Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,22,Mod(1,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.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: | \(134.149125258\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{537541}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 134385 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3^{2}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 24) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-366.086\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 48.1 |
$q$-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 | ||||||||
\(3\) | −59049.0 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.57551e7 | 1.17944 | 0.589722 | − | 0.807606i | \(-0.299237\pi\) | ||||
0.589722 | + | 0.807606i | \(0.299237\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.59057e8 | −0.480434 | −0.240217 | − | 0.970719i | \(-0.577219\pi\) | ||||
−0.240217 | + | 0.970719i | \(0.577219\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.48678e9 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.36294e11 | 1.58435 | 0.792177 | − | 0.610292i | \(-0.208948\pi\) | ||||
0.792177 | + | 0.610292i | \(0.208948\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.92453e11 | −0.789555 | −0.394777 | − | 0.918777i | \(-0.629178\pi\) | ||||
−0.394777 | + | 0.918777i | \(0.629178\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.52081e12 | −0.680952 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.39882e13 | −1.68286 | −0.841432 | − | 0.540364i | \(-0.818287\pi\) | ||||
−0.841432 | + | 0.540364i | \(0.818287\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.50746e13 | 0.564069 | 0.282034 | − | 0.959404i | \(-0.408991\pi\) | ||||
0.282034 | + | 0.959404i | \(0.408991\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.12020e13 | 0.277379 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.76097e13 | 0.440971 | 0.220486 | − | 0.975390i | \(-0.429236\pi\) | ||||
0.220486 | + | 0.975390i | \(0.429236\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.86486e14 | 0.391089 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.05891e14 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.21409e15 | −0.977272 | −0.488636 | − | 0.872488i | \(-0.662505\pi\) | ||||
−0.488636 | + | 0.872488i | \(0.662505\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.94349e14 | −0.195979 | −0.0979894 | − | 0.995187i | \(-0.531241\pi\) | ||||
−0.0979894 | + | 0.995187i | \(0.531241\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.04800e15 | −0.914727 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.24753e15 | −0.566645 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.48898e16 | −1.19284 | −0.596418 | − | 0.802674i | \(-0.703410\pi\) | ||||
−0.596418 | + | 0.802674i | \(0.703410\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.31739e16 | 0.455850 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.42605e17 | 1.65923 | 0.829613 | − | 0.558339i | \(-0.188561\pi\) | ||||
0.829613 | + | 0.558339i | \(0.188561\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.89687e17 | −1.33850 | −0.669251 | − | 0.743037i | \(-0.733385\pi\) | ||||
−0.669251 | + | 0.743037i | \(0.733385\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.98023e16 | 0.393148 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.48311e17 | 0.965918 | 0.482959 | − | 0.875643i | \(-0.339562\pi\) | ||||
0.482959 | + | 0.875643i | \(0.339562\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.29624e17 | −0.769183 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.25990e17 | 0.971601 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.82306e18 | 1.43188 | 0.715938 | − | 0.698164i | \(-0.245999\pi\) | ||||
0.715938 | + | 0.698164i | \(0.245999\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.51025e18 | 1.86866 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.90138e17 | −0.325665 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.09411e18 | −0.533402 | −0.266701 | − | 0.963779i | \(-0.585934\pi\) | ||||
−0.266701 | + | 0.963779i | \(0.585934\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.46472e18 | −0.262900 | −0.131450 | − | 0.991323i | \(-0.541963\pi\) | ||||
−0.131450 | + | 0.991323i | \(0.541963\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.25195e18 | −0.160145 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.01076e19 | −0.931236 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.86063e18 | −0.124702 | −0.0623511 | − | 0.998054i | \(-0.519860\pi\) | ||||
−0.0623511 | + | 0.998054i | \(0.519860\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.17327e18 | −0.254595 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.89991e19 | 1.78639 | 0.893194 | − | 0.449672i | \(-0.148459\pi\) | ||||
0.893194 | + | 0.449672i | \(0.148459\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.41519e19 | −0.385413 | −0.192706 | − | 0.981256i | \(-0.561726\pi\) | ||||
−0.192706 | + | 0.981256i | \(0.561726\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.10118e19 | −0.225795 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.89372e19 | −0.761178 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.80140e18 | −0.0570537 | −0.0285268 | − | 0.999593i | \(-0.509082\pi\) | ||||
−0.0285268 | + | 0.999593i | \(0.509082\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.21577e19 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.73723e20 | 1.22896 | 0.614480 | − | 0.788932i | \(-0.289366\pi\) | ||||
0.614480 | + | 0.788932i | \(0.289366\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.60267e20 | −1.98484 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.30740e20 | 0.564229 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.41275e20 | −0.480252 | −0.240126 | − | 0.970742i | \(-0.577189\pi\) | ||||
−0.240126 | + | 0.970742i | \(0.577189\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.40913e20 | 0.379329 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.28104e19 | 0.113148 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.88246e20 | 0.665288 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.17758e20 | −1.26364 | −0.631822 | − | 0.775113i | \(-0.717693\pi\) | ||||
−0.631822 | + | 0.775113i | \(0.717693\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.75226e20 | 0.528118 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.47601e19 | 0.0223037 | 0.0111519 | − | 0.999938i | \(-0.496450\pi\) | ||||
0.0111519 | + | 0.999938i | \(0.496450\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.69839e21 | −1.24522 | −0.622612 | − | 0.782531i | \(-0.713928\pi\) | ||||
−0.622612 | + | 0.782531i | \(0.713928\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.46058e20 | 0.327153 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.41055e21 | −1.18464 | −0.592320 | − | 0.805703i | \(-0.701788\pi\) | ||||
−0.592320 | + | 0.805703i | \(0.701788\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.85834e21 | −0.751878 | −0.375939 | − | 0.926644i | \(-0.622680\pi\) | ||||
−0.375939 | + | 0.926644i | \(0.622680\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.06021e21 | 0.688684 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.42812e21 | 0.672893 | 0.336446 | − | 0.941703i | \(-0.390775\pi\) | ||||
0.336446 | + | 0.941703i | \(0.390775\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.25639e21 | 0.520101 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.36840e21 | −0.263185 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.02257e21 | 0.808505 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.11757e22 | 1.51018 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.42071e21 | −0.957955 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.47802e21 | −0.718177 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.03194e22 | −1.65185 | −0.825926 | − | 0.563779i | \(-0.809347\pi\) | ||||
−0.825926 | + | 0.563779i | \(0.809347\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.12008e22 | 0.772784 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.93767e22 | −1.13745 | −0.568725 | − | 0.822528i | \(-0.692563\pi\) | ||||
−0.568725 | + | 0.822528i | \(0.692563\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.41263e21 | −0.270998 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.30274e21 | −0.226984 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.85640e22 | 0.680935 | 0.340468 | − | 0.940256i | \(-0.389415\pi\) | ||||
0.340468 | + | 0.940256i | \(0.389415\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.06791e22 | −0.966466 | −0.483233 | − | 0.875492i | \(-0.660538\pi\) | ||||
−0.483233 | + | 0.875492i | \(0.660538\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.05674e22 | −0.557673 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.34888e22 | −1.25093 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.70239e22 | −1.15264 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.53689e22 | 0.444088 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.03106e23 | −1.56614 | −0.783069 | − | 0.621934i | \(-0.786347\pi\) | ||||
−0.783069 | + | 0.621934i | \(0.786347\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.43298e22 | −0.717431 | −0.358716 | − | 0.933447i | \(-0.616785\pi\) | ||||
−0.358716 | + | 0.933447i | \(0.616785\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.87739e22 | −0.560954 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.30340e22 | −0.231146 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.24116e22 | 0.547417 | 0.273709 | − | 0.961813i | \(-0.411750\pi\) | ||||
0.273709 | + | 0.961813i | \(0.411750\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.07650e23 | −0.826694 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.14569e22 | −0.211858 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.75747e23 | 1.63132 | 0.815662 | − | 0.578529i | \(-0.196373\pi\) | ||||
0.815662 | + | 0.578529i | \(0.196373\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.07277e23 | −1.07887 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.31299e22 | 0.197813 | 0.0989067 | − | 0.995097i | \(-0.468465\pi\) | ||||
0.0989067 | + | 0.995097i | \(0.468465\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.30453e22 | −0.376603 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.25618e22 | 0.188023 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.96523e23 | −1.57201 | −0.786005 | − | 0.618220i | \(-0.787854\pi\) | ||||
−0.786005 | + | 0.618220i | \(0.787854\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.69590e22 | −0.187892 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.23655e23 | 0.307960 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.59980e23 | −0.354086 | −0.177043 | − | 0.984203i | \(-0.556653\pi\) | ||||
−0.177043 | + | 0.984203i | \(0.556653\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.04239e23 | −0.205307 | −0.102654 | − | 0.994717i | \(-0.532733\pi\) | ||||
−0.102654 | + | 0.994717i | \(0.532733\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.64901e22 | 0.151785 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.98589e23 | −1.40688 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.90650e24 | −2.66625 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.39267e22 | 0.0924596 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.53991e21 | 0.0106830 | 0.00534151 | − | 0.999986i | \(-0.498300\pi\) | ||||
0.00534151 | + | 0.999986i | \(0.498300\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.63574e24 | −1.64196 | −0.820982 | − | 0.570955i | \(-0.806573\pi\) | ||||
−0.820982 | + | 0.570955i | \(0.806573\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.96846e23 | 0.537649 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.78920e23 | −0.144798 | −0.0723990 | − | 0.997376i | \(-0.523065\pi\) | ||||
−0.0723990 | + | 0.997376i | \(0.523065\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.27224e24 | −0.926000 | −0.463000 | − | 0.886358i | \(-0.653227\pi\) | ||||
−0.463000 | + | 0.886358i | \(0.653227\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.09868e23 | 0.0719969 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.94983e23 | 0.469515 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.67281e24 | 1.95697 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.05476e23 | 0.146990 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.05457e24 | 0.893684 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.28008e24 | −0.503814 | −0.251907 | − | 0.967751i | \(-0.581058\pi\) | ||||
−0.251907 | + | 0.967751i | \(0.581058\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.89335e24 | −1.03137 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.88540e24 | −1.57869 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.21122e23 | 0.0941549 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.35658e23 | 0.222518 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.48972e24 | 1.32871 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.50398e24 | −1.87250 | −0.936249 | − | 0.351337i | \(-0.885727\pi\) | ||||
−0.936249 | + | 0.351337i | \(0.885727\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.50235e23 | 0.130363 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.87384e24 | 1.07313 | 0.536563 | − | 0.843860i | \(-0.319722\pi\) | ||||
0.536563 | + | 0.843860i | \(0.319722\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.22784e24 | 0.871064 | 0.435532 | − | 0.900173i | \(-0.356560\pi\) | ||||
0.435532 | + | 0.900173i | \(0.356560\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.88969e24 | 0.439466 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.21665e25 | −1.69016 | −0.845080 | − | 0.534639i | \(-0.820447\pi\) | ||||
−0.845080 | + | 0.534639i | \(0.820447\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.97078e24 | 1.13925 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.83518e23 | 0.0329400 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.48569e25 | 1.58034 | 0.790172 | − | 0.612885i | \(-0.209991\pi\) | ||||
0.790172 | + | 0.612885i | \(0.209991\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.92207e25 | 1.87322 | 0.936611 | − | 0.350371i | \(-0.113944\pi\) | ||||
0.936611 | + | 0.350371i | \(0.113944\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.17898e23 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.10650e25 | −0.907208 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.91606e24 | −0.445363 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.02582e25 | −0.709541 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.32687e25 | 0.843827 | 0.421913 | − | 0.906636i | \(-0.361359\pi\) | ||||
0.421913 | + | 0.906636i | \(0.361359\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.19406e25 | 0.698654 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.12734e25 | 1.14595 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.26688e25 | 0.628690 | 0.314345 | − | 0.949309i | \(-0.398215\pi\) | ||||
0.314345 | + | 0.949309i | \(0.398215\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.25274e25 | 0.573079 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.72004e24 | −0.325757 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.53269e25 | 0.596925 | 0.298463 | − | 0.954421i | \(-0.403526\pi\) | ||||
0.298463 | + | 0.954421i | \(0.403526\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.69531e25 | 1.68882 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.34213e24 | 0.277274 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.89875e25 | −0.583537 | −0.291769 | − | 0.956489i | \(-0.594244\pi\) | ||||
−0.291769 | + | 0.956489i | \(0.594244\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.77343e24 | 0.221022 | 0.110511 | − | 0.993875i | \(-0.464751\pi\) | ||||
0.110511 | + | 0.993875i | \(0.464751\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.32077e24 | −0.219006 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.54168e25 | 0.619623 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.49025e25 | −1.01445 | −0.507227 | − | 0.861812i | \(-0.669330\pi\) | ||||
−0.507227 | + | 0.861812i | \(0.669330\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.11840e24 | −0.0653263 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.01753e25 | −0.780804 | −0.390402 | − | 0.920644i | \(-0.627664\pi\) | ||||
−0.390402 | + | 0.920644i | \(0.627664\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.95046e25 | −0.712673 | −0.356336 | − | 0.934358i | \(-0.615974\pi\) | ||||
−0.356336 | + | 0.934358i | \(0.615974\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.29256e25 | −0.384104 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.12035e25 | −0.797149 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.26578e26 | 1.83203 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.41927e25 | 0.729565 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.06017e26 | 1.32821 | 0.664105 | − | 0.747639i | \(-0.268813\pi\) | ||||
0.664105 | + | 0.747639i | \(0.268813\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.39340e25 | −0.629117 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.80616e25 | −0.304909 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.43827e25 | −0.348171 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.81085e25 | 0.643062 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.46206e24 | −0.0128771 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.77239e25 | −0.310076 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.27333e26 | −0.977207 | −0.488603 | − | 0.872506i | \(-0.662493\pi\) | ||||
−0.488603 | + | 0.872506i | \(0.662493\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.00288e26 | 0.718930 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.10303e26 | 1.40884 | 0.704420 | − | 0.709784i | \(-0.251207\pi\) | ||||
0.704420 | + | 0.709784i | \(0.251207\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.27161e25 | −0.267532 | −0.133766 | − | 0.991013i | \(-0.542707\pi\) | ||||
−0.133766 | + | 0.991013i | \(0.542707\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.22442e25 | −0.188882 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.06128e25 | −0.0581713 | −0.0290856 | − | 0.999577i | \(-0.509260\pi\) | ||||
−0.0290856 | + | 0.999577i | \(0.509260\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.01766e26 | −1.54835 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.42340e26 | 0.683952 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.10866e26 | −0.949250 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.31868e25 | −0.308786 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.09733e26 | 0.434097 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.25064e26 | −0.464060 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.50096e24 | 0.0295988 | 0.0147994 | − | 0.999890i | \(-0.495289\pi\) | ||||
0.0147994 | + | 0.999890i | \(0.495289\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.21653e26 | −0.397612 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.79206e25 | −0.147079 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.53863e26 | −1.59694 | −0.798469 | − | 0.602035i | \(-0.794357\pi\) | ||||
−0.798469 | + | 0.602035i | \(0.794357\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.43378e26 | −0.388495 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.21894e26 | −0.310500 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.54809e26 | 0.849976 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.33238e26 | −0.300280 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.87571e26 | −1.67044 | −0.835218 | − | 0.549919i | \(-0.814659\pi\) | ||||
−0.835218 | + | 0.549919i | \(0.814659\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.59188e26 | −0.717223 | −0.358612 | − | 0.933487i | \(-0.616750\pi\) | ||||
−0.358612 | + | 0.933487i | \(0.616750\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.08026e25 | 0.151950 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.07852e27 | −1.91071 | −0.955357 | − | 0.295454i | \(-0.904529\pi\) | ||||
−0.955357 | + | 0.295454i | \(0.904529\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.26198e27 | 2.10694 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.96578e26 | −0.466791 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.47071e26 | −1.10884 | −0.554421 | − | 0.832236i | \(-0.687060\pi\) | ||||
−0.554421 | + | 0.832236i | \(0.687060\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.86967e26 | −0.681827 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.59913e26 | −0.871900 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.64484e26 | −0.454573 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.12481e25 | −0.0603510 | −0.0301755 | − | 0.999545i | \(-0.509607\pi\) | ||||
−0.0301755 | + | 0.999545i | \(0.509607\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.97234e26 | 0.553075 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.54584e26 | −0.687922 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.85350e27 | 1.84098 | 0.920492 | − | 0.390761i | \(-0.127788\pi\) | ||||
0.920492 | + | 0.390761i | \(0.127788\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.41569e26 | 0.414640 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.68925e26 | 0.771610 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.88527e27 | 1.58366 | 0.791832 | − | 0.610740i | \(-0.209128\pi\) | ||||
0.791832 | + | 0.610740i | \(0.209128\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.19984e27 | 0.953697 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.86685e27 | 1.40450 | 0.702252 | − | 0.711928i | \(-0.252178\pi\) | ||||
0.702252 | + | 0.711928i | \(0.252178\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.26038e27 | −0.897767 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.61398e26 | −0.446167 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.56908e26 | −0.483696 | −0.241848 | − | 0.970314i | \(-0.577753\pi\) | ||||
−0.241848 | + | 0.970314i | \(0.577753\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.22550e27 | −0.742094 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.14418e27 | 0.656707 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.23660e26 | −0.0672916 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.42415e27 | −1.76706 | −0.883532 | − | 0.468371i | \(-0.844841\pi\) | ||||
−0.883532 | + | 0.468371i | \(0.844841\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.19610e26 | 0.156461 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.10952e27 | 1.90886 | 0.954431 | − | 0.298430i | \(-0.0964631\pi\) | ||||
0.954431 | + | 0.298430i | \(0.0964631\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.50990e26 | 0.154736 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.13121e26 | 0.131049 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.75526e27 | −1.88987 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.66757e27 | 1.00698 | 0.503490 | − | 0.864001i | \(-0.332049\pi\) | ||||
0.503490 | + | 0.864001i | \(0.332049\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.09619e27 | −0.393138 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.51907e26 | 0.256264 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.47425e27 | 1.44949 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.81157e27 | 0.557990 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.19630e27 | −0.643346 | −0.321673 | − | 0.946851i | \(-0.604245\pi\) | ||||
−0.321673 | + | 0.946851i | \(0.604245\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.66044e27 | 1.57721 | 0.788603 | − | 0.614903i | \(-0.210805\pi\) | ||||
0.788603 | + | 0.614903i | \(0.210805\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.21449e27 | 0.321973 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.60860e27 | −0.658149 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.25917e26 | 0.126306 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.15846e27 | 0.722227 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.11367e27 | 0.242519 | 0.121260 | − | 0.992621i | \(-0.461307\pi\) | ||||
0.121260 | + | 0.992621i | \(0.461307\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.02630e27 | −0.212888 | −0.106444 | − | 0.994319i | \(-0.533946\pi\) | ||||
−0.106444 | + | 0.994319i | \(0.533946\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.36721e27 | 0.665476 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.32068e27 | 0.248738 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.22966e26 | −0.147742 | −0.0738710 | − | 0.997268i | \(-0.523535\pi\) | ||||
−0.0738710 | + | 0.997268i | \(0.523535\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.49801e27 | −0.256394 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.65938e27 | −0.597267 | −0.298633 | − | 0.954368i | \(-0.596531\pi\) | ||||
−0.298633 | + | 0.954368i | \(0.596531\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.63854e27 | −0.566431 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.08834e27 | 0.904211 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.66489e27 | −0.661081 | −0.330541 | − | 0.943792i | \(-0.607231\pi\) | ||||
−0.330541 | + | 0.943792i | \(0.607231\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.94362e28 | 2.62880 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.20812e27 | 0.414209 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.62922e27 | 0.447398 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.25704e27 | 0.265717 | 0.132859 | − | 0.991135i | \(-0.457584\pi\) | ||||
0.132859 | + | 0.991135i | \(0.457584\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.88005e27 | 0.323867 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.22216e27 | −0.346168 | −0.173084 | − | 0.984907i | \(-0.555373\pi\) | ||||
−0.173084 | + | 0.984907i | \(0.555373\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.52787e28 | −1.56850 | −0.784252 | − | 0.620442i | \(-0.786953\pi\) | ||||
−0.784252 | + | 0.620442i | \(0.786953\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.36013e27 | 0.133452 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.38717e27 | 0.505282 | 0.252641 | − | 0.967560i | \(-0.418701\pi\) | ||||
0.252641 | + | 0.967560i | \(0.418701\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.68072e26 | 0.0599113 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.68534e27 | −0.316052 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.58531e28 | −2.12066 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.81119e27 | 0.220601 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.35663e27 | 0.477292 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.99749e27 | −0.143536 | −0.0717680 | − | 0.997421i | \(-0.522864\pi\) | ||||
−0.0717680 | + | 0.997421i | \(0.522864\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.36926e28 | 0.941809 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.85750e27 | 0.122316 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.36369e28 | −1.49040 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.07531e27 | −0.366872 | −0.183436 | − | 0.983032i | \(-0.558722\pi\) | ||||
−0.183436 | + | 0.983032i | \(0.558722\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.62826e28 | −0.941845 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.63125e28 | −0.903990 | −0.451995 | − | 0.892020i | \(-0.649288\pi\) | ||||
−0.451995 | + | 0.892020i | \(0.649288\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.09711e28 | 1.64462 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.22395e28 | 0.622886 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.75935e28 | −0.858242 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.96493e27 | 0.232197 | 0.116099 | − | 0.993238i | \(-0.462961\pi\) | ||||
0.116099 | + | 0.993238i | \(0.462961\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.54678e27 | −0.114208 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.73937e28 | −1.60818 | −0.804090 | − | 0.594507i | \(-0.797347\pi\) | ||||
−0.804090 | + | 0.594507i | \(0.797347\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.37697e26 | 0.0263060 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.49423e27 | 0.217432 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.97440e28 | 1.12944 | 0.564719 | − | 0.825283i | \(-0.308984\pi\) | ||||
0.564719 | + | 0.825283i | \(0.308984\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.08135e27 | 0.185165 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.10372e27 | −0.108555 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.37422e28 | −1.46867 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.74726e28 | 1.53035 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.93192e28 | 0.907600 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.22606e28 | −1.25643 | −0.628217 | − | 0.778038i | \(-0.716215\pi\) | ||||
−0.628217 | + | 0.778038i | \(0.716215\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.42283e28 | −1.83425 | −0.917125 | − | 0.398600i | \(-0.869496\pi\) | ||||
−0.917125 | + | 0.398600i | \(0.869496\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.95386e27 | 0.108480 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.25103e28 | 0.329805 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.17961e28 | −0.805545 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.30173e27 | −0.177801 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.59659e28 | −1.31005 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.20838e28 | −1.39722 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.44665e27 | 0.204431 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.85550e28 | −1.21866 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.00894e28 | 0.201974 | 0.100987 | − | 0.994888i | \(-0.467800\pi\) | ||||
0.100987 | + | 0.994888i | \(0.467800\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.15520e27 | 0.118534 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.78617e28 | −0.886798 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.94342e25 | −0.00177284 | −0.000886419 | − | 1.00000i | \(-0.500282\pi\) | ||||
−0.000886419 | 1.00000i | \(0.500282\pi\) | ||||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.10715e27 | −0.0876333 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.33764e28 | −0.551249 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.72398e27 | 0.0274105 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.30608e28 | 0.812264 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.03071e28 | −0.151935 | −0.0759676 | − | 0.997110i | \(-0.524205\pi\) | ||||
−0.0759676 | + | 0.997110i | \(0.524205\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.44432e28 | 1.05682 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.12577e29 | 1.53936 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.09973e28 | 1.06692 | 0.533461 | − | 0.845825i | \(-0.320891\pi\) | ||||
0.533461 | + | 0.845825i | \(0.320891\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.25363e28 | 0.793639 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.36530e27 | −0.0533816 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.57054e28 | 0.538628 | 0.269314 | − | 0.963052i | \(-0.413203\pi\) | ||||
0.269314 | + | 0.963052i | \(0.413203\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.57917e28 | −0.974465 | −0.487232 | − | 0.873272i | \(-0.661993\pi\) | ||||
−0.487232 | + | 0.873272i | \(0.661993\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.63322e26 | −0.00616785 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.63380e28 | 0.172459 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.50127e28 | −0.763464 | −0.381732 | − | 0.924273i | \(-0.624672\pi\) | ||||
−0.381732 | + | 0.924273i | \(0.624672\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.65890e28 | 0.947988 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.23766e28 | −0.590435 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.48472e29 | 2.26860 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.52432e28 | −0.310412 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.80794e29 | 1.53633 | 0.768163 | − | 0.640254i | \(-0.221171\pi\) | ||||
0.768163 | + | 0.640254i | \(0.221171\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.34819e28 | −0.110546 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.05650e28 | 0.0835991 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.00538e29 | −1.53152 | −0.765759 | − | 0.643128i | \(-0.777636\pi\) | ||||
−0.765759 | + | 0.643128i | \(0.777636\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.29357e29 | 0.953587 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.51244e28 | 0.534626 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.43168e29 | −1.67080 | −0.835401 | − | 0.549641i | \(-0.814765\pi\) | ||||
−0.835401 | + | 0.549641i | \(0.814765\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.21456e28 | 0.478661 | 0.239331 | − | 0.970938i | \(-0.423072\pi\) | ||||
0.239331 | + | 0.970938i | \(0.423072\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.48761e27 | −0.0415674 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.87830e29 | 1.78117 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.08349e29 | 1.84315 | 0.921575 | − | 0.388199i | \(-0.126903\pi\) | ||||
0.921575 | + | 0.388199i | \(0.126903\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.69430e28 | −0.271075 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.36696e29 | −0.762645 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.74135e29 | 0.938754 | 0.469377 | − | 0.882998i | \(-0.344478\pi\) | ||||
0.469377 | + | 0.882998i | \(0.344478\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.16876e29 | −1.12985 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.09708e29 | −0.552386 | −0.276193 | − | 0.961102i | \(-0.589073\pi\) | ||||
−0.276193 | + | 0.961102i | \(0.589073\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.18534e28 | −0.203695 | −0.101847 | − | 0.994800i | \(-0.532475\pi\) | ||||
−0.101847 | + | 0.994800i | \(0.532475\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.80381e28 | −0.0848649 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.07257e28 | 0.230730 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.81520e29 | −1.23814 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.21320e29 | −0.515969 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.88046e29 | 2.00738 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.19034e28 | 0.286049 | 0.143025 | − | 0.989719i | \(-0.454317\pi\) | ||||
0.143025 | + | 0.989719i | \(0.454317\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.55873e28 | 0.290877 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.23326e29 | −1.94827 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.68607e29 | 0.607312 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.70849e29 | 0.595462 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.94295e28 | −0.267900 | −0.133950 | − | 0.990988i | \(-0.542766\pi\) | ||||
−0.133950 | + | 0.990988i | \(0.542766\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.98801e29 | 0.975363 | 0.487682 | − | 0.873022i | \(-0.337843\pi\) | ||||
0.487682 | + | 0.873022i | \(0.337843\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.88478e29 | 0.911456 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.99749e29 | 0.610926 | 0.305463 | − | 0.952204i | \(-0.401189\pi\) | ||||
0.305463 | + | 0.952204i | \(0.401189\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.85414e29 | −0.845097 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.89619e28 | −0.0543604 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.93075e28 | 0.220154 | 0.110077 | − | 0.993923i | \(-0.464890\pi\) | ||||
0.110077 | + | 0.993923i | \(0.464890\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.99049e29 | −1.34156 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.93448e28 | −0.128471 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.45555e29 | 1.37576 | 0.687878 | − | 0.725826i | \(-0.258542\pi\) | ||||
0.687878 | + | 0.725826i | \(0.258542\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.69429e28 | 0.0902435 | 0.0451218 | − | 0.998981i | \(-0.485632\pi\) | ||||
0.0451218 | + | 0.998981i | \(0.485632\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.24162e29 | −0.767133 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.39403e29 | −0.319627 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.93976e29 | −0.430949 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.02152e29 | 1.08109 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.99632e29 | −0.416526 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.85053e29 | 0.374230 | 0.187115 | − | 0.982338i | \(-0.440086\pi\) | ||||
0.187115 | + | 0.982338i | \(0.440086\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.83958e28 | −0.0752651 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.29001e29 | 0.815225 | 0.407612 | − | 0.913155i | \(-0.366361\pi\) | ||||
0.407612 | + | 0.913155i | \(0.366361\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.29527e29 | 0.607098 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.46844e29 | −0.619570 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.06550e29 | −0.184559 | −0.0922796 | − | 0.995733i | \(-0.529415\pi\) | ||||
−0.0922796 | + | 0.995733i | \(0.529415\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.78117e29 | 0.803125 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.08699e29 | −0.502909 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.15467e29 | −1.13054 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.17173e29 | 0.792714 | 0.396357 | − | 0.918096i | \(-0.370274\pi\) | ||||
0.396357 | + | 0.918096i | \(0.370274\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.70633e29 | −0.253726 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.90141e29 | −1.13989 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.99480e30 | −2.79225 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.18419e29 | 0.975815 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.77924e29 | 0.761784 | 0.380892 | − | 0.924620i | \(-0.375617\pi\) | ||||
0.380892 | + | 0.924620i | \(0.375617\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.25949e29 | −0.672841 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.29715e29 | −0.657744 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.89028e27 | −0.0107155 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.60050e30 | −1.87270 | −0.936352 | − | 0.351063i | \(-0.885820\pi\) | ||||
−0.936352 | + | 0.351063i | \(0.885820\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.67415e28 | −0.0190179 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.83536e28 | −0.0864210 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.37761e30 | −1.47541 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.77288e29 | −0.912412 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.62814e29 | 0.669482 | 0.334741 | − | 0.942310i | \(-0.391351\pi\) | ||||
0.334741 | + | 0.942310i | \(0.391351\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.09820e29 | 0.598248 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.13496e30 | −1.08151 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.12896e29 | −0.382200 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.75931e29 | 0.338062 | 0.169031 | − | 0.985611i | \(-0.445936\pi\) | ||||
0.169031 | + | 0.985611i | \(0.445936\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.23912e28 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.65338e30 | 2.25251 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.05971e29 | 0.252400 | 0.126200 | − | 0.992005i | \(-0.459722\pi\) | ||||
0.126200 | + | 0.992005i | \(0.459722\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.53376e29 | 0.523777 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.53592e29 | −0.197573 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.09955e30 | −1.58987 | −0.794933 | − | 0.606698i | \(-0.792494\pi\) | ||||
−0.794933 | + | 0.606698i | \(0.792494\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.49337e29 | 0.257131 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.40094e30 | 1.00239 | 0.501196 | − | 0.865334i | \(-0.332893\pi\) | ||||
0.501196 | + | 0.865334i | \(0.332893\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.65551e30 | −1.84717 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.05736e29 | 0.409654 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.65524e29 | 0.569141 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.12216e30 | −1.35694 | −0.678468 | − | 0.734630i | \(-0.737356\pi\) | ||||
−0.678468 | + | 0.734630i | \(0.737356\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.83502e29 | −0.487184 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.39927e30 | −0.846170 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.95242e30 | 1.73649 | 0.868244 | − | 0.496138i | \(-0.165249\pi\) | ||||
0.868244 | + | 0.496138i | \(0.165249\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.05083e29 | −0.403368 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.69651e29 | 0.539606 | 0.269803 | − | 0.962916i | \(-0.413041\pi\) | ||||
0.269803 | + | 0.962916i | \(0.413041\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.67250e29 | 0.361228 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.25617e30 | −0.661614 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.21841e29 | 0.421150 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.29748e30 | 1.14558 | 0.572790 | − | 0.819702i | \(-0.305861\pi\) | ||||
0.572790 | + | 0.819702i | \(0.305861\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.48078e29 | −0.362974 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.39639e30 | −0.659361 | −0.329681 | − | 0.944093i | \(-0.606941\pi\) | ||||
−0.329681 | + | 0.944093i | \(0.606941\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.66783e29 | −0.0766451 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.39732e29 | −0.330867 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.14972e30 | 0.935918 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.67826e30 | 2.83027 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.55861e29 | 0.188076 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.60741e30 | 0.645648 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.65709e30 | 0.648053 | 0.324027 | − | 0.946048i | \(-0.394963\pi\) | ||||
0.324027 | + | 0.946048i | \(0.394963\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.05040e29 | −0.344635 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.71832e29 | −0.323281 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.74832e29 | 0.207574 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.77253e30 | −0.975039 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.83413e30 | 1.65579 | 0.827896 | − | 0.560882i | \(-0.189538\pi\) | ||||
0.827896 | + | 0.560882i | \(0.189538\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.87226e30 | −1.62551 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.92595e29 | −0.160084 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.92882e30 | −0.610630 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.10174e29 | −0.249874 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.12119e30 | 0.336905 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.24758e30 | −0.950823 | −0.475412 | − | 0.879763i | \(-0.657701\pi\) | ||||
−0.475412 | + | 0.879763i | \(0.657701\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.41163e30 | 0.402719 | 0.201360 | − | 0.979517i | \(-0.435464\pi\) | ||||
0.201360 | + | 0.979517i | \(0.435464\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.59013e29 | −0.127607 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.10187e30 | 1.92406 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.85945e30 | −0.755007 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.91333e29 | 0.126443 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.90028e30 | 1.73087 | 0.865433 | − | 0.501024i | \(-0.167043\pi\) | ||||
0.865433 | + | 0.501024i | \(0.167043\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.25832e30 | 0.796702 | 0.398351 | − | 0.917233i | \(-0.369583\pi\) | ||||
0.398351 | + | 0.917233i | \(0.369583\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.50084e30 | −0.357740 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.21005e30 | 0.281187 | 0.140593 | − | 0.990067i | \(-0.455099\pi\) | ||||
0.140593 | + | 0.990067i | \(0.455099\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.20920e30 | −0.500510 | −0.250255 | − | 0.968180i | \(-0.580514\pi\) | ||||
−0.250255 | + | 0.968180i | \(0.580514\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.65145e30 | 0.585696 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.00967e30 | 1.29443 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.11081e30 | 0.233310 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.84138e29 | 0.0377161 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.04315e30 | 1.80642 | 0.903211 | − | 0.429198i | \(-0.141204\pi\) | ||||
0.903211 | + | 0.429198i | \(0.141204\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.30662e29 | −0.0449385 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.37231e30 | 0.450798 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.39639e30 | −0.444183 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.01271e30 | −0.725540 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.33271e30 | 0.411462 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.05669e30 | −0.526006 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.44589e30 | 0.410650 | 0.205325 | − | 0.978694i | \(-0.434175\pi\) | ||||
0.205325 | + | 0.978694i | \(0.434175\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.35373e30 | 0.221763 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.48470e30 | −0.557015 | −0.278508 | − | 0.960434i | \(-0.589840\pi\) | ||||
−0.278508 | + | 0.960434i | \(0.589840\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.03387e30 | −0.473226 | −0.236613 | − | 0.971604i | \(-0.576037\pi\) | ||||
−0.236613 | + | 0.971604i | \(0.576037\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.02351e30 | 0.460234 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.80822e30 | −0.268620 | −0.134310 | − | 0.990939i | \(-0.542882\pi\) | ||||
−0.134310 | + | 0.990939i | \(0.542882\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.27880e31 | −1.85410 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.47433e30 | −1.05772 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.54400e29 | −0.0903932 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.30209e29 | 0.0984593 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.20002e30 | −0.421215 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.68503e30 | 0.345037 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.01880e31 | −1.27818 | −0.639089 | − | 0.769133i | \(-0.720689\pi\) | ||||
−0.639089 | + | 0.769133i | \(0.720689\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.26021e30 | −0.766842 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.65056e30 | −1.03466 | −0.517330 | − | 0.855786i | \(-0.673074\pi\) | ||||
−0.517330 | + | 0.855786i | \(0.673074\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.16043e31 | 1.35529 | 0.677643 | − | 0.735391i | \(-0.263002\pi\) | ||||
0.677643 | + | 0.735391i | \(0.263002\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.18475e30 | 0.363221 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.27819e30 | 0.365120 | 0.182560 | − | 0.983195i | \(-0.441562\pi\) | ||||
0.182560 | + | 0.983195i | \(0.441562\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.29581e30 | 0.793606 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.65701e30 | 0.176039 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.25064e30 | 0.544844 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.12029e30 | −0.417624 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.03026e30 | 0.201016 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.98017e30 | 0.191525 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.55014e31 | −2.40965 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.02174e30 | −0.371272 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.68468e30 | −0.242149 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.71433e30 | 0.239213 | 0.119607 | − | 0.992821i | \(-0.461837\pi\) | ||||
0.119607 | + | 0.992821i | \(0.461837\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.63331e28 | 0.00743458 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.50470e31 | −1.26621 | −0.633107 | − | 0.774064i | \(-0.718221\pi\) | ||||
−0.633107 | + | 0.774064i | \(0.718221\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.36774e31 | 1.94711 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.22756e30 | 0.179022 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.95735e30 | 0.546470 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.22782e31 | 0.942585 | 0.471292 | − | 0.881977i | \(-0.343788\pi\) | ||||
0.471292 | + | 0.881977i | \(0.343788\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.51886e30 | 0.564191 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.92298e31 | −1.41045 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.50645e30 | −0.466505 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.92193e30 | −0.415074 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.63481e31 | 1.80545 | 0.902724 | − | 0.430221i | \(-0.141564\pi\) | ||||
0.902724 | + | 0.430221i | \(0.141564\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.47639e30 | −0.433872 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.24182e31 | −0.813394 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.91021e31 | −3.14469 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.75508e30 | 0.548270 | 0.274135 | − | 0.961691i | \(-0.411608\pi\) | ||||
0.274135 | + | 0.961691i | \(0.411608\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.52235e30 | 0.154460 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.13855e31 | −1.28064 | −0.640321 | − | 0.768107i | \(-0.721199\pi\) | ||||
−0.640321 | + | 0.768107i | \(0.721199\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.24936e31 | 0.731671 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.90399e30 | 0.109051 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.33092e30 | 0.522697 | 0.261348 | − | 0.965245i | \(-0.415833\pi\) | ||||
0.261348 | + | 0.965245i | \(0.415833\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.55397e30 | 0.304304 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.26677e29 | 0.0335852 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.95374e30 | −0.364538 | −0.182269 | − | 0.983249i | \(-0.558344\pi\) | ||||
−0.182269 | + | 0.983249i | \(0.558344\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.45701e29 | 0.0126000 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.78190e31 | 0.893937 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.66554e30 | −0.327145 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.00256e31 | −0.961592 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.40506e30 | −0.394880 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.21287e31 | −1.93660 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.93817e30 | −0.312081 | −0.156040 | − | 0.987751i | \(-0.549873\pi\) | ||||
−0.156040 | + | 0.987751i | \(0.549873\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.24514e31 | 0.548050 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.25351e30 | −0.269353 | −0.134676 | − | 0.990890i | \(-0.543000\pi\) | ||||
−0.134676 | + | 0.990890i | \(0.543000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.10155e31 | 0.464324 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.32161e30 | 0.178278 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.80828e30 | −0.153757 | −0.0768787 | − | 0.997040i | \(-0.524495\pi\) | ||||
−0.0768787 | + | 0.997040i | \(0.524495\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.92548e31 | −0.760889 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.47964e30 | −0.250626 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.71631e31 | 0.649807 | 0.324903 | − | 0.945747i | \(-0.394668\pi\) | ||||
0.324903 | + | 0.945747i | \(0.394668\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.60808e30 | −0.170781 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.38488e30 | 0.267925 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.66184e31 | −0.590240 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.07510e31 | 0.373830 | 0.186915 | − | 0.982376i | \(-0.440151\pi\) | ||||
0.186915 | + | 0.982376i | \(0.440151\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.01973e29 | −0.0170889 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.27666e31 | −1.09217 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.35137e31 | −0.767399 | −0.383699 | − | 0.923458i | \(-0.625350\pi\) | ||||
−0.383699 | + | 0.923458i | \(0.625350\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.18350e30 | 0.229561 |
(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 | 48.22.a.h.1.2 | 2 | ||
4.3 | odd | 2 | 24.22.a.a.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 72.22.a.a.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.22.a.a.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
48.22.a.h.1.2 | 2 | 1.1 | even | 1 | trivial | ||
72.22.a.a.1.1 | 2 | 12.11 | even | 2 |