Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,7,Mod(127,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.127");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.d (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(58.8938454067\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{15})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 7x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 4) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.3 | ||
Root | \(-1.93649 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 256.127 |
Dual form | 256.7.d.f.127.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 30.9839 | 1.14755 | 0.573775 | − | 0.819013i | \(-0.305478\pi\) | ||||
0.573775 | + | 0.819013i | \(0.305478\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 10.0000i | − 0.0800000i | −0.999200 | − | 0.0400000i | \(-0.987264\pi\) | ||||
0.999200 | − | 0.0400000i | \(-0.0127358\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 309.839i | − 0.903320i | −0.892190 | − | 0.451660i | \(-0.850832\pi\) | ||||
0.892190 | − | 0.451660i | \(-0.149168\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 231.000 | 0.316872 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −960.500 | −0.721638 | −0.360819 | − | 0.932636i | \(-0.617503\pi\) | ||||
−0.360819 | + | 0.932636i | \(0.617503\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1466.00i | 0.667274i | 0.942702 | + | 0.333637i | \(0.108276\pi\) | ||||
−0.942702 | + | 0.333637i | \(0.891724\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 309.839i | − 0.0918040i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4766.00 | −0.970079 | −0.485040 | − | 0.874492i | \(-0.661195\pi\) | ||||
−0.485040 | + | 0.874492i | \(0.661195\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7529.08 | −1.09769 | −0.548847 | − | 0.835923i | \(-0.684933\pi\) | ||||
−0.548847 | + | 0.835923i | \(0.684933\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 9600.00i | − 1.03661i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 10472.5i | 0.860734i | 0.902654 | + | 0.430367i | \(0.141616\pi\) | ||||
−0.902654 | + | 0.430367i | \(0.858384\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 15525.0 | 0.993600 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −15430.0 | −0.783923 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 25498.0i | 1.04547i | 0.852495 | + | 0.522736i | \(0.175089\pi\) | ||||
−0.852495 | + | 0.522736i | \(0.824911\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 41890.2i | 1.40614i | 0.711123 | + | 0.703068i | \(0.248187\pi\) | ||||
−0.711123 | + | 0.703068i | \(0.751813\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −29760.0 | −0.828116 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3098.39 | −0.0722656 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 1994.00i | − 0.0393659i | −0.999806 | − | 0.0196829i | \(-0.993734\pi\) | ||||
0.999806 | − | 0.0196829i | \(-0.00626568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 45422.3i | 0.765730i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −29362.0 | −0.426024 | −0.213012 | − | 0.977050i | \(-0.568327\pi\) | ||||
−0.213012 | + | 0.977050i | \(0.568327\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −21533.8 | −0.270841 | −0.135421 | − | 0.990788i | \(-0.543239\pi\) | ||||
−0.135421 | + | 0.990788i | \(0.543239\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 2310.00i | − 0.0253498i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 7560.06i | − 0.0728168i | −0.999337 | − | 0.0364084i | \(-0.988408\pi\) | ||||
0.999337 | − | 0.0364084i | \(-0.0115917\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 21649.0 | 0.184013 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −147669. | −1.11322 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 192854.i | 1.29539i | 0.761899 | + | 0.647696i | \(0.224267\pi\) | ||||
−0.761899 | + | 0.647696i | \(0.775733\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9605.00i | 0.0577310i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −233280. | −1.25966 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −78420.2 | −0.381831 | −0.190916 | − | 0.981606i | \(-0.561146\pi\) | ||||
−0.190916 | + | 0.981606i | \(0.561146\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 10918.0i | − 0.0481009i | −0.999711 | − | 0.0240505i | \(-0.992344\pi\) | ||||
0.999711 | − | 0.0240505i | \(-0.00765624\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 71572.7i | − 0.286237i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14660.0 | 0.0533819 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 394146. | 1.31049 | 0.655243 | − | 0.755418i | \(-0.272566\pi\) | ||||
0.655243 | + | 0.755418i | \(0.272566\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 324480.i | 0.987735i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 532241.i | − 1.48708i | −0.668694 | − | 0.743538i | \(-0.733146\pi\) | ||||
0.668694 | − | 0.743538i | \(-0.266854\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −288626. | −0.741937 | −0.370968 | − | 0.928646i | \(-0.620974\pi\) | ||||
−0.370968 | + | 0.928646i | \(0.620974\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 481025. | 1.14021 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 297600.i | 0.651870i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 310706.i | − 0.630186i | −0.949061 | − | 0.315093i | \(-0.897964\pi\) | ||||
0.949061 | − | 0.315093i | \(-0.102036\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −646479. | −1.21646 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 204153. | 0.357043 | 0.178522 | − | 0.983936i | \(-0.442869\pi\) | ||||
0.178522 | + | 0.983936i | \(0.442869\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 47660.0i | 0.0776064i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 790027.i | 1.19973i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −310738. | −0.440783 | −0.220391 | − | 0.975412i | \(-0.570733\pi\) | ||||
−0.220391 | + | 0.975412i | \(0.570733\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 454223. | 0.602761 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.29792e6i | 1.61361i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 75290.8i | 0.0878155i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.45709e6 | −1.59650 | −0.798252 | − | 0.602324i | \(-0.794242\pi\) | ||||
−0.798252 | + | 0.602324i | \(0.794242\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −221875. | −0.228667 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 639158.i | 0.620360i | 0.950678 | + | 0.310180i | \(0.100389\pi\) | ||||
−0.950678 | + | 0.310180i | \(0.899611\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 1.38913e6i | − 1.27125i | −0.771997 | − | 0.635626i | \(-0.780742\pi\) | ||||
0.771997 | − | 0.635626i | \(-0.219258\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −96000.0 | −0.0829284 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.14935e6 | −0.938209 | −0.469105 | − | 0.883143i | \(-0.655423\pi\) | ||||
−0.469105 | + | 0.883143i | \(0.655423\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.53574e6i | 1.18587i | 0.805250 | + | 0.592936i | \(0.202031\pi\) | ||||
−0.805250 | + | 0.592936i | \(0.797969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 61781.8i | − 0.0451743i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −601694. | −0.417004 | −0.208502 | − | 0.978022i | \(-0.566859\pi\) | ||||
−0.208502 | + | 0.978022i | \(0.566859\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 104725. | 0.0688587 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 338646.i | 0.211441i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.47669e6i | 0.876292i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −849001. | −0.479239 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −909748. | −0.488884 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 311500.i | − 0.159488i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.67462e6i | 0.817531i | 0.912640 | + | 0.408765i | \(0.134041\pi\) | ||||
−0.912640 | + | 0.408765i | \(0.865959\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −667200. | −0.310804 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.84454e6 | −1.26531 | −0.632656 | − | 0.774433i | \(-0.718035\pi\) | ||||
−0.632656 | + | 0.774433i | \(0.718035\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.33280e6i | 0.991568i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 154300.i | 0.0627139i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.81003e6 | −1.48172 | −0.740862 | − | 0.671658i | \(-0.765583\pi\) | ||||
−0.740862 | + | 0.671658i | \(0.765583\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 138839. | 0.0516971 | 0.0258485 | − | 0.999666i | \(-0.491771\pi\) | ||||
0.0258485 | + | 0.999666i | \(0.491771\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 234240.i | − 0.0835610i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 1.40809e6i | − 0.481530i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 254980. | 0.0836377 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 670770. | 0.211165 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.27426e6i | 0.989816i | 0.868945 | + | 0.494908i | \(0.164798\pi\) | ||||
−0.868945 | + | 0.494908i | \(0.835202\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.59352e6i | 1.62463i | 0.583220 | + | 0.812314i | \(0.301793\pi\) | ||||
−0.583220 | + | 0.812314i | \(0.698207\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.10095e6 | −0.307391 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 418902. | 0.112491 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 816794.i | 0.211064i | 0.994416 | + | 0.105532i | \(0.0336545\pi\) | ||||
−0.994416 | + | 0.105532i | \(0.966345\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.97536e6i | 1.48653i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.24480e6 | 0.777518 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.84593e6 | 0.426237 | 0.213119 | − | 0.977026i | \(-0.431638\pi\) | ||||
0.213119 | + | 0.977026i | \(0.431638\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 297600.i | 0.0662493i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 7.96515e6i | − 1.71019i | −0.518471 | − | 0.855095i | \(-0.673499\pi\) | ||||
0.518471 | − | 0.855095i | \(-0.326501\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.67765e6 | 0.554746 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.73922e6 | −0.347829 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 5.12653e6i | − 0.990115i | −0.868860 | − | 0.495057i | \(-0.835147\pi\) | ||||
0.868860 | − | 0.495057i | \(-0.164853\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 4.81025e6i | − 0.897538i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.42976e6 | −0.438171 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.33411e6 | 0.406969 | 0.203485 | − | 0.979078i | \(-0.434773\pi\) | ||||
0.203485 | + | 0.979078i | \(0.434773\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 9.69156e6i | − 1.63440i | −0.576355 | − | 0.817199i | \(-0.695525\pi\) | ||||
0.576355 | − | 0.817199i | \(-0.304475\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 338282.i | − 0.0551983i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −19940.0 | −0.00314927 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.57774e6 | 0.700046 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.78080e6i | 0.708134i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 1.14164e7i | − 1.63844i | −0.573479 | − | 0.819220i | \(-0.694407\pi\) | ||||
0.573479 | − | 0.819220i | \(-0.305593\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.43033e6 | −0.338060 | −0.169030 | − | 0.985611i | \(-0.554064\pi\) | ||||
−0.169030 | + | 0.985611i | \(0.554064\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 454223. | 0.0612584 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.23065e6i | 0.291764i | 0.989302 | + | 0.145882i | \(0.0466020\pi\) | ||||
−0.989302 | + | 0.145882i | \(0.953398\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 4.89576e6i | − 0.621242i | −0.950534 | − | 0.310621i | \(-0.899463\pi\) | ||||
0.950534 | − | 0.310621i | \(-0.100537\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.22122e7 | 1.50385 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.90027e6 | 0.944395 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 293620.i | 0.0340819i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.41916e6i | 0.272743i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.23168e6 | 0.792137 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.90951e6 | −0.416174 | −0.208087 | − | 0.978110i | \(-0.566724\pi\) | ||||
−0.208087 | + | 0.978110i | \(0.566724\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 1.64909e7i | − 1.70650i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 215338.i | 0.0216673i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.29792e7 | 1.27019 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.94275e6 | −0.851410 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 6.98696e6i | − 0.647308i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.33114e6i | 0.300385i | 0.988657 | + | 0.150192i | \(0.0479893\pi\) | ||||
−0.988657 | + | 0.150192i | \(0.952011\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.58628e6 | 0.314844 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.35033e7 | 1.15442 | 0.577208 | − | 0.816597i | \(-0.304142\pi\) | ||||
0.577208 | + | 0.816597i | \(0.304142\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 1.59598e6i | − 0.132899i | −0.997790 | − | 0.0664493i | \(-0.978833\pi\) | ||||
0.997790 | − | 0.0664493i | \(-0.0211671\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.22080e6i | 0.748053i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.04383e6 | −0.635909 | −0.317954 | − | 0.948106i | \(-0.602996\pi\) | ||||
−0.317954 | + | 0.948106i | \(0.602996\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −75600.6 | −0.00582535 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 9.62688e6i | − 0.723170i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.12532e7i | 0.824296i | 0.911117 | + | 0.412148i | \(0.135221\pi\) | ||||
−0.911117 | + | 0.412148i | \(0.864779\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.05104e6 | 0.360853 | 0.180426 | − | 0.983589i | \(-0.442252\pi\) | ||||
0.180426 | + | 0.983589i | \(0.442252\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.78197e6 | −0.612031 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 216490.i | − 0.0147211i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 1.10376e7i | − 0.732462i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.32544e6 | 0.409725 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.71590e6 | 0.298225 | 0.149112 | − | 0.988820i | \(-0.452358\pi\) | ||||
0.149112 | + | 0.988820i | \(0.452358\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 1.00589e7i | − 0.621138i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.47669e6i | 0.0890572i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.34552e7 | 1.38178 | 0.690892 | − | 0.722958i | \(-0.257218\pi\) | ||||
0.690892 | + | 0.722958i | \(0.257218\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −617818. | −0.0355600 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.89004e6i | 0.331281i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.16993e7i | 1.19283i | 0.802676 | + | 0.596415i | \(0.203409\pi\) | ||||
−0.802676 | + | 0.596415i | \(0.796591\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.92854e6 | 0.103631 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.62786e6 | −0.505820 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 2.94278e7i | − 1.51182i | −0.654674 | − | 0.755911i | \(-0.727194\pi\) | ||||
0.654674 | − | 0.755911i | \(-0.272806\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 8.51474e6i | − 0.427822i | −0.976853 | − | 0.213911i | \(-0.931380\pi\) | ||||
0.976853 | − | 0.213911i | \(-0.0686203\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.40736e7 | 0.691699 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.49118e7 | −0.717019 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 2.76226e7i | − 1.29965i | −0.760085 | − | 0.649824i | \(-0.774843\pi\) | ||||
0.760085 | − | 0.649824i | \(-0.225157\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.67663e6i | 0.445566i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.64008e6 | −0.389403 | −0.194701 | − | 0.980863i | \(-0.562374\pi\) | ||||
−0.194701 | + | 0.980863i | \(0.562374\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.27350e7 | −0.561873 | −0.280937 | − | 0.959726i | \(-0.590645\pi\) | ||||
−0.280937 | + | 0.959726i | \(0.590645\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.33280e6i | 0.100773i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.09748e6i | 0.384836i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.42281e6 | −0.0589460 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.51462e7 | −1.83207 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.45415e7i | 1.77077i | 0.464859 | + | 0.885385i | \(0.346105\pi\) | ||||
−0.464859 | + | 0.885385i | \(0.653895\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 784202.i | 0.0305465i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.48205e7 | 0.565709 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.53528e7 | −0.574345 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.67200e6i | 0.244656i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.98036e7i | 0.711895i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −109180. | −0.00384808 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.89051e7 | 1.69020 | 0.845102 | − | 0.534606i | \(-0.179540\pi\) | ||||
0.845102 | + | 0.534606i | \(0.179540\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 4.30406e7i | − 1.45883i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 5.00220e7i | − 1.66295i | −0.555559 | − | 0.831477i | \(-0.687496\pi\) | ||||
0.555559 | − | 0.831477i | \(-0.312504\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.12719e6 | −0.0367589 | −0.0183795 | − | 0.999831i | \(-0.505851\pi\) | ||||
−0.0183795 | + | 0.999831i | \(0.505851\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −715727. | −0.0228990 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.44882e7i | 1.08266i | 0.840810 | + | 0.541330i | \(0.182079\pi\) | ||||
−0.840810 | + | 0.541330i | \(0.817921\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 2.44908e7i | − 0.754452i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.56112e7 | −1.07664 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.58836e7 | 1.06485 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.27596e7i | 0.663003i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.75831e7i | 1.36085i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.34240e6 | −0.0657769 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.02696e7 | 1.11044 | 0.555218 | − | 0.831705i | \(-0.312635\pi\) | ||||
0.555218 | + | 0.831705i | \(0.312635\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 460614.i | − 0.0124740i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 3.94146e6i | − 0.104839i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.42531e7 | −0.894973 | −0.447487 | − | 0.894291i | \(-0.647681\pi\) | ||||
−0.447487 | + | 0.894291i | \(0.647681\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.86428e7 | −0.478533 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 4.02355e7i | − 1.01472i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 4.31599e7i | − 1.06954i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.24480e6 | 0.0790188 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.45496e7 | 1.30558 | 0.652790 | − | 0.757539i | \(-0.273599\pi\) | ||||
0.652790 | + | 0.757539i | \(0.273599\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.70009e7i | 1.10568i | 0.833287 | + | 0.552840i | \(0.186456\pi\) | ||||
−0.833287 | + | 0.552840i | \(0.813544\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 2.26203e7i | − 0.523091i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.27231e7 | −0.289248 | −0.144624 | − | 0.989487i | \(-0.546197\pi\) | ||||
−0.144624 | + | 0.989487i | \(0.546197\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.32241e6 | −0.118966 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.57536e7i | 1.00559i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.02153e7i | 0.436915i | 0.975846 | + | 0.218457i | \(0.0701025\pi\) | ||||
−0.975846 | + | 0.218457i | \(0.929898\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.64116e6 | 0.204931 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.63053e7 | −0.549951 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.88626e6i | 0.0593549i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 1.11057e7i | − 0.224672i | −0.993670 | − | 0.112336i | \(-0.964167\pi\) | ||||
0.993670 | − | 0.112336i | \(-0.0358333\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.78262e6 | −0.134995 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.97536e7 | 1.17015 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 687146.i | − 0.0132411i | −0.999978 | − | 0.00662053i | \(-0.997893\pi\) | ||||
0.999978 | − | 0.00662053i | \(-0.00210739\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 9.65147e6i | − 0.183021i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.73801e7 | −0.697615 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.48499e7 | 0.272775 | 0.136388 | − | 0.990656i | \(-0.456451\pi\) | ||||
0.136388 | + | 0.990656i | \(0.456451\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.18861e7i | 0.938158i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 3.35885e7i | − 0.597853i | −0.954276 | − | 0.298926i | \(-0.903372\pi\) | ||||
0.954276 | − | 0.298926i | \(-0.0966285\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.97600e6 | 0.0521496 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.97430e6 | −0.0858222 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.01122e8i | 1.71789i | 0.512066 | + | 0.858946i | \(0.328880\pi\) | ||||
−0.512066 | + | 0.858946i | \(0.671120\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 4.99122e7i | − 0.834980i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.81347e7 | −1.45201 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.10706e6 | −0.0504149 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 3.48266e7i | − 0.556595i | −0.960495 | − | 0.278297i | \(-0.910230\pi\) | ||||
0.960495 | − | 0.278297i | \(-0.0897701\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.22792e7i | 1.13787i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.88398e7 | −1.06760 | −0.533798 | − | 0.845612i | \(-0.679236\pi\) | ||||
−0.533798 | + | 0.845612i | \(0.679236\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.14110e7 | −0.938277 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.46479e6i | 0.0973171i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.91524e6i | 0.0284079i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.59959e7 | −0.672278 | −0.336139 | − | 0.941812i | \(-0.609121\pi\) | ||||
−0.336139 | + | 0.941812i | \(0.609121\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.18050e8 | −1.70035 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.42976e7i | 0.344916i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 2.04153e6i | − 0.0285635i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.30176e6 | 0.0593250 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.71153e7 | −0.368615 | −0.184307 | − | 0.982869i | \(-0.559004\pi\) | ||||
−0.184307 | + | 0.982869i | \(0.559004\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.42078e7i | 1.26253i | 0.775569 | + | 0.631263i | \(0.217463\pi\) | ||||
−0.775569 | + | 0.631263i | \(0.782537\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 1.74637e6i | − 0.0230737i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.39922e7 | −0.963871 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.38282e6 | −0.0434505 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 4.36282e7i | − 0.552580i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 5.19187e7i | − 0.648473i | −0.945976 | − | 0.324236i | \(-0.894893\pi\) | ||||
0.945976 | − | 0.324236i | \(-0.105107\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.40210e7 | 1.03496 | 0.517481 | − | 0.855695i | \(-0.326870\pi\) | ||||
0.517481 | + | 0.855695i | \(0.326870\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.90027e6 | 0.0959785 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 7.88486e7i | − 0.944822i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.48115e8i | 1.75068i | 0.483512 | + | 0.875338i | \(0.339361\pi\) | ||||
−0.483512 | + | 0.875338i | \(0.660639\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.00092e6 | 0.0583088 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.03735e7 | 0.924489 | 0.462245 | − | 0.886752i | \(-0.347044\pi\) | ||||
0.462245 | + | 0.886752i | \(0.347044\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.10738e6i | 0.0352626i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.01449e8i | 1.13586i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.80925e7 | −0.973196 | −0.486598 | − | 0.873626i | \(-0.661762\pi\) | ||||
−0.486598 | + | 0.873626i | \(0.661762\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.82022e7 | 0.307435 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.73309e8i | 1.86434i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 4.54223e6i | − 0.0482209i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.75423e7 | 0.393344 | 0.196672 | − | 0.980469i | \(-0.436987\pi\) | ||||
0.196672 | + | 0.980469i | \(0.436987\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.35392e7 | 0.760468 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.15260e8i | 1.17646i | 0.808695 | + | 0.588228i | \(0.200174\pi\) | ||||
−0.808695 | + | 0.588228i | \(0.799826\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 1.03415e7i | − 0.104194i | −0.998642 | − | 0.0520970i | \(-0.983410\pi\) | ||||
0.998642 | − | 0.0520970i | \(-0.0165905\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.29792e7 | 0.129089 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.64223e8 | −1.61243 | −0.806217 | − | 0.591620i | \(-0.798489\pi\) | ||||
−0.806217 | + | 0.591620i | \(0.798489\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 1.22122e8i | − 1.18379i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.53074e7i | 0.242206i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.06832e7 | 0.195449 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.16889e8 | −1.09067 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.45493e7i | 0.410474i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.76230e7i | 0.706291i | 0.935568 | + | 0.353146i | \(0.114888\pi\) | ||||
−0.935568 | + | 0.353146i | \(0.885112\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.92320e6 | 0.0262678 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.00536e8 | 0.892241 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.45709e7i | 0.127720i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.08071e7i | 0.0935670i | 0.998905 | + | 0.0467835i | \(0.0148971\pi\) | ||||
−0.998905 | + | 0.0467835i | \(0.985103\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.71939e7 | 0.489129 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.85067e8 | −1.56345 | −0.781724 | − | 0.623624i | \(-0.785660\pi\) | ||||
−0.781724 | + | 0.623624i | \(0.785660\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 1.21523e8i | − 1.01419i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.21875e6i | 0.0182934i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.64909e8 | −1.34331 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.83704e7 | 0.550258 | 0.275129 | − | 0.961407i | \(-0.411279\pi\) | ||||
0.275129 | + | 0.961407i | \(0.411279\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 2.46791e8i | − 1.96253i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 1.31562e7i | − 0.103377i | −0.998663 | − | 0.0516887i | \(-0.983540\pi\) | ||||
0.998663 | − | 0.0516887i | \(-0.0164604\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.39158e6 | 0.0496288 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.29640e7 | 0.636599 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.34186e8i | 1.01755i | 0.860900 | + | 0.508775i | \(0.169901\pi\) | ||||
−0.860900 | + | 0.508775i | \(0.830099\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.94275e7i | 0.670206i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.16173e8 | 0.860508 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.38913e7 | −0.101700 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.26144e6i | 0.0525474i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 1.58840e8i | − 1.13621i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.98565e8 | 1.40407 | 0.702036 | − | 0.712142i | \(-0.252275\pi\) | ||||
0.702036 | + | 0.712142i | \(0.252275\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.15512e8 | 1.50649 | 0.753245 | − | 0.657740i | \(-0.228487\pi\) | ||||
0.753245 | + | 0.657740i | \(0.228487\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 1.49040e8i | − 1.02997i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 1.99649e8i | − 1.36406i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.83616e7 | 0.259137 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.81151e7 | −0.120992 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 4.30447e7i | − 0.284275i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.14935e7i | 0.0750567i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.23197e7 | 0.467018 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.07939e7 | −0.132791 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.44188e7i | 0.0910623i | 0.998963 | + | 0.0455311i | \(0.0144980\pi\) | ||||
−0.998963 | + | 0.0455311i | \(0.985502\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 3.00282e8i | − 1.87556i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.53574e7 | 0.0948697 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.24129e7 | −0.259141 | −0.129571 | − | 0.991570i | \(-0.541360\pi\) | ||||
−0.129571 | + | 0.991570i | \(0.541360\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 2.52206e6i | − 0.0152419i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 1.91976e8i | − 1.14761i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.62688e7 | −0.569259 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −617818. | −0.00361395 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.90848e7i | 0.515511i | 0.966210 | + | 0.257756i | \(0.0829829\pi\) | ||||
−0.966210 | + | 0.257756i | \(0.917017\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 3.15685e7i | − 0.180725i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.41836e8 | 0.803338 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.41576e8 | 1.35372 | 0.676860 | − | 0.736112i | \(-0.263340\pi\) | ||||
0.676860 | + | 0.736112i | \(0.263340\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.01694e6i | 0.0333603i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.00304e8i | 1.09886i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.56141e7 | 0.139041 | 0.0695203 | − | 0.997581i | \(-0.477853\pi\) | ||||
0.0695203 | + | 0.997581i | \(0.477853\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.10781e8 | 0.595057 | 0.297528 | − | 0.954713i | \(-0.403838\pi\) | ||||
0.297528 | + | 0.954713i | \(0.403838\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 3.53725e8i | − 1.88019i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.62586e8i | 0.855225i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.07272e8 | 0.558415 | 0.279208 | − | 0.960231i | \(-0.409928\pi\) | ||||
0.279208 | + | 0.960231i | \(0.409928\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.53011e7 | −0.387941 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 6.32544e7i | − 0.322524i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 1.85236e8i | − 0.934803i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.38646e6 | 0.0169152 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.16397e7 | 0.106988 | 0.0534941 | − | 0.998568i | \(-0.482964\pi\) | ||||
0.0534941 | + | 0.998568i | \(0.482964\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 3.15395e8i | − 1.54351i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.91140e7i | 0.334814i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.00341e8 | 0.960738 | 0.480369 | − | 0.877066i | \(-0.340503\pi\) | ||||
0.480369 | + | 0.877066i | \(0.340503\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.47669e7 | 0.0701033 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 1.51690e8i | − 0.712907i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.37592e8i | 0.640197i | 0.947384 | + | 0.320098i | \(0.103716\pi\) | ||||
−0.947384 | + | 0.320098i | \(0.896284\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.90306e8 | 0.876655 | 0.438327 | − | 0.898815i | \(-0.355571\pi\) | ||||
0.438327 | + | 0.898815i | \(0.355571\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.10477e7 | 0.415257 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.49001e6i | 0.0383391i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.25461e8i | 0.560974i | 0.959858 | + | 0.280487i | \(0.0904960\pi\) | ||||
−0.959858 | + | 0.280487i | \(0.909504\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.44781e8 | 1.08374 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.10831e7 | 0.0485888 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.91111e7i | 0.430270i | 0.976584 | + | 0.215135i | \(0.0690191\pi\) | ||||
−0.976584 | + | 0.215135i | \(0.930981\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.09748e6i | 0.0391107i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.70827e7 | −0.157876 | −0.0789379 | − | 0.996880i | \(-0.525153\pi\) | ||||
−0.0789379 | + | 0.996880i | \(0.525153\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.05274e8 | −1.70874 | −0.854372 | − | 0.519662i | \(-0.826058\pi\) | ||||
−0.854372 | + | 0.519662i | \(0.826058\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 1.61591e8i | − 0.674749i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.62786e7i | 0.398168i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.39463e8 | 0.980841 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.24065e8 | 0.909017 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.50340e6i | 0.0381880i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.52648e7i | 0.100561i | 0.998735 | + | 0.0502803i | \(0.0160115\pi\) | ||||
−0.998735 | + | 0.0502803i | \(0.983989\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.21132e8 | −0.477581 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.67462e7 | 0.0654025 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.17374e7i | 0.122787i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 1.22948e8i | − 0.471213i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.21293e8 | −1.59959 | −0.799797 | − | 0.600270i | \(-0.795060\pi\) | ||||
−0.799797 | + | 0.600270i | \(0.795060\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.17706e7 | −0.307584 | −0.153792 | − | 0.988103i | \(-0.549149\pi\) | ||||
−0.153792 | + | 0.988103i | \(0.549149\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.67200e6i | 0.0248643i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.84284e8i | 0.680416i | 0.940350 | + | 0.340208i | \(0.110497\pi\) | ||||
−0.940350 | + | 0.340208i | \(0.889503\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.53226e7 | 0.275544 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.02146e8 | 1.45761 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.43842e7i | 0.231228i | 0.993294 | + | 0.115614i | \(0.0368835\pi\) | ||||
−0.993294 | + | 0.115614i | \(0.963117\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.84454e7i | 0.101225i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.66726e7 | −0.235099 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.38099e8 | −1.88021 | −0.940103 | − | 0.340889i | \(-0.889272\pi\) | ||||
−0.940103 | + | 0.340889i | \(0.889272\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 2.83897e8i | − 0.983008i | −0.870875 | − | 0.491504i | \(-0.836447\pi\) | ||||
0.870875 | − | 0.491504i | \(-0.163553\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 2.16483e8i | − 0.742819i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.33280e7 | 0.0793255 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.67029e8 | −0.899872 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.03212e8i | 0.344707i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.04867e7i | 0.0347115i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.77693e8 | 0.911002 | 0.455501 | − | 0.890235i | \(-0.349460\pi\) | ||||
0.455501 | + | 0.890235i | \(0.349460\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.39550e8 | −0.778906 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.23026e7i | 0.297473i | 0.988877 | + | 0.148737i | \(0.0475207\pi\) | ||||
−0.988877 | + | 0.148737i | \(0.952479\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.51462e8i | 1.44215i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.18384e8 | 1.32475 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.70862e8 | −0.850132 | −0.425066 | − | 0.905162i | \(-0.639749\pi\) | ||||
−0.425066 | + | 0.905162i | \(0.639749\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.81003e7i | 0.118538i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 4.94496e7i | − 0.152508i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.82724e8 | −0.864380 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.92568e7 | 0.0583645 | 0.0291823 | − | 0.999574i | \(-0.490710\pi\) | ||||
0.0291823 | + | 0.999574i | \(0.490710\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.87456e7i | 0.206560i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 1.38839e6i | − 0.00413577i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.39939e8 | 0.413277 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.49229e8 | −0.729738 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.52234e8i | 1.02253i | 0.859423 | + | 0.511266i | \(0.170823\pi\) | ||||
−0.859423 | + | 0.511266i | \(0.829177\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.50130e7i | 0.0432117i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.34240e6 | −0.00668488 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.98036e8 | 0.560384 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 4.62733e8i | − 1.29835i | −0.760639 | − | 0.649175i | \(-0.775114\pi\) | ||||
0.760639 | − | 0.649175i | \(-0.224886\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 7.17731e7i | − 0.199689i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.38697e8 | −1.21031 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.40809e7 | −0.0385224 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.48668e8i | 0.945921i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.60385e8i | 1.23861i | 0.785150 | + | 0.619305i | \(0.212586\pi\) | ||||
−0.785150 | + | 0.619305i | \(0.787414\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.30406e8 | −1.14835 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.56501e8 | 0.414097 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.95856e8i | 1.03878i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 4.82173e8i | − 1.25487i | −0.778668 | − | 0.627437i | \(-0.784104\pi\) | ||||
0.778668 | − | 0.627437i | \(-0.215896\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.99184e8 | 0.514128 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.02630e8 | 0.262738 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 5.08270e8i | − 1.29057i | −0.763941 | − | 0.645287i | \(-0.776738\pi\) | ||||
0.763941 | − | 0.645287i | \(-0.223262\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 6.70770e6i | − 0.0168932i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.78577e8 | −0.945696 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.27767e8 | −0.316582 | −0.158291 | − | 0.987392i | \(-0.550598\pi\) | ||||
−0.158291 | + | 0.987392i | \(0.550598\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 3.41988e8i | − 0.840537i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.83312e8i | 0.690716i | 0.938471 | + | 0.345358i | \(0.112242\pi\) | ||||
−0.938471 | + | 0.345358i | \(0.887758\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.27426e7 | 0.0791853 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.71593e7 | 0.113137 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.56112e8i | 0.847503i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 2.15309e8i | − 0.508325i | −0.967161 | − | 0.254163i | \(-0.918200\pi\) | ||||
0.967161 | − | 0.254163i | \(-0.0817999\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.46117e8 | 0.342228 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.59352e7 | 0.129970 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.03985e8i | 0.700753i | 0.936609 | + | 0.350377i | \(0.113946\pi\) | ||||
−0.936609 | + | 0.350377i | \(0.886054\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 3.11663e8i | − 0.712787i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.63611e8 | −1.95959 | −0.979793 | − | 0.200014i | \(-0.935901\pi\) | ||||
−0.979793 | + | 0.200014i | \(0.935901\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.75831e8 | 1.07122 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.10095e7i | 0.0245913i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 1.14964e8i | − 0.254786i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.97898e7 | −0.0435174 | −0.0217587 | − | 0.999763i | \(-0.506927\pi\) | ||||
−0.0217587 | + | 0.999763i | \(0.506927\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.26734e8 | 1.58567 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.64048e8i | 1.22117i | 0.791949 | + | 0.610587i | \(0.209067\pi\) | ||||
−0.791949 | + | 0.610587i | \(0.790933\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.50345e8i | 1.39714i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.91424e7 | −0.0408069 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.21069e8 | 0.467644 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.11217e8i | 1.07313i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 3.93433e8i | − 0.819570i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.16794e6 | 0.0168851 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.04198e8 | −0.829220 | −0.414610 | − | 0.909999i | \(-0.636082\pi\) | ||||
−0.414610 | + | 0.909999i | \(0.636082\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.72328e8i | 1.36883i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.86428e8i | 0.376688i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.60058e7 | 0.0320965 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.97536e7 | 0.118922 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 2.15998e7i | − 0.0426654i | −0.999772 | − | 0.0213327i | \(-0.993209\pi\) | ||||
0.999772 | − | 0.0213327i | \(-0.00679092\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.60313e7i | 0.0706381i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.17805e7 | −0.139672 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.77225e8 | 0.535410 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 3.24480e7i | − 0.0622014i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 9.11786e8i | − 1.73489i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.51310e8 | −1.23011 | −0.615053 | − | 0.788486i | \(-0.710865\pi\) | ||||
−0.615053 | + | 0.788486i | \(0.710865\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.52891e8 | 1.03652 | 0.518259 | − | 0.855223i | \(-0.326580\pi\) | ||||
0.518259 | + | 0.855223i | \(0.326580\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 2.63820e8i | − 0.490948i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 1.84593e7i | − 0.0340990i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.62130e8 | 0.297301 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.04926e8 | 0.190998 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.94865e8i | 1.61707i | 0.588450 | + | 0.808534i | \(0.299738\pi\) | ||||
−0.588450 | + | 0.808534i | \(0.700262\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 8.44482e8i | − 1.51492i | −0.652879 | − | 0.757462i | \(-0.726439\pi\) | ||||
0.652879 | − | 0.757462i | \(-0.273561\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.62024e8 | −0.822816 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.11099e7 | −0.0550024 | −0.0275012 | − | 0.999622i | \(-0.508755\pi\) | ||||
−0.0275012 | + | 0.999622i | \(0.508755\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 4.05444e7i | − 0.0711652i | −0.999367 | − | 0.0355826i | \(-0.988671\pi\) | ||||
0.999367 | − | 0.0355826i | \(-0.0113287\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 8.55856e8i | − 1.49141i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.03179e8 | −0.178508 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.96515e7 | −0.136815 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 6.46364e8i | − 1.10230i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.17820e8i | 0.707463i | 0.935347 | + | 0.353731i | \(0.115087\pi\) | ||||
−0.935347 | + | 0.353731i | \(0.884913\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.53247e7 | −0.0930103 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.67703e8 | −0.446859 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 2.67765e7i | − 0.0443797i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.63053e8i | 0.432906i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.94578e8 | −0.644778 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.08823e7 | 0.0338835 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.28994e8i | 0.691201i | 0.938382 | + | 0.345601i | \(0.112325\pi\) | ||||
−0.938382 | + | 0.345601i | \(0.887675\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.73922e7i | 0.0278263i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.20598e8 | −0.350476 | −0.175238 | − | 0.984526i | \(-0.556070\pi\) | ||||
−0.175238 | + | 0.984526i | \(0.556070\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.14768e9 | −1.81068 | −0.905339 | − | 0.424689i | \(-0.860383\pi\) | ||||
−0.905339 | + | 0.424689i | \(0.860383\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.81875e8i | 0.441619i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.44987e7i | 0.100350i | 0.998740 | + | 0.0501752i | \(0.0159780\pi\) | ||||
−0.998740 | + | 0.0501752i | \(0.984022\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.12653e7 | −0.0792092 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.40842e7 | −0.0676435 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.98433e8i | 0.454766i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.77818e8i | 0.874453i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.36587e8 | −0.505888 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.65147e7 | −0.144069 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.15252e8i | 0.763873i | 0.924189 | + | 0.381937i | \(0.124743\pi\) | ||||
−0.924189 | + | 0.381937i | \(0.875257\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.38007e9i | 2.03205i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.18519e8 | −0.173324 | −0.0866622 | − | 0.996238i | \(-0.527620\pi\) | ||||
−0.0866622 | + | 0.996238i | \(0.527620\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.28669e8 | 0.186893 | 0.0934466 | − | 0.995624i | \(-0.470212\pi\) | ||||
0.0934466 | + | 0.995624i | \(0.470212\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.42976e7i | 0.0350537i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 5.09948e8i | − 0.730727i | −0.930865 | − | 0.365363i | \(-0.880945\pi\) | ||||
0.930865 | − | 0.365363i | \(-0.119055\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.18861e8 | 0.738492 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.20943e8 | 0.877847 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.69203e7i | 0.0799306i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 2.33411e7i | − 0.0325576i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.75688e8 | −0.659090 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.06812e9 | −1.47007 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 9.19142e8i | − 1.25663i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.06724e8i | 0.280756i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.69156e7 | −0.130752 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.43212e8 | −0.728027 | −0.364014 | − | 0.931394i | \(-0.618594\pi\) | ||||
−0.364014 | + | 0.931394i | \(0.618594\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.47645e8i | 0.196575i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 5.99585e8i | − 0.793041i | −0.918026 | − | 0.396520i | \(-0.870218\pi\) | ||||
0.918026 | − | 0.396520i | \(-0.129782\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.96089e8 | −0.257656 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.38282e6 | −0.00441586 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.81347e8i | 1.14298i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.66486e8i | 1.24523i | 0.782529 | + | 0.622614i | \(0.213929\pi\) | ||||
−0.782529 | + | 0.622614i | \(0.786071\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.51527e9 | 1.93959 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.80265e8 | 0.992286 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 3.09568e7i | − 0.0391139i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 3.20889e8i | − 0.402825i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.22626e8 | 0.901295 | 0.450647 | − | 0.892702i | \(-0.351193\pi\) | ||||
0.450647 | + | 0.892702i | \(0.351193\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.62997e8 | −0.201990 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 1.54988e9i | − 1.90832i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 4.57774e7i | − 0.0560037i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.12016e8 | 0.500836 | 0.250418 | − | 0.968138i | \(-0.419432\pi\) | ||||
0.250418 | + | 0.968138i | \(0.419432\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.49246e7 | −0.0421827 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.87666e8i | 0.945308i | 0.881248 | + | 0.472654i | \(0.156704\pi\) | ||||
−0.881248 | + | 0.472654i | \(0.843296\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 3.07495e8i | − 0.366693i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.78080e7 | 0.0566507 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.29504e8 | 0.623475 | 0.311738 | − | 0.950168i | \(-0.399089\pi\) | ||||
0.311738 | + | 0.950168i | \(0.399089\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 4.23126e8i | − 0.495075i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.06858e9i | 1.24241i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.18323e9 | −1.36706 | −0.683532 | − | 0.729920i | \(-0.739557\pi\) | ||||
−0.683532 | + | 0.729920i | \(0.739557\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.14164e8 | −0.131075 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 7.58820e8i | − 0.865771i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.18050e9i | 1.33847i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.67284e8 | −0.977218 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.65499e8 | −0.297293 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.43033e7i | 0.0270448i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 4.78688e8i | − 0.529387i | −0.964333 | − | 0.264693i | \(-0.914729\pi\) | ||||
0.964333 | − | 0.264693i | \(-0.0852708\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.11181e9 | 1.22197 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.02914e8 | −0.767793 | −0.383897 | − | 0.923376i | \(-0.625418\pi\) | ||||
−0.383897 | + | 0.923376i | \(0.625418\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 4.30176e7i | − 0.0466990i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.05182e8i | 0.760830i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.21323e8 | −0.987934 | −0.493967 | − | 0.869481i | \(-0.664454\pi\) | ||||
−0.493967 | + | 0.869481i | \(0.664454\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.98464e8 | 0.318085 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.54755e8i | 0.375770i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 2.44410e8i | − 0.257311i | −0.991689 | − | 0.128655i | \(-0.958934\pi\) | ||||
0.991689 | − | 0.128655i | \(-0.0410661\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.23065e7 | 0.0233411 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.25766e7 | −0.0754823 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 2.25514e8i | − 0.233122i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.78184e9i | 1.83083i | 0.402516 | + | 0.915413i | \(0.368136\pi\) | ||||
−0.402516 | + | 0.915413i | \(0.631864\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.24771e9 | 1.27428 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.89576e7 | −0.0496994 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1.36790e9i | − 1.38029i | −0.723673 | − | 0.690143i | \(-0.757548\pi\) | ||||
0.723673 | − | 0.690143i | \(-0.242452\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.07674e7i | 0.0308598i |
(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 | 256.7.d.f.127.3 | 4 | ||
4.3 | odd | 2 | inner | 256.7.d.f.127.1 | 4 | ||
8.3 | odd | 2 | inner | 256.7.d.f.127.4 | 4 | ||
8.5 | even | 2 | inner | 256.7.d.f.127.2 | 4 | ||
16.3 | odd | 4 | 64.7.c.c.63.1 | 2 | |||
16.5 | even | 4 | 4.7.b.a.3.2 | yes | 2 | ||
16.11 | odd | 4 | 4.7.b.a.3.1 | ✓ | 2 | ||
16.13 | even | 4 | 64.7.c.c.63.2 | 2 | |||
48.5 | odd | 4 | 36.7.d.c.19.1 | 2 | |||
48.11 | even | 4 | 36.7.d.c.19.2 | 2 | |||
48.29 | odd | 4 | 576.7.g.h.127.2 | 2 | |||
48.35 | even | 4 | 576.7.g.h.127.1 | 2 | |||
80.27 | even | 4 | 100.7.d.a.99.4 | 4 | |||
80.37 | odd | 4 | 100.7.d.a.99.2 | 4 | |||
80.43 | even | 4 | 100.7.d.a.99.1 | 4 | |||
80.53 | odd | 4 | 100.7.d.a.99.3 | 4 | |||
80.59 | odd | 4 | 100.7.b.c.51.2 | 2 | |||
80.69 | even | 4 | 100.7.b.c.51.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.7.b.a.3.1 | ✓ | 2 | 16.11 | odd | 4 | ||
4.7.b.a.3.2 | yes | 2 | 16.5 | even | 4 | ||
36.7.d.c.19.1 | 2 | 48.5 | odd | 4 | |||
36.7.d.c.19.2 | 2 | 48.11 | even | 4 | |||
64.7.c.c.63.1 | 2 | 16.3 | odd | 4 | |||
64.7.c.c.63.2 | 2 | 16.13 | even | 4 | |||
100.7.b.c.51.1 | 2 | 80.69 | even | 4 | |||
100.7.b.c.51.2 | 2 | 80.59 | odd | 4 | |||
100.7.d.a.99.1 | 4 | 80.43 | even | 4 | |||
100.7.d.a.99.2 | 4 | 80.37 | odd | 4 | |||
100.7.d.a.99.3 | 4 | 80.53 | odd | 4 | |||
100.7.d.a.99.4 | 4 | 80.27 | even | 4 | |||
256.7.d.f.127.1 | 4 | 4.3 | odd | 2 | inner | ||
256.7.d.f.127.2 | 4 | 8.5 | even | 2 | inner | ||
256.7.d.f.127.3 | 4 | 1.1 | even | 1 | trivial | ||
256.7.d.f.127.4 | 4 | 8.3 | odd | 2 | inner | ||
576.7.g.h.127.1 | 2 | 48.35 | even | 4 | |||
576.7.g.h.127.2 | 2 | 48.29 | odd | 4 |