413 | ||||||||
\(295\) | −2.33236e18 | −0.698443 | ||||||||
\(296\) | 1.43848e18 | 0.419968 | ||||||||
\(297\) | −3.42096e18 | −0.973810 | ||||||||
\(298\) | 2.01179e17 | 0.0558421 | ||||||||
\(299\) | −7.85979e18 | −2.12754 | ||||||||
\(300\) | −5.81658e17 | −0.153553 | ||||||||
\(301\) | 1.05553e18 | 0.271784 | ||||||||
\(302\) | −8.48161e17 | −0.213023 | ||||||||
\(303\) | 4.00727e18 | 0.981814 | ||||||||
\(304\) | 1.00403e18 | 0.239990 | ||||||||
\(305\) | 1.21913e18 | 0.284316 | ||||||||
\(306\) | 1.93676e18 | 0.440722 | ||||||||
\(307\) | 3.91067e18 | 0.868387 | 0.434194 | − | 0.900820i | \(-0.357033\pi\) | ||||
0.434194 | + | 0.900820i | \(0.357033\pi\) | |||||||
\(308\) | −4.80956e18 | −1.04226 | ||||||||
\(309\) | 1.01258e19 | 2.14160 | ||||||||
\(310\) | 2.79408e16 | 0.00576801 | ||||||||
\(311\) | 3.92589e18 | 0.791108 | 0.395554 | − | 0.918443i | \(-0.370553\pi\) | ||||
0.395554 | + | 0.918443i | \(0.370553\pi\) | |||||||
\(312\) | −3.46903e18 | −0.682414 | ||||||||
\(313\) | −7.05946e18 | −1.35578 | −0.677889 | − | 0.735164i | \(-0.737105\pi\) | ||||
−0.677889 | + | 0.735164i | \(0.737105\pi\) | |||||||
\(314\) | −4.39531e18 | −0.824171 | ||||||||
\(315\) | −3.90111e18 | −0.714264 | ||||||||
\(316\) | 3.04472e18 | 0.544370 | ||||||||
\(317\) | 6.33185e18 | 1.10557 | 0.552785 | − | 0.833324i | \(-0.313565\pi\) | ||||
0.552785 | + | 0.833324i | \(0.313565\pi\) | |||||||
\(318\) | −8.28742e18 | −1.41324 | ||||||||
\(319\) | 1.82956e18 | 0.304732 | ||||||||
\(320\) | 3.43597e17 | 0.0559017 | ||||||||
\(321\) | −1.39128e19 | −2.21120 | ||||||||
\(322\) | 9.06647e18 | 1.40773 | ||||||||
\(323\) | 2.90469e18 | 0.440637 | ||||||||
\(324\) | −1.73419e18 | −0.257046 | ||||||||
\(325\) | 1.73576e18 | 0.251400 | ||||||||
\(326\) | −6.50956e18 | −0.921340 | ||||||||
\(327\) | −1.30819e19 | −1.80952 | ||||||||
\(328\) | 1.90675e18 | 0.257775 | ||||||||
\(329\) | 1.10179e18 | 0.145589 | ||||||||
\(330\) | −6.66233e18 | −0.860541 | ||||||||
\(331\) | 6.29584e18 | 0.794957 | 0.397478 | − | 0.917612i | \(-0.369885\pi\) | ||||
0.397478 | + | 0.917612i | \(0.369885\pi\) | |||||||
\(332\) | −5.04040e18 | −0.622200 | ||||||||
\(333\) | 1.33643e19 | 1.61292 | ||||||||
\(334\) | 4.14105e18 | 0.488666 | ||||||||
\(335\) | 5.05809e18 | 0.583647 | ||||||||
\(336\) | 4.00161e18 | 0.451533 | ||||||||
\(337\) | −5.64981e18 | −0.623461 | −0.311730 | − | 0.950171i | \(-0.600909\pi\) | ||||
−0.311730 | + | 0.950171i | \(0.600909\pi\) | |||||||
\(338\) | 3.80035e18 | 0.410155 | ||||||||
\(339\) | 2.90219e18 | 0.306358 | ||||||||
\(340\) | 9.94040e17 | 0.102639 | ||||||||
\(341\) | 3.20035e17 | 0.0323251 | ||||||||
\(342\) | 9.32796e18 | 0.921703 | ||||||||
\(343\) | 7.50103e18 | 0.725129 | ||||||||
\(344\) | −8.63724e17 | −0.0816934 | ||||||||
\(345\) | 1.25591e19 | 1.16229 | ||||||||
\(346\) | −1.31209e18 | −0.118821 | ||||||||
\(347\) | 9.94333e17 | 0.0881172 | 0.0440586 | − | 0.999029i | \(-0.485971\pi\) | ||||
0.0440586 | + | 0.999029i | \(0.485971\pi\) | |||||||
\(348\) | −1.52222e18 | −0.132018 | ||||||||
\(349\) | −1.39253e19 | −1.18199 | −0.590996 | − | 0.806674i | \(-0.701265\pi\) | ||||
−0.590996 | + | 0.806674i | \(0.701265\pi\) | |||||||
\(350\) | −2.00224e18 | −0.166344 | ||||||||
\(351\) | −8.49374e18 | −0.690710 | ||||||||
\(352\) | 3.93558e18 | 0.313284 | ||||||||
\(353\) | 4.63332e18 | 0.361062 | 0.180531 | − | 0.983569i | \(-0.442218\pi\) | ||||
0.180531 | + | 0.983569i | \(0.442218\pi\) | |||||||
\(354\) | 2.22271e19 | 1.69574 | ||||||||
\(355\) | 1.08094e19 | 0.807399 | ||||||||
\(356\) | −2.97723e18 | −0.217740 | ||||||||
\(357\) | 1.15768e19 | 0.829043 | ||||||||
\(358\) | −1.33491e19 | −0.936115 | ||||||||
\(359\) | 1.14313e19 | 0.785030 | 0.392515 | − | 0.919746i | \(-0.371605\pi\) | ||||
0.392515 | + | 0.919746i | \(0.371605\pi\) | |||||||
\(360\) | 3.19221e18 | 0.214695 | ||||||||
\(361\) | −1.19132e18 | −0.0784738 | ||||||||
\(362\) | −1.73374e18 | −0.111858 | ||||||||
\(363\) | −5.20133e19 | −3.28711 | ||||||||
\(364\) | −1.19415e19 | −0.739259 | ||||||||
\(365\) | −4.50387e18 | −0.273143 | ||||||||
\(366\) | −1.16182e19 | −0.690287 | ||||||||
\(367\) | −1.89910e19 | −1.10549 | −0.552743 | − | 0.833352i | \(-0.686419\pi\) | ||||
−0.552743 | + | 0.833352i | \(0.686419\pi\) | |||||||
\(368\) | −7.41893e18 | −0.423138 | ||||||||
\(369\) | 1.77148e19 | 0.990006 | ||||||||
\(370\) | 6.85921e18 | 0.375631 | ||||||||
\(371\) | −2.85278e19 | −1.53096 | ||||||||
\(372\) | −2.66272e17 | −0.0140041 | ||||||||
\(373\) | −2.59363e18 | −0.133688 | −0.0668439 | − | 0.997763i | \(-0.521293\pi\) | ||||
−0.0668439 | + | 0.997763i | \(0.521293\pi\) | |||||||
\(374\) | 1.13858e19 | 0.575209 | ||||||||
\(375\) | −2.77356e18 | −0.137342 | ||||||||
\(376\) | −9.01573e17 | −0.0437615 | ||||||||
\(377\) | 4.54255e18 | 0.216142 | ||||||||
\(378\) | 9.79774e18 | 0.457022 | ||||||||
\(379\) | −2.69599e19 | −1.23289 | −0.616446 | − | 0.787397i | \(-0.711428\pi\) | ||||
−0.616446 | + | 0.787397i | \(0.711428\pi\) | |||||||
\(380\) | 4.78758e18 | 0.214654 | ||||||||
\(381\) | 4.94110e19 | 2.17213 | ||||||||
\(382\) | 2.05739e19 | 0.886830 | ||||||||
\(383\) | 7.21341e17 | 0.0304895 | 0.0152447 | − | 0.999884i | \(-0.495147\pi\) | ||||
0.0152447 | + | 0.999884i | \(0.495147\pi\) | |||||||
\(384\) | −3.27444e18 | −0.135723 | ||||||||
\(385\) | −2.29338e19 | −0.932224 | ||||||||
\(386\) | 8.61663e18 | 0.343505 | ||||||||
\(387\) | −8.02447e18 | −0.313750 | ||||||||
\(388\) | −2.98577e18 | −0.114503 | ||||||||
\(389\) | 1.58276e19 | 0.595378 | 0.297689 | − | 0.954663i | \(-0.403784\pi\) | ||||
0.297689 | + | 0.954663i | \(0.403784\pi\) | |||||||
\(390\) | −1.65416e19 | −0.610370 | ||||||||
\(391\) | −2.14632e19 | −0.776908 | ||||||||
\(392\) | 3.81840e18 | 0.135593 | ||||||||
\(393\) | −2.01321e19 | −0.701365 | ||||||||
\(394\) | 1.21138e19 | 0.414057 | ||||||||
\(395\) | 1.45183e19 | 0.486899 | ||||||||
\(396\) | 3.65637e19 | 1.20319 | ||||||||
\(397\) | −1.94707e19 | −0.628713 | −0.314356 | − | 0.949305i | \(-0.601789\pi\) | ||||
−0.314356 | + | 0.949305i | \(0.601789\pi\) | |||||||
\(398\) | 2.77222e18 | 0.0878426 | ||||||||
\(399\) | 5.57571e19 | 1.73382 | ||||||||
\(400\) | 1.63840e18 | 0.0500000 | ||||||||
\(401\) | 1.04806e19 | 0.313908 | 0.156954 | − | 0.987606i | \(-0.449833\pi\) | ||||
0.156954 | + | 0.987606i | \(0.449833\pi\) | |||||||
\(402\) | −4.82030e19 | −1.41703 | ||||||||
\(403\) | 7.94600e17 | 0.0229277 | ||||||||
\(404\) | −1.12876e19 | −0.319699 | ||||||||
\(405\) | −8.26929e18 | −0.229909 | ||||||||
\(406\) | −5.23994e18 | −0.143015 | ||||||||
\(407\) | 7.85656e19 | 2.10511 | ||||||||
\(408\) | −9.47309e18 | −0.249196 | ||||||||
\(409\) | 7.27248e17 | 0.0187827 | 0.00939134 | − | 0.999956i | \(-0.497011\pi\) | ||||
0.00939134 | + | 0.999956i | \(0.497011\pi\) | |||||||
\(410\) | 9.09210e18 | 0.230561 | ||||||||
\(411\) | −4.92034e18 | −0.122513 | ||||||||
\(412\) | −2.85220e19 | −0.697350 | ||||||||
\(413\) | 7.65126e19 | 1.83699 | ||||||||
\(414\) | −6.89258e19 | −1.62510 | ||||||||
\(415\) | −2.40345e19 | −0.556512 | ||||||||
\(416\) | 9.77147e18 | 0.222208 | ||||||||
\(417\) | 5.85010e19 | 1.30660 | ||||||||
\(418\) | 5.48371e19 | 1.20296 | ||||||||
\(419\) | 4.89919e19 | 1.05565 | 0.527824 | − | 0.849354i | \(-0.323008\pi\) | ||||
0.527824 | + | 0.849354i | \(0.323008\pi\) | |||||||
\(420\) | 1.90812e19 | 0.403864 | ||||||||
\(421\) | −4.22149e18 | −0.0877707 | −0.0438854 | − | 0.999037i | \(-0.513974\pi\) | ||||
−0.0438854 | + | 0.999037i | \(0.513974\pi\) | |||||||
\(422\) | −4.83845e19 | −0.988241 | ||||||||
\(423\) | −8.37611e18 | −0.168070 | ||||||||
\(424\) | 2.33438e19 | 0.460180 | ||||||||
\(425\) | 4.73995e18 | 0.0918031 | ||||||||
\(426\) | −1.03012e20 | −1.96027 | ||||||||
\(427\) | −3.99933e19 | −0.747787 | ||||||||
\(428\) | 3.91893e19 | 0.720012 | ||||||||
\(429\) | −1.89468e20 | −3.42063 | ||||||||
\(430\) | −4.11856e18 | −0.0730688 | ||||||||
\(431\) | 1.61261e18 | 0.0281157 | 0.0140579 | − | 0.999901i | \(-0.495525\pi\) | ||||
0.0140579 | + | 0.999901i | \(0.495525\pi\) | |||||||
\(432\) | −8.01731e18 | −0.137373 | ||||||||
\(433\) | −6.08830e19 | −1.02527 | −0.512633 | − | 0.858608i | \(-0.671330\pi\) | ||||
−0.512633 | + | 0.858608i | \(0.671330\pi\) | |||||||
\(434\) | −9.16591e17 | −0.0151706 | ||||||||
\(435\) | −7.25850e18 | −0.118080 | ||||||||
\(436\) | 3.68489e19 | 0.589218 | ||||||||
\(437\) | −1.03373e20 | −1.62479 | ||||||||
\(438\) | 4.29214e19 | 0.663159 | ||||||||
\(439\) | 5.81533e19 | 0.883264 | 0.441632 | − | 0.897196i | \(-0.354400\pi\) | ||||
0.441632 | + | 0.897196i | \(0.354400\pi\) | |||||||
\(440\) | 1.87663e19 | 0.280210 | ||||||||
\(441\) | 3.54750e19 | 0.520755 | ||||||||
\(442\) | 2.82692e19 | 0.407988 | ||||||||
\(443\) | 1.06230e20 | 1.50736 | 0.753682 | − | 0.657239i | \(-0.228276\pi\) | ||||
0.753682 | + | 0.657239i | \(0.228276\pi\) | |||||||
\(444\) | −6.53674e19 | −0.911988 | ||||||||
\(445\) | −1.41966e19 | −0.194752 | ||||||||
\(446\) | 9.03814e18 | 0.121918 | ||||||||
\(447\) | −9.14200e18 | −0.121265 | ||||||||
\(448\) | −1.12716e19 | −0.147029 | ||||||||
\(449\) | −1.17735e20 | −1.51028 | −0.755140 | − | 0.655564i | \(-0.772431\pi\) | ||||
−0.755140 | + | 0.655564i | \(0.772431\pi\) | |||||||
\(450\) | 1.52216e19 | 0.192029 | ||||||||
\(451\) | 1.04141e20 | 1.29211 | ||||||||
\(452\) | −8.17483e18 | −0.0997564 | ||||||||
\(453\) | 3.85421e19 | 0.462593 | ||||||||
\(454\) | 8.95570e19 | 1.05726 | ||||||||
\(455\) | −5.69413e19 | −0.661213 | ||||||||
\(456\) | −4.56251e19 | −0.521155 | ||||||||
\(457\) | 1.15681e20 | 1.29984 | 0.649918 | − | 0.760004i | \(-0.274803\pi\) | ||||
0.649918 | + | 0.760004i | \(0.274803\pi\) | |||||||
\(458\) | 9.83212e18 | 0.108682 | ||||||||
\(459\) | −2.31944e19 | −0.252225 | ||||||||
\(460\) | −3.53762e19 | −0.378466 | ||||||||
\(461\) | −8.04744e19 | −0.847034 | −0.423517 | − | 0.905888i | \(-0.639205\pi\) | ||||
−0.423517 | + | 0.905888i | \(0.639205\pi\) | |||||||
\(462\) | 2.18556e20 | 2.26333 | ||||||||
\(463\) | −9.29651e19 | −0.947245 | −0.473623 | − | 0.880728i | \(-0.657054\pi\) | ||||
−0.473623 | + | 0.880728i | \(0.657054\pi\) | |||||||
\(464\) | 4.28775e18 | 0.0429877 | ||||||||
\(465\) | −1.26969e18 | −0.0125256 | ||||||||
\(466\) | −8.98103e19 | −0.871830 | ||||||||
\(467\) | 1.37482e19 | 0.131332 | 0.0656659 | − | 0.997842i | \(-0.479083\pi\) | ||||
0.0656659 | + | 0.997842i | \(0.479083\pi\) | |||||||
\(468\) | 9.07823e19 | 0.853409 | ||||||||
\(469\) | −1.65930e20 | −1.53507 | ||||||||
\(470\) | −4.29904e18 | −0.0391415 | ||||||||
\(471\) | 1.99732e20 | 1.78974 | ||||||||
\(472\) | −6.26089e19 | −0.552167 | ||||||||
\(473\) | −4.71741e19 | −0.409492 | ||||||||
\(474\) | −1.38358e20 | −1.18213 | ||||||||
\(475\) | 2.28289e19 | 0.191992 | ||||||||
\(476\) | −3.26093e19 | −0.269953 | ||||||||
\(477\) | 2.16877e20 | 1.76736 | ||||||||
\(478\) | −6.17164e19 | −0.495098 | ||||||||
\(479\) | 6.69948e19 | 0.529084 | 0.264542 | − | 0.964374i | \(-0.414779\pi\) | ||||
0.264542 | + | 0.964374i | \(0.414779\pi\) | |||||||
\(480\) | −1.56138e19 | −0.121394 | ||||||||
\(481\) | 1.95067e20 | 1.49312 | ||||||||
\(482\) | 1.75860e19 | 0.132530 | ||||||||
\(483\) | −4.11999e20 | −3.05698 | ||||||||
\(484\) | 1.46510e20 | 1.07035 | ||||||||
\(485\) | −1.42372e19 | −0.102415 | ||||||||
\(486\) | 1.33661e20 | 0.946741 | ||||||||
\(487\) | −1.80792e19 | −0.126099 | −0.0630495 | − | 0.998010i | \(-0.520083\pi\) | ||||
−0.0630495 | + | 0.998010i | \(0.520083\pi\) | |||||||
\(488\) | 3.27258e19 | 0.224772 | ||||||||
\(489\) | 2.95808e20 | 2.00075 | ||||||||
\(490\) | 1.82076e19 | 0.121278 | ||||||||
\(491\) | −1.08152e20 | −0.709450 | −0.354725 | − | 0.934971i | \(-0.615426\pi\) | ||||
−0.354725 | + | 0.934971i | \(0.615426\pi\) | |||||||
\(492\) | −8.66467e19 | −0.559775 | ||||||||
\(493\) | 1.24046e19 | 0.0789280 | ||||||||
\(494\) | 1.36153e20 | 0.853245 | ||||||||
\(495\) | 1.74349e20 | 1.07617 | ||||||||
\(496\) | 7.50029e17 | 0.00456001 | ||||||||
\(497\) | −3.54599e20 | −2.12356 | ||||||||
\(498\) | 2.29046e20 | 1.35115 | ||||||||
\(499\) | 6.92079e19 | 0.402163 | 0.201081 | − | 0.979575i | \(-0.435554\pi\) | ||||
0.201081 | + | 0.979575i | \(0.435554\pi\) | |||||||
\(500\) | 7.81250e18 | 0.0447214 | ||||||||
\(501\) | −1.88178e20 | −1.06117 | ||||||||
\(502\) | −8.25849e19 | −0.458799 | ||||||||
\(503\) | 1.85647e20 | 1.01608 | 0.508040 | − | 0.861333i | \(-0.330370\pi\) | ||||
0.508040 | + | 0.861333i | \(0.330370\pi\) | |||||||
\(504\) | −1.04720e20 | −0.564675 | ||||||||
\(505\) | −5.38235e19 | −0.285947 | ||||||||
\(506\) | −4.05200e20 | −2.12100 | ||||||||
\(507\) | −1.72695e20 | −0.890679 | ||||||||
\(508\) | −1.39180e20 | −0.707291 | ||||||||
\(509\) | −1.26957e20 | −0.635730 | −0.317865 | − | 0.948136i | \(-0.602966\pi\) | ||||
−0.317865 | + | 0.948136i | \(0.602966\pi\) | |||||||
\(510\) | −4.51712e19 | −0.222887 | ||||||||
\(511\) | 1.47748e20 | 0.718400 | ||||||||
\(512\) | 9.22337e18 | 0.0441942 | ||||||||
\(513\) | −1.11711e20 | −0.527490 | ||||||||
\(514\) | −1.56436e20 | −0.727968 | ||||||||
\(515\) | −1.36003e20 | −0.623728 | ||||||||
\(516\) | 3.92494e19 | 0.177403 | ||||||||
\(517\) | −4.92413e19 | −0.219357 | ||||||||
\(518\) | −2.25015e20 | −0.987956 | ||||||||
\(519\) | 5.96242e19 | 0.258028 | ||||||||
\(520\) | 4.65940e19 | 0.198749 | ||||||||
\(521\) | −1.53600e20 | −0.645817 | −0.322908 | − | 0.946430i | \(-0.604661\pi\) | ||||
−0.322908 | + | 0.946430i | \(0.604661\pi\) | |||||||
\(522\) | 3.98355e19 | 0.165098 | ||||||||
\(523\) | 4.35314e20 | 1.77844 | 0.889222 | − | 0.457477i | \(-0.151247\pi\) | ||||
0.889222 | + | 0.457477i | \(0.151247\pi\) | |||||||
\(524\) | 5.67075e19 | 0.228379 | ||||||||
\(525\) | 9.09860e19 | 0.361227 | ||||||||
\(526\) | 2.02192e20 | 0.791352 | ||||||||
\(527\) | 2.16986e18 | 0.00837246 | ||||||||
\(528\) | −1.78841e20 | −0.680318 | ||||||||
\(529\) | 4.97204e20 | 1.86474 | ||||||||
\(530\) | 1.11312e20 | 0.411598 | ||||||||
\(531\) | −5.81670e20 | −2.12064 | ||||||||
\(532\) | −1.57055e20 | −0.564567 | ||||||||
\(533\) | 2.58568e20 | 0.916475 | ||||||||
\(534\) | 1.35292e20 | 0.472837 | ||||||||
\(535\) | 1.86869e20 | 0.643998 | ||||||||
\(536\) | 1.35777e20 | 0.461414 | ||||||||
\(537\) | 6.06610e20 | 2.03284 | ||||||||
\(538\) | −2.36035e20 | −0.780027 | ||||||||
\(539\) | 2.08550e20 | 0.679664 | ||||||||
\(540\) | −3.82295e19 | −0.122870 | ||||||||
\(541\) | −1.00466e20 | −0.318448 | −0.159224 | − | 0.987243i | \(-0.550899\pi\) | ||||
−0.159224 | + | 0.987243i | \(0.550899\pi\) | |||||||
\(542\) | −2.37347e20 | −0.741975 | ||||||||
\(543\) | 7.87845e19 | 0.242908 | ||||||||
\(544\) | 2.66836e19 | 0.0811432 | ||||||||
\(545\) | 1.75709e20 | 0.527013 | ||||||||
\(546\) | 5.42644e20 | 1.60535 | ||||||||
\(547\) | −3.68217e20 | −1.07448 | −0.537240 | − | 0.843429i | \(-0.680533\pi\) | ||||
−0.537240 | + | 0.843429i | \(0.680533\pi\) | |||||||
\(548\) | 1.38595e19 | 0.0398927 | ||||||||
\(549\) | 3.04040e20 | 0.863254 | ||||||||
\(550\) | 8.94847e19 | 0.250627 | ||||||||
\(551\) | 5.97441e19 | 0.165066 | ||||||||
\(552\) | 3.37131e20 | 0.918873 | ||||||||
\(553\) | −4.76271e20 | −1.28061 | ||||||||
\(554\) | 2.92010e20 | 0.774594 | ||||||||
\(555\) | −3.11696e20 | −0.815707 | ||||||||
\(556\) | −1.64784e20 | −0.425456 | ||||||||
\(557\) | 8.61313e19 | 0.219405 | 0.109703 | − | 0.993964i | \(-0.465010\pi\) | ||||
0.109703 | + | 0.993964i | \(0.465010\pi\) | |||||||
\(558\) | 6.96818e18 | 0.0175131 | ||||||||
\(559\) | −1.17127e20 | −0.290447 | ||||||||
\(560\) | −5.37473e19 | −0.131506 | ||||||||
\(561\) | −5.17393e20 | −1.24910 | ||||||||
\(562\) | −3.03348e20 | −0.722634 | ||||||||
\(563\) | −4.59219e20 | −1.07946 | −0.539731 | − | 0.841838i | \(-0.681474\pi\) | ||||
−0.539731 | + | 0.841838i | \(0.681474\pi\) | |||||||
\(564\) | 4.09693e19 | 0.0950310 | ||||||||
\(565\) | −3.89806e19 | −0.0892248 | ||||||||
\(566\) | 3.50890e20 | 0.792589 | ||||||||
\(567\) | 2.71272e20 | 0.604689 | ||||||||
\(568\) | 2.90162e20 | 0.638305 | ||||||||
\(569\) | −7.18099e20 | −1.55899 | −0.779493 | − | 0.626410i | \(-0.784523\pi\) | ||||
−0.779493 | + | 0.626410i | \(0.784523\pi\) | |||||||
\(570\) | −2.17557e20 | −0.466135 | ||||||||
\(571\) | 1.98256e20 | 0.419233 | 0.209616 | − | 0.977784i | \(-0.432778\pi\) | ||||
0.209616 | + | 0.977784i | \(0.432778\pi\) | |||||||
\(572\) | 5.33690e20 | 1.11383 | ||||||||
\(573\) | −9.34918e20 | −1.92581 | ||||||||
\(574\) | −2.98264e20 | −0.606404 | ||||||||
\(575\) | −1.68687e20 | −0.338511 | ||||||||
\(576\) | 8.56901e19 | 0.169731 | ||||||||
\(577\) | 1.51016e20 | 0.295259 | 0.147630 | − | 0.989043i | \(-0.452836\pi\) | ||||
0.147630 | + | 0.989043i | \(0.452836\pi\) | |||||||
\(578\) | −2.89194e20 | −0.558123 | ||||||||
\(579\) | −3.91557e20 | −0.745943 | ||||||||
\(580\) | 2.04456e19 | 0.0384494 | ||||||||
\(581\) | 7.88447e20 | 1.46370 | ||||||||
\(582\) | 1.35679e20 | 0.248651 | ||||||||
\(583\) | 1.27497e21 | 2.30668 | ||||||||
\(584\) | −1.20900e20 | −0.215938 | ||||||||
\(585\) | 4.32884e20 | 0.763312 | ||||||||
\(586\) | 9.08964e19 | 0.158239 | ||||||||
\(587\) | −4.98278e20 | −0.856418 | −0.428209 | − | 0.903680i | \(-0.640855\pi\) | ||||
−0.428209 | + | 0.903680i | \(0.640855\pi\) | |||||||
\(588\) | −1.73516e20 | −0.294448 | ||||||||
\(589\) | 1.04507e19 | 0.0175097 | ||||||||
\(590\) | −2.98542e20 | −0.493874 | ||||||||
\(591\) | −5.50477e20 | −0.899152 | ||||||||
\(592\) | 1.84125e20 | 0.296962 | ||||||||
\(593\) | 1.37436e20 | 0.218871 | 0.109436 | − | 0.993994i | \(-0.465096\pi\) | ||||
0.109436 | + | 0.993994i | \(0.465096\pi\) | |||||||
\(594\) | −4.37882e20 | −0.688587 | ||||||||
\(595\) | −1.55493e20 | −0.241454 | ||||||||
\(596\) | 2.57510e19 | 0.0394863 | ||||||||
\(597\) | −1.25975e20 | −0.190756 | ||||||||
\(598\) | −1.00605e21 | −1.50440 | ||||||||
\(599\) | −1.07343e21 | −1.58516 | −0.792582 | − | 0.609765i | \(-0.791264\pi\) | ||||
−0.792582 | + | 0.609765i | \(0.791264\pi\) | |||||||
\(600\) | −7.44522e19 | −0.108578 | ||||||||
\(601\) | −1.27438e20 | −0.183544 | −0.0917721 | − | 0.995780i | \(-0.529253\pi\) | ||||
−0.0917721 | + | 0.995780i | \(0.529253\pi\) | |||||||
\(602\) | 1.35108e20 | 0.192180 | ||||||||
\(603\) | 1.26144e21 | 1.77210 | ||||||||
\(604\) | −1.08565e20 | −0.150630 | ||||||||
\(605\) | 6.98613e20 | 0.957352 | ||||||||
\(606\) | 5.12931e20 | 0.694248 | ||||||||
\(607\) | −3.63227e20 | −0.485582 | −0.242791 | − | 0.970079i | \(-0.578063\pi\) | ||||
−0.242791 | + | 0.970079i | \(0.578063\pi\) | |||||||
\(608\) | 1.28516e20 | 0.169699 | ||||||||
\(609\) | 2.38113e20 | 0.310566 | ||||||||
\(610\) | 1.56049e20 | 0.201042 | ||||||||
\(611\) | −1.22259e20 | −0.155587 | ||||||||
\(612\) | 2.47905e20 | 0.311637 | ||||||||
\(613\) | 1.06315e21 | 1.32021 | 0.660104 | − | 0.751174i | \(-0.270512\pi\) | ||||
0.660104 | + | 0.751174i | \(0.270512\pi\) | |||||||
\(614\) | 5.00566e20 | 0.614042 | ||||||||
\(615\) | −4.13164e20 | −0.500678 | ||||||||
\(616\) | −6.15624e20 | −0.736988 | ||||||||
\(617\) | 8.94081e20 | 1.05740 | 0.528699 | − | 0.848810i | \(-0.322680\pi\) | ||||
0.528699 | + | 0.848810i | \(0.322680\pi\) | |||||||
\(618\) | 1.29610e21 | 1.51434 | ||||||||
\(619\) | −1.24002e21 | −1.43136 | −0.715681 | − | 0.698427i | \(-0.753884\pi\) | ||||
−0.715681 | + | 0.698427i | \(0.753884\pi\) | |||||||
\(620\) | 3.57642e18 | 0.00407860 | ||||||||
\(621\) | 8.25448e20 | 0.930043 | ||||||||
\(622\) | 5.02514e20 | 0.559398 | ||||||||
\(623\) | 4.65715e20 | 0.512224 | ||||||||
\(624\) | −4.44035e20 | −0.482540 | ||||||||
\(625\) | 3.72529e19 | 0.0400000 | ||||||||
\(626\) | −9.03610e20 | −0.958680 | ||||||||
\(627\) | −2.49191e21 | −2.61231 | ||||||||
\(628\) | −5.62600e20 | −0.582777 | ||||||||
\(629\) | 5.32682e20 | 0.545240 | ||||||||
\(630\) | −4.99342e20 | −0.505061 | ||||||||
\(631\) | 1.22882e21 | 1.22820 | 0.614099 | − | 0.789229i | \(-0.289519\pi\) | ||||
0.614099 | + | 0.789229i | \(0.289519\pi\) | |||||||
\(632\) | 3.89724e20 | 0.384927 | ||||||||
\(633\) | 2.19869e21 | 2.14603 | ||||||||
\(634\) | 8.10477e20 | 0.781756 | ||||||||
\(635\) | −6.63661e20 | −0.632620 | ||||||||
\(636\) | −1.06079e21 | −0.999312 | ||||||||
\(637\) | 5.17800e20 | 0.482076 | ||||||||
\(638\) | 2.34184e20 | 0.215478 | ||||||||
\(639\) | 2.69577e21 | 2.45146 | ||||||||
\(640\) | 4.39805e19 | 0.0395285 | ||||||||
\(641\) | −1.91614e21 | −1.70213 | −0.851063 | − | 0.525063i | \(-0.824042\pi\) | ||||
−0.851063 | + | 0.525063i | \(0.824042\pi\) | |||||||
\(642\) | −1.78084e21 | −1.56355 | ||||||||
\(643\) | −8.56056e20 | −0.742882 | −0.371441 | − | 0.928457i | \(-0.621136\pi\) | ||||
−0.371441 | + | 0.928457i | \(0.621136\pi\) | |||||||
\(644\) | 1.16051e21 | 0.995415 | ||||||||
\(645\) | 1.87156e20 | 0.158674 | ||||||||
\(646\) | 3.71800e20 | 0.311577 | ||||||||
\(647\) | 1.91833e21 | 1.58906 | 0.794531 | − | 0.607224i | \(-0.207717\pi\) | ||||
0.794531 | + | 0.607224i | \(0.207717\pi\) | |||||||
\(648\) | −2.21977e20 | −0.181759 | ||||||||
\(649\) | −3.41951e21 | −2.76777 | ||||||||
\(650\) | 2.22178e20 | 0.177767 | ||||||||
\(651\) | 4.16517e19 | 0.0329439 | ||||||||
\(652\) | −8.33224e20 | −0.651486 | ||||||||
\(653\) | −1.17776e21 | −0.910353 | −0.455176 | − | 0.890401i | \(-0.650424\pi\) | ||||
−0.455176 | + | 0.890401i | \(0.650424\pi\) | |||||||
\(654\) | −1.67449e21 | −1.27953 | ||||||||
\(655\) | 2.70403e20 | 0.204268 | ||||||||
\(656\) | 2.44064e20 | 0.182274 | ||||||||
\(657\) | −1.12323e21 | −0.829329 | ||||||||
\(658\) | 1.41029e20 | 0.102947 | ||||||||
\(659\) | 3.65308e20 | 0.263644 | 0.131822 | − | 0.991273i | \(-0.457917\pi\) | ||||
0.131822 | + | 0.991273i | \(0.457917\pi\) | |||||||
\(660\) | −8.52778e20 | −0.608495 | ||||||||
\(661\) | 2.48240e21 | 1.75130 | 0.875650 | − | 0.482947i | \(-0.160433\pi\) | ||||
0.875650 | + | 0.482947i | \(0.160433\pi\) | |||||||
\(662\) | 8.05867e20 | 0.562119 | ||||||||
\(663\) | −1.28461e21 | −0.885973 | ||||||||
\(664\) | −6.45172e20 | −0.439961 | ||||||||
\(665\) | −7.48898e20 | −0.504964 | ||||||||
\(666\) | 1.71062e21 | 1.14051 | ||||||||
\(667\) | −4.41459e20 | −0.291036 | ||||||||
\(668\) | 5.30055e20 | 0.345539 | ||||||||
\(669\) | −4.10711e20 | −0.264753 | ||||||||
\(670\) | 6.47436e20 | 0.412701 | ||||||||
\(671\) | 1.78739e21 | 1.12668 | ||||||||
\(672\) | 5.12206e20 | 0.319282 | ||||||||
\(673\) | −2.25249e21 | −1.38851 | −0.694257 | − | 0.719728i | \(-0.744267\pi\) | ||||
−0.694257 | + | 0.719728i | \(0.744267\pi\) | |||||||
\(674\) | −7.23175e20 | −0.440853 | ||||||||
\(675\) | −1.82293e20 | −0.109898 | ||||||||
\(676\) | 4.86444e20 | 0.290023 | ||||||||
\(677\) | 1.00846e21 | 0.594628 | 0.297314 | − | 0.954780i | \(-0.403909\pi\) | ||||
0.297314 | + | 0.954780i | \(0.403909\pi\) | |||||||
\(678\) | 3.71481e20 | 0.216628 | ||||||||
\(679\) | 4.67049e20 | 0.269364 | ||||||||
\(680\) | 1.27237e20 | 0.0725767 | ||||||||
\(681\) | −4.06965e21 | −2.29591 | ||||||||
\(682\) | 4.09644e19 | 0.0228573 | ||||||||
\(683\) | 1.61840e20 | 0.0893160 | 0.0446580 | − | 0.999002i | \(-0.485780\pi\) | ||||
0.0446580 | + | 0.999002i | \(0.485780\pi\) | |||||||
\(684\) | 1.19398e21 | 0.651742 | ||||||||
\(685\) | 6.60873e19 | 0.0356811 | ||||||||
\(686\) | 9.60132e20 | 0.512743 | ||||||||
\(687\) | −4.46791e20 | −0.236009 | ||||||||
\(688\) | −1.10557e20 | −0.0577659 | ||||||||
\(689\) | 3.16557e21 | 1.63609 | ||||||||
\(690\) | 1.60757e21 | 0.821865 | ||||||||
\(691\) | −2.04771e21 | −1.03558 | −0.517788 | − | 0.855509i | \(-0.673244\pi\) | ||||
−0.517788 | + | 0.855509i | \(0.673244\pi\) | |||||||
\(692\) | −1.67948e20 | −0.0840193 | ||||||||
\(693\) | −5.71948e21 | −2.83046 | ||||||||
\(694\) | 1.27275e20 | 0.0623083 | ||||||||
\(695\) | −7.85752e20 | −0.380539 | ||||||||
\(696\) | −1.94844e20 | −0.0933507 | ||||||||
\(697\) | 7.06087e20 | 0.334667 | ||||||||
\(698\) | −1.78244e21 | −0.835795 | ||||||||
\(699\) | 4.08116e21 | 1.89324 | ||||||||
\(700\) | −2.56287e20 | −0.117623 | ||||||||
\(701\) | −2.28411e21 | −1.03713 | −0.518564 | − | 0.855039i | \(-0.673533\pi\) | ||||
−0.518564 | + | 0.855039i | \(0.673533\pi\) | |||||||
\(702\) | −1.08720e21 | −0.488406 | ||||||||
\(703\) | 2.56555e21 | 1.14029 | ||||||||
\(704\) | 5.03754e20 | 0.221525 | ||||||||
\(705\) | 1.95357e20 | 0.0849983 | ||||||||
\(706\) | 5.93065e20 | 0.255310 | ||||||||
\(707\) | 1.76567e21 | 0.752078 | ||||||||
\(708\) | 2.84507e21 | 1.19907 | ||||||||
\(709\) | 7.23937e20 | 0.301894 | 0.150947 | − | 0.988542i | \(-0.451768\pi\) | ||||
0.150947 | + | 0.988542i | \(0.451768\pi\) | |||||||
\(710\) | 1.38360e21 | 0.570918 | ||||||||
\(711\) | 3.62075e21 | 1.47835 | ||||||||
\(712\) | −3.81086e20 | −0.153965 | ||||||||
\(713\) | −7.72217e19 | −0.0308722 | ||||||||
\(714\) | 1.48183e21 | 0.586222 | ||||||||
\(715\) | 2.54483e21 | 0.996239 | ||||||||
\(716\) | −1.70868e21 | −0.661933 | ||||||||
\(717\) | 2.80452e21 | 1.07514 | ||||||||
\(718\) | 1.46320e21 | 0.555100 | ||||||||
\(719\) | −2.52991e20 | −0.0949815 | −0.0474907 | − | 0.998872i | \(-0.515122\pi\) | ||||
−0.0474907 | + | 0.998872i | \(0.515122\pi\) | |||||||
\(720\) | 4.08602e20 | 0.151812 | ||||||||
\(721\) | 4.46156e21 | 1.64049 | ||||||||
\(722\) | −1.52489e20 | −0.0554893 | ||||||||
\(723\) | −7.99143e20 | −0.287798 | ||||||||
\(724\) | −2.21918e20 | −0.0790959 | ||||||||
\(725\) | 9.74921e19 | 0.0343902 | ||||||||
\(726\) | −6.65770e21 | −2.32434 | ||||||||
\(727\) | −2.20533e21 | −0.762019 | −0.381009 | − | 0.924571i | \(-0.624423\pi\) | ||||
−0.381009 | + | 0.924571i | \(0.624423\pi\) | |||||||
\(728\) | −1.52851e21 | −0.522735 | ||||||||
\(729\) | −4.55502e21 | −1.54182 | ||||||||
\(730\) | −5.76496e20 | −0.193141 | ||||||||
\(731\) | −3.19845e20 | −0.106062 | ||||||||
\(732\) | −1.48713e21 | −0.488106 | ||||||||
\(733\) | −1.83621e21 | −0.596544 | −0.298272 | − | 0.954481i | \(-0.596410\pi\) | ||||
−0.298272 | + | 0.954481i | \(0.596410\pi\) | |||||||
\(734\) | −2.43085e21 | −0.781697 | ||||||||
\(735\) | −8.27388e20 | −0.263363 | ||||||||
\(736\) | −9.49622e20 | −0.299204 | ||||||||
\(737\) | 7.41575e21 | 2.31286 | ||||||||
\(738\) | 2.26749e21 | 0.700040 | ||||||||
\(739\) | −1.19943e21 | −0.366556 | −0.183278 | − | 0.983061i | \(-0.558671\pi\) | ||||
−0.183278 | + | 0.983061i | \(0.558671\pi\) | |||||||
\(740\) | 8.77978e20 | 0.265611 | ||||||||
\(741\) | −6.18705e21 | −1.85288 | ||||||||
\(742\) | −3.65156e21 | −1.08255 | ||||||||
\(743\) | 5.61963e20 | 0.164927 | 0.0824635 | − | 0.996594i | \(-0.473721\pi\) | ||||
0.0824635 | + | 0.996594i | \(0.473721\pi\) | |||||||
\(744\) | −3.40829e19 | −0.00990236 | ||||||||
\(745\) | 1.22790e20 | 0.0353176 | ||||||||
\(746\) | −3.31985e20 | −0.0945315 | ||||||||
\(747\) | −5.99399e21 | −1.68971 | ||||||||
\(748\) | 1.45738e21 | 0.406734 | ||||||||
\(749\) | −6.13021e21 | −1.69380 | ||||||||
\(750\) | −3.55016e20 | −0.0971154 | ||||||||
\(751\) | −6.45789e21 | −1.74901 | −0.874503 | − | 0.485020i | \(-0.838812\pi\) | ||||
−0.874503 | + | 0.485020i | \(0.838812\pi\) | |||||||
\(752\) | −1.15401e20 | −0.0309441 | ||||||||
\(753\) | 3.75283e21 | 0.996314 | ||||||||
\(754\) | 5.81446e20 | 0.152835 | ||||||||
\(755\) | −5.17676e20 | −0.134727 | ||||||||
\(756\) | 1.25411e21 | 0.323164 | ||||||||
\(757\) | −2.17355e21 | −0.554561 | −0.277281 | − | 0.960789i | \(-0.589433\pi\) | ||||
−0.277281 | + | 0.960789i | \(0.589433\pi\) | |||||||
\(758\) | −3.45087e21 | −0.871786 | ||||||||
\(759\) | 1.84131e22 | 4.60589 | ||||||||
\(760\) | 6.12810e20 | 0.151783 | ||||||||
\(761\) | 6.38965e21 | 1.56708 | 0.783542 | − | 0.621339i | \(-0.213411\pi\) | ||||
0.783542 | + | 0.621339i | \(0.213411\pi\) | |||||||
\(762\) | 6.32461e21 | 1.53593 | ||||||||
\(763\) | −5.76410e21 | −1.38611 | ||||||||
\(764\) | 2.63345e21 | 0.627084 | ||||||||
\(765\) | 1.18210e21 | 0.278737 | ||||||||
\(766\) | 9.23317e19 | 0.0215593 | ||||||||
\(767\) | −8.49016e21 | −1.96314 | ||||||||
\(768\) | −4.19129e20 | −0.0959706 | ||||||||
\(769\) | −4.63352e21 | −1.05066 | −0.525331 | − | 0.850898i | \(-0.676059\pi\) | ||||
−0.525331 | + | 0.850898i | \(0.676059\pi\) | |||||||
\(770\) | −2.93552e21 | −0.659182 | ||||||||
\(771\) | 7.10876e21 | 1.58083 | ||||||||
\(772\) | 1.10293e21 | 0.242895 | ||||||||
\(773\) | −2.62638e21 | −0.572811 | −0.286406 | − | 0.958108i | \(-0.592460\pi\) | ||||
−0.286406 | + | 0.958108i | \(0.592460\pi\) | |||||||
\(774\) | −1.02713e21 | −0.221855 | ||||||||
\(775\) | 1.70537e19 | 0.00364801 | ||||||||
\(776\) | −3.82178e20 | −0.0809660 | ||||||||
\(777\) | 1.02251e22 | 2.14541 | ||||||||
\(778\) | 2.02593e21 | 0.420996 | ||||||||
\(779\) | 3.40071e21 | 0.699905 | ||||||||
\(780\) | −2.11733e21 | −0.431597 | ||||||||
\(781\) | 1.58478e22 | 3.19954 | ||||||||
\(782\) | −2.74729e21 | −0.549357 | ||||||||
\(783\) | −4.77066e20 | −0.0944854 | ||||||||
\(784\) | 4.88755e20 | 0.0958784 | ||||||||
\(785\) | −2.68269e21 | −0.521252 | ||||||||
\(786\) | −2.57691e21 | −0.495940 | ||||||||
\(787\) | −9.12707e21 | −1.73989 | −0.869944 | − | 0.493151i | \(-0.835845\pi\) | ||||
−0.869944 | + | 0.493151i | \(0.835845\pi\) | |||||||
\(788\) | 1.55057e21 | 0.292782 | ||||||||
\(789\) | −9.18799e21 | −1.71847 | ||||||||
\(790\) | 1.85835e21 | 0.344290 | ||||||||
\(791\) | 1.27875e21 | 0.234673 | ||||||||
\(792\) | 4.68015e21 | 0.850787 | ||||||||
\(793\) | 4.43782e21 | 0.799137 | ||||||||
\(794\) | −2.49225e21 | −0.444567 | ||||||||
\(795\) | −5.05824e21 | −0.893812 | ||||||||
\(796\) | 3.54845e20 | 0.0621141 | ||||||||
\(797\) | −6.57555e21 | −1.14024 | −0.570118 | − | 0.821563i | \(-0.693102\pi\) | ||||
−0.570118 | + | 0.821563i | \(0.693102\pi\) | |||||||
\(798\) | 7.13691e21 | 1.22600 | ||||||||
\(799\) | −3.33861e20 | −0.0568152 | ||||||||
\(800\) | 2.09715e20 | 0.0353553 | ||||||||
\(801\) | −3.54049e21 | −0.591317 | ||||||||
\(802\) | 1.34151e21 | 0.221966 | ||||||||
\(803\) | −6.60320e21 | −1.08240 | ||||||||
\(804\) | −6.16999e21 | −1.00199 | ||||||||
\(805\) | 5.53373e21 | 0.890326 | ||||||||
\(806\) | 1.01709e20 | 0.0162123 | ||||||||
\(807\) | 1.07259e22 | 1.69388 | ||||||||
\(808\) | −1.44481e21 | −0.226061 | ||||||||
\(809\) | 1.80991e21 | 0.280572 | 0.140286 | − | 0.990111i | \(-0.455198\pi\) | ||||
0.140286 | + | 0.990111i | \(0.455198\pi\) | |||||||
\(810\) | −1.05847e21 | −0.162570 | ||||||||
\(811\) | 3.19559e21 | 0.486290 | 0.243145 | − | 0.969990i | \(-0.421821\pi\) | ||||
0.243145 | + | 0.969990i | \(0.421821\pi\) | |||||||
\(812\) | −6.70712e20 | −0.101127 | ||||||||
\(813\) | 1.07855e22 | 1.61125 | ||||||||
\(814\) | 1.00564e22 | 1.48854 | ||||||||
\(815\) | −3.97312e21 | −0.582707 | ||||||||
\(816\) | −1.21256e21 | −0.176208 | ||||||||
\(817\) | −1.54046e21 | −0.221812 | ||||||||
\(818\) | 9.30877e19 | 0.0132814 | ||||||||
\(819\) | −1.42006e22 | −2.00761 | ||||||||
\(820\) | 1.16379e21 | 0.163031 | ||||||||
\(821\) | −8.98711e21 | −1.24752 | −0.623758 | − | 0.781617i | \(-0.714395\pi\) | ||||
−0.623758 | + | 0.781617i | \(0.714395\pi\) | |||||||
\(822\) | −6.29804e20 | −0.0866297 | ||||||||
\(823\) | 5.82230e21 | 0.793589 | 0.396795 | − | 0.917907i | \(-0.370123\pi\) | ||||
0.396795 | + | 0.917907i | \(0.370123\pi\) | |||||||
\(824\) | −3.65081e21 | −0.493101 | ||||||||
\(825\) | −4.06636e21 | −0.544254 | ||||||||
\(826\) | 9.79361e21 | 1.29895 | ||||||||
\(827\) | 1.32555e22 | 1.74223 | 0.871113 | − | 0.491083i | \(-0.163399\pi\) | ||||
0.871113 | + | 0.491083i | \(0.163399\pi\) | |||||||
\(828\) | −8.82251e21 | −1.14912 | ||||||||
\(829\) | −1.11966e22 | −1.44520 | −0.722598 | − | 0.691269i | \(-0.757052\pi\) | ||||
−0.722598 | + | 0.691269i | \(0.757052\pi\) | |||||||
\(830\) | −3.07642e21 | −0.393514 | ||||||||
\(831\) | −1.32695e22 | −1.68208 | ||||||||
\(832\) | 1.25075e21 | 0.157125 | ||||||||
\(833\) | 1.41399e21 | 0.176039 | ||||||||
\(834\) | 7.48812e21 | 0.923906 | ||||||||
\(835\) | 2.52750e21 | 0.309060 | ||||||||
\(836\) | 7.01915e21 | 0.850623 | ||||||||
\(837\) | −8.34502e19 | −0.0100227 | ||||||||
\(838\) | 6.27096e21 | 0.746455 | ||||||||
\(839\) | −1.04808e21 | −0.123646 | −0.0618228 | − | 0.998087i | \(-0.519691\pi\) | ||||
−0.0618228 | + | 0.998087i | \(0.519691\pi\) | |||||||
\(840\) | 2.44239e21 | 0.285575 | ||||||||
\(841\) | −8.37405e21 | −0.970433 | ||||||||
\(842\) | −5.40350e20 | −0.0620633 | ||||||||
\(843\) | 1.37847e22 | 1.56925 | ||||||||
\(844\) | −6.19322e21 | −0.698792 | ||||||||
\(845\) | 2.31955e21 | 0.259405 | ||||||||
\(846\) | −1.07214e21 | −0.118843 | ||||||||
\(847\) | −2.29179e22 | −2.51796 | ||||||||
\(848\) | 2.98801e21 | 0.325397 | ||||||||
\(849\) | −1.59452e22 | −1.72116 | ||||||||
\(850\) | 6.06714e20 | 0.0649146 | ||||||||
\(851\) | −1.89572e22 | −2.01050 | ||||||||
\(852\) | −1.31856e22 | −1.38612 | ||||||||
\(853\) | 9.43153e21 | 0.982799 | 0.491399 | − | 0.870934i | \(-0.336486\pi\) | ||||
0.491399 | + | 0.870934i | \(0.336486\pi\) | |||||||
\(854\) | −5.11914e21 | −0.528765 | ||||||||
\(855\) | 5.69334e21 | 0.582936 | ||||||||
\(856\) | 5.01624e21 | 0.509125 | ||||||||
\(857\) | 1.23081e22 | 1.23832 | 0.619161 | − | 0.785264i | \(-0.287473\pi\) | ||||
0.619161 | + | 0.785264i | \(0.287473\pi\) | |||||||
\(858\) | −2.42519e22 | −2.41875 | ||||||||
\(859\) | 1.76754e22 | 1.74752 | 0.873759 | − | 0.486360i | \(-0.161675\pi\) | ||||
0.873759 | + | 0.486360i | \(0.161675\pi\) | |||||||
\(860\) | −5.27175e20 | −0.0516674 | ||||||||
\(861\) | 1.35537e22 | 1.31685 | ||||||||
\(862\) | 2.06414e20 | 0.0198808 | ||||||||
\(863\) | 4.26192e21 | 0.406934 | 0.203467 | − | 0.979082i | \(-0.434779\pi\) | ||||
0.203467 | + | 0.979082i | \(0.434779\pi\) | |||||||
\(864\) | −1.02622e21 | −0.0971372 | ||||||||
\(865\) | −8.00838e20 | −0.0751491 | ||||||||
\(866\) | −7.79302e21 | −0.724973 | ||||||||
\(867\) | 1.31415e22 | 1.21200 | ||||||||
\(868\) | −1.17324e20 | −0.0107272 | ||||||||
\(869\) | 2.12856e22 | 1.92947 | ||||||||
\(870\) | −9.29088e20 | −0.0834954 | ||||||||
\(871\) | 1.84122e22 | 1.64048 | ||||||||
\(872\) | 4.71666e21 | 0.416640 | ||||||||
\(873\) | −3.55064e21 | −0.310957 | ||||||||
\(874\) | −1.32317e22 | −1.14890 | ||||||||
\(875\) | −1.22207e21 | −0.105205 | ||||||||
\(876\) | 5.49394e21 | 0.468924 | ||||||||
\(877\) | −3.22309e21 | −0.272757 | −0.136378 | − | 0.990657i | \(-0.543546\pi\) | ||||
−0.136378 | + | 0.990657i | \(0.543546\pi\) | |||||||
\(878\) | 7.44363e21 | 0.624562 | ||||||||
\(879\) | −4.13051e21 | −0.343627 | ||||||||
\(880\) | 2.40209e21 | 0.198138 | ||||||||
\(881\) | −1.48852e22 | −1.21740 | −0.608702 | − | 0.793399i | \(-0.708310\pi\) | ||||
−0.608702 | + | 0.793399i | \(0.708310\pi\) | |||||||
\(882\) | 4.54080e21 | 0.368229 | ||||||||
\(883\) | −8.42699e21 | −0.677590 | −0.338795 | − | 0.940860i | \(-0.610019\pi\) | ||||
−0.338795 | + | 0.940860i | \(0.610019\pi\) | |||||||
\(884\) | 3.61846e21 | 0.288491 | ||||||||
\(885\) | 1.35664e22 | 1.07248 | ||||||||
\(886\) | 1.35974e22 | 1.06587 | ||||||||
\(887\) | −1.54780e22 | −1.20306 | −0.601529 | − | 0.798851i | \(-0.705442\pi\) | ||||
−0.601529 | + | 0.798851i | \(0.705442\pi\) | |||||||
\(888\) | −8.36703e21 | −0.644873 | ||||||||
\(889\) | 2.17712e22 | 1.66387 | ||||||||
\(890\) | −1.81716e21 | −0.137711 | ||||||||
\(891\) | −1.21237e22 | −0.911074 | ||||||||
\(892\) | 1.15688e21 | 0.0862090 | ||||||||
\(893\) | −1.60797e21 | −0.118820 | ||||||||
\(894\) | −1.17018e21 | −0.0857471 | ||||||||
\(895\) | −8.14764e21 | −0.592051 | ||||||||
\(896\) | −1.44277e21 | −0.103965 | ||||||||
\(897\) | 4.57171e22 | 3.26690 | ||||||||
\(898\) | −1.50701e22 | −1.06793 | ||||||||
\(899\) | 4.46301e19 | 0.00313639 | ||||||||
\(900\) | 1.94837e21 | 0.135785 | ||||||||
\(901\) | 8.64442e21 | 0.597448 | ||||||||
\(902\) | 1.33301e22 | 0.913659 | ||||||||
\(903\) | −6.13960e21 | −0.417332 | ||||||||
\(904\) | −1.04638e21 | −0.0705384 | ||||||||
\(905\) | −1.05819e21 | −0.0707455 | ||||||||
\(906\) | 4.93339e21 | 0.327103 | ||||||||
\(907\) | −2.19678e22 | −1.44455 | −0.722275 | − | 0.691606i | \(-0.756903\pi\) | ||||
−0.722275 | + | 0.691606i | \(0.756903\pi\) | |||||||
\(908\) | 1.14633e22 | 0.747594 | ||||||||
\(909\) | −1.34231e22 | −0.868207 | ||||||||
\(910\) | −7.28848e21 | −0.467549 | ||||||||
\(911\) | 1.84376e22 | 1.17305 | 0.586525 | − | 0.809931i | \(-0.300496\pi\) | ||||
0.586525 | + | 0.809931i | \(0.300496\pi\) | |||||||
\(912\) | −5.84001e21 | −0.368512 | ||||||||
\(913\) | −3.52374e22 | −2.20533 | ||||||||
\(914\) | 1.48071e22 | 0.919123 | ||||||||
\(915\) | −7.09117e21 | −0.436576 | ||||||||
\(916\) | 1.25851e21 | 0.0768495 | ||||||||
\(917\) | −8.87050e21 | −0.537252 | ||||||||
\(918\) | −2.96888e21 | −0.178350 | ||||||||
\(919\) | −1.29719e22 | −0.772927 | −0.386464 | − | 0.922305i | \(-0.626304\pi\) | ||||
−0.386464 | + | 0.922305i | \(0.626304\pi\) | |||||||
\(920\) | −4.52815e21 | −0.267616 | ||||||||
\(921\) | −2.27467e22 | −1.33343 | ||||||||
\(922\) | −1.03007e22 | −0.598944 | ||||||||
\(923\) | 3.93479e22 | 2.26939 | ||||||||
\(924\) | 2.79752e22 | 1.60042 | ||||||||
\(925\) | 4.18653e21 | 0.237570 | ||||||||
\(926\) | −1.18995e22 | −0.669803 | ||||||||
\(927\) | −3.39180e22 | −1.89379 | ||||||||
\(928\) | 5.48831e20 | 0.0303969 | ||||||||
\(929\) | 2.38798e22 | 1.31194 | 0.655969 | − | 0.754788i | \(-0.272260\pi\) | ||||
0.655969 | + | 0.754788i | \(0.272260\pi\) | |||||||
\(930\) | −1.62520e20 | −0.00885694 | ||||||||
\(931\) | 6.81016e21 | 0.368158 | ||||||||
\(932\) | −1.14957e22 | −0.616477 | ||||||||
\(933\) | −2.28353e22 | −1.21477 | ||||||||
\(934\) | 1.75977e21 | 0.0928655 | ||||||||
\(935\) | 6.94933e21 | 0.363794 | ||||||||
\(936\) | 1.16201e22 | 0.603451 | ||||||||
\(937\) | −1.55876e22 | −0.803033 | −0.401516 | − | 0.915852i | \(-0.631517\pi\) | ||||
−0.401516 | + | 0.915852i | \(0.631517\pi\) | |||||||
\(938\) | −2.12390e22 | −1.08546 | ||||||||
\(939\) | 4.10619e22 | 2.08184 | ||||||||
\(940\) | −5.50277e20 | −0.0276772 | ||||||||
\(941\) | −1.19037e21 | −0.0593964 | −0.0296982 | − | 0.999559i | \(-0.509455\pi\) | ||||
−0.0296982 | + | 0.999559i | \(0.509455\pi\) | |||||||
\(942\) | 2.55657e22 | 1.26554 | ||||||||
\(943\) | −2.51284e22 | −1.23404 | ||||||||
\(944\) | −8.01393e21 | −0.390441 | ||||||||
\(945\) | 5.98007e21 | 0.289046 | ||||||||
\(946\) | −6.03829e21 | −0.289554 | ||||||||
\(947\) | −1.18652e22 | −0.564482 | −0.282241 | − | 0.959343i | \(-0.591078\pi\) | ||||
−0.282241 | + | 0.959343i | \(0.591078\pi\) | |||||||
\(948\) | −1.77098e22 | −0.835896 | ||||||||
\(949\) | −1.63948e22 | −0.767732 | ||||||||
\(950\) | 2.92211e21 | 0.135759 | ||||||||
\(951\) | −3.68297e22 | −1.69763 | ||||||||
\(952\) | −4.17399e21 | −0.190886 | ||||||||
\(953\) | −7.68749e21 | −0.348809 | −0.174404 | − | 0.984674i | \(-0.555800\pi\) | ||||
−0.174404 | + | 0.984674i | \(0.555800\pi\) | |||||||
\(954\) | 2.77602e22 | 1.24971 | ||||||||
\(955\) | 1.25573e22 | 0.560881 | ||||||||
\(956\) | −7.89970e21 | −0.350087 | ||||||||
\(957\) | −1.06418e22 | −0.467925 | ||||||||
\(958\) | 8.57533e21 | 0.374119 | ||||||||
\(959\) | −2.16798e21 | −0.0938459 | ||||||||
\(960\) | −1.99856e21 | −0.0858387 | ||||||||
\(961\) | −2.34575e22 | −0.999667 | ||||||||
\(962\) | 2.49686e22 | 1.05580 | ||||||||
\(963\) | 4.66036e22 | 1.95534 | ||||||||
\(964\) | 2.25101e21 | 0.0937129 | ||||||||
\(965\) | 5.25917e21 | 0.217251 | ||||||||
\(966\) | −5.27358e22 | −2.16161 | ||||||||
\(967\) | 2.96436e22 | 1.20568 | 0.602840 | − | 0.797862i | \(-0.294036\pi\) | ||||
0.602840 | + | 0.797862i | \(0.294036\pi\) | |||||||
\(968\) | 1.87533e22 | 0.756853 | ||||||||
\(969\) | −1.68954e22 | −0.676611 | ||||||||
\(970\) | −1.82237e21 | −0.0724182 | ||||||||
\(971\) | 3.79674e22 | 1.49715 | 0.748577 | − | 0.663047i | \(-0.230737\pi\) | ||||
0.748577 | + | 0.663047i | \(0.230737\pi\) | |||||||
\(972\) | 1.71085e22 | 0.669447 | ||||||||
\(973\) | 2.57764e22 | 1.00087 | ||||||||
\(974\) | −2.31414e21 | −0.0891655 | ||||||||
\(975\) | −1.00962e22 | −0.386032 | ||||||||
\(976\) | 4.18890e21 | 0.158937 | ||||||||
\(977\) | −1.73025e21 | −0.0651479 | −0.0325739 | − | 0.999469i | \(-0.510370\pi\) | ||||
−0.0325739 | + | 0.999469i | \(0.510370\pi\) | |||||||
\(978\) | 3.78634e22 | 1.41474 | ||||||||
\(979\) | −2.08138e22 | −0.771758 | ||||||||
\(980\) | 2.33057e21 | 0.0857563 | ||||||||
\(981\) | 4.38203e22 | 1.60014 | ||||||||
\(982\) | −1.38434e22 | −0.501657 | ||||||||
\(983\) | 2.72751e22 | 0.980878 | 0.490439 | − | 0.871476i | \(-0.336836\pi\) | ||||
0.490439 | + | 0.871476i | \(0.336836\pi\) | |||||||
\(984\) | −1.10908e22 | −0.395821 | ||||||||
\(985\) | 7.39370e21 | 0.261873 | ||||||||
\(986\) | 1.58779e21 | 0.0558106 | ||||||||
\(987\) | −6.40864e21 | −0.223556 | ||||||||
\(988\) | 1.74275e22 | 0.603335 | ||||||||
\(989\) | 1.13827e22 | 0.391088 | ||||||||
\(990\) | 2.23167e22 | 0.760967 | ||||||||
\(991\) | 4.94891e22 | 1.67478 | 0.837389 | − | 0.546607i | \(-0.184081\pi\) | ||||
0.837389 | + | 0.546607i | \(0.184081\pi\) | |||||||
\(992\) | 9.60038e19 | 0.00322441 | ||||||||
\(993\) | −3.66202e22 | −1.22068 | ||||||||
\(994\) | −4.53887e22 | −1.50159 | ||||||||
\(995\) | 1.69203e21 | 0.0555565 | ||||||||
\(996\) | 2.93179e22 | 0.955406 | ||||||||
\(997\) | 6.46309e21 | 0.209039 | 0.104519 | − | 0.994523i | \(-0.466670\pi\) | ||||
0.104519 | + | 0.994523i | \(0.466670\pi\) | |||||||
\(998\) | 8.85861e21 | 0.284372 | ||||||||
\(999\) | −2.04863e22 | −0.652712 |
(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 | 10.16.a.d.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 90.16.a.j.1.1 | 2 | |||
4.3 | odd | 2 | 80.16.a.f.1.2 | 2 | |||
5.2 | odd | 4 | 50.16.b.e.49.4 | 4 | |||
5.3 | odd | 4 | 50.16.b.e.49.1 | 4 | |||
5.4 | even | 2 | 50.16.a.f.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.16.a.d.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
50.16.a.f.1.2 | 2 | 5.4 | even | 2 | |||
50.16.b.e.49.1 | 4 | 5.3 | odd | 4 | |||
50.16.b.e.49.4 | 4 | 5.2 | odd | 4 | |||
80.16.a.f.1.2 | 2 | 4.3 | odd | 2 | |||
90.16.a.j.1.1 | 2 | 3.2 | odd | 2 |