Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [64,20,Mod(1,64)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(64, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 20, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("64.1");
S:= CuspForms(chi, 20);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 64 = 2^{6} \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 64.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: | \(146.442685796\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{1453}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 363 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{7}\cdot 3\cdot 5 \) |
Twist minimal: | no (minimal twist has level 8) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(19.5591\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 64.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −50549.5 | −1.48274 | −0.741370 | − | 0.671096i | \(-0.765824\pi\) | ||||
−0.741370 | + | 0.671096i | \(0.765824\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.22342e6 | −0.509105 | −0.254552 | − | 0.967059i | \(-0.581928\pi\) | ||||
−0.254552 | + | 0.967059i | \(0.581928\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.60989e8 | −1.50787 | −0.753934 | − | 0.656950i | \(-0.771846\pi\) | ||||
−0.753934 | + | 0.656950i | \(0.771846\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.39299e9 | 1.19852 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.17593e10 | −1.50367 | −0.751835 | − | 0.659352i | \(-0.770831\pi\) | ||||
−0.751835 | + | 0.659352i | \(0.770831\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.44117e9 | 0.0638464 | 0.0319232 | − | 0.999490i | \(-0.489837\pi\) | ||||
0.0319232 | + | 0.999490i | \(0.489837\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.12393e11 | 0.754870 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.98454e11 | 1.22396 | 0.611978 | − | 0.790874i | \(-0.290374\pi\) | ||||
0.611978 | + | 0.790874i | \(0.290374\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.51671e12 | −1.78927 | −0.894633 | − | 0.446802i | \(-0.852563\pi\) | ||||
−0.894633 | + | 0.446802i | \(0.852563\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.13789e12 | 2.23578 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.35737e11 | 0.0735975 | 0.0367988 | − | 0.999323i | \(-0.488284\pi\) | ||||
0.0367988 | + | 0.999323i | \(0.488284\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.41299e13 | −0.740812 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.16633e13 | −0.294351 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.78062e13 | 0.611932 | 0.305966 | − | 0.952043i | \(-0.401021\pi\) | ||||
0.305966 | + | 0.952043i | \(0.401021\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.03104e14 | 1.37970 | 0.689848 | − | 0.723954i | \(-0.257677\pi\) | ||||
0.689848 | + | 0.723954i | \(0.257677\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.94429e14 | 2.22955 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.57946e14 | 0.767664 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.95266e14 | −1.13249 | −0.566246 | − | 0.824236i | \(-0.691605\pi\) | ||||
−0.566246 | + | 0.824236i | \(0.691605\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.23400e14 | −0.0946676 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.61047e14 | −0.219937 | −0.109969 | − | 0.993935i | \(-0.535075\pi\) | ||||
−0.109969 | + | 0.993935i | \(0.535075\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.21551e15 | −0.672238 | −0.336119 | − | 0.941820i | \(-0.609114\pi\) | ||||
−0.336119 | + | 0.941820i | \(0.609114\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.09721e15 | −0.610171 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.04653e16 | 1.36403 | 0.682013 | − | 0.731340i | \(-0.261105\pi\) | ||||
0.682013 | + | 0.731340i | \(0.261105\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.45184e16 | 1.27367 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.02516e16 | −1.81481 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.43716e16 | 1.43080 | 0.715400 | − | 0.698715i | \(-0.246244\pi\) | ||||
0.715400 | + | 0.698715i | \(0.246244\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.61460e16 | 0.765525 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.27219e17 | 2.65302 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.13126e16 | 1.37226 | 0.686130 | − | 0.727479i | \(-0.259308\pi\) | ||||
0.686130 | + | 0.727479i | \(0.259308\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.19474e17 | 1.30809 | 0.654047 | − | 0.756454i | \(-0.273070\pi\) | ||||
0.654047 | + | 0.756454i | \(0.273070\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.24256e17 | −1.80721 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.42776e15 | −0.0325045 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.98838e17 | −0.892872 | −0.446436 | − | 0.894816i | \(-0.647307\pi\) | ||||
−0.446436 | + | 0.894816i | \(0.647307\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.21362e16 | −0.109126 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.38863e17 | 0.359446 | 0.179723 | − | 0.983717i | \(-0.442480\pi\) | ||||
0.179723 | + | 0.983717i | \(0.442480\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.63434e16 | −0.0722533 | −0.0361267 | − | 0.999347i | \(-0.511502\pi\) | ||||
−0.0361267 | + | 0.999347i | \(0.511502\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.14258e17 | 1.09843 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.89312e18 | 2.26734 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.36121e17 | 0.409402 | 0.204701 | − | 0.978825i | \(-0.434378\pi\) | ||||
0.204701 | + | 0.978825i | \(0.434378\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.02945e18 | −0.762073 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.52389e17 | 0.265626 | 0.132813 | − | 0.991141i | \(-0.457599\pi\) | ||||
0.132813 | + | 0.991141i | \(0.457599\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.33062e18 | −0.623123 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.41658e18 | −0.907335 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.30628e18 | 1.00031 | 0.500154 | − | 0.865936i | \(-0.333277\pi\) | ||||
0.500154 | + | 0.865936i | \(0.333277\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.93001e17 | −0.0962720 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.02668e19 | −2.04573 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.59572e18 | 0.910924 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.03558e18 | −0.806097 | −0.403049 | − | 0.915179i | \(-0.632049\pi\) | ||||
−0.403049 | + | 0.915179i | \(0.632049\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.63807e19 | −1.80217 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.09027e18 | −0.827034 | −0.413517 | − | 0.910496i | \(-0.635700\pi\) | ||||
−0.413517 | + | 0.910496i | \(0.635700\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.16083e19 | −0.876628 | −0.438314 | − | 0.898822i | \(-0.644424\pi\) | ||||
−0.438314 | + | 0.898822i | \(0.644424\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.80940e19 | −1.13825 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.99623e18 | 0.525642 | 0.262821 | − | 0.964845i | \(-0.415347\pi\) | ||||
0.262821 | + | 0.964845i | \(0.415347\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.34179e18 | 0.191477 | 0.0957385 | − | 0.995407i | \(-0.469479\pi\) | ||||
0.0957385 | + | 0.995407i | \(0.469479\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.52552e19 | 1.67919 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.09237e18 | −0.284729 | −0.142365 | − | 0.989814i | \(-0.545471\pi\) | ||||
−0.142365 | + | 0.989814i | \(0.545471\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.41351e18 | −0.0374689 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.40053e18 | 0.0765210 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.63443e19 | −1.84557 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.71229e19 | 1.26102 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.33057e19 | 0.326110 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.38252e19 | 0.886256 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.31085e19 | −0.961289 | −0.480645 | − | 0.876915i | \(-0.659597\pi\) | ||||
−0.480645 | + | 0.876915i | \(0.659597\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.11993e20 | 0.996753 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.87606e19 | 0.144268 | 0.0721340 | − | 0.997395i | \(-0.477019\pi\) | ||||
0.0721340 | + | 0.997395i | \(0.477019\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.05162e20 | 2.69798 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.59324e19 | 0.149855 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.84318e20 | −0.926240 | −0.463120 | − | 0.886296i | \(-0.653270\pi\) | ||||
−0.463120 | + | 0.886296i | \(0.653270\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.59539e20 | −0.698597 | −0.349299 | − | 0.937011i | \(-0.613580\pi\) | ||||
−0.349299 | + | 0.937011i | \(0.613580\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.29017e20 | −2.02250 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.87065e19 | −0.0960038 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.06293e20 | −0.311537 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.33899e20 | −1.88852 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.21712e20 | −0.728111 | −0.364055 | − | 0.931377i | \(-0.618608\pi\) | ||||
−0.364055 | + | 0.931377i | \(0.618608\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.55272e20 | 0.309607 | 0.154804 | − | 0.987945i | \(-0.450526\pi\) | ||||
0.154804 | + | 0.987945i | \(0.450526\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.33641e20 | 1.46693 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.51587e20 | −0.702410 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.54202e20 | 0.625464 | 0.312732 | − | 0.949841i | \(-0.398756\pi\) | ||||
0.312732 | + | 0.949841i | \(0.398756\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.73747e21 | −2.12150 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.02346e20 | −0.110975 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.72395e20 | 0.744830 | 0.372415 | − | 0.928066i | \(-0.378530\pi\) | ||||
0.372415 | + | 0.928066i | \(0.378530\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.32167e21 | −1.13508 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.02583e21 | −0.785725 | −0.392862 | − | 0.919597i | \(-0.628515\pi\) | ||||
−0.392862 | + | 0.919597i | \(0.628515\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.45596e21 | −0.995924 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.50576e21 | −2.14447 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.92487e20 | −0.379292 | −0.189646 | − | 0.981853i | \(-0.560734\pi\) | ||||
−0.189646 | + | 0.981853i | \(0.560734\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.27475e21 | 1.11705 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.61581e21 | −2.03471 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.42385e21 | 0.960290 | 0.480145 | − | 0.877189i | \(-0.340584\pi\) | ||||
0.480145 | + | 0.877189i | \(0.340584\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.72457e20 | 0.346676 | 0.173338 | − | 0.984862i | \(-0.444545\pi\) | ||||
0.173338 | + | 0.984862i | \(0.444545\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.03934e21 | −1.93956 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.99056e21 | 0.576558 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.03742e21 | −1.84043 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.87765e21 | 0.443842 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.76037e21 | −1.44595 | −0.722975 | − | 0.690874i | \(-0.757226\pi\) | ||||
−0.722975 | + | 0.690874i | \(0.757226\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.53000e21 | 0.296413 | 0.148206 | − | 0.988956i | \(-0.452650\pi\) | ||||
0.148206 | + | 0.988956i | \(0.452650\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.74371e20 | 0.0481957 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.79113e21 | 1.08271 | 0.541356 | − | 0.840793i | \(-0.317911\pi\) | ||||
0.541356 | + | 0.840793i | \(0.317911\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.45465e21 | −1.36943 | −0.684717 | − | 0.728809i | \(-0.740074\pi\) | ||||
−0.684717 | + | 0.728809i | \(0.740074\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.00512e22 | 1.32390 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.69624e21 | −0.922713 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.02510e21 | 0.111971 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.85577e20 | 0.0882080 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.95949e22 | 2.69046 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.14995e22 | −1.78544 | −0.892721 | − | 0.450610i | \(-0.851207\pi\) | ||||
−0.892721 | + | 0.450610i | \(0.851207\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.01948e21 | −0.532965 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.92601e21 | 0.342239 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.26975e22 | −2.08040 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.83714e21 | 0.107133 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.46093e21 | 0.0781452 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.89942e22 | 1.91471 | 0.957356 | − | 0.288910i | \(-0.0932927\pi\) | ||||
0.957356 | + | 0.288910i | \(0.0932927\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.96828e22 | −0.887877 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.69117e21 | 0.0701361 | 0.0350680 | − | 0.999385i | \(-0.488835\pi\) | ||||
0.0350680 | + | 0.999385i | \(0.488835\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.34630e21 | −0.127681 | −0.0638407 | − | 0.997960i | \(-0.520335\pi\) | ||||
−0.0638407 | + | 0.997960i | \(0.520335\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.56962e22 | −3.36187 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.27609e22 | 0.413049 | 0.206524 | − | 0.978441i | \(-0.433785\pi\) | ||||
0.206524 | + | 0.978441i | \(0.433785\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.32688e22 | −0.694433 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.20457e22 | −0.607037 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.15938e21 | 0.232855 | 0.116428 | − | 0.993199i | \(-0.462856\pi\) | ||||
0.116428 | + | 0.993199i | \(0.462856\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.54596e22 | −1.06774 | −0.533868 | − | 0.845568i | \(-0.679262\pi\) | ||||
−0.533868 | + | 0.845568i | \(0.679262\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.55938e22 | 1.42431 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.22806e22 | −0.648431 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.14373e21 | −0.114238 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.28680e22 | −0.393854 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.68788e22 | −0.588677 | −0.294338 | − | 0.955701i | \(-0.595099\pi\) | ||||
−0.294338 | + | 0.955701i | \(0.595099\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.47585e21 | −0.110666 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.72621e22 | 0.923929 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.84420e22 | 0.617813 | 0.308907 | − | 0.951092i | \(-0.400037\pi\) | ||||
0.308907 | + | 0.951092i | \(0.400037\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.44128e23 | 1.70765 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.65936e22 | 0.733411 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.84645e22 | −0.701271 | −0.350635 | − | 0.936512i | \(-0.614034\pi\) | ||||
−0.350635 | + | 0.936512i | \(0.614034\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.64226e22 | −0.728427 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.67131e23 | −1.48320 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.17729e23 | 1.79999 | 0.899995 | − | 0.435900i | \(-0.143570\pi\) | ||||
0.899995 | + | 0.435900i | \(0.143570\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.88487e23 | 1.45236 | 0.726180 | − | 0.687505i | \(-0.241294\pi\) | ||||
0.726180 | + | 0.687505i | \(0.241294\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.98660e22 | 0.142746 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.66158e23 | 1.11394 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.07964e23 | −1.30146 | −0.650729 | − | 0.759310i | \(-0.725537\pi\) | ||||
−0.650729 | + | 0.759310i | \(0.725537\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.82923e23 | 1.65359 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.33849e23 | 1.82322 | 0.911612 | − | 0.411052i | \(-0.134838\pi\) | ||||
0.911612 | + | 0.411052i | \(0.134838\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.26611e22 | −0.115694 | −0.0578470 | − | 0.998325i | \(-0.518424\pi\) | ||||
−0.0578470 | + | 0.998325i | \(0.518424\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.82861e23 | −1.35066 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.42233e22 | 0.331636 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.19075e23 | 0.498070 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.05095e23 | 1.19523 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.85421e23 | 0.680639 | 0.340319 | − | 0.940310i | \(-0.389465\pi\) | ||||
0.340319 | + | 0.940310i | \(0.389465\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.03027e23 | −0.698625 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.37152e23 | 0.442606 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.55194e21 | 0.00469894 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.56671e23 | 1.01365 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.59508e23 | 1.22628 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.65641e23 | −0.665958 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.93628e23 | 1.86983 | 0.934916 | − | 0.354870i | \(-0.115475\pi\) | ||||
0.934916 | + | 0.354870i | \(0.115475\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.86794e23 | 1.29981 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.20440e23 | 1.08429 | 0.542147 | − | 0.840284i | \(-0.317612\pi\) | ||||
0.542147 | + | 0.840284i | \(0.317612\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.65345e23 | −0.324130 | −0.162065 | − | 0.986780i | \(-0.551815\pi\) | ||||
−0.162065 | + | 0.986780i | \(0.551815\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.98615e23 | 0.920059 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.50226e23 | −0.956044 | −0.478022 | − | 0.878348i | \(-0.658646\pi\) | ||||
−0.478022 | + | 0.878348i | \(0.658646\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.62169e23 | −0.920143 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.05304e23 | −0.779391 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.50614e24 | −2.18998 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.44934e22 | −0.0472982 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.19475e23 | −0.283911 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.68480e24 | −2.05677 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.52973e23 | 0.637291 | 0.318646 | − | 0.947874i | \(-0.396772\pi\) | ||||
0.318646 | + | 0.947874i | \(0.396772\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.24710e24 | −1.35731 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.42102e23 | 0.454565 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.19323e23 | 0.504607 | 0.252303 | − | 0.967648i | \(-0.418812\pi\) | ||||
0.252303 | + | 0.967648i | \(0.418812\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.59615e23 | 0.422179 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.38837e24 | −2.07461 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.02207e23 | −0.412657 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.14524e22 | 0.0555566 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.43821e24 | 1.05850 | 0.529250 | − | 0.848466i | \(-0.322473\pi\) | ||||
0.529250 | + | 0.848466i | \(0.322473\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.46494e23 | 0.589905 | 0.294952 | − | 0.955512i | \(-0.404696\pi\) | ||||
0.294952 | + | 0.955512i | \(0.404696\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.84721e22 | −0.0187932 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.34329e24 | 0.840063 | 0.420031 | − | 0.907510i | \(-0.362019\pi\) | ||||
0.420031 | + | 0.907510i | \(0.362019\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.08752e23 | −0.182996 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.87015e24 | 2.73650 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.45409e24 | 0.774805 | 0.387403 | − | 0.921911i | \(-0.373372\pi\) | ||||
0.387403 | + | 0.921911i | \(0.373372\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.35543e24 | 2.20147 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.89852e24 | −1.86977 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.08067e22 | 0.0367845 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.21387e24 | 0.524620 | 0.262310 | − | 0.964984i | \(-0.415516\pi\) | ||||
0.262310 | + | 0.964984i | \(0.415516\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.42234e23 | −0.263599 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.53343e24 | −2.15746 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.39082e24 | −1.25624 | −0.628118 | − | 0.778118i | \(-0.716174\pi\) | ||||
−0.628118 | + | 0.778118i | \(0.716174\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.73183e24 | −1.31409 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.16703e23 | 0.0390696 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.13450e24 | 1.31629 | 0.658144 | − | 0.752892i | \(-0.271342\pi\) | ||||
0.658144 | + | 0.752892i | \(0.271342\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.70659e24 | 1.42534 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.88317e24 | −1.11892 | −0.559459 | − | 0.828858i | \(-0.688991\pi\) | ||||
−0.559459 | + | 0.828858i | \(0.688991\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.20921e24 | −1.15431 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.08618e24 | −0.805689 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.58080e24 | −0.641553 | −0.320777 | − | 0.947155i | \(-0.603944\pi\) | ||||
−0.320777 | + | 0.947155i | \(0.603944\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.80460e23 | 0.0900802 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.48340e23 | −0.213912 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.69683e23 | −0.208429 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.11532e24 | 0.843129 | 0.421564 | − | 0.906799i | \(-0.361481\pi\) | ||||
0.421564 | + | 0.906799i | \(0.361481\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.04807e25 | −4.00040 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.60175e24 | 1.22967 | 0.614833 | − | 0.788657i | \(-0.289223\pi\) | ||||
0.614833 | + | 0.788657i | \(0.289223\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.95813e23 | 0.0880886 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.28890e24 | 0.387975 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.05277e25 | 1.70289 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.13278e25 | −1.74893 | −0.874467 | − | 0.485084i | \(-0.838789\pi\) | ||||
−0.874467 | + | 0.485084i | \(0.838789\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.31721e24 | 1.37337 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.47003e25 | −2.06919 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.00585e24 | −0.135231 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.06463e24 | 1.03584 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.26882e25 | −1.55729 | −0.778643 | − | 0.627468i | \(-0.784092\pi\) | ||||
−0.778643 | + | 0.627468i | \(0.784092\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.67974e24 | 0.314349 | 0.157175 | − | 0.987571i | \(-0.449761\pi\) | ||||
0.157175 | + | 0.987571i | \(0.449761\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.45781e25 | 1.63481 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.45608e24 | −0.906722 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.92339e25 | −1.97244 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.45110e24 | 0.142349 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.37367e24 | −0.692069 | −0.346035 | − | 0.938222i | \(-0.612472\pi\) | ||||
−0.346035 | + | 0.938222i | \(0.612472\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.67233e25 | −1.50206 | −0.751028 | − | 0.660271i | \(-0.770442\pi\) | ||||
−0.751028 | + | 0.660271i | \(0.770442\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.37308e24 | 0.461929 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.59997e24 | −0.131686 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.48622e25 | −1.17130 | −0.585651 | − | 0.810563i | \(-0.699161\pi\) | ||||
−0.585651 | + | 0.810563i | \(0.699161\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.02240e25 | 1.52651 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.05393e24 | 0.510030 | 0.255015 | − | 0.966937i | \(-0.417920\pi\) | ||||
0.255015 | + | 0.966937i | \(0.417920\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.35126e24 | −0.509262 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.62624e25 | 1.07960 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.86136e24 | 0.436586 | 0.218293 | − | 0.975883i | \(-0.429951\pi\) | ||||
0.218293 | + | 0.975883i | \(0.429951\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.42161e24 | 0.330713 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.84891e24 | −0.459067 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.73807e23 | 0.0490125 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.33077e25 | −0.715975 | −0.357988 | − | 0.933726i | \(-0.616537\pi\) | ||||
−0.357988 | + | 0.933726i | \(0.616537\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.97994e24 | −0.360272 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.20176e25 | −1.09046 | −0.545231 | − | 0.838286i | \(-0.683558\pi\) | ||||
−0.545231 | + | 0.838286i | \(0.683558\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.34544e25 | 1.11482 | 0.557410 | − | 0.830237i | \(-0.311795\pi\) | ||||
0.557410 | + | 0.830237i | \(0.311795\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.28275e25 | 1.04149 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.76282e25 | 0.772143 | 0.386071 | − | 0.922469i | \(-0.373832\pi\) | ||||
0.386071 | + | 0.922469i | \(0.373832\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.20107e25 | 1.34633 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.29597e25 | −0.927400 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.60529e25 | 1.01082 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.55609e25 | 1.32551 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.78793e25 | 1.71484 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.55873e25 | 0.880719 | 0.440359 | − | 0.897822i | \(-0.354851\pi\) | ||||
0.440359 | + | 0.897822i | \(0.354851\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.18550e24 | −0.0723056 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.17356e24 | 0.164548 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.34197e25 | 0.410388 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.39237e25 | −0.409478 | −0.204739 | − | 0.978817i | \(-0.565635\pi\) | ||||
−0.204739 | + | 0.978817i | \(0.565635\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.90442e25 | −1.10439 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.82993e24 | −0.158631 | −0.0793157 | − | 0.996850i | \(-0.525274\pi\) | ||||
−0.0793157 | + | 0.996850i | \(0.525274\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.86098e25 | 0.748978 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.64211e25 | 0.917496 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.23554e25 | −0.541997 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.49503e25 | 0.348895 | 0.174447 | − | 0.984666i | \(-0.444186\pi\) | ||||
0.174447 | + | 0.984666i | \(0.444186\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.18554e25 | 1.16503 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.92509e25 | 0.416443 | 0.208222 | − | 0.978082i | \(-0.433232\pi\) | ||||
0.208222 | + | 0.978082i | \(0.433232\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.02115e25 | 0.421047 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.35981e25 | 1.47670 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.27794e25 | −1.02011 | −0.510053 | − | 0.860143i | \(-0.670374\pi\) | ||||
−0.510053 | + | 0.860143i | \(0.670374\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.85086e24 | 0.108949 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.93531e25 | 0.526671 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.58102e25 | 0.446296 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.23065e26 | −2.05104 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.50049e25 | 0.562391 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.00961e25 | 0.621074 | 0.310537 | − | 0.950561i | \(-0.399491\pi\) | ||||
0.310537 | + | 0.950561i | \(0.399491\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.30249e25 | −0.791979 | −0.395989 | − | 0.918255i | \(-0.629598\pi\) | ||||
−0.395989 | + | 0.918255i | \(0.629598\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.14987e26 | −1.65629 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.21549e26 | 1.68869 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.42113e25 | −0.994583 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.27198e26 | 1.64468 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.12549e24 | −0.0140422 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.22259e25 | −0.267607 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.22525e26 | −1.42386 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.70727e26 | −1.91518 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.31942e26 | −1.42892 | −0.714461 | − | 0.699676i | \(-0.753328\pi\) | ||||
−0.714461 | + | 0.699676i | \(0.753328\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.91572e25 | −0.514031 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.65363e24 | −0.0974819 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.18692e25 | 0.310807 | 0.155404 | − | 0.987851i | \(-0.450332\pi\) | ||||
0.155404 | + | 0.987851i | \(0.450332\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.66426e26 | 1.56778 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.20314e26 | −1.09491 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.02106e25 | −0.617325 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.00622e26 | −0.854885 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.30222e26 | 1.06920 | 0.534600 | − | 0.845105i | \(-0.320462\pi\) | ||||
0.534600 | + | 0.845105i | \(0.320462\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.40843e24 | −0.0429199 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.55738e26 | 2.72887 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.14771e23 | −0.00604235 | −0.00302118 | − | 0.999995i | \(-0.500962\pi\) | ||||
−0.00302118 | + | 0.999995i | \(0.500962\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.02162e25 | 0.144957 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.65729e26 | 1.14911 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.13811e26 | −0.763161 | −0.381580 | − | 0.924336i | \(-0.624620\pi\) | ||||
−0.381580 | + | 0.924336i | \(0.624620\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.33817e25 | −0.411075 | −0.205537 | − | 0.978649i | \(-0.565894\pi\) | ||||
−0.205537 | + | 0.978649i | \(0.565894\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.41733e26 | 2.14397 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.98289e24 | −0.0545220 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.26802e26 | 0.744654 | 0.372327 | − | 0.928102i | \(-0.378560\pi\) | ||||
0.372327 | + | 0.928102i | \(0.378560\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.73408e25 | −0.439503 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.28295e25 | −0.400529 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.04187e26 | −2.15145 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.56082e24 | −0.0389572 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.28792e26 | 1.14125 | 0.570623 | − | 0.821212i | \(-0.306702\pi\) | ||||
0.570623 | + | 0.821212i | \(0.306702\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.11156e26 | −2.46864 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.43288e26 | −1.60538 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.87324e26 | −0.848348 | −0.424174 | − | 0.905581i | \(-0.639435\pi\) | ||||
−0.424174 | + | 0.905581i | \(0.639435\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.14214e26 | 0.939587 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.77928e26 | 2.03051 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.85467e25 | 0.364433 | 0.182217 | − | 0.983258i | \(-0.441673\pi\) | ||||
0.182217 | + | 0.983258i | \(0.441673\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.61951e25 | −0.144325 | −0.0721625 | − | 0.997393i | \(-0.522990\pi\) | ||||
−0.0721625 | + | 0.997393i | \(0.522990\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.76980e26 | −1.07012 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.71477e26 | −0.641992 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.25964e26 | 0.819873 | 0.409936 | − | 0.912114i | \(-0.365551\pi\) | ||||
0.409936 | + | 0.912114i | \(0.365551\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.89041e26 | 1.36814 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.55476e25 | 0.0870882 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.22922e26 | 1.06714 | 0.533572 | − | 0.845755i | \(-0.320849\pi\) | ||||
0.533572 | + | 0.845755i | \(0.320849\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.18184e25 | −0.166024 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.57559e26 | −1.73213 | −0.866067 | − | 0.499927i | \(-0.833360\pi\) | ||||
−0.866067 | + | 0.499927i | \(0.833360\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.69876e26 | −1.11428 | −0.557141 | − | 0.830418i | \(-0.688102\pi\) | ||||
−0.557141 | + | 0.830418i | \(0.688102\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.41478e24 | −0.0216635 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.32273e26 | −1.50833 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.05361e26 | 0.289615 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.49601e27 | −3.98926 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.35775e26 | −1.38612 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.48829e26 | 0.373603 | 0.186801 | − | 0.982398i | \(-0.440188\pi\) | ||||
0.186801 | + | 0.982398i | \(0.440188\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.08679e27 | 2.64735 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.07020e26 | 0.489397 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.54419e25 | 0.0813192 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.93435e26 | 0.430802 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.74129e26 | −0.592657 | −0.296329 | − | 0.955086i | \(-0.595762\pi\) | ||||
−0.296329 | + | 0.955086i | \(0.595762\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.47762e26 | −0.520032 | −0.260016 | − | 0.965604i | \(-0.583728\pi\) | ||||
−0.260016 | + | 0.965604i | \(0.583728\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.49007e26 | −0.507452 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.36261e26 | 0.269638 | 0.134819 | − | 0.990870i | \(-0.456955\pi\) | ||||
0.134819 | + | 0.990870i | \(0.456955\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.07378e27 | −2.06343 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.65284e27 | 3.08469 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.13257e25 | 0.111165 | 0.0555824 | − | 0.998454i | \(-0.482298\pi\) | ||||
0.0555824 | + | 0.998454i | \(0.482298\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.17128e25 | −0.0734475 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.06260e25 | −0.0865969 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.67926e26 | −0.445250 | −0.222625 | − | 0.974904i | \(-0.571463\pi\) | ||||
−0.222625 | + | 0.974904i | \(0.571463\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.12853e26 | −0.505157 | −0.252578 | − | 0.967576i | \(-0.581279\pi\) | ||||
−0.252578 | + | 0.967576i | \(0.581279\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.38492e25 | −0.115869 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.00848e26 | −1.37355 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.03922e25 | 0.0450367 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.97114e27 | −2.83902 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.40493e27 | −1.96694 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.60450e26 | 1.03497 | 0.517485 | − | 0.855692i | \(-0.326868\pi\) | ||||
0.517485 | + | 0.855692i | \(0.326868\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.64801e26 | 0.218058 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.44198e27 | 1.85510 | 0.927550 | − | 0.373700i | \(-0.121911\pi\) | ||||
0.927550 | + | 0.373700i | \(0.121911\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.71659e26 | 1.21549 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.54878e25 | −0.103994 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.31240e26 | 0.983399 | 0.491700 | − | 0.870765i | \(-0.336376\pi\) | ||||
0.491700 | + | 0.870765i | \(0.336376\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.09818e26 | 0.471553 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.69154e26 | 0.189318 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.39069e25 | 0.0913514 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.10819e26 | −0.223290 | −0.111645 | − | 0.993748i | \(-0.535612\pi\) | ||||
−0.111645 | + | 0.993748i | \(0.535612\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.63710e27 | 2.71744 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.54723e26 | 0.355659 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.75915e26 | −0.269194 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.45059e26 | −0.612444 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.41456e26 | −0.869919 | −0.434959 | − | 0.900450i | \(-0.643237\pi\) | ||||
−0.434959 | + | 0.900450i | \(0.643237\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.25313e27 | 2.02633 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.17623e27 | 1.02966 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.46343e27 | 1.24706 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.83074e27 | 1.51875 | 0.759376 | − | 0.650652i | \(-0.225505\pi\) | ||||
0.759376 | + | 0.650652i | \(0.225505\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.07513e26 | 0.490676 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.29121e26 | 0.101542 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.38268e25 | 0.0488760 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.63002e26 | −0.345264 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.73532e27 | −1.26025 | −0.630124 | − | 0.776495i | \(-0.716996\pi\) | ||||
−0.630124 | + | 0.776495i | \(0.716996\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.86880e27 | 1.32184 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.29796e27 | 1.58317 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.75495e26 | −0.453326 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.33232e26 | −0.348610 | −0.174305 | − | 0.984692i | \(-0.555768\pi\) | ||||
−0.174305 | + | 0.984692i | \(0.555768\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.11925e27 | −1.34980 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.32588e27 | −0.822790 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.90931e26 | −0.236381 | −0.118190 | − | 0.992991i | \(-0.537709\pi\) | ||||
−0.118190 | + | 0.992991i | \(0.537709\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.63177e27 | 0.961455 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.33820e27 | 1.34258 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.87032e26 | 0.440423 | 0.220212 | − | 0.975452i | \(-0.429325\pi\) | ||||
0.220212 | + | 0.975452i | \(0.429325\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.10563e26 | 0.169385 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.68492e27 | 1.95900 | 0.979500 | − | 0.201445i | \(-0.0645637\pi\) | ||||
0.979500 | + | 0.201445i | \(0.0645637\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.15302e26 | 0.370685 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.30174e26 | 0.318357 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.60928e27 | −0.792600 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.86208e26 | −0.185457 | −0.0927283 | − | 0.995691i | \(-0.529559\pi\) | ||||
−0.0927283 | + | 0.995691i | \(0.529559\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.86421e27 | 0.872855 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.45235e26 | −0.157623 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.93310e27 | −1.75116 | −0.875578 | − | 0.483078i | \(-0.839519\pi\) | ||||
−0.875578 | + | 0.483078i | \(0.839519\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.77900e26 | 0.164089 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.44215e27 | −0.610742 | −0.305371 | − | 0.952234i | \(-0.598780\pi\) | ||||
−0.305371 | + | 0.952234i | \(0.598780\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.98978e26 | −0.288722 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.85354e27 | −0.746824 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.22910e26 | 0.0876139 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.77621e27 | −1.83140 | −0.915701 | − | 0.401861i | \(-0.868364\pi\) | ||||
−0.915701 | + | 0.401861i | \(0.868364\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.44872e27 | −0.916056 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.06095e27 | 1.11725 | 0.558625 | − | 0.829420i | \(-0.311329\pi\) | ||||
0.558625 | + | 0.829420i | \(0.311329\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.86984e27 | −1.02210 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.28557e27 | −2.53200 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.16032e27 | 0.393526 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.63294e27 | −0.540488 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.57576e26 | −0.180122 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.00988e27 | −0.318427 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.46755e27 | 0.759461 | 0.379731 | − | 0.925097i | \(-0.376017\pi\) | ||||
0.379731 | + | 0.925097i | \(0.376017\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.46084e27 | 1.03980 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.46377e27 | 0.429334 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.91656e26 | 0.0835171 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.86313e27 | 1.08007 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.72784e27 | 1.29065 | 0.645326 | − | 0.763907i | \(-0.276722\pi\) | ||||
0.645326 | + | 0.763907i | \(0.276722\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.26301e27 | 1.66951 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.60561e27 | 1.19889 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.27374e26 | 0.108645 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.27560e26 | 0.0564981 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.10061e28 | −2.66892 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.73872e27 | 1.12241 | 0.561203 | − | 0.827678i | \(-0.310339\pi\) | ||||
0.561203 | + | 0.827678i | \(0.310339\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.55266e27 | −0.359234 | −0.179617 | − | 0.983737i | \(-0.557486\pi\) | ||||
−0.179617 | + | 0.983737i | \(0.557486\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.52795e27 | −2.15347 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.71736e27 | −0.379197 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.57580e27 | 1.20281 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.47446e26 | −0.115384 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.90129e27 | 1.62719 | 0.813595 | − | 0.581432i | \(-0.197507\pi\) | ||||
0.813595 | + | 0.581432i | \(0.197507\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.55379e27 | −1.52008 | −0.760040 | − | 0.649877i | \(-0.774820\pi\) | ||||
−0.760040 | + | 0.649877i | \(0.774820\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.39920e27 | −1.65168 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.52722e27 | −1.83090 | −0.915448 | − | 0.402436i | \(-0.868164\pi\) | ||||
−0.915448 | + | 0.402436i | \(0.868164\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.29069e27 | −0.242412 | −0.121206 | − | 0.992627i | \(-0.538676\pi\) | ||||
−0.121206 | + | 0.992627i | \(0.538676\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.05125e28 | 1.92973 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.68861e27 | 1.55892 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.28086e27 | 0.400016 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.36886e27 | −0.406114 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.22538e27 | −1.54613 | −0.773065 | − | 0.634327i | \(-0.781277\pi\) | ||||
−0.773065 | + | 0.634327i | \(0.781277\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.81783e27 | −0.625540 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.68759e28 | −2.70337 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.23722e27 | 0.507030 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.24159e28 | −1.90145 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.14551e27 | 0.171544 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.69154e26 | −0.0833487 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.63470e27 | 0.950180 | 0.475090 | − | 0.879937i | \(-0.342416\pi\) | ||||
0.475090 | + | 0.879937i | \(0.342416\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.79479e27 | 1.09176 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.92147e27 | 0.400206 | 0.200103 | − | 0.979775i | \(-0.435872\pi\) | ||||
0.200103 | + | 0.979775i | \(0.435872\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.47684e27 | 1.13579 | 0.567896 | − | 0.823100i | \(-0.307757\pi\) | ||||
0.567896 | + | 0.823100i | \(0.307757\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.75195e27 | −0.491730 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.99055e27 | 1.28082 | 0.640408 | − | 0.768035i | \(-0.278765\pi\) | ||||
0.640408 | + | 0.768035i | \(0.278765\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.53969e27 | 0.193099 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.01918e27 | −0.738509 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.12850e27 | −0.615605 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.85398e26 | −0.0570066 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.40751e27 | −0.966122 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.18850e28 | −1.33636 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.66387e27 | 0.403129 | 0.201564 | − | 0.979475i | \(-0.435397\pi\) | ||||
0.201564 | + | 0.979475i | \(0.435397\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.37294e27 | −1.00921 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.90178e27 | 0.411141 | 0.205571 | − | 0.978642i | \(-0.434095\pi\) | ||||
0.205571 | + | 0.978642i | \(0.434095\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.02824e27 | −0.621676 | −0.310838 | − | 0.950463i | \(-0.600610\pi\) | ||||
−0.310838 | + | 0.950463i | \(0.600610\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.02629e28 | 1.03588 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.43600e28 | 1.41867 | 0.709333 | − | 0.704874i | \(-0.248996\pi\) | ||||
0.709333 | + | 0.704874i | \(0.248996\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.49894e28 | 1.44950 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.21056e28 | 1.14591 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.63382e28 | −2.44061 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.38925e27 | −0.488888 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.84500e25 | −0.00696730 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.70964e27 | 0.844279 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.05698e28 | 1.75124 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.80296e28 | −1.50297 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.16218e27 | −0.176495 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.84058e27 | 0.706662 | 0.353331 | − | 0.935498i | \(-0.385049\pi\) | ||||
0.353331 | + | 0.935498i | \(0.385049\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.26627e28 | −0.991215 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.77289e28 | −1.35912 | −0.679561 | − | 0.733619i | \(-0.737830\pi\) | ||||
−0.679561 | + | 0.733619i | \(0.737830\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.31979e27 | −0.399413 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.34280e28 | 0.987442 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.02024e27 | −0.217537 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.67320e28 | 1.18046 | 0.590230 | − | 0.807235i | \(-0.299037\pi\) | ||||
0.590230 | + | 0.807235i | \(0.299037\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.01175e28 | −2.77247 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.38989e26 | 0.0229493 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.26500e28 | 0.838965 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.61703e28 | −1.05065 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.04557e28 | −1.30216 | −0.651082 | − | 0.759008i | \(-0.725685\pi\) | ||||
−0.651082 | + | 0.759008i | \(0.725685\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.65387e28 | −2.27893 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.63080e28 | −1.60772 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.56472e28 | 0.936970 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.17132e27 | −0.127408 | −0.0637042 | − | 0.997969i | \(-0.520291\pi\) | ||||
−0.0637042 | + | 0.997969i | \(0.520291\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.35809e27 | 0.480600 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.37859e27 | −0.472138 | −0.236069 | − | 0.971736i | \(-0.575859\pi\) | ||||
−0.236069 | + | 0.971736i | \(0.575859\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.93105e26 | −0.0161868 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.17482e27 | −0.225962 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.69589e28 | 0.899648 | 0.449824 | − | 0.893117i | \(-0.351487\pi\) | ||||
0.449824 | + | 0.893117i | \(0.351487\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.87204e25 | −0.00461311 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.78136e28 | 1.41756 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.53298e27 | 0.176506 | 0.0882529 | − | 0.996098i | \(-0.471872\pi\) | ||||
0.0882529 | + | 0.996098i | \(0.471872\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.50312e28 | 0.736140 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.84173e28 | 1.36433 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.96732e28 | 1.39665 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.95807e28 | 0.903560 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.39247e28 | 0.629992 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.40184e27 | −0.150905 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.62859e27 | 0.418805 | 0.209402 | − | 0.977830i | \(-0.432848\pi\) | ||||
0.209402 | + | 0.977830i | \(0.432848\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.61345e28 | 3.24718 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.59014e28 | −1.08328 | −0.541640 | − | 0.840611i | \(-0.682196\pi\) | ||||
−0.541640 | + | 0.840611i | \(0.682196\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.56840e28 | 1.05339 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.74363e27 | 0.0701309 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.99288e28 | 1.57503 | 0.787514 | − | 0.616297i | \(-0.211368\pi\) | ||||
0.787514 | + | 0.616297i | \(0.211368\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.88796e28 | −1.50413 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.04807e27 | 0.229489 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.74542e27 | −0.139393 | −0.0696966 | − | 0.997568i | \(-0.522203\pi\) | ||||
−0.0696966 | + | 0.997568i | \(0.522203\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.50996e28 | −0.551214 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.51656e28 | 3.04966 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.40848e27 | −0.0494750 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.40811e28 | 1.17440 | 0.587198 | − | 0.809443i | \(-0.300231\pi\) | ||||
0.587198 | + | 0.809443i | \(0.300231\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.79525e28 | −0.944937 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.10217e28 | 0.697186 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.93862e27 | 0.160695 | 0.0803473 | − | 0.996767i | \(-0.474397\pi\) | ||||
0.0803473 | + | 0.996767i | \(0.474397\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.04417e28 | 0.333350 |
(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 | 64.20.a.j.1.1 | 2 | ||
4.3 | odd | 2 | 64.20.a.k.1.2 | 2 | |||
8.3 | odd | 2 | 8.20.a.a.1.1 | ✓ | 2 | ||
8.5 | even | 2 | 16.20.a.e.1.2 | 2 | |||
24.11 | even | 2 | 72.20.a.a.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.20.a.a.1.1 | ✓ | 2 | 8.3 | odd | 2 | ||
16.20.a.e.1.2 | 2 | 8.5 | even | 2 | |||
64.20.a.j.1.1 | 2 | 1.1 | even | 1 | trivial | ||
64.20.a.k.1.2 | 2 | 4.3 | odd | 2 | |||
72.20.a.a.1.1 | 2 | 24.11 | even | 2 |