Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9,64,Mod(1,9)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 64, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.1");
S:= CuspForms(chi, 64);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 64 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.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: | \(226.224870226\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2 x^{4} + \cdots - 35\!\cdots\!34 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{37}\cdot 3^{22}\cdot 5^{3}\cdot 7^{2}\cdot 13 \) |
Twist minimal: | no (minimal twist has level 1) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.73795e7\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.14986e9 | 0.378616 | 0.189308 | − | 0.981918i | \(-0.439376\pi\) | ||||
0.189308 | + | 0.981918i | \(0.439376\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.90120e18 | −0.856650 | ||||||||
\(5\) | 9.56939e21 | 0.919029 | 0.459514 | − | 0.888170i | \(-0.348023\pi\) | ||||
0.459514 | + | 0.888170i | \(0.348023\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.15073e26 | −0.275667 | −0.137833 | − | 0.990455i | \(-0.544014\pi\) | ||||
−0.137833 | + | 0.990455i | \(0.544014\pi\) | |||||||
\(8\) | −1.96908e28 | −0.702958 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.10034e31 | 0.347959 | ||||||||
\(11\) | 2.43908e32 | 0.383139 | 0.191570 | − | 0.981479i | \(-0.438642\pi\) | ||||
0.191570 | + | 0.981479i | \(0.438642\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.25036e35 | 1.01817 | 0.509084 | − | 0.860717i | \(-0.329984\pi\) | ||||
0.509084 | + | 0.860717i | \(0.329984\pi\) | |||||||
\(14\) | −1.32317e35 | −0.104372 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.02341e37 | 0.590499 | ||||||||
\(17\) | −7.86280e38 | −1.36910 | −0.684552 | − | 0.728964i | \(-0.740002\pi\) | ||||
−0.684552 | + | 0.728964i | \(0.740002\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.70961e39 | −0.141961 | −0.0709805 | − | 0.997478i | \(-0.522613\pi\) | ||||
−0.0709805 | + | 0.997478i | \(0.522613\pi\) | |||||||
\(20\) | −7.56097e40 | −0.787286 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.80460e41 | 0.145063 | ||||||||
\(23\) | −3.63454e42 | −0.463471 | −0.231735 | − | 0.972779i | \(-0.574440\pi\) | ||||
−0.231735 | + | 0.972779i | \(0.574440\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.68470e43 | −0.155386 | ||||||||
\(26\) | 1.43774e44 | 0.385495 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 9.09213e44 | 0.236150 | ||||||||
\(29\) | −3.93841e45 | −0.338675 | −0.169338 | − | 0.985558i | \(-0.554163\pi\) | ||||
−0.169338 | + | 0.985558i | \(0.554163\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.18807e47 | 1.25011 | 0.625055 | − | 0.780581i | \(-0.285076\pi\) | ||||
0.625055 | + | 0.780581i | \(0.285076\pi\) | |||||||
\(32\) | 2.39378e47 | 0.926530 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −9.04110e47 | −0.518365 | ||||||||
\(35\) | −1.10118e48 | −0.253346 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.80510e49 | 0.721350 | 0.360675 | − | 0.932692i | \(-0.382546\pi\) | ||||
0.360675 | + | 0.932692i | \(0.382546\pi\) | |||||||
\(38\) | −3.11567e48 | −0.0537487 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.88429e50 | −0.646038 | ||||||||
\(41\) | −3.23583e50 | −0.509677 | −0.254838 | − | 0.966984i | \(-0.582022\pi\) | ||||
−0.254838 | + | 0.966984i | \(0.582022\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.59653e50 | 0.302042 | 0.151021 | − | 0.988531i | \(-0.451744\pi\) | ||||
0.151021 | + | 0.988531i | \(0.451744\pi\) | |||||||
\(44\) | −1.92717e51 | −0.328216 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.17920e51 | −0.175477 | ||||||||
\(47\) | −1.26451e52 | −0.269674 | −0.134837 | − | 0.990868i | \(-0.543051\pi\) | ||||
−0.134837 | + | 0.990868i | \(0.543051\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.61010e53 | −0.924008 | ||||||||
\(50\) | −1.93716e52 | −0.0588315 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −9.87934e53 | −0.872213 | ||||||||
\(53\) | 5.19617e53 | 0.251764 | 0.125882 | − | 0.992045i | \(-0.459824\pi\) | ||||
0.125882 | + | 0.992045i | \(0.459824\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.33405e54 | 0.352116 | ||||||||
\(56\) | 2.26588e54 | 0.193782 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.52860e54 | −0.128228 | ||||||||
\(59\) | 4.37498e55 | 0.722999 | 0.361500 | − | 0.932372i | \(-0.382265\pi\) | ||||
0.361500 | + | 0.932372i | \(0.382265\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.79669e56 | 1.61716 | 0.808582 | − | 0.588383i | \(-0.200235\pi\) | ||||
0.808582 | + | 0.588383i | \(0.200235\pi\) | |||||||
\(62\) | 1.36611e56 | 0.473312 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.88077e56 | −0.239700 | ||||||||
\(65\) | 1.19652e57 | 0.935726 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.12890e57 | 0.339860 | 0.169930 | − | 0.985456i | \(-0.445646\pi\) | ||||
0.169930 | + | 0.985456i | \(0.445646\pi\) | |||||||
\(68\) | 6.21256e57 | 1.17284 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.26620e57 | −0.0959208 | ||||||||
\(71\) | −1.56870e58 | −0.760154 | −0.380077 | − | 0.924955i | \(-0.624103\pi\) | ||||
−0.380077 | + | 0.924955i | \(0.624103\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.21857e58 | −1.86206 | −0.931030 | − | 0.364943i | \(-0.881088\pi\) | ||||
−0.931030 | + | 0.364943i | \(0.881088\pi\) | |||||||
\(74\) | 2.07560e58 | 0.273115 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.14092e58 | 0.121611 | ||||||||
\(77\) | −2.80672e58 | −0.105619 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.18902e59 | −0.702844 | −0.351422 | − | 0.936217i | \(-0.614302\pi\) | ||||
−0.351422 | + | 0.936217i | \(0.614302\pi\) | |||||||
\(80\) | 4.80710e59 | 0.542685 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.72075e59 | −0.192972 | ||||||||
\(83\) | 3.28273e60 | 1.16218 | 0.581092 | − | 0.813838i | \(-0.302626\pi\) | ||||
0.581092 | + | 0.813838i | \(0.302626\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.52422e60 | −1.25825 | ||||||||
\(86\) | 9.88478e59 | 0.114358 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.80275e60 | −0.269331 | ||||||||
\(89\) | 3.02241e61 | 1.18732 | 0.593660 | − | 0.804716i | \(-0.297683\pi\) | ||||
0.593660 | + | 0.804716i | \(0.297683\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.43882e61 | −0.280675 | ||||||||
\(92\) | 2.87172e61 | 0.397032 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.45400e61 | −0.102103 | ||||||||
\(95\) | −2.59294e61 | −0.130466 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.45642e61 | 0.142429 | 0.0712145 | − | 0.997461i | \(-0.477313\pi\) | ||||
0.0712145 | + | 0.997461i | \(0.477313\pi\) | |||||||
\(98\) | −1.85138e62 | −0.349844 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.33111e62 | 0.133111 | ||||||||
\(101\) | −7.79995e62 | −0.570123 | −0.285061 | − | 0.958509i | \(-0.592014\pi\) | ||||
−0.285061 | + | 0.958509i | \(0.592014\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.40638e63 | 0.948401 | 0.474200 | − | 0.880417i | \(-0.342737\pi\) | ||||
0.474200 | + | 0.880417i | \(0.342737\pi\) | |||||||
\(104\) | −2.46206e63 | −0.715729 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.97486e62 | 0.0953219 | ||||||||
\(107\) | −9.53357e63 | −1.13153 | −0.565766 | − | 0.824566i | \(-0.691419\pi\) | ||||
−0.565766 | + | 0.824566i | \(0.691419\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.35388e63 | −0.288365 | −0.144182 | − | 0.989551i | \(-0.546055\pi\) | ||||
−0.144182 | + | 0.989551i | \(0.546055\pi\) | |||||||
\(110\) | 2.68383e63 | 0.133317 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.78057e63 | −0.162781 | ||||||||
\(113\) | 3.09629e64 | 0.658978 | 0.329489 | − | 0.944159i | \(-0.393123\pi\) | ||||
0.329489 | + | 0.944159i | \(0.393123\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.47803e64 | −0.425943 | ||||||||
\(116\) | 3.11181e64 | 0.290126 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.03060e64 | 0.273739 | ||||||||
\(119\) | 9.04794e64 | 0.377416 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.45774e65 | −0.853204 | ||||||||
\(122\) | 3.21579e65 | 0.612285 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.38717e65 | −1.07091 | ||||||||
\(125\) | −1.19873e66 | −1.06183 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.71483e66 | −0.921308 | −0.460654 | − | 0.887580i | \(-0.652385\pi\) | ||||
−0.460654 | + | 0.887580i | \(0.652385\pi\) | |||||||
\(128\) | −2.42413e66 | −1.01728 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.37583e66 | 0.354281 | ||||||||
\(131\) | 4.29490e66 | 0.868774 | 0.434387 | − | 0.900726i | \(-0.356965\pi\) | ||||
0.434387 | + | 0.900726i | \(0.356965\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.11803e65 | 0.0391339 | ||||||||
\(134\) | 1.29808e66 | 0.128676 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.54825e67 | 0.962422 | ||||||||
\(137\) | −2.53921e67 | −1.25315 | −0.626573 | − | 0.779363i | \(-0.715543\pi\) | ||||
−0.626573 | + | 0.779363i | \(0.715543\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.60697e67 | 0.502390 | 0.251195 | − | 0.967937i | \(-0.419176\pi\) | ||||
0.251195 | + | 0.967937i | \(0.419176\pi\) | |||||||
\(140\) | 8.70062e66 | 0.217029 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.80378e67 | −0.287807 | ||||||||
\(143\) | 3.04973e67 | 0.390100 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.76881e67 | −0.311252 | ||||||||
\(146\) | −1.06000e68 | −0.705006 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.42624e68 | −0.617944 | ||||||||
\(149\) | 1.60985e68 | 0.564181 | 0.282091 | − | 0.959388i | \(-0.408972\pi\) | ||||
0.282091 | + | 0.959388i | \(0.408972\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.49704e68 | −0.574979 | −0.287490 | − | 0.957784i | \(-0.592821\pi\) | ||||
−0.287490 | + | 0.957784i | \(0.592821\pi\) | |||||||
\(152\) | 5.33545e67 | 0.0997925 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.22733e67 | −0.0399890 | ||||||||
\(155\) | 1.13691e69 | 1.14889 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.93952e69 | 1.30875 | 0.654373 | − | 0.756172i | \(-0.272933\pi\) | ||||
0.654373 | + | 0.756172i | \(0.272933\pi\) | |||||||
\(158\) | −4.81678e68 | −0.266108 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.29070e69 | 0.851508 | ||||||||
\(161\) | 4.18236e68 | 0.127763 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.46413e69 | −0.717274 | −0.358637 | − | 0.933477i | \(-0.616758\pi\) | ||||
−0.358637 | + | 0.933477i | \(0.616758\pi\) | |||||||
\(164\) | 2.55670e69 | 0.436614 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.77467e69 | 0.440021 | ||||||||
\(167\) | −1.46319e70 | −1.41166 | −0.705831 | − | 0.708380i | \(-0.749426\pi\) | ||||
−0.705831 | + | 0.708380i | \(0.749426\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.52965e68 | 0.0366662 | ||||||||
\(170\) | −8.65178e69 | −0.476392 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.79229e69 | −0.258744 | ||||||||
\(173\) | −6.95687e69 | −0.220781 | −0.110390 | − | 0.993888i | \(-0.535210\pi\) | ||||
−0.110390 | + | 0.993888i | \(0.535210\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.93863e69 | 0.0428347 | ||||||||
\(176\) | 1.22525e70 | 0.226243 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.47534e70 | 0.449538 | ||||||||
\(179\) | 7.72748e70 | 0.837852 | 0.418926 | − | 0.908020i | \(-0.362407\pi\) | ||||
0.418926 | + | 0.908020i | \(0.362407\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.40823e71 | −1.84002 | −0.920011 | − | 0.391892i | \(-0.871821\pi\) | ||||
−0.920011 | + | 0.391892i | \(0.871821\pi\) | |||||||
\(182\) | −1.65444e70 | −0.106268 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.15670e70 | 0.325800 | ||||||||
\(185\) | 1.72737e71 | 0.662941 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.91780e71 | −0.524557 | ||||||||
\(188\) | 9.99113e70 | 0.231016 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.98151e70 | −0.0493966 | ||||||||
\(191\) | −1.08495e72 | −1.52356 | −0.761780 | − | 0.647836i | \(-0.775674\pi\) | ||||
−0.761780 | + | 0.647836i | \(0.775674\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.08691e71 | 0.109936 | 0.0549679 | − | 0.998488i | \(-0.482494\pi\) | ||||
0.0549679 | + | 0.998488i | \(0.482494\pi\) | |||||||
\(194\) | 6.27410e70 | 0.0539259 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.27217e72 | 0.791551 | ||||||||
\(197\) | −1.84925e72 | −0.980186 | −0.490093 | − | 0.871670i | \(-0.663037\pi\) | ||||
−0.490093 | + | 0.871670i | \(0.663037\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.80760e72 | 0.696997 | 0.348498 | − | 0.937309i | \(-0.386692\pi\) | ||||
0.348498 | + | 0.937309i | \(0.386692\pi\) | |||||||
\(200\) | 3.31730e71 | 0.109230 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.96883e71 | −0.215858 | ||||||||
\(203\) | 4.53203e71 | 0.0933615 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.09650e72 | −0.468408 | ||||||||
\(206\) | 2.76700e72 | 0.359080 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.28107e72 | 0.601227 | ||||||||
\(209\) | −6.60897e71 | −0.0543908 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.54379e73 | −0.941221 | −0.470611 | − | 0.882341i | \(-0.655966\pi\) | ||||
−0.470611 | + | 0.882341i | \(0.655966\pi\) | |||||||
\(212\) | −4.10560e72 | −0.215674 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.09622e73 | −0.428416 | ||||||||
\(215\) | 8.22636e72 | 0.277585 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.36714e73 | −0.344614 | ||||||||
\(218\) | −5.00635e72 | −0.109180 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.84418e73 | −0.301640 | ||||||||
\(221\) | −9.83133e73 | −1.39398 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.35527e73 | 0.251442 | 0.125721 | − | 0.992066i | \(-0.459876\pi\) | ||||
0.125721 | + | 0.992066i | \(0.459876\pi\) | |||||||
\(224\) | −2.75459e73 | −0.255413 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.56030e73 | 0.249500 | ||||||||
\(227\) | −2.46957e74 | −1.50594 | −0.752968 | − | 0.658057i | \(-0.771378\pi\) | ||||
−0.752968 | + | 0.658057i | \(0.771378\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.99938e74 | −1.38744 | −0.693719 | − | 0.720245i | \(-0.744029\pi\) | ||||
−0.693719 | + | 0.720245i | \(0.744029\pi\) | |||||||
\(230\) | −3.99924e73 | −0.161269 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.75504e73 | 0.238074 | ||||||||
\(233\) | −4.83092e74 | −1.29514 | −0.647572 | − | 0.762004i | \(-0.724216\pi\) | ||||
−0.647572 | + | 0.762004i | \(0.724216\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.21006e74 | −0.247838 | ||||||||
\(236\) | −3.45676e74 | −0.619357 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.04038e74 | 0.142896 | ||||||||
\(239\) | 6.21166e74 | 0.747608 | 0.373804 | − | 0.927508i | \(-0.378053\pi\) | ||||
0.373804 | + | 0.927508i | \(0.378053\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.17493e74 | −0.293898 | −0.146949 | − | 0.989144i | \(-0.546945\pi\) | ||||
−0.146949 | + | 0.989144i | \(0.546945\pi\) | |||||||
\(242\) | −3.97591e74 | −0.323037 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.20972e75 | −1.38534 | ||||||||
\(245\) | −1.54077e75 | −0.849190 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.38799e74 | −0.144540 | ||||||||
\(248\) | −2.33941e75 | −0.878775 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.37837e75 | −0.402027 | ||||||||
\(251\) | −3.82426e75 | −0.983615 | −0.491807 | − | 0.870704i | \(-0.663664\pi\) | ||||
−0.491807 | + | 0.870704i | \(0.663664\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.86493e74 | −0.177574 | ||||||||
\(254\) | −1.97182e75 | −0.348822 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.05270e75 | −0.145461 | ||||||||
\(257\) | −7.62665e75 | −0.932052 | −0.466026 | − | 0.884771i | \(-0.654315\pi\) | ||||
−0.466026 | + | 0.884771i | \(0.654315\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.07717e75 | −0.198852 | ||||||||
\(260\) | −9.45393e75 | −0.801589 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.93852e75 | 0.328932 | ||||||||
\(263\) | −1.28572e76 | −0.759521 | −0.379760 | − | 0.925085i | \(-0.623994\pi\) | ||||
−0.379760 | + | 0.925085i | \(0.623994\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.97242e75 | 0.231378 | ||||||||
\(266\) | 3.58529e74 | 0.0148167 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.91968e75 | −0.291141 | ||||||||
\(269\) | −3.17052e76 | −0.920310 | −0.460155 | − | 0.887838i | \(-0.652206\pi\) | ||||
−0.460155 | + | 0.887838i | \(0.652206\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.69145e76 | −1.30825 | −0.654125 | − | 0.756387i | \(-0.726963\pi\) | ||||
−0.654125 | + | 0.756387i | \(0.726963\pi\) | |||||||
\(272\) | −3.94980e76 | −0.808454 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.91973e76 | −0.474461 | ||||||||
\(275\) | −4.10911e75 | −0.0595344 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.83488e76 | −0.442221 | −0.221110 | − | 0.975249i | \(-0.570968\pi\) | ||||
−0.221110 | + | 0.975249i | \(0.570968\pi\) | |||||||
\(278\) | 1.84778e76 | 0.190213 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.16831e76 | 0.178091 | ||||||||
\(281\) | −9.26162e76 | −0.679888 | −0.339944 | − | 0.940446i | \(-0.610408\pi\) | ||||
−0.339944 | + | 0.940446i | \(0.610408\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.27051e77 | −1.33306 | −0.666532 | − | 0.745477i | \(-0.732222\pi\) | ||||
−0.666532 | + | 0.745477i | \(0.732222\pi\) | |||||||
\(284\) | 1.23946e77 | 0.651186 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.50675e76 | 0.147698 | ||||||||
\(287\) | 3.72356e76 | 0.140501 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.88412e77 | 0.874444 | ||||||||
\(290\) | −4.33360e76 | −0.117845 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.28378e77 | 1.59513 | ||||||||
\(293\) | 7.85286e77 | 1.54418 | 0.772090 | − | 0.635513i | \(-0.219212\pi\) | ||||
0.772090 | + | 0.635513i | \(0.219212\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.18659e77 | 0.664457 | ||||||||
\(296\) | −3.55438e77 | −0.507078 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.85110e77 | 0.213608 | ||||||||
\(299\) | −4.54448e77 | −0.471891 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.89227e76 | −0.0832628 | ||||||||
\(302\) | −2.87124e77 | −0.217697 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.36115e77 | −0.0838278 | ||||||||
\(305\) | 2.67626e78 | 1.48622 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.46188e78 | −1.11278 | −0.556388 | − | 0.830923i | \(-0.687813\pi\) | ||||
−0.556388 | + | 0.830923i | \(0.687813\pi\) | |||||||
\(308\) | 2.21764e77 | 0.0904783 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.30728e78 | 0.434987 | ||||||||
\(311\) | 4.46651e78 | 1.34281 | 0.671407 | − | 0.741089i | \(-0.265690\pi\) | ||||
0.671407 | + | 0.741089i | \(0.265690\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.75654e78 | 0.677201 | 0.338601 | − | 0.940930i | \(-0.390046\pi\) | ||||
0.338601 | + | 0.940930i | \(0.390046\pi\) | |||||||
\(314\) | 2.23017e78 | 0.495512 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.30983e78 | 0.602092 | ||||||||
\(317\) | 1.07470e79 | 1.76978 | 0.884888 | − | 0.465803i | \(-0.154234\pi\) | ||||
0.884888 | + | 0.465803i | \(0.154234\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.60609e77 | −0.129760 | ||||||||
\(320\) | −1.79979e78 | −0.220291 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.80912e77 | 0.0483733 | ||||||||
\(323\) | 2.13051e78 | 0.194359 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.10648e78 | −0.158209 | ||||||||
\(326\) | −3.98326e78 | −0.271571 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.37162e78 | 0.358281 | ||||||||
\(329\) | 1.45510e78 | 0.0743402 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.07542e79 | 0.876041 | 0.438021 | − | 0.898965i | \(-0.355680\pi\) | ||||
0.438021 | + | 0.898965i | \(0.355680\pi\) | |||||||
\(332\) | −2.59375e79 | −0.995584 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.68246e79 | −0.534478 | ||||||||
\(335\) | 1.08029e79 | 0.312341 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.57458e79 | −0.617114 | −0.308557 | − | 0.951206i | \(-0.599846\pi\) | ||||
−0.308557 | + | 0.951206i | \(0.599846\pi\) | |||||||
\(338\) | 6.35831e77 | 0.0138824 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.94504e79 | 1.07788 | ||||||||
\(341\) | 2.89780e79 | 0.478966 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.85794e79 | 0.530385 | ||||||||
\(344\) | −1.69273e79 | −0.212322 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.99941e78 | −0.0835912 | ||||||||
\(347\) | 4.77104e78 | 0.0455234 | 0.0227617 | − | 0.999741i | \(-0.492754\pi\) | ||||
0.0227617 | + | 0.999741i | \(0.492754\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.34138e80 | −1.86411 | −0.932053 | − | 0.362323i | \(-0.881984\pi\) | ||||
−0.932053 | + | 0.362323i | \(0.881984\pi\) | |||||||
\(350\) | 2.22914e78 | 0.0162179 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.83862e79 | 0.354990 | ||||||||
\(353\) | 7.30803e79 | 0.406347 | 0.203173 | − | 0.979143i | \(-0.434874\pi\) | ||||
0.203173 | + | 0.979143i | \(0.434874\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.50115e80 | −0.698604 | ||||||||
\(356\) | −2.38806e80 | −1.01712 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.88549e79 | 0.317224 | ||||||||
\(359\) | −3.10624e80 | −1.01569 | −0.507844 | − | 0.861449i | \(-0.669557\pi\) | ||||
−0.507844 | + | 0.861449i | \(0.669557\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.56973e80 | −0.979847 | ||||||||
\(362\) | −2.76912e80 | −0.696662 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.13684e80 | 0.240440 | ||||||||
\(365\) | −8.82161e80 | −1.71129 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.95687e80 | −0.482893 | −0.241447 | − | 0.970414i | \(-0.577622\pi\) | ||||
−0.241447 | + | 0.970414i | \(0.577622\pi\) | |||||||
\(368\) | −1.82578e80 | −0.273679 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.98623e80 | 0.251000 | ||||||||
\(371\) | −5.97938e79 | −0.0694029 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.53601e80 | 0.640449 | 0.320224 | − | 0.947342i | \(-0.396242\pi\) | ||||
0.320224 | + | 0.947342i | \(0.396242\pi\) | |||||||
\(374\) | −2.20520e80 | −0.198606 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.48992e80 | 0.189569 | ||||||||
\(377\) | −4.92442e80 | −0.344828 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.70057e81 | −1.00800 | −0.503998 | − | 0.863705i | \(-0.668138\pi\) | ||||
−0.503998 | + | 0.863705i | \(0.668138\pi\) | |||||||
\(380\) | 2.04873e80 | 0.111764 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.24754e81 | −0.576844 | ||||||||
\(383\) | 4.22264e81 | 1.79814 | 0.899068 | − | 0.437808i | \(-0.144245\pi\) | ||||
0.899068 | + | 0.437808i | \(0.144245\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.68586e80 | −0.0970667 | ||||||||
\(386\) | 1.24979e80 | 0.0416235 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.31123e80 | −0.122012 | ||||||||
\(389\) | −1.74537e81 | −0.455487 | −0.227744 | − | 0.973721i | \(-0.573135\pi\) | ||||
−0.227744 | + | 0.973721i | \(0.573135\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.85776e81 | 0.634539 | ||||||||
\(392\) | 3.17041e81 | 0.649538 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.12637e81 | −0.371114 | ||||||||
\(395\) | −4.00864e81 | −0.645934 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.07185e82 | 1.47310 | 0.736551 | − | 0.676382i | \(-0.236453\pi\) | ||||
0.736551 | + | 0.676382i | \(0.236453\pi\) | |||||||
\(398\) | 2.07848e81 | 0.263894 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.46291e80 | −0.0917551 | ||||||||
\(401\) | 1.05350e82 | 1.05582 | 0.527908 | − | 0.849301i | \(-0.322976\pi\) | ||||
0.527908 | + | 0.849301i | \(0.322976\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.48551e82 | 1.27282 | ||||||||
\(404\) | 6.16290e81 | 0.488396 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.21119e80 | 0.0353482 | ||||||||
\(407\) | 4.40278e81 | 0.276377 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.74020e81 | −0.254984 | −0.127492 | − | 0.991840i | \(-0.540693\pi\) | ||||
−0.127492 | + | 0.991840i | \(0.540693\pi\) | |||||||
\(410\) | −3.56053e81 | −0.177347 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.90133e82 | −0.812447 | ||||||||
\(413\) | −5.03441e81 | −0.199307 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.14137e82 | 1.06808 | ||||||||
\(416\) | 2.99308e82 | 0.943363 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.59937e80 | −0.0205932 | ||||||||
\(419\) | 4.38377e82 | 1.10181 | 0.550904 | − | 0.834569i | \(-0.314283\pi\) | ||||
0.550904 | + | 0.834569i | \(0.314283\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.14158e82 | −0.246956 | −0.123478 | − | 0.992347i | \(-0.539405\pi\) | ||||
−0.123478 | + | 0.992347i | \(0.539405\pi\) | |||||||
\(422\) | −1.77514e82 | −0.356362 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.02317e82 | −0.176979 | ||||||||
\(425\) | 1.32464e82 | 0.212739 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.21823e82 | −0.445798 | ||||||||
\(428\) | 7.53266e82 | 0.969326 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 9.45914e81 | 0.105098 | ||||||||
\(431\) | −1.31107e83 | −1.35391 | −0.676956 | − | 0.736023i | \(-0.736701\pi\) | ||||
−0.676956 | + | 0.736023i | \(0.736701\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.01725e82 | −0.447813 | −0.223907 | − | 0.974611i | \(-0.571881\pi\) | ||||
−0.223907 | + | 0.974611i | \(0.571881\pi\) | |||||||
\(434\) | −1.57202e82 | −0.130476 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.44009e82 | 0.247028 | ||||||||
\(437\) | 9.84819e81 | 0.0657947 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.75059e82 | 0.390579 | 0.195290 | − | 0.980746i | \(-0.437435\pi\) | ||||
0.195290 | + | 0.980746i | \(0.437435\pi\) | |||||||
\(440\) | −4.59594e82 | −0.247523 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.13046e83 | −0.527782 | ||||||||
\(443\) | −2.29536e83 | −0.998005 | −0.499002 | − | 0.866601i | \(-0.666300\pi\) | ||||
−0.499002 | + | 0.866601i | \(0.666300\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.89226e83 | 1.09118 | ||||||||
\(446\) | 2.70822e82 | 0.0951999 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.16426e82 | 0.0660772 | ||||||||
\(449\) | −2.84021e83 | −0.808333 | −0.404167 | − | 0.914685i | \(-0.632438\pi\) | ||||
−0.404167 | + | 0.914685i | \(0.632438\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.89246e82 | −0.195277 | ||||||||
\(452\) | −2.44644e83 | −0.564514 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.83965e83 | −0.570172 | ||||||||
\(455\) | −1.37687e83 | −0.257948 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.53890e83 | −0.577442 | −0.288721 | − | 0.957413i | \(-0.593230\pi\) | ||||
−0.288721 | + | 0.957413i | \(0.593230\pi\) | |||||||
\(458\) | −3.44886e83 | −0.525307 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.74806e83 | 0.364884 | ||||||||
\(461\) | 9.02523e83 | 1.11913 | 0.559563 | − | 0.828788i | \(-0.310969\pi\) | ||||
0.559563 | + | 0.828788i | \(0.310969\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.17555e84 | −1.27187 | −0.635933 | − | 0.771744i | \(-0.719385\pi\) | ||||
−0.635933 | + | 0.771744i | \(0.719385\pi\) | |||||||
\(464\) | −1.97842e83 | −0.199987 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.55487e83 | −0.490363 | ||||||||
\(467\) | −1.78581e84 | −1.47351 | −0.736757 | − | 0.676157i | \(-0.763644\pi\) | ||||
−0.736757 | + | 0.676157i | \(0.763644\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.29906e83 | −0.0936881 | ||||||||
\(470\) | −1.39139e83 | −0.0938356 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.61469e83 | −0.508238 | ||||||||
\(473\) | 2.09676e83 | 0.115724 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.56487e82 | 0.0220587 | ||||||||
\(476\) | −7.14896e83 | −0.323313 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.14253e83 | 0.283056 | ||||||||
\(479\) | 4.37337e84 | 1.62274 | 0.811368 | − | 0.584536i | \(-0.198723\pi\) | ||||
0.811368 | + | 0.584536i | \(0.198723\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.25702e84 | 0.734455 | ||||||||
\(482\) | −3.65071e83 | −0.111275 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.73203e84 | 0.730897 | ||||||||
\(485\) | 5.22146e83 | 0.130896 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.62469e84 | 1.01841 | 0.509203 | − | 0.860647i | \(-0.329940\pi\) | ||||
0.509203 | + | 0.860647i | \(0.329940\pi\) | |||||||
\(488\) | −5.50691e84 | −1.13680 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.77166e84 | −0.321517 | ||||||||
\(491\) | 1.06620e85 | 1.81455 | 0.907277 | − | 0.420533i | \(-0.138157\pi\) | ||||
0.907277 | + | 0.420533i | \(0.138157\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.09669e84 | 0.463681 | ||||||||
\(494\) | −3.89571e83 | −0.0547252 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.96816e84 | 0.738189 | ||||||||
\(497\) | 1.80515e84 | 0.209549 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.87919e84 | −0.908252 | −0.454126 | − | 0.890938i | \(-0.650048\pi\) | ||||
−0.454126 | + | 0.890938i | \(0.650048\pi\) | |||||||
\(500\) | 9.47141e84 | 0.909619 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.39735e84 | −0.372412 | ||||||||
\(503\) | −1.82243e84 | −0.144964 | −0.0724818 | − | 0.997370i | \(-0.523092\pi\) | ||||
−0.0724818 | + | 0.997370i | \(0.523092\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.46408e84 | −0.523959 | ||||||||
\(506\) | −1.01934e84 | −0.0672323 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.35493e85 | 0.789239 | ||||||||
\(509\) | 1.57331e85 | 0.861401 | 0.430700 | − | 0.902495i | \(-0.358267\pi\) | ||||
0.430700 | + | 0.902495i | \(0.358267\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.06081e85 | 0.513308 | ||||||||
\(512\) | 2.11482e85 | 0.962210 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8.76956e84 | −0.352890 | ||||||||
\(515\) | 2.30276e85 | 0.871608 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.08424e84 | −0.103323 | ||||||||
\(518\) | −2.38845e84 | −0.0752886 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.35604e85 | −0.657776 | ||||||||
\(521\) | −2.23640e85 | −0.587707 | −0.293853 | − | 0.955850i | \(-0.594938\pi\) | ||||
−0.293853 | + | 0.955850i | \(0.594938\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.37853e85 | 1.95148 | 0.975741 | − | 0.218927i | \(-0.0702555\pi\) | ||||
0.975741 | + | 0.218927i | \(0.0702555\pi\) | |||||||
\(524\) | −3.39348e85 | −0.744235 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.47839e85 | −0.287567 | ||||||||
\(527\) | −9.34155e85 | −1.71153 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.82871e85 | −0.785195 | ||||||||
\(530\) | 5.71757e84 | 0.0876036 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.46362e84 | −0.0335241 | ||||||||
\(533\) | −4.04596e85 | −0.518937 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.12305e85 | −1.03991 | ||||||||
\(536\) | −2.22290e85 | −0.238907 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.64565e85 | −0.348444 | ||||||||
\(539\) | −3.92716e85 | −0.354024 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.46553e86 | 1.17565 | 0.587827 | − | 0.808986i | \(-0.299983\pi\) | ||||
0.587827 | + | 0.808986i | \(0.299983\pi\) | |||||||
\(542\) | −6.54436e85 | −0.495324 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.88218e86 | −1.26852 | ||||||||
\(545\) | −4.16640e85 | −0.265016 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.03373e83 | 0.000585878 0 | 0.000292939 | − | 1.00000i | \(-0.499907\pi\) | ||||
0.000292939 | 1.00000i | \(0.499907\pi\) | ||||||||
\(548\) | 2.00628e86 | 1.07351 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.72489e84 | −0.0225407 | ||||||||
\(551\) | 1.06716e85 | 0.0480787 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.82042e85 | 0.193751 | ||||||||
\(554\) | −4.40956e85 | −0.167432 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.26970e86 | −0.430372 | ||||||||
\(557\) | 1.52548e86 | 0.488616 | 0.244308 | − | 0.969698i | \(-0.421439\pi\) | ||||
0.244308 | + | 0.969698i | \(0.421439\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.07488e86 | 0.307529 | ||||||||
\(560\) | −5.53166e85 | −0.149600 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.06495e86 | −0.257417 | ||||||||
\(563\) | −6.23004e86 | −1.42389 | −0.711945 | − | 0.702235i | \(-0.752186\pi\) | ||||
−0.711945 | + | 0.702235i | \(0.752186\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.96296e86 | 0.605620 | ||||||||
\(566\) | −2.61076e86 | −0.504719 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.08890e86 | 0.534356 | ||||||||
\(569\) | 2.01891e86 | 0.330431 | 0.165216 | − | 0.986257i | \(-0.447168\pi\) | ||||
0.165216 | + | 0.986257i | \(0.447168\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.80331e86 | −1.29006 | −0.645028 | − | 0.764159i | \(-0.723154\pi\) | ||||
−0.645028 | + | 0.764159i | \(0.723154\pi\) | |||||||
\(572\) | −2.40965e86 | −0.334179 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.28157e85 | 0.0531959 | ||||||||
\(575\) | 6.12309e85 | 0.0720167 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.21339e86 | 0.444215 | 0.222107 | − | 0.975022i | \(-0.428706\pi\) | ||||
0.222107 | + | 0.975022i | \(0.428706\pi\) | |||||||
\(578\) | 3.31633e86 | 0.331079 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.97782e86 | 0.266634 | ||||||||
\(581\) | −3.77752e86 | −0.320375 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.26739e86 | 0.0964607 | ||||||||
\(584\) | 1.81521e87 | 1.30895 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.02967e86 | 0.584651 | ||||||||
\(587\) | 1.93457e87 | 1.18709 | 0.593545 | − | 0.804801i | \(-0.297728\pi\) | ||||
0.593545 | + | 0.804801i | \(0.297728\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.21921e86 | −0.177467 | ||||||||
\(590\) | 4.81398e86 | 0.251574 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.06773e86 | 0.425956 | ||||||||
\(593\) | 3.07531e87 | 1.36983 | 0.684914 | − | 0.728624i | \(-0.259840\pi\) | ||||
0.684914 | + | 0.728624i | \(0.259840\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.65833e86 | 0.346856 | ||||||||
\(596\) | −1.27198e87 | −0.483306 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.22550e86 | −0.178666 | ||||||||
\(599\) | 3.29040e87 | 1.06734 | 0.533672 | − | 0.845692i | \(-0.320812\pi\) | ||||
0.533672 | + | 0.845692i | \(0.320812\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.89130e87 | −1.13645 | −0.568224 | − | 0.822874i | \(-0.692369\pi\) | ||||
−0.568224 | + | 0.822874i | \(0.692369\pi\) | |||||||
\(602\) | −1.13747e86 | −0.0315247 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.97296e87 | 0.492556 | ||||||||
\(605\) | −3.30885e87 | −0.784119 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.00692e87 | −0.642212 | −0.321106 | − | 0.947043i | \(-0.604055\pi\) | ||||
−0.321106 | + | 0.947043i | \(0.604055\pi\) | |||||||
\(608\) | −6.48621e86 | −0.131531 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.07732e87 | 0.562707 | ||||||||
\(611\) | −1.58109e87 | −0.274574 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.23158e87 | 1.13300 | 0.566498 | − | 0.824063i | \(-0.308298\pi\) | ||||
0.566498 | + | 0.824063i | \(0.308298\pi\) | |||||||
\(614\) | −2.83081e87 | −0.421315 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.52666e86 | 0.0742455 | ||||||||
\(617\) | 6.75048e87 | 0.861691 | 0.430846 | − | 0.902426i | \(-0.358215\pi\) | ||||
0.430846 | + | 0.902426i | \(0.358215\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.11084e87 | 0.819720 | 0.409860 | − | 0.912149i | \(-0.365578\pi\) | ||||
0.409860 | + | 0.912149i | \(0.365578\pi\) | |||||||
\(620\) | −8.98295e87 | −0.984194 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.13585e87 | 0.508411 | ||||||||
\(623\) | −3.47797e87 | −0.327304 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.64457e87 | −0.820470 | ||||||||
\(626\) | 3.16963e87 | 0.256399 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.53245e88 | −1.12114 | ||||||||
\(629\) | −1.41931e88 | −0.987603 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.17327e88 | −0.738708 | −0.369354 | − | 0.929289i | \(-0.620421\pi\) | ||||
−0.369354 | + | 0.929289i | \(0.620421\pi\) | |||||||
\(632\) | 8.24853e87 | 0.494070 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.23575e88 | 0.670066 | ||||||||
\(635\) | −1.64099e88 | −0.846709 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.01320e88 | −0.940795 | ||||||||
\(638\) | −1.10456e87 | −0.0491291 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.31975e88 | −0.934914 | ||||||||
\(641\) | 5.85075e87 | 0.224483 | 0.112241 | − | 0.993681i | \(-0.464197\pi\) | ||||
0.112241 | + | 0.993681i | \(0.464197\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.09879e88 | −1.07782 | −0.538910 | − | 0.842363i | \(-0.681164\pi\) | ||||
−0.538910 | + | 0.842363i | \(0.681164\pi\) | |||||||
\(644\) | −3.30457e87 | −0.109448 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.44979e87 | 0.0735875 | ||||||||
\(647\) | −3.14549e88 | −0.899919 | −0.449959 | − | 0.893049i | \(-0.648562\pi\) | ||||
−0.449959 | + | 0.893049i | \(0.648562\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.06709e88 | 0.277009 | ||||||||
\(650\) | −2.42215e87 | −0.0599004 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.73708e88 | 0.614452 | ||||||||
\(653\) | −1.00332e88 | −0.214622 | −0.107311 | − | 0.994226i | \(-0.534224\pi\) | ||||
−0.107311 | + | 0.994226i | \(0.534224\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.10995e88 | 0.798428 | ||||||||
\(656\) | −1.62549e88 | −0.300963 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.67316e87 | 0.0281464 | ||||||||
\(659\) | −3.87613e88 | −0.621595 | −0.310798 | − | 0.950476i | \(-0.600596\pi\) | ||||
−0.310798 | + | 0.950476i | \(0.600596\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.13511e88 | 0.748521 | 0.374261 | − | 0.927324i | \(-0.377897\pi\) | ||||
0.374261 | + | 0.927324i | \(0.377897\pi\) | |||||||
\(662\) | 2.38644e88 | 0.331683 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.46395e88 | −0.816966 | ||||||||
\(665\) | 2.98376e87 | 0.0359652 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.43143e88 | 0.156966 | ||||||||
\(668\) | 1.15609e89 | 1.20930 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.24218e88 | 0.118257 | ||||||||
\(671\) | 6.82135e88 | 0.619599 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.51230e89 | 1.25073 | 0.625366 | − | 0.780332i | \(-0.284950\pi\) | ||||
0.625366 | + | 0.780332i | \(0.284950\pi\) | |||||||
\(674\) | −2.96040e88 | −0.233649 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.36909e87 | −0.0314101 | ||||||||
\(677\) | −9.60349e87 | −0.0659001 | −0.0329500 | − | 0.999457i | \(-0.510490\pi\) | ||||
−0.0329500 | + | 0.999457i | \(0.510490\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.27885e87 | −0.0392629 | ||||||||
\(680\) | 1.48158e89 | 0.884493 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.33205e88 | 0.181344 | ||||||||
\(683\) | 1.20923e89 | 0.628431 | 0.314215 | − | 0.949352i | \(-0.398259\pi\) | ||||
0.314215 | + | 0.949352i | \(0.398259\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.42987e89 | −1.15168 | ||||||||
\(686\) | 4.43609e88 | 0.200812 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.31839e88 | 0.178355 | ||||||||
\(689\) | 6.49708e88 | 0.256338 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.63672e88 | −0.202987 | −0.101494 | − | 0.994836i | \(-0.532362\pi\) | ||||
−0.101494 | + | 0.994836i | \(0.532362\pi\) | |||||||
\(692\) | 5.49676e88 | 0.189132 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.48602e87 | 0.0172359 | ||||||||
\(695\) | 1.53777e89 | 0.461711 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.54427e89 | 0.697800 | ||||||||
\(698\) | −2.69225e89 | −0.705780 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.53175e88 | −0.0366943 | ||||||||
\(701\) | 3.32347e89 | 0.761158 | 0.380579 | − | 0.924748i | \(-0.375725\pi\) | ||||
0.380579 | + | 0.924748i | \(0.375725\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.89111e88 | −0.102404 | ||||||||
\(704\) | −4.58736e88 | −0.0918383 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.40319e88 | 0.153849 | ||||||||
\(707\) | 8.97562e88 | 0.157164 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.99117e89 | 0.639357 | 0.319678 | − | 0.947526i | \(-0.396425\pi\) | ||||
0.319678 | + | 0.947526i | \(0.396425\pi\) | |||||||
\(710\) | −1.72611e89 | −0.264503 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.95136e89 | −0.834635 | ||||||||
\(713\) | −4.31808e89 | −0.579389 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.91841e89 | 0.358513 | ||||||||
\(716\) | −6.10563e89 | −0.717745 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.57174e89 | −0.384556 | ||||||||
\(719\) | −2.39039e89 | −0.246325 | −0.123162 | − | 0.992387i | \(-0.539304\pi\) | ||||
−0.123162 | + | 0.992387i | \(0.539304\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.76909e89 | −0.261442 | ||||||||
\(722\) | −4.10468e89 | −0.370986 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.90279e90 | 1.57626 | ||||||||
\(725\) | 6.63501e88 | 0.0526253 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.96567e88 | −0.0506558 | −0.0253279 | − | 0.999679i | \(-0.508063\pi\) | ||||
−0.0253279 | + | 0.999679i | \(0.508063\pi\) | |||||||
\(728\) | 2.83316e89 | 0.197303 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.01436e90 | −0.647921 | ||||||||
\(731\) | −6.75928e89 | −0.413526 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.46414e90 | −0.821880 | −0.410940 | − | 0.911662i | \(-0.634799\pi\) | ||||
−0.410940 | + | 0.911662i | \(0.634799\pi\) | |||||||
\(734\) | −3.39998e89 | −0.182831 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.70027e89 | −0.429419 | ||||||||
\(737\) | 2.75348e89 | 0.130214 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.24476e90 | −1.40891 | −0.704454 | − | 0.709749i | \(-0.748808\pi\) | ||||
−0.704454 | + | 0.709749i | \(0.748808\pi\) | |||||||
\(740\) | −1.36483e90 | −0.567909 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.87543e88 | −0.0262771 | ||||||||
\(743\) | −1.23913e90 | −0.453909 | −0.226955 | − | 0.973905i | \(-0.572877\pi\) | ||||
−0.226955 | + | 0.973905i | \(0.572877\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.54053e90 | 0.518499 | ||||||||
\(746\) | 7.51548e89 | 0.242484 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.51529e90 | 0.449362 | ||||||||
\(749\) | 1.09705e90 | 0.311925 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.90019e90 | −0.758172 | −0.379086 | − | 0.925361i | \(-0.623762\pi\) | ||||
−0.379086 | + | 0.925361i | \(0.623762\pi\) | |||||||
\(752\) | −6.35214e89 | −0.159242 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.66239e89 | −0.130558 | ||||||||
\(755\) | −2.38952e90 | −0.528423 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.88673e90 | 1.19772 | 0.598858 | − | 0.800855i | \(-0.295621\pi\) | ||||
0.598858 | + | 0.800855i | \(0.295621\pi\) | |||||||
\(758\) | −1.95541e90 | −0.381643 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.10570e89 | 0.0917122 | ||||||||
\(761\) | −6.18701e90 | −1.06626 | −0.533131 | − | 0.846033i | \(-0.678985\pi\) | ||||
−0.533131 | + | 0.846033i | \(0.678985\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.01013e89 | 0.0794926 | ||||||||
\(764\) | 8.57242e90 | 1.30516 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.85543e90 | 0.680804 | ||||||||
\(767\) | 5.47030e90 | 0.736135 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.95075e88 | −0.00985663 | −0.00492832 | − | 0.999988i | \(-0.501569\pi\) | ||||
−0.00492832 | + | 0.999988i | \(0.501569\pi\) | |||||||
\(770\) | −3.08835e89 | −0.0367510 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.58791e89 | −0.0941765 | ||||||||
\(773\) | 2.44555e90 | 0.257468 | 0.128734 | − | 0.991679i | \(-0.458909\pi\) | ||||
0.128734 | + | 0.991679i | \(0.458909\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.00153e90 | −0.194249 | ||||||||
\(776\) | −1.07441e90 | −0.100121 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.00693e90 | −0.172455 | ||||||||
\(779\) | 8.76786e89 | 0.0723542 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.82619e90 | −0.291245 | ||||||||
\(782\) | 3.28602e90 | 0.240247 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.08818e90 | −0.545625 | ||||||||
\(785\) | 1.85600e91 | 1.20278 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.22272e91 | 0.731345 | 0.365673 | − | 0.930744i | \(-0.380839\pi\) | ||||
0.365673 | + | 0.930744i | \(0.380839\pi\) | |||||||
\(788\) | 1.46113e91 | 0.839676 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.60936e90 | −0.244561 | ||||||||
\(791\) | −3.56299e90 | −0.181658 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.49687e91 | 1.64655 | ||||||||
\(794\) | 1.23247e91 | 0.557740 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.42822e91 | −0.597082 | ||||||||
\(797\) | 3.33569e91 | 1.34044 | 0.670222 | − | 0.742161i | \(-0.266199\pi\) | ||||
0.670222 | + | 0.742161i | \(0.266199\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.94258e90 | 0.369212 | ||||||||
\(800\) | −4.03279e90 | −0.143970 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.21138e91 | 0.399749 | ||||||||
\(803\) | −2.24848e91 | −0.713428 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.00227e90 | 0.117418 | ||||||||
\(806\) | 1.70813e91 | 0.481911 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.53587e91 | 0.400772 | ||||||||
\(809\) | −5.41859e91 | −1.35990 | −0.679952 | − | 0.733257i | \(-0.737999\pi\) | ||||
−0.679952 | + | 0.733257i | \(0.737999\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.10679e91 | −0.953556 | −0.476778 | − | 0.879024i | \(-0.658195\pi\) | ||||
−0.476778 | + | 0.879024i | \(0.658195\pi\) | |||||||
\(812\) | −3.58085e90 | −0.0799781 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.06256e90 | 0.104641 | ||||||||
\(815\) | −3.31496e91 | −0.659195 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.32933e90 | −0.0428781 | ||||||||
\(818\) | −5.45056e90 | −0.0965410 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.44660e91 | 0.401261 | ||||||||
\(821\) | −7.47546e91 | −1.17986 | −0.589928 | − | 0.807456i | \(-0.700844\pi\) | ||||
−0.589928 | + | 0.807456i | \(0.700844\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.00127e92 | −1.46372 | −0.731859 | − | 0.681456i | \(-0.761347\pi\) | ||||
−0.731859 | + | 0.681456i | \(0.761347\pi\) | |||||||
\(824\) | −4.73836e91 | −0.666685 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.78886e90 | −0.0754608 | ||||||||
\(827\) | −7.70914e91 | −0.967348 | −0.483674 | − | 0.875248i | \(-0.660698\pi\) | ||||
−0.483674 | + | 0.875248i | \(0.660698\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.89462e90 | 0.103433 | 0.0517166 | − | 0.998662i | \(-0.483531\pi\) | ||||
0.0517166 | + | 0.998662i | \(0.483531\pi\) | |||||||
\(830\) | 3.61213e91 | 0.404392 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.35164e91 | −0.244054 | ||||||||
\(833\) | 1.26599e92 | 1.26506 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.40018e92 | −1.29736 | ||||||||
\(836\) | 5.22188e90 | 0.0465939 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.04071e91 | 0.417162 | ||||||||
\(839\) | −1.70386e91 | −0.135810 | −0.0679049 | − | 0.997692i | \(-0.521631\pi\) | ||||
−0.0679049 | + | 0.997692i | \(0.521631\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.19719e92 | −0.885299 | ||||||||
\(842\) | −1.31265e91 | −0.0935015 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.21978e92 | 0.806297 | ||||||||
\(845\) | 5.29154e90 | 0.0336973 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.97892e91 | 0.235200 | ||||||||
\(848\) | 2.61025e91 | 0.148666 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.52315e91 | 0.0805465 | ||||||||
\(851\) | −6.56069e91 | −0.334324 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.48680e91 | 0.117692 | 0.0588460 | − | 0.998267i | \(-0.481258\pi\) | ||||
0.0588460 | + | 0.998267i | \(0.481258\pi\) | |||||||
\(854\) | −3.70050e91 | −0.168786 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.87724e92 | 0.795418 | ||||||||
\(857\) | −1.41839e92 | −0.579296 | −0.289648 | − | 0.957133i | \(-0.593538\pi\) | ||||
−0.289648 | + | 0.957133i | \(0.593538\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.07690e91 | −0.116769 | −0.0583847 | − | 0.998294i | \(-0.518595\pi\) | ||||
−0.0583847 | + | 0.998294i | \(0.518595\pi\) | |||||||
\(860\) | −6.49981e91 | −0.237793 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.50754e92 | −0.512613 | ||||||||
\(863\) | 2.87438e91 | 0.0942334 | 0.0471167 | − | 0.998889i | \(-0.484997\pi\) | ||||
0.0471167 | + | 0.998889i | \(0.484997\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.65730e91 | −0.202904 | ||||||||
\(866\) | −5.76912e91 | −0.169549 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.08021e92 | 0.295213 | ||||||||
\(869\) | −1.02174e92 | −0.269287 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.41153e92 | 0.346035 | ||||||||
\(872\) | 8.57315e91 | 0.202708 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.13240e91 | 0.0249109 | ||||||||
\(875\) | 1.37941e92 | 0.292712 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.89285e92 | 1.55864 | 0.779322 | − | 0.626624i | \(-0.215564\pi\) | ||||
0.779322 | + | 0.626624i | \(0.215564\pi\) | |||||||
\(878\) | 7.76222e91 | 0.147880 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.17249e92 | 0.207924 | ||||||||
\(881\) | 1.02239e93 | 1.74934 | 0.874671 | − | 0.484717i | \(-0.161077\pi\) | ||||
0.874671 | + | 0.484717i | \(0.161077\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.60718e92 | −1.05258 | −0.526289 | − | 0.850306i | \(-0.676417\pi\) | ||||
−0.526289 | + | 0.850306i | \(0.676417\pi\) | |||||||
\(884\) | 7.76793e92 | 1.19415 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.63933e92 | −0.377861 | ||||||||
\(887\) | 2.71527e92 | 0.375162 | 0.187581 | − | 0.982249i | \(-0.439935\pi\) | ||||
0.187581 | + | 0.982249i | \(0.439935\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.97331e92 | 0.253974 | ||||||||
\(890\) | 3.32568e92 | 0.413139 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.86095e92 | −0.215398 | ||||||||
\(893\) | 3.42633e91 | 0.0382832 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.39472e92 | 0.770010 | ||||||||
\(896\) | 2.78952e92 | 0.280431 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.26583e92 | −0.306048 | ||||||||
\(899\) | −4.67910e92 | −0.423381 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.08565e92 | −0.344691 | ||||||||
\(902\) | −9.07521e91 | −0.0739351 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.09685e92 | −0.463234 | ||||||||
\(905\) | −2.30453e93 | −1.69103 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.32414e92 | −0.638233 | −0.319116 | − | 0.947716i | \(-0.603386\pi\) | ||||
−0.319116 | + | 0.947716i | \(0.603386\pi\) | |||||||
\(908\) | 1.95125e93 | 1.29006 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.58320e92 | −0.0976635 | ||||||||
\(911\) | −6.82273e92 | −0.406564 | −0.203282 | − | 0.979120i | \(-0.565161\pi\) | ||||
−0.203282 | + | 0.979120i | \(0.565161\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.00683e92 | 0.445278 | ||||||||
\(914\) | −4.06923e92 | −0.218629 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.36987e93 | 1.18855 | ||||||||
\(917\) | −4.94226e92 | −0.239492 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.29916e92 | 0.375487 | 0.187744 | − | 0.982218i | \(-0.439883\pi\) | ||||
0.187744 | + | 0.982218i | \(0.439883\pi\) | |||||||
\(920\) | 6.84853e92 | 0.299420 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.03777e93 | 0.423719 | ||||||||
\(923\) | −1.96144e93 | −0.773965 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.04104e92 | −0.112087 | ||||||||
\(926\) | −1.35172e93 | −0.481549 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −9.42767e92 | −0.313793 | ||||||||
\(929\) | −3.38716e93 | −1.08978 | −0.544892 | − | 0.838506i | \(-0.683429\pi\) | ||||
−0.544892 | + | 0.838506i | \(0.683429\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.36274e92 | 0.131173 | ||||||||
\(932\) | 3.81701e93 | 1.10949 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.05343e93 | −0.557896 | ||||||||
\(935\) | −1.83522e93 | −0.482083 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.03836e93 | −0.746179 | −0.373089 | − | 0.927795i | \(-0.621702\pi\) | ||||
−0.373089 | + | 0.927795i | \(0.621702\pi\) | |||||||
\(938\) | −1.49373e92 | −0.0354718 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.56091e92 | 0.212311 | ||||||||
\(941\) | 2.32725e93 | 0.499769 | 0.249884 | − | 0.968276i | \(-0.419607\pi\) | ||||
0.249884 | + | 0.968276i | \(0.419607\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.17608e93 | 0.236220 | ||||||||
\(944\) | 2.19773e93 | 0.426930 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.41098e92 | 0.0438150 | ||||||||
\(947\) | −6.25689e93 | −1.09985 | −0.549926 | − | 0.835213i | \(-0.685344\pi\) | ||||
−0.549926 | + | 0.835213i | \(0.685344\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.15265e94 | −1.89589 | ||||||||
\(950\) | 5.24895e91 | 0.00835178 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.78161e93 | −0.265308 | ||||||||
\(953\) | −6.65569e93 | −0.958885 | −0.479443 | − | 0.877573i | \(-0.659161\pi\) | ||||
−0.479443 | + | 0.877573i | \(0.659161\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.03823e94 | −1.40020 | ||||||||
\(956\) | −4.90796e93 | −0.640438 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.02876e93 | 0.614394 | ||||||||
\(959\) | 2.92194e93 | 0.345450 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.08303e93 | 0.562776 | ||||||||
\(962\) | 2.59525e93 | 0.278077 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.50857e93 | 0.251768 | ||||||||
\(965\) | 1.04011e93 | 0.101034 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.16513e94 | 1.06033 | 0.530165 | − | 0.847895i | \(-0.322130\pi\) | ||||
0.530165 | + | 0.847895i | \(0.322130\pi\) | |||||||
\(968\) | 6.80857e93 | 0.599766 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.00394e92 | 0.0495594 | ||||||||
\(971\) | −3.52112e93 | −0.281368 | −0.140684 | − | 0.990055i | \(-0.544930\pi\) | ||||
−0.140684 | + | 0.990055i | \(0.544930\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.84918e93 | −0.138492 | ||||||||
\(974\) | 5.31774e93 | 0.385585 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.40489e94 | 0.954934 | ||||||||
\(977\) | −1.56288e94 | −1.02860 | −0.514301 | − | 0.857610i | \(-0.671948\pi\) | ||||
−0.514301 | + | 0.857610i | \(0.671948\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.37189e93 | 0.454909 | ||||||||
\(980\) | 1.21739e94 | 0.727458 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.22597e94 | 0.687020 | ||||||||
\(983\) | 2.15640e94 | 1.17029 | 0.585146 | − | 0.810928i | \(-0.301037\pi\) | ||||
0.585146 | + | 0.810928i | \(0.301037\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.76962e94 | −0.900819 | ||||||||
\(986\) | 3.56075e93 | 0.175557 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.67692e93 | 0.123820 | ||||||||
\(989\) | −3.12444e93 | −0.139987 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.31180e94 | 0.551501 | 0.275750 | − | 0.961229i | \(-0.411074\pi\) | ||||
0.275750 | + | 0.961229i | \(0.411074\pi\) | |||||||
\(992\) | 2.84397e94 | 1.15826 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.07566e93 | 0.0793387 | ||||||||
\(995\) | 1.72976e94 | 0.640560 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.78877e94 | −1.31705 | −0.658523 | − | 0.752560i | \(-0.728819\pi\) | ||||
−0.658523 | + | 0.752560i | \(0.728819\pi\) | |||||||
\(998\) | −1.02098e94 | −0.343879 | ||||||||
\(999\) | 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 | 9.64.a.c.1.4 | 5 | ||
3.2 | odd | 2 | 1.64.a.a.1.2 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.64.a.a.1.2 | ✓ | 5 | 3.2 | odd | 2 | ||
9.64.a.c.1.4 | 5 | 1.1 | even | 1 | trivial |