Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,8,Mod(1,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.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: | \(165.876448532\) |
Analytic rank: | \(1\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} - 1798 x^{16} + 11087 x^{15} + 1326765 x^{14} - 8403720 x^{13} - 518334228 x^{12} + \cdots + 51\!\cdots\!48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{5} \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Root | \(-17.7235\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 531.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 16.7235 | 1.47816 | 0.739082 | − | 0.673616i | \(-0.235260\pi\) | ||||
0.739082 | + | 0.673616i | \(0.235260\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 151.676 | 1.18497 | ||||||||
\(5\) | 298.819 | 1.06909 | 0.534543 | − | 0.845141i | \(-0.320484\pi\) | ||||
0.534543 | + | 0.845141i | \(0.320484\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 200.095 | 0.220493 | 0.110246 | − | 0.993904i | \(-0.464836\pi\) | ||||
0.110246 | + | 0.993904i | \(0.464836\pi\) | |||||||
\(8\) | 395.941 | 0.273411 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4997.30 | 1.58028 | ||||||||
\(11\) | −6819.80 | −1.54489 | −0.772444 | − | 0.635082i | \(-0.780966\pi\) | ||||
−0.772444 | + | 0.635082i | \(0.780966\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7653.89 | −0.966230 | −0.483115 | − | 0.875557i | \(-0.660495\pi\) | ||||
−0.483115 | + | 0.875557i | \(0.660495\pi\) | |||||||
\(14\) | 3346.30 | 0.325924 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −12793.0 | −0.780821 | ||||||||
\(17\) | 23868.2 | 1.17828 | 0.589141 | − | 0.808030i | \(-0.299466\pi\) | ||||
0.589141 | + | 0.808030i | \(0.299466\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 41453.1 | 1.38650 | 0.693249 | − | 0.720698i | \(-0.256179\pi\) | ||||
0.693249 | + | 0.720698i | \(0.256179\pi\) | |||||||
\(20\) | 45323.6 | 1.26683 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −114051. | −2.28360 | ||||||||
\(23\) | −87045.3 | −1.49176 | −0.745878 | − | 0.666082i | \(-0.767970\pi\) | ||||
−0.745878 | + | 0.666082i | \(0.767970\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11167.7 | 0.142947 | ||||||||
\(26\) | −128000. | −1.42825 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 30349.6 | 0.261276 | ||||||||
\(29\) | 28849.4 | 0.219657 | 0.109828 | − | 0.993951i | \(-0.464970\pi\) | ||||
0.109828 | + | 0.993951i | \(0.464970\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −136082. | −0.820419 | −0.410209 | − | 0.911991i | \(-0.634544\pi\) | ||||
−0.410209 | + | 0.911991i | \(0.634544\pi\) | |||||||
\(32\) | −264624. | −1.42759 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 399161. | 1.74169 | ||||||||
\(35\) | 59792.3 | 0.235726 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −238332. | −0.773527 | −0.386764 | − | 0.922179i | \(-0.626407\pi\) | ||||
−0.386764 | + | 0.922179i | \(0.626407\pi\) | |||||||
\(38\) | 693241. | 2.04947 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 118315. | 0.292300 | ||||||||
\(41\) | 387202. | 0.877394 | 0.438697 | − | 0.898635i | \(-0.355440\pi\) | ||||
0.438697 | + | 0.898635i | \(0.355440\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −560156. | −1.07441 | −0.537204 | − | 0.843452i | \(-0.680519\pi\) | ||||
−0.537204 | + | 0.843452i | \(0.680519\pi\) | |||||||
\(44\) | −1.03440e6 | −1.83064 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.45570e6 | −2.20506 | ||||||||
\(47\) | −343766. | −0.482970 | −0.241485 | − | 0.970405i | \(-0.577635\pi\) | ||||
−0.241485 | + | 0.970405i | \(0.577635\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −783505. | −0.951383 | ||||||||
\(50\) | 186763. | 0.211298 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.16091e6 | −1.14495 | ||||||||
\(53\) | −1.90828e6 | −1.76066 | −0.880332 | − | 0.474358i | \(-0.842680\pi\) | ||||
−0.880332 | + | 0.474358i | \(0.842680\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.03788e6 | −1.65162 | ||||||||
\(56\) | 79226.0 | 0.0602851 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 482464. | 0.324689 | ||||||||
\(59\) | −205379. | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.52219e6 | 1.42273 | 0.711366 | − | 0.702822i | \(-0.248077\pi\) | ||||
0.711366 | + | 0.702822i | \(0.248077\pi\) | |||||||
\(62\) | −2.27577e6 | −1.21271 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.78794e6 | −1.32939 | ||||||||
\(65\) | −2.28713e6 | −1.03298 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.23640e6 | 0.502224 | 0.251112 | − | 0.967958i | \(-0.419204\pi\) | ||||
0.251112 | + | 0.967958i | \(0.419204\pi\) | |||||||
\(68\) | 3.62023e6 | 1.39622 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 999937. | 0.348441 | ||||||||
\(71\) | 5.34185e6 | 1.77128 | 0.885640 | − | 0.464373i | \(-0.153720\pi\) | ||||
0.885640 | + | 0.464373i | \(0.153720\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.51521e6 | −1.35846 | −0.679232 | − | 0.733923i | \(-0.737687\pi\) | ||||
−0.679232 | + | 0.733923i | \(0.737687\pi\) | |||||||
\(74\) | −3.98574e6 | −1.14340 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.28743e6 | 1.64295 | ||||||||
\(77\) | −1.36461e6 | −0.340637 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.40570e6 | −0.320772 | −0.160386 | − | 0.987054i | \(-0.551274\pi\) | ||||
−0.160386 | + | 0.987054i | \(0.551274\pi\) | |||||||
\(80\) | −3.82278e6 | −0.834765 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.47538e6 | 1.29693 | ||||||||
\(83\) | −8.95946e6 | −1.71992 | −0.859961 | − | 0.510361i | \(-0.829512\pi\) | ||||
−0.859961 | + | 0.510361i | \(0.829512\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.13228e6 | 1.25969 | ||||||||
\(86\) | −9.36777e6 | −1.58815 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.70024e6 | −0.422389 | ||||||||
\(89\) | 1.30962e6 | 0.196916 | 0.0984581 | − | 0.995141i | \(-0.468609\pi\) | ||||
0.0984581 | + | 0.995141i | \(0.468609\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.53151e6 | −0.213047 | ||||||||
\(92\) | −1.32027e7 | −1.76768 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.74897e6 | −0.713909 | ||||||||
\(95\) | 1.23870e7 | 1.48229 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.27503e7 | 1.41847 | 0.709236 | − | 0.704971i | \(-0.249040\pi\) | ||||
0.709236 | + | 0.704971i | \(0.249040\pi\) | |||||||
\(98\) | −1.31029e7 | −1.40630 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.69387e6 | 0.169387 | ||||||||
\(101\) | −1.88135e7 | −1.81696 | −0.908478 | − | 0.417933i | \(-0.862755\pi\) | ||||
−0.908478 | + | 0.417933i | \(0.862755\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.54829e7 | 1.39611 | 0.698057 | − | 0.716042i | \(-0.254048\pi\) | ||||
0.698057 | + | 0.716042i | \(0.254048\pi\) | |||||||
\(104\) | −3.03049e6 | −0.264178 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.19131e7 | −2.60255 | ||||||||
\(107\) | −2.71022e6 | −0.213876 | −0.106938 | − | 0.994266i | \(-0.534105\pi\) | ||||
−0.106938 | + | 0.994266i | \(0.534105\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.25363e6 | 0.314606 | 0.157303 | − | 0.987550i | \(-0.449720\pi\) | ||||
0.157303 | + | 0.987550i | \(0.449720\pi\) | |||||||
\(110\) | −3.40806e7 | −2.44136 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.55981e6 | −0.172165 | ||||||||
\(113\) | −1.36740e7 | −0.891501 | −0.445750 | − | 0.895157i | \(-0.647063\pi\) | ||||
−0.445750 | + | 0.895157i | \(0.647063\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.60108e7 | −1.59482 | ||||||||
\(116\) | 4.37576e6 | 0.260286 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.43466e6 | −0.192440 | ||||||||
\(119\) | 4.77593e6 | 0.259802 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.70225e7 | 1.38668 | ||||||||
\(122\) | 4.21798e7 | 2.10303 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.06404e7 | −0.972169 | ||||||||
\(125\) | −2.00081e7 | −0.916264 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.13310e7 | 1.35726 | 0.678628 | − | 0.734482i | \(-0.262575\pi\) | ||||
0.678628 | + | 0.734482i | \(0.262575\pi\) | |||||||
\(128\) | −1.27523e7 | −0.537468 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.82488e7 | −1.52692 | ||||||||
\(131\) | 2.66364e6 | 0.103520 | 0.0517602 | − | 0.998660i | \(-0.483517\pi\) | ||||
0.0517602 | + | 0.998660i | \(0.483517\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.29457e6 | 0.305713 | ||||||||
\(134\) | 2.06770e7 | 0.742369 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.45042e6 | 0.322155 | ||||||||
\(137\) | −2.83551e6 | −0.0942126 | −0.0471063 | − | 0.998890i | \(-0.515000\pi\) | ||||
−0.0471063 | + | 0.998890i | \(0.515000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.75740e7 | 1.18669 | 0.593343 | − | 0.804950i | \(-0.297808\pi\) | ||||
0.593343 | + | 0.804950i | \(0.297808\pi\) | |||||||
\(140\) | 9.06904e6 | 0.279327 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.93344e7 | 2.61824 | ||||||||
\(143\) | 5.21980e7 | 1.49272 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.62076e6 | 0.234832 | ||||||||
\(146\) | −7.55102e7 | −2.00803 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.61491e7 | −0.916604 | ||||||||
\(149\) | −2.26234e7 | −0.560280 | −0.280140 | − | 0.959959i | \(-0.590381\pi\) | ||||
−0.280140 | + | 0.959959i | \(0.590381\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.07436e7 | −0.490303 | −0.245152 | − | 0.969485i | \(-0.578838\pi\) | ||||
−0.245152 | + | 0.969485i | \(0.578838\pi\) | |||||||
\(152\) | 1.64130e7 | 0.379084 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.28211e7 | −0.503516 | ||||||||
\(155\) | −4.06639e7 | −0.877099 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.37534e7 | −1.10855 | −0.554277 | − | 0.832332i | \(-0.687005\pi\) | ||||
−0.554277 | + | 0.832332i | \(0.687005\pi\) | |||||||
\(158\) | −2.35082e7 | −0.474154 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −7.90746e7 | −1.52622 | ||||||||
\(161\) | −1.74174e7 | −0.328921 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.39837e7 | 0.433769 | 0.216885 | − | 0.976197i | \(-0.430410\pi\) | ||||
0.216885 | + | 0.976197i | \(0.430410\pi\) | |||||||
\(164\) | 5.87292e7 | 1.03968 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.49834e8 | −2.54232 | ||||||||
\(167\) | −7.25545e7 | −1.20547 | −0.602736 | − | 0.797941i | \(-0.705923\pi\) | ||||
−0.602736 | + | 0.797941i | \(0.705923\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.16645e6 | −0.0663992 | ||||||||
\(170\) | 1.19277e8 | 1.86202 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.49620e7 | −1.27314 | ||||||||
\(173\) | −8.99082e7 | −1.32020 | −0.660098 | − | 0.751180i | \(-0.729485\pi\) | ||||
−0.660098 | + | 0.751180i | \(0.729485\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.23461e6 | 0.0315187 | ||||||||
\(176\) | 8.72455e7 | 1.20628 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.19015e7 | 0.291074 | ||||||||
\(179\) | −2.66685e7 | −0.347547 | −0.173774 | − | 0.984786i | \(-0.555596\pi\) | ||||
−0.173774 | + | 0.984786i | \(0.555596\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.27888e8 | −1.60308 | −0.801539 | − | 0.597943i | \(-0.795985\pi\) | ||||
−0.801539 | + | 0.597943i | \(0.795985\pi\) | |||||||
\(182\) | −2.56122e7 | −0.314918 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.44648e7 | −0.407862 | ||||||||
\(185\) | −7.12180e7 | −0.826968 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.62777e8 | −1.82031 | ||||||||
\(188\) | −5.21410e7 | −0.572304 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.07153e8 | 2.19106 | ||||||||
\(191\) | 3.33882e7 | 0.346718 | 0.173359 | − | 0.984859i | \(-0.444538\pi\) | ||||
0.173359 | + | 0.984859i | \(0.444538\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.61151e7 | 0.661988 | 0.330994 | − | 0.943633i | \(-0.392616\pi\) | ||||
0.330994 | + | 0.943633i | \(0.392616\pi\) | |||||||
\(194\) | 2.13230e8 | 2.09673 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.18839e8 | −1.12736 | ||||||||
\(197\) | 7.50492e6 | 0.0699381 | 0.0349691 | − | 0.999388i | \(-0.488867\pi\) | ||||
0.0349691 | + | 0.999388i | \(0.488867\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.88579e7 | 0.259584 | 0.129792 | − | 0.991541i | \(-0.458569\pi\) | ||||
0.129792 | + | 0.991541i | \(0.458569\pi\) | |||||||
\(200\) | 4.42175e6 | 0.0390832 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.14627e8 | −2.68576 | ||||||||
\(203\) | 5.77264e6 | 0.0484327 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.15703e8 | 0.938010 | ||||||||
\(206\) | 2.58928e8 | 2.06368 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 9.79160e7 | 0.754453 | ||||||||
\(209\) | −2.82702e8 | −2.14199 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.61521e8 | −1.18370 | −0.591849 | − | 0.806049i | \(-0.701602\pi\) | ||||
−0.591849 | + | 0.806049i | \(0.701602\pi\) | |||||||
\(212\) | −2.89440e8 | −2.08633 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.53245e7 | −0.316144 | ||||||||
\(215\) | −1.67385e8 | −1.14863 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.72294e7 | −0.180896 | ||||||||
\(218\) | 7.11356e7 | 0.465039 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.09098e8 | −1.95711 | ||||||||
\(221\) | −1.82685e8 | −1.13849 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.37272e8 | 0.828924 | 0.414462 | − | 0.910067i | \(-0.363970\pi\) | ||||
0.414462 | + | 0.910067i | \(0.363970\pi\) | |||||||
\(224\) | −5.29500e7 | −0.314773 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.28678e8 | −1.31778 | ||||||||
\(227\) | 5.03590e7 | 0.285750 | 0.142875 | − | 0.989741i | \(-0.454365\pi\) | ||||
0.142875 | + | 0.989741i | \(0.454365\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.29634e8 | 1.81388 | 0.906938 | − | 0.421264i | \(-0.138413\pi\) | ||||
0.906938 | + | 0.421264i | \(0.138413\pi\) | |||||||
\(230\) | −4.34991e8 | −2.35740 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.14227e7 | 0.0600565 | ||||||||
\(233\) | −4.35459e7 | −0.225529 | −0.112764 | − | 0.993622i | \(-0.535971\pi\) | ||||
−0.112764 | + | 0.993622i | \(0.535971\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.02724e8 | −0.516337 | ||||||||
\(236\) | −3.11510e7 | −0.154270 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.98703e7 | 0.384030 | ||||||||
\(239\) | 1.16895e8 | 0.553865 | 0.276933 | − | 0.960889i | \(-0.410682\pi\) | ||||
0.276933 | + | 0.960889i | \(0.410682\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.76459e8 | −1.73244 | −0.866219 | − | 0.499664i | \(-0.833457\pi\) | ||||
−0.866219 | + | 0.499664i | \(0.833457\pi\) | |||||||
\(242\) | 4.51911e8 | 2.04974 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.82555e8 | 1.68589 | ||||||||
\(245\) | −2.34126e8 | −1.01711 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.17277e8 | −1.33968 | ||||||||
\(248\) | −5.38806e7 | −0.224311 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.34606e8 | −1.35439 | ||||||||
\(251\) | −3.72328e8 | −1.48617 | −0.743084 | − | 0.669198i | \(-0.766638\pi\) | ||||
−0.743084 | + | 0.669198i | \(0.766638\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.93631e8 | 2.30460 | ||||||||
\(254\) | 5.23965e8 | 2.00625 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.43594e8 | 0.534928 | ||||||||
\(257\) | 4.73110e8 | 1.73859 | 0.869294 | − | 0.494296i | \(-0.164574\pi\) | ||||
0.869294 | + | 0.494296i | \(0.164574\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.76891e7 | −0.170557 | ||||||||
\(260\) | −3.46902e8 | −1.22405 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.45454e7 | 0.153020 | ||||||||
\(263\) | 4.08150e8 | 1.38349 | 0.691743 | − | 0.722144i | \(-0.256843\pi\) | ||||
0.691743 | + | 0.722144i | \(0.256843\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.70230e8 | −1.88230 | ||||||||
\(266\) | 1.38714e8 | 0.451893 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.87532e8 | 0.595119 | ||||||||
\(269\) | −5.16986e8 | −1.61937 | −0.809684 | − | 0.586865i | \(-0.800362\pi\) | ||||
−0.809684 | + | 0.586865i | \(0.800362\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.66936e7 | −0.173038 | −0.0865189 | − | 0.996250i | \(-0.527574\pi\) | ||||
−0.0865189 | + | 0.996250i | \(0.527574\pi\) | |||||||
\(272\) | −3.05346e8 | −0.920027 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.74196e7 | −0.139262 | ||||||||
\(275\) | −7.61615e7 | −0.220837 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.31128e8 | 0.653392 | 0.326696 | − | 0.945129i | \(-0.394065\pi\) | ||||
0.326696 | + | 0.945129i | \(0.394065\pi\) | |||||||
\(278\) | 6.28370e8 | 1.75412 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.36742e7 | 0.0644500 | ||||||||
\(281\) | −3.68378e8 | −0.990426 | −0.495213 | − | 0.868772i | \(-0.664910\pi\) | ||||
−0.495213 | + | 0.868772i | \(0.664910\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.19507e8 | 1.36251 | 0.681254 | − | 0.732047i | \(-0.261435\pi\) | ||||
0.681254 | + | 0.732047i | \(0.261435\pi\) | |||||||
\(284\) | 8.10228e8 | 2.09891 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.72934e8 | 2.20648 | ||||||||
\(287\) | 7.74774e7 | 0.193459 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.59354e8 | 0.388349 | ||||||||
\(290\) | 1.44169e8 | 0.347120 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.84848e8 | −1.60974 | ||||||||
\(293\) | 8.25048e8 | 1.91621 | 0.958104 | − | 0.286421i | \(-0.0924657\pi\) | ||||
0.958104 | + | 0.286421i | \(0.0924657\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.13711e7 | −0.139183 | ||||||||
\(296\) | −9.43653e7 | −0.211491 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.78342e8 | −0.828186 | ||||||||
\(299\) | 6.66235e8 | 1.44138 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.12085e8 | −0.236899 | ||||||||
\(302\) | −3.46906e8 | −0.724748 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.30308e8 | −1.08261 | ||||||||
\(305\) | 7.53677e8 | 1.52102 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.01480e8 | −0.397418 | −0.198709 | − | 0.980059i | \(-0.563675\pi\) | ||||
−0.198709 | + | 0.980059i | \(0.563675\pi\) | |||||||
\(308\) | −2.06978e8 | −0.403643 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.80044e8 | −1.29650 | ||||||||
\(311\) | −1.01602e8 | −0.191533 | −0.0957663 | − | 0.995404i | \(-0.530530\pi\) | ||||
−0.0957663 | + | 0.995404i | \(0.530530\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.09494e8 | −0.939148 | −0.469574 | − | 0.882893i | \(-0.655592\pi\) | ||||
−0.469574 | + | 0.882893i | \(0.655592\pi\) | |||||||
\(314\) | −8.98946e8 | −1.63863 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.13210e8 | −0.380104 | ||||||||
\(317\) | −5.25634e8 | −0.926779 | −0.463389 | − | 0.886155i | \(-0.653367\pi\) | ||||
−0.463389 | + | 0.886155i | \(0.653367\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.96747e8 | −0.339345 | ||||||||
\(320\) | −8.33088e8 | −1.42124 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.91279e8 | −0.486199 | ||||||||
\(323\) | 9.89412e8 | 1.63369 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.54764e7 | −0.138119 | ||||||||
\(326\) | 4.01091e8 | 0.641182 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.53309e8 | 0.239889 | ||||||||
\(329\) | −6.87860e7 | −0.106491 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.47062e8 | 0.374463 | 0.187231 | − | 0.982316i | \(-0.440049\pi\) | ||||
0.187231 | + | 0.982316i | \(0.440049\pi\) | |||||||
\(332\) | −1.35893e9 | −2.03805 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.21337e9 | −1.78188 | ||||||||
\(335\) | 3.69460e8 | 0.536921 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.28783e9 | 1.83296 | 0.916482 | − | 0.400076i | \(-0.131016\pi\) | ||||
0.916482 | + | 0.400076i | \(0.131016\pi\) | |||||||
\(338\) | −6.96777e7 | −0.0981488 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.08179e9 | 1.49269 | ||||||||
\(341\) | 9.28054e8 | 1.26746 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.21563e8 | −0.430266 | ||||||||
\(344\) | −2.21789e8 | −0.293755 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.50358e9 | −1.95146 | ||||||||
\(347\) | 1.16047e9 | 1.49101 | 0.745504 | − | 0.666502i | \(-0.232209\pi\) | ||||
0.745504 | + | 0.666502i | \(0.232209\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.00669e9 | 1.26767 | 0.633836 | − | 0.773467i | \(-0.281479\pi\) | ||||
0.633836 | + | 0.773467i | \(0.281479\pi\) | |||||||
\(350\) | 3.73705e7 | 0.0465897 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.80468e9 | 2.20547 | ||||||||
\(353\) | −2.36378e8 | −0.286019 | −0.143010 | − | 0.989721i | \(-0.545678\pi\) | ||||
−0.143010 | + | 0.989721i | \(0.545678\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.59624e9 | 1.89365 | ||||||||
\(356\) | 1.98638e8 | 0.233339 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.45992e8 | −0.513731 | ||||||||
\(359\) | 4.28699e8 | 0.489015 | 0.244507 | − | 0.969647i | \(-0.421374\pi\) | ||||
0.244507 | + | 0.969647i | \(0.421374\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.24486e8 | 0.922377 | ||||||||
\(362\) | −2.13873e9 | −2.36961 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.32293e8 | −0.252453 | ||||||||
\(365\) | −1.34923e9 | −1.45232 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.21528e9 | 1.28335 | 0.641677 | − | 0.766975i | \(-0.278239\pi\) | ||||
0.641677 | + | 0.766975i | \(0.278239\pi\) | |||||||
\(368\) | 1.11357e9 | 1.16479 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.19101e9 | −1.22239 | ||||||||
\(371\) | −3.81838e8 | −0.388213 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.41218e8 | 0.939094 | 0.469547 | − | 0.882907i | \(-0.344417\pi\) | ||||
0.469547 | + | 0.882907i | \(0.344417\pi\) | |||||||
\(374\) | −2.72220e9 | −2.69072 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.36111e8 | −0.132049 | ||||||||
\(377\) | −2.20811e8 | −0.212239 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.27326e8 | 0.214492 | 0.107246 | − | 0.994233i | \(-0.465797\pi\) | ||||
0.107246 | + | 0.994233i | \(0.465797\pi\) | |||||||
\(380\) | 1.87880e9 | 1.75646 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.58368e8 | 0.512506 | ||||||||
\(383\) | −1.40852e9 | −1.28105 | −0.640525 | − | 0.767938i | \(-0.721283\pi\) | ||||
−0.640525 | + | 0.767938i | \(0.721283\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.07771e8 | −0.364170 | ||||||||
\(386\) | 1.10568e9 | 0.978527 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.93392e9 | 1.68084 | ||||||||
\(389\) | −1.22433e9 | −1.05457 | −0.527285 | − | 0.849689i | \(-0.676790\pi\) | ||||
−0.527285 | + | 0.849689i | \(0.676790\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.07762e9 | −1.75771 | ||||||||
\(392\) | −3.10222e8 | −0.260118 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.25509e8 | 0.103380 | ||||||||
\(395\) | −4.20049e8 | −0.342933 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.38844e8 | −0.271790 | −0.135895 | − | 0.990723i | \(-0.543391\pi\) | ||||
−0.135895 | + | 0.990723i | \(0.543391\pi\) | |||||||
\(398\) | 4.82605e8 | 0.383708 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.42868e8 | −0.111616 | ||||||||
\(401\) | −1.32434e8 | −0.102564 | −0.0512820 | − | 0.998684i | \(-0.516331\pi\) | ||||
−0.0512820 | + | 0.998684i | \(0.516331\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.04156e9 | 0.792713 | ||||||||
\(404\) | −2.85355e9 | −2.15303 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.65388e7 | 0.0715914 | ||||||||
\(407\) | 1.62537e9 | 1.19501 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.81103e9 | 1.30886 | 0.654431 | − | 0.756122i | \(-0.272908\pi\) | ||||
0.654431 | + | 0.756122i | \(0.272908\pi\) | |||||||
\(410\) | 1.93497e9 | 1.38653 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.34837e9 | 1.65435 | ||||||||
\(413\) | −4.10954e7 | −0.0287057 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.67726e9 | −1.83874 | ||||||||
\(416\) | 2.02540e9 | 1.37938 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.72776e9 | −3.16620 | ||||||||
\(419\) | 2.75900e9 | 1.83233 | 0.916164 | − | 0.400805i | \(-0.131269\pi\) | ||||
0.916164 | + | 0.400805i | \(0.131269\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.24044e8 | −0.407594 | −0.203797 | − | 0.979013i | \(-0.565328\pi\) | ||||
−0.203797 | + | 0.979013i | \(0.565328\pi\) | |||||||
\(422\) | −2.70120e9 | −1.74970 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.55566e8 | −0.481385 | ||||||||
\(425\) | 2.66554e8 | 0.168431 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.04678e8 | 0.313702 | ||||||||
\(428\) | −4.11075e8 | −0.253436 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.79927e9 | −1.69787 | ||||||||
\(431\) | −2.11891e9 | −1.27480 | −0.637401 | − | 0.770532i | \(-0.719990\pi\) | ||||
−0.637401 | + | 0.770532i | \(0.719990\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.12211e9 | −0.664244 | −0.332122 | − | 0.943236i | \(-0.607765\pi\) | ||||
−0.332122 | + | 0.943236i | \(0.607765\pi\) | |||||||
\(434\) | −4.55372e8 | −0.267394 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.45172e8 | 0.372797 | ||||||||
\(437\) | −3.60830e9 | −2.06832 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.19818e9 | −0.675922 | −0.337961 | − | 0.941160i | \(-0.609737\pi\) | ||||
−0.337961 | + | 0.941160i | \(0.609737\pi\) | |||||||
\(440\) | −8.06882e8 | −0.451571 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.05513e9 | −1.68288 | ||||||||
\(443\) | 5.64409e8 | 0.308447 | 0.154224 | − | 0.988036i | \(-0.450712\pi\) | ||||
0.154224 | + | 0.988036i | \(0.450712\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.91340e8 | 0.210521 | ||||||||
\(446\) | 2.29567e9 | 1.22529 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.57854e8 | −0.293121 | ||||||||
\(449\) | 1.48373e9 | 0.773558 | 0.386779 | − | 0.922172i | \(-0.373588\pi\) | ||||
0.386779 | + | 0.922172i | \(0.373588\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.64064e9 | −1.35548 | ||||||||
\(452\) | −2.07402e9 | −1.05640 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.42179e8 | 0.422386 | ||||||||
\(455\) | −4.57644e8 | −0.227765 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.51906e9 | −0.744505 | −0.372253 | − | 0.928131i | \(-0.621415\pi\) | ||||
−0.372253 | + | 0.928131i | \(0.621415\pi\) | |||||||
\(458\) | 5.51264e9 | 2.68121 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.94520e9 | −1.88980 | ||||||||
\(461\) | −8.02602e8 | −0.381546 | −0.190773 | − | 0.981634i | \(-0.561099\pi\) | ||||
−0.190773 | + | 0.981634i | \(0.561099\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.47165e8 | 0.443499 | 0.221749 | − | 0.975104i | \(-0.428823\pi\) | ||||
0.221749 | + | 0.975104i | \(0.428823\pi\) | |||||||
\(464\) | −3.69070e8 | −0.171513 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.28241e8 | −0.333368 | ||||||||
\(467\) | −1.58449e9 | −0.719914 | −0.359957 | − | 0.932969i | \(-0.617209\pi\) | ||||
−0.359957 | + | 0.932969i | \(0.617209\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.47398e8 | 0.110737 | ||||||||
\(470\) | −1.71790e9 | −0.763231 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.13180e7 | −0.0355951 | ||||||||
\(473\) | 3.82015e9 | 1.65984 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.62936e8 | 0.198195 | ||||||||
\(476\) | 7.24392e8 | 0.307857 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.95490e9 | 0.818703 | ||||||||
\(479\) | 2.85017e6 | 0.00118494 | 0.000592471 | − | 1.00000i | \(-0.499811\pi\) | ||||
0.000592471 | 1.00000i | \(0.499811\pi\) | ||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.82416e9 | 0.747405 | ||||||||
\(482\) | −6.29571e9 | −2.56083 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.09866e9 | 1.64317 | ||||||||
\(485\) | 3.81004e9 | 1.51647 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.28087e9 | 0.502521 | 0.251260 | − | 0.967920i | \(-0.419155\pi\) | ||||
0.251260 | + | 0.967920i | \(0.419155\pi\) | |||||||
\(488\) | 9.98638e8 | 0.388990 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.91541e9 | −1.50346 | ||||||||
\(491\) | 1.37484e8 | 0.0524164 | 0.0262082 | − | 0.999657i | \(-0.491657\pi\) | ||||
0.0262082 | + | 0.999657i | \(0.491657\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.88586e8 | 0.258818 | ||||||||
\(494\) | −5.30599e9 | −1.98026 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.74090e9 | 0.640600 | ||||||||
\(497\) | 1.06888e9 | 0.390554 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.97156e8 | 0.0710327 | 0.0355163 | − | 0.999369i | \(-0.488692\pi\) | ||||
0.0355163 | + | 0.999369i | \(0.488692\pi\) | |||||||
\(500\) | −3.03474e9 | −1.08574 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.22663e9 | −2.19680 | ||||||||
\(503\) | 2.00636e9 | 0.702946 | 0.351473 | − | 0.936198i | \(-0.385681\pi\) | ||||
0.351473 | + | 0.936198i | \(0.385681\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.62182e9 | −1.94248 | ||||||||
\(506\) | 9.92760e9 | 3.40657 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.75216e9 | 1.60830 | ||||||||
\(509\) | −4.88057e9 | −1.64043 | −0.820216 | − | 0.572053i | \(-0.806147\pi\) | ||||
−0.820216 | + | 0.572053i | \(0.806147\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.03474e8 | −0.299531 | ||||||||
\(512\) | 4.03368e9 | 1.32818 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.91206e9 | 2.56992 | ||||||||
\(515\) | 4.62657e9 | 1.49257 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.34442e9 | 0.746135 | ||||||||
\(518\) | −7.97528e8 | −0.252111 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −9.05568e8 | −0.282429 | ||||||||
\(521\) | −3.48111e9 | −1.07842 | −0.539208 | − | 0.842173i | \(-0.681276\pi\) | ||||
−0.539208 | + | 0.842173i | \(0.681276\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.79645e8 | −0.268876 | −0.134438 | − | 0.990922i | \(-0.542923\pi\) | ||||
−0.134438 | + | 0.990922i | \(0.542923\pi\) | |||||||
\(524\) | 4.04010e8 | 0.122668 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.82570e9 | 2.04502 | ||||||||
\(527\) | −3.24804e9 | −0.966685 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.17206e9 | 1.22534 | ||||||||
\(530\) | −9.53625e9 | −2.78235 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.25809e9 | 0.362259 | ||||||||
\(533\) | −2.96360e9 | −0.847764 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.09866e8 | −0.228652 | ||||||||
\(536\) | 4.89542e8 | 0.137314 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.64582e9 | −2.39369 | ||||||||
\(539\) | 5.34335e9 | 1.46978 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.31588e9 | −1.44339 | −0.721697 | − | 0.692209i | \(-0.756638\pi\) | ||||
−0.721697 | + | 0.692209i | \(0.756638\pi\) | |||||||
\(542\) | −9.48115e8 | −0.255778 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.31611e9 | −1.68211 | ||||||||
\(545\) | 1.27106e9 | 0.336341 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.68079e9 | 1.22282 | 0.611412 | − | 0.791313i | \(-0.290602\pi\) | ||||
0.611412 | + | 0.791313i | \(0.290602\pi\) | |||||||
\(548\) | −4.30078e8 | −0.111639 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.27369e9 | −0.326433 | ||||||||
\(551\) | 1.19590e9 | 0.304554 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.81274e8 | −0.0707279 | ||||||||
\(554\) | 3.86527e9 | 0.965820 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.69907e9 | 1.40618 | ||||||||
\(557\) | −9.19162e8 | −0.225371 | −0.112686 | − | 0.993631i | \(-0.535945\pi\) | ||||
−0.112686 | + | 0.993631i | \(0.535945\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.28737e9 | 1.03813 | ||||||||
\(560\) | −7.64921e8 | −0.184060 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.16058e9 | −1.46401 | ||||||||
\(563\) | −2.14197e9 | −0.505865 | −0.252933 | − | 0.967484i | \(-0.581395\pi\) | ||||
−0.252933 | + | 0.967484i | \(0.581395\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.08606e9 | −0.953092 | ||||||||
\(566\) | 8.68798e9 | 2.01401 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.11506e9 | 0.484287 | ||||||||
\(569\) | 6.07580e9 | 1.38265 | 0.691323 | − | 0.722546i | \(-0.257028\pi\) | ||||
0.691323 | + | 0.722546i | \(0.257028\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.78352e9 | −1.52486 | −0.762428 | − | 0.647073i | \(-0.775993\pi\) | ||||
−0.762428 | + | 0.647073i | \(0.775993\pi\) | |||||||
\(572\) | 7.91717e9 | 1.76882 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.29569e9 | 0.285964 | ||||||||
\(575\) | −9.72096e8 | −0.213242 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.20797e9 | −0.478495 | −0.239248 | − | 0.970959i | \(-0.576901\pi\) | ||||
−0.239248 | + | 0.970959i | \(0.576901\pi\) | |||||||
\(578\) | 2.66497e9 | 0.574043 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.30756e9 | 0.278268 | ||||||||
\(581\) | −1.79275e9 | −0.379230 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.30141e10 | 2.72003 | ||||||||
\(584\) | −1.78776e9 | −0.371419 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.37977e10 | 2.83247 | ||||||||
\(587\) | 3.43972e9 | 0.701924 | 0.350962 | − | 0.936390i | \(-0.385855\pi\) | ||||
0.350962 | + | 0.936390i | \(0.385855\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.64103e9 | −1.13751 | ||||||||
\(590\) | −1.02634e9 | −0.205736 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.04897e9 | 0.603986 | ||||||||
\(593\) | 3.62804e9 | 0.714464 | 0.357232 | − | 0.934016i | \(-0.383721\pi\) | ||||
0.357232 | + | 0.934016i | \(0.383721\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.42714e9 | 0.277751 | ||||||||
\(596\) | −3.43142e9 | −0.663914 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.11418e10 | 2.13059 | ||||||||
\(599\) | −3.45165e9 | −0.656194 | −0.328097 | − | 0.944644i | \(-0.606407\pi\) | ||||
−0.328097 | + | 0.944644i | \(0.606407\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.18642e9 | 1.35037 | 0.675184 | − | 0.737649i | \(-0.264064\pi\) | ||||
0.675184 | + | 0.737649i | \(0.264064\pi\) | |||||||
\(602\) | −1.87445e9 | −0.350175 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.14630e9 | −0.580993 | ||||||||
\(605\) | 8.07483e9 | 1.48248 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.76353e9 | 1.40896 | 0.704480 | − | 0.709724i | \(-0.251180\pi\) | ||||
0.704480 | + | 0.709724i | \(0.251180\pi\) | |||||||
\(608\) | −1.09695e10 | −1.97935 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.26041e10 | 2.24832 | ||||||||
\(611\) | 2.63115e9 | 0.466660 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.87864e9 | 0.504750 | 0.252375 | − | 0.967630i | \(-0.418788\pi\) | ||||
0.252375 | + | 0.967630i | \(0.418788\pi\) | |||||||
\(614\) | −3.36945e9 | −0.587449 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.40306e8 | −0.0931337 | ||||||||
\(617\) | −9.59531e9 | −1.64460 | −0.822301 | − | 0.569053i | \(-0.807310\pi\) | ||||
−0.822301 | + | 0.569053i | \(0.807310\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.93284e8 | 0.117488 | 0.0587441 | − | 0.998273i | \(-0.481290\pi\) | ||||
0.0587441 | + | 0.998273i | \(0.481290\pi\) | |||||||
\(620\) | −6.16773e9 | −1.03933 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.69915e9 | −0.283116 | ||||||||
\(623\) | 2.62050e8 | 0.0434186 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.85127e9 | −1.12251 | ||||||||
\(626\) | −8.52053e9 | −1.38821 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.15309e9 | −1.31360 | ||||||||
\(629\) | −5.68856e9 | −0.911433 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.90432e9 | 0.777099 | 0.388549 | − | 0.921428i | \(-0.372976\pi\) | ||||
0.388549 | + | 0.921428i | \(0.372976\pi\) | |||||||
\(632\) | −5.56573e8 | −0.0877026 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.79044e9 | −1.36993 | ||||||||
\(635\) | 9.36231e9 | 1.45102 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.99686e9 | 0.919255 | ||||||||
\(638\) | −3.29031e9 | −0.501608 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.81062e9 | −0.574599 | ||||||||
\(641\) | 9.16838e9 | 1.37496 | 0.687479 | − | 0.726204i | \(-0.258717\pi\) | ||||
0.687479 | + | 0.726204i | \(0.258717\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.70285e9 | 0.697626 | 0.348813 | − | 0.937192i | \(-0.386585\pi\) | ||||
0.348813 | + | 0.937192i | \(0.386585\pi\) | |||||||
\(644\) | −2.64179e9 | −0.389761 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.65464e10 | 2.41485 | ||||||||
\(647\) | −5.90195e9 | −0.856703 | −0.428352 | − | 0.903612i | \(-0.640906\pi\) | ||||
−0.428352 | + | 0.903612i | \(0.640906\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.40064e9 | 0.201127 | ||||||||
\(650\) | −1.42947e9 | −0.204163 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.63774e9 | 0.514002 | ||||||||
\(653\) | −7.53884e9 | −1.05952 | −0.529759 | − | 0.848148i | \(-0.677718\pi\) | ||||
−0.529759 | + | 0.848148i | \(0.677718\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.95947e8 | 0.110672 | ||||||||
\(656\) | −4.95347e9 | −0.685087 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.15034e9 | −0.157412 | ||||||||
\(659\) | 8.90395e9 | 1.21195 | 0.605974 | − | 0.795484i | \(-0.292784\pi\) | ||||
0.605974 | + | 0.795484i | \(0.292784\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.51361e9 | −0.338527 | −0.169264 | − | 0.985571i | \(-0.554139\pi\) | ||||
−0.169264 | + | 0.985571i | \(0.554139\pi\) | |||||||
\(662\) | 4.13175e9 | 0.553517 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.54742e9 | −0.470245 | ||||||||
\(665\) | 2.47857e9 | 0.326833 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.51121e9 | −0.327674 | ||||||||
\(668\) | −1.10048e10 | −1.42844 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.17867e9 | 0.793657 | ||||||||
\(671\) | −1.72008e10 | −2.19796 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.80021e9 | 0.227651 | 0.113826 | − | 0.993501i | \(-0.463690\pi\) | ||||
0.113826 | + | 0.993501i | \(0.463690\pi\) | |||||||
\(674\) | 2.15370e10 | 2.70942 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.31949e8 | −0.0786808 | ||||||||
\(677\) | −7.89862e9 | −0.978343 | −0.489171 | − | 0.872188i | \(-0.662701\pi\) | ||||
−0.489171 | + | 0.872188i | \(0.662701\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.55128e9 | 0.312762 | ||||||||
\(680\) | 2.82396e9 | 0.344412 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.55203e10 | 1.87351 | ||||||||
\(683\) | −3.31446e9 | −0.398053 | −0.199026 | − | 0.979994i | \(-0.563778\pi\) | ||||
−0.199026 | + | 0.979994i | \(0.563778\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.47303e8 | −0.100721 | ||||||||
\(686\) | −5.37766e9 | −0.636003 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.16605e9 | 0.838920 | ||||||||
\(689\) | 1.46058e10 | 1.70121 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.78938e9 | −0.667512 | −0.333756 | − | 0.942659i | \(-0.608316\pi\) | ||||
−0.333756 | + | 0.942659i | \(0.608316\pi\) | |||||||
\(692\) | −1.36369e10 | −1.56439 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.94071e10 | 2.20395 | ||||||||
\(695\) | 1.12278e10 | 1.26867 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.24184e9 | 1.03382 | ||||||||
\(698\) | 1.68354e10 | 1.87383 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.38936e8 | 0.0373486 | ||||||||
\(701\) | 1.14194e10 | 1.25207 | 0.626036 | − | 0.779794i | \(-0.284676\pi\) | ||||
0.626036 | + | 0.779794i | \(0.284676\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.87958e9 | −1.07249 | ||||||||
\(704\) | 1.90132e10 | 2.05376 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.95307e9 | −0.422783 | ||||||||
\(707\) | −3.76449e9 | −0.400625 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.23857e10 | −1.30515 | −0.652575 | − | 0.757725i | \(-0.726311\pi\) | ||||
−0.652575 | + | 0.757725i | \(0.726311\pi\) | |||||||
\(710\) | 2.66948e10 | 2.79913 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.18534e8 | 0.0538390 | ||||||||
\(713\) | 1.18453e10 | 1.22386 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.55978e10 | 1.59585 | ||||||||
\(716\) | −4.04497e9 | −0.411832 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.16935e9 | 0.722844 | ||||||||
\(719\) | 1.16266e10 | 1.16655 | 0.583274 | − | 0.812275i | \(-0.301771\pi\) | ||||
0.583274 | + | 0.812275i | \(0.301771\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.09805e9 | 0.307833 | ||||||||
\(722\) | 1.37883e10 | 1.36342 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.93975e10 | −1.89959 | ||||||||
\(725\) | 3.22182e8 | 0.0313992 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.72736e9 | 0.842389 | 0.421194 | − | 0.906970i | \(-0.361611\pi\) | ||||
0.421194 | + | 0.906970i | \(0.361611\pi\) | |||||||
\(728\) | −6.06387e8 | −0.0582492 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.25639e10 | −2.14676 | ||||||||
\(731\) | −1.33699e10 | −1.26596 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.02816e10 | 1.90212 | 0.951062 | − | 0.309000i | \(-0.0999943\pi\) | ||||
0.951062 | + | 0.309000i | \(0.0999943\pi\) | |||||||
\(734\) | 2.03238e10 | 1.89701 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.30343e10 | 2.12962 | ||||||||
\(737\) | −8.43201e9 | −0.775881 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.02731e9 | −0.275932 | −0.137966 | − | 0.990437i | \(-0.544056\pi\) | ||||
−0.137966 | + | 0.990437i | \(0.544056\pi\) | |||||||
\(740\) | −1.08020e10 | −0.979929 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.38567e9 | −0.573843 | ||||||||
\(743\) | −1.35696e10 | −1.21369 | −0.606843 | − | 0.794822i | \(-0.707564\pi\) | ||||
−0.606843 | + | 0.794822i | \(0.707564\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.76029e9 | −0.598988 | ||||||||
\(746\) | 1.57405e10 | 1.38813 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.46893e10 | −2.15701 | ||||||||
\(749\) | −5.42304e8 | −0.0471581 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.38238e10 | −1.19094 | −0.595469 | − | 0.803378i | \(-0.703034\pi\) | ||||
−0.595469 | + | 0.803378i | \(0.703034\pi\) | |||||||
\(752\) | 4.39779e9 | 0.377113 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.69273e9 | −0.313724 | ||||||||
\(755\) | −6.19858e9 | −0.524177 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.53342e9 | −0.128477 | −0.0642386 | − | 0.997935i | \(-0.520462\pi\) | ||||
−0.0642386 | + | 0.997935i | \(0.520462\pi\) | |||||||
\(758\) | 3.80168e9 | 0.317054 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.90451e9 | 0.405273 | ||||||||
\(761\) | 8.31351e9 | 0.683814 | 0.341907 | − | 0.939734i | \(-0.388927\pi\) | ||||
0.341907 | + | 0.939734i | \(0.388927\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.51131e8 | 0.0693682 | ||||||||
\(764\) | 5.06418e9 | 0.410849 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.35553e10 | −1.89360 | ||||||||
\(767\) | 1.57195e9 | 0.125792 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.21279e10 | 0.961710 | 0.480855 | − | 0.876800i | \(-0.340326\pi\) | ||||
0.480855 | + | 0.876800i | \(0.340326\pi\) | |||||||
\(770\) | −6.81937e9 | −0.538303 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.00281e10 | 0.784434 | ||||||||
\(773\) | 8.47150e9 | 0.659678 | 0.329839 | − | 0.944037i | \(-0.393006\pi\) | ||||
0.329839 | + | 0.944037i | \(0.393006\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.51973e9 | −0.117276 | ||||||||
\(776\) | 5.04838e9 | 0.387825 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.04751e10 | −1.55883 | ||||||||
\(779\) | 1.60507e10 | 1.21650 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.64303e10 | −2.73643 | ||||||||
\(782\) | −3.47451e10 | −2.59818 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00234e10 | 0.742860 | ||||||||
\(785\) | −1.60625e10 | −1.18514 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.35820e10 | −0.993233 | −0.496617 | − | 0.867970i | \(-0.665424\pi\) | ||||
−0.496617 | + | 0.867970i | \(0.665424\pi\) | |||||||
\(788\) | 1.13831e9 | 0.0828744 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7.02469e9 | −0.506912 | ||||||||
\(791\) | −2.73611e9 | −0.196569 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.93045e10 | −1.37469 | ||||||||
\(794\) | −5.66666e9 | −0.401750 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.37704e9 | 0.307599 | ||||||||
\(797\) | 2.11682e10 | 1.48108 | 0.740542 | − | 0.672010i | \(-0.234569\pi\) | ||||
0.740542 | + | 0.672010i | \(0.234569\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.20509e9 | −0.569075 | ||||||||
\(800\) | −2.95524e9 | −0.204069 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.21477e9 | −0.151606 | ||||||||
\(803\) | 3.07929e10 | 2.09868 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.20464e9 | −0.351645 | ||||||||
\(806\) | 1.74185e10 | 1.17176 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.44903e9 | −0.496775 | ||||||||
\(809\) | 5.28973e9 | 0.351248 | 0.175624 | − | 0.984457i | \(-0.443806\pi\) | ||||
0.175624 | + | 0.984457i | \(0.443806\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.57240e10 | 1.69342 | 0.846710 | − | 0.532054i | \(-0.178580\pi\) | ||||
0.846710 | + | 0.532054i | \(0.178580\pi\) | |||||||
\(812\) | 8.75570e8 | 0.0573911 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.71819e10 | 1.76642 | ||||||||
\(815\) | 7.16677e9 | 0.463737 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.32202e10 | −1.48966 | ||||||||
\(818\) | 3.02868e10 | 1.93471 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.75494e10 | 1.11151 | ||||||||
\(821\) | 3.97061e8 | 0.0250413 | 0.0125206 | − | 0.999922i | \(-0.496014\pi\) | ||||
0.0125206 | + | 0.999922i | \(0.496014\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.17465e10 | −1.35985 | −0.679923 | − | 0.733283i | \(-0.737987\pi\) | ||||
−0.679923 | + | 0.733283i | \(0.737987\pi\) | |||||||
\(824\) | 6.13030e9 | 0.381713 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.87259e8 | −0.0424317 | ||||||||
\(827\) | −1.11227e10 | −0.683821 | −0.341910 | − | 0.939733i | \(-0.611074\pi\) | ||||
−0.341910 | + | 0.939733i | \(0.611074\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.06605e9 | −0.552684 | −0.276342 | − | 0.961059i | \(-0.589122\pi\) | ||||
−0.276342 | + | 0.961059i | \(0.589122\pi\) | |||||||
\(830\) | −4.47731e10 | −2.71797 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.13386e10 | 1.28450 | ||||||||
\(833\) | −1.87009e10 | −1.12100 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.16807e10 | −1.28875 | ||||||||
\(836\) | −4.28790e10 | −2.53818 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.61402e10 | 2.70848 | ||||||||
\(839\) | −5.43132e9 | −0.317496 | −0.158748 | − | 0.987319i | \(-0.550746\pi\) | ||||
−0.158748 | + | 0.987319i | \(0.550746\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.64176e10 | −0.951751 | ||||||||
\(842\) | −1.04362e10 | −0.602491 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.44988e10 | −1.40264 | ||||||||
\(845\) | −1.24501e9 | −0.0709865 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.40708e9 | 0.305753 | ||||||||
\(848\) | 2.44126e10 | 1.37476 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.45771e9 | 0.248969 | ||||||||
\(851\) | 2.07456e10 | 1.15391 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.82993e9 | −0.376786 | −0.188393 | − | 0.982094i | \(-0.560328\pi\) | ||||
−0.188393 | + | 0.982094i | \(0.560328\pi\) | |||||||
\(854\) | 8.43999e9 | 0.463702 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.07309e9 | −0.0584760 | ||||||||
\(857\) | −3.60369e10 | −1.95576 | −0.977878 | − | 0.209178i | \(-0.932921\pi\) | ||||
−0.977878 | + | 0.209178i | \(0.932921\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.90837e10 | 1.02727 | 0.513637 | − | 0.858008i | \(-0.328298\pi\) | ||||
0.513637 | + | 0.858008i | \(0.328298\pi\) | |||||||
\(860\) | −2.53882e10 | −1.36109 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.54357e10 | −1.88437 | ||||||||
\(863\) | 3.33278e10 | 1.76510 | 0.882550 | − | 0.470218i | \(-0.155825\pi\) | ||||
0.882550 | + | 0.470218i | \(0.155825\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.68663e10 | −1.41140 | ||||||||
\(866\) | −1.87656e10 | −0.981861 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.13004e9 | −0.214356 | ||||||||
\(869\) | 9.58657e9 | 0.495558 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.46328e9 | −0.485264 | ||||||||
\(872\) | 1.68419e9 | 0.0860166 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.03434e10 | −3.05731 | ||||||||
\(875\) | −4.00353e9 | −0.202030 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.92873e10 | 1.46616 | 0.733079 | − | 0.680143i | \(-0.238082\pi\) | ||||
0.733079 | + | 0.680143i | \(0.238082\pi\) | |||||||
\(878\) | −2.00378e10 | −0.999124 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.60706e10 | 1.28962 | ||||||||
\(881\) | 7.06390e9 | 0.348040 | 0.174020 | − | 0.984742i | \(-0.444324\pi\) | ||||
0.174020 | + | 0.984742i | \(0.444324\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.11700e10 | −1.03480 | −0.517401 | − | 0.855743i | \(-0.673100\pi\) | ||||
−0.517401 | + | 0.855743i | \(0.673100\pi\) | |||||||
\(884\) | −2.77089e10 | −1.34907 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.43890e9 | 0.455935 | ||||||||
\(887\) | −3.92843e9 | −0.189011 | −0.0945053 | − | 0.995524i | \(-0.530127\pi\) | ||||
−0.0945053 | + | 0.995524i | \(0.530127\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.26920e9 | 0.299265 | ||||||||
\(890\) | 6.54458e9 | 0.311184 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.08208e10 | 0.982248 | ||||||||
\(893\) | −1.42502e10 | −0.669637 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.96906e9 | −0.371558 | ||||||||
\(896\) | −2.55167e9 | −0.118508 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.48132e10 | 1.14345 | ||||||||
\(899\) | −3.92590e9 | −0.180211 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.55473e10 | −2.07456 | ||||||||
\(902\) | −4.41608e10 | −2.00361 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.41411e9 | −0.243746 | ||||||||
\(905\) | −3.82153e10 | −1.71383 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.73810e10 | 0.773482 | 0.386741 | − | 0.922188i | \(-0.373601\pi\) | ||||
0.386741 | + | 0.922188i | \(0.373601\pi\) | |||||||
\(908\) | 7.63824e9 | 0.338605 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.65341e9 | −0.336674 | ||||||||
\(911\) | −3.94515e9 | −0.172882 | −0.0864409 | − | 0.996257i | \(-0.527549\pi\) | ||||
−0.0864409 | + | 0.996257i | \(0.527549\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.11017e10 | 2.65709 | ||||||||
\(914\) | −2.54040e10 | −1.10050 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.99975e10 | 2.14938 | ||||||||
\(917\) | 5.32983e8 | 0.0228255 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.68687e10 | −0.716930 | −0.358465 | − | 0.933543i | \(-0.616700\pi\) | ||||
−0.358465 | + | 0.933543i | \(0.616700\pi\) | |||||||
\(920\) | −1.02987e10 | −0.436040 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.34223e10 | −0.563987 | ||||||||
\(923\) | −4.08859e10 | −1.71146 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.66162e9 | −0.110573 | ||||||||
\(926\) | 1.58399e10 | 0.655564 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.63425e9 | −0.313580 | ||||||||
\(929\) | −5.86634e9 | −0.240056 | −0.120028 | − | 0.992771i | \(-0.538298\pi\) | ||||
−0.120028 | + | 0.992771i | \(0.538298\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.24787e10 | −1.31909 | ||||||||
\(932\) | −6.60486e9 | −0.267244 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.64983e10 | −1.06415 | ||||||||
\(935\) | −4.86407e10 | −1.94607 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.42022e10 | 0.961093 | 0.480546 | − | 0.876969i | \(-0.340438\pi\) | ||||
0.480546 | + | 0.876969i | \(0.340438\pi\) | |||||||
\(938\) | 4.13737e9 | 0.163687 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.55807e10 | −0.611842 | ||||||||
\(941\) | −2.22320e10 | −0.869792 | −0.434896 | − | 0.900481i | \(-0.643215\pi\) | ||||
−0.434896 | + | 0.900481i | \(0.643215\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.37041e10 | −1.30886 | ||||||||
\(944\) | 2.62741e9 | 0.101654 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.38863e10 | 2.45351 | ||||||||
\(947\) | −2.37539e9 | −0.0908889 | −0.0454444 | − | 0.998967i | \(-0.514470\pi\) | ||||
−0.0454444 | + | 0.998967i | \(0.514470\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.45590e10 | 1.31259 | ||||||||
\(950\) | 7.74191e9 | 0.292965 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.89099e9 | 0.0710328 | ||||||||
\(953\) | 2.11402e10 | 0.791197 | 0.395599 | − | 0.918423i | \(-0.370537\pi\) | ||||
0.395599 | + | 0.918423i | \(0.370537\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.97702e9 | 0.370671 | ||||||||
\(956\) | 1.77302e10 | 0.656312 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.76649e7 | 0.00175154 | ||||||||
\(959\) | −5.67372e8 | −0.0207732 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.99423e9 | −0.326913 | ||||||||
\(962\) | 3.05064e10 | 1.10479 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.70996e10 | −2.05288 | ||||||||
\(965\) | 1.97564e10 | 0.707723 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.04540e9 | −0.321688 | −0.160844 | − | 0.986980i | \(-0.551422\pi\) | ||||
−0.160844 | + | 0.986980i | \(0.551422\pi\) | |||||||
\(968\) | 1.06993e10 | 0.379134 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.37173e10 | 2.24159 | ||||||||
\(971\) | 4.75592e9 | 0.166712 | 0.0833560 | − | 0.996520i | \(-0.473436\pi\) | ||||
0.0833560 | + | 0.996520i | \(0.473436\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.51839e9 | 0.261656 | ||||||||
\(974\) | 2.14207e10 | 0.742808 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.22663e10 | −1.11090 | ||||||||
\(977\) | −1.97475e9 | −0.0677456 | −0.0338728 | − | 0.999426i | \(-0.510784\pi\) | ||||
−0.0338728 | + | 0.999426i | \(0.510784\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.93137e9 | −0.304214 | ||||||||
\(980\) | −3.55112e10 | −1.20524 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.29922e9 | 0.0774801 | ||||||||
\(983\) | −1.84818e10 | −0.620592 | −0.310296 | − | 0.950640i | \(-0.600428\pi\) | ||||
−0.310296 | + | 0.950640i | \(0.600428\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.24261e9 | 0.0747699 | ||||||||
\(986\) | 1.15156e10 | 0.382575 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.81233e10 | −1.58747 | ||||||||
\(989\) | 4.87589e10 | 1.60275 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.09246e9 | 0.0356573 | 0.0178286 | − | 0.999841i | \(-0.494325\pi\) | ||||
0.0178286 | + | 0.999841i | \(0.494325\pi\) | |||||||
\(992\) | 3.60106e10 | 1.17122 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.78754e10 | 0.577303 | ||||||||
\(995\) | 8.62327e9 | 0.277518 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.48711e9 | −0.239266 | −0.119633 | − | 0.992818i | \(-0.538172\pi\) | ||||
−0.119633 | + | 0.992818i | \(0.538172\pi\) | |||||||
\(998\) | 3.29714e9 | 0.104998 | ||||||||
\(999\) | 0 | 0 |
(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 | 531.8.a.e.1.16 | 18 | ||
3.2 | odd | 2 | 177.8.a.d.1.3 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.d.1.3 | ✓ | 18 | 3.2 | odd | 2 | ||
531.8.a.e.1.16 | 18 | 1.1 | even | 1 | trivial |