Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,11,Mod(255,256)]
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, 0]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.255");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.c (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: | \(162.651456684\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4 x^{9} - 9850 x^{8} - 22678 x^{7} + 31760900 x^{6} + 262382084 x^{5} - 36066825359 x^{4} + \cdots + 11\!\cdots\!28 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{85}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 128) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 255.5 | ||
Root | \(-59.8851 - 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 256.255 |
Dual form | 256.11.c.j.255.6 |
$q$-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 | ||||||||
\(3\) | − 121.681i | − 0.500746i | −0.968149 | − | 0.250373i | \(-0.919447\pi\) | ||||
0.968149 | − | 0.250373i | \(-0.0805533\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2688.94 | −0.860461 | −0.430231 | − | 0.902719i | \(-0.641568\pi\) | ||||
−0.430231 | + | 0.902719i | \(0.641568\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 30265.0i | 1.80074i | 0.435125 | + | 0.900370i | \(0.356704\pi\) | ||||
−0.435125 | + | 0.900370i | \(0.643296\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 44242.7 | 0.749253 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 33112.3i | 0.205601i | 0.994702 | + | 0.102801i | \(0.0327804\pi\) | ||||
−0.994702 | + | 0.102801i | \(0.967220\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −510285. | −1.37434 | −0.687172 | − | 0.726495i | \(-0.741148\pi\) | ||||
−0.687172 | + | 0.726495i | \(0.741148\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 327194.i | 0.430873i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.64540e6 | −1.86314 | −0.931572 | − | 0.363557i | \(-0.881562\pi\) | ||||
−0.931572 | + | 0.363557i | \(0.881562\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 3.77448e6i | − 1.52436i | −0.647362 | − | 0.762182i | \(-0.724128\pi\) | ||||
0.647362 | − | 0.762182i | \(-0.275872\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.68269e6 | 0.901714 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 6.21786e6i | − 0.966056i | −0.875605 | − | 0.483028i | \(-0.839537\pi\) | ||||
0.875605 | − | 0.483028i | \(-0.160463\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.53522e6 | −0.259606 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 1.25687e7i | − 0.875932i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.22858e7 | 1.57406 | 0.787031 | − | 0.616914i | \(-0.211617\pi\) | ||||
0.787031 | + | 0.616914i | \(0.211617\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.24973e7i | 0.436523i | 0.975890 | + | 0.218261i | \(0.0700385\pi\) | ||||
−0.975890 | + | 0.218261i | \(0.929961\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.02915e6 | 0.102954 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 8.13809e7i | − 1.54947i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.65303e7 | −0.959425 | −0.479713 | − | 0.877426i | \(-0.659259\pi\) | ||||
−0.479713 | + | 0.877426i | \(0.659259\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.20921e7i | 0.688198i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.97485e6 | −0.0860969 | −0.0430484 | − | 0.999073i | \(-0.513707\pi\) | ||||
−0.0430484 | + | 0.999073i | \(0.513707\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 2.31833e8i | − 1.57700i | −0.615033 | − | 0.788501i | \(-0.710857\pi\) | ||||
0.615033 | − | 0.788501i | \(-0.289143\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.18966e8 | −0.644703 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 4.86716e7i | − 0.212220i | −0.994354 | − | 0.106110i | \(-0.966160\pi\) | ||||
0.994354 | − | 0.106110i | \(-0.0338396\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.33498e8 | −2.24267 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.21896e8i | 0.932962i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.33989e8 | 0.320397 | 0.160198 | − | 0.987085i | \(-0.448787\pi\) | ||||
0.160198 | + | 0.987085i | \(0.448787\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 8.90370e7i | − 0.176912i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.59284e8 | −0.763320 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.52337e8i | 1.19221i | 0.802908 | + | 0.596103i | \(0.203285\pi\) | ||||
−0.802908 | + | 0.596103i | \(0.796715\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.10213e8 | 0.485691 | 0.242846 | − | 0.970065i | \(-0.421919\pi\) | ||||
0.242846 | + | 0.970065i | \(0.421919\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.33901e9i | 1.34921i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.37213e9 | 1.18257 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.27704e9i | 0.945869i | 0.881098 | + | 0.472934i | \(0.156805\pi\) | ||||
−0.881098 | + | 0.472934i | \(0.843195\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.56598e8 | −0.483749 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.06151e8i | 0.0588347i | 0.999567 | + | 0.0294174i | \(0.00936519\pi\) | ||||
−0.999567 | + | 0.0294174i | \(0.990635\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.60337e8 | −0.173818 | −0.0869089 | − | 0.996216i | \(-0.527699\pi\) | ||||
−0.0869089 | + | 0.996216i | \(0.527699\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.08489e8i | 0.129997i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00214e9 | −0.370234 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.41105e9i | 0.783557i | 0.920060 | + | 0.391778i | \(0.128140\pi\) | ||||
−0.920060 | + | 0.391778i | \(0.871860\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.08311e9 | 0.310634 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.05140e9i | 0.520788i | 0.965502 | + | 0.260394i | \(0.0838524\pi\) | ||||
−0.965502 | + | 0.260394i | \(0.916148\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.11332e9 | 1.60316 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 3.92858e9i | − 0.788205i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.58898e9 | 1.17996 | 0.589981 | − | 0.807417i | \(-0.299135\pi\) | ||||
0.589981 | + | 0.807417i | \(0.299135\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 1.54438e10i | − 2.47484i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.52068e9 | 0.218587 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.01494e10i | 1.31166i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.54022e9 | −0.179360 | −0.0896799 | − | 0.995971i | \(-0.528584\pi\) | ||||
−0.0896799 | + | 0.995971i | \(0.528584\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.46498e9i | 0.154047i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.77466e9 | −0.834879 | −0.417440 | − | 0.908705i | \(-0.637072\pi\) | ||||
−0.417440 | + | 0.908705i | \(0.637072\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.25173e9i | 0.798062i | 0.916937 | + | 0.399031i | \(0.130653\pi\) | ||||
−0.916937 | + | 0.399031i | \(0.869347\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.90254e9 | −0.775890 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1.42627e10i | − 1.01691i | −0.861088 | − | 0.508456i | \(-0.830217\pi\) | ||||
0.861088 | − | 0.508456i | \(-0.169783\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.17215e9 | 0.0761814 | 0.0380907 | − | 0.999274i | \(-0.487872\pi\) | ||||
0.0380907 | + | 0.999274i | \(0.487872\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.09550e9i | 0.480428i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.16559e10 | 0.632637 | 0.316318 | − | 0.948653i | \(-0.397553\pi\) | ||||
0.316318 | + | 0.948653i | \(0.397553\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.67195e10i | 0.831253i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.25763e10 | −1.02973 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 8.00631e10i | − 3.35504i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.48410e10 | 0.957728 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.21375e9i | 0.0431127i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.30762e10 | 1.08384 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.27548e10i | 1.59677i | 0.602144 | + | 0.798387i | \(0.294313\pi\) | ||||
−0.602144 | + | 0.798387i | \(0.705687\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.82097e10 | −0.789678 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.15388e10i | 1.59512i | 0.603241 | + | 0.797559i | \(0.293876\pi\) | ||||
−0.603241 | + | 0.797559i | \(0.706124\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.14235e11 | 2.74499 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.37964e10i | 0.753706i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.06375e10 | −0.634821 | −0.317410 | − | 0.948288i | \(-0.602813\pi\) | ||||
−0.317410 | + | 0.948288i | \(0.602813\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 1.64390e10i | − 0.316811i | −0.987374 | − | 0.158406i | \(-0.949365\pi\) | ||||
0.987374 | − | 0.158406i | \(-0.0506354\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.92243e9 | −0.106268 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 1.68967e10i | − 0.282567i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.68146e10 | −1.35442 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.70848e10i | 1.12301i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.16257e10 | −0.294469 | −0.147234 | − | 0.989102i | \(-0.547037\pi\) | ||||
−0.147234 | + | 0.989102i | \(0.547037\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 1.16957e11i | − 1.48985i | −0.667147 | − | 0.744926i | \(-0.732485\pi\) | ||||
0.667147 | − | 0.744926i | \(-0.267515\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.17039e11 | −1.39597 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 3.36044e10i | − 0.375611i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.13296e10 | 0.747776 | 0.373888 | − | 0.927474i | \(-0.378024\pi\) | ||||
0.373888 | + | 0.927474i | \(0.378024\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 1.63039e10i | − 0.160438i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.88184e11 | 1.73962 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 2.67639e10i | − 0.232601i | −0.993214 | − | 0.116300i | \(-0.962896\pi\) | ||||
0.993214 | − | 0.116300i | \(-0.0371035\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.08341e10 | −0.0885879 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.70185e9i | 0.0746917i | 0.999302 | + | 0.0373459i | \(0.0118903\pi\) | ||||
−0.999302 | + | 0.0373459i | \(0.988110\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.22532e11 | 0.888823 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 1.66993e11i | − 1.14214i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.37621e10 | 0.153340 | 0.0766698 | − | 0.997057i | \(-0.475571\pi\) | ||||
0.0766698 | + | 0.997057i | \(0.475571\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 7.67285e10i | − 0.467484i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.03714e11 | 0.596993 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 2.62781e11i | − 1.42997i | −0.699138 | − | 0.714987i | \(-0.746433\pi\) | ||||
0.699138 | − | 0.714987i | \(-0.253567\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.05356e11 | 1.57186 | 0.785931 | − | 0.618314i | \(-0.212184\pi\) | ||||
0.785931 | + | 0.618314i | \(0.212184\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 4.99152e10i | − 0.243208i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.78896e11 | 0.825548 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 8.75952e10i | − 0.383065i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.80391e11 | 1.57733 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.65071e11i | 0.649389i | 0.945819 | + | 0.324694i | \(0.105261\pi\) | ||||
−0.945819 | + | 0.324694i | \(0.894739\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.00796e11 | −1.12327 | −0.561636 | − | 0.827384i | \(-0.689828\pi\) | ||||
−0.561636 | + | 0.827384i | \(0.689828\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 1.66962e11i | − 0.592168i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.68648e11 | 1.24245 | 0.621227 | − | 0.783631i | \(-0.286634\pi\) | ||||
0.621227 | + | 0.783631i | \(0.286634\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.81728e11i | 0.902744i | 0.892336 | + | 0.451372i | \(0.149065\pi\) | ||||
−0.892336 | + | 0.451372i | \(0.850935\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.55392e11 | 0.473640 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.77131e11i | 2.83448i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.68218e10 | 0.0740830 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 2.75095e11i | − 0.723820i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.24982e11 | 0.313411 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.97682e10i | 0.118998i | 0.998228 | + | 0.0594990i | \(0.0189503\pi\) | ||||
−0.998228 | + | 0.0594990i | \(0.981050\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.29166e10 | 0.0294613 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.23384e11i | 1.35695i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.78230e11 | −0.786064 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.38463e10i | 0.0870386i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.34991e12 | 2.56060 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 7.53050e11i | − 1.36552i | −0.730641 | − | 0.682762i | \(-0.760778\pi\) | ||||
0.730641 | − | 0.682762i | \(-0.239222\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.12165e11 | −0.194511 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.78118e11i | 0.793241i | 0.917983 | + | 0.396621i | \(0.129817\pi\) | ||||
−0.917983 | + | 0.396621i | \(0.870183\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.93341e11 | 0.624586 | 0.312293 | − | 0.949986i | \(-0.398903\pi\) | ||||
0.312293 | + | 0.949986i | \(0.398903\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.21942e11i | 0.185393i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.62943e11 | −0.382896 | −0.191448 | − | 0.981503i | \(-0.561318\pi\) | ||||
−0.191448 | + | 0.981503i | \(0.561318\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.30875e11i | 0.182607i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.93380e11 | 0.392363 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.35317e11i | 0.686470i | 0.939250 | + | 0.343235i | \(0.111523\pi\) | ||||
−0.939250 | + | 0.343235i | \(0.888477\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.32117e11 | 0.654518 | 0.327259 | − | 0.944935i | \(-0.393875\pi\) | ||||
0.327259 | + | 0.944935i | \(0.393875\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 8.73962e11i | − 1.03148i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.70344e12 | 1.92973 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.92606e12i | 2.09500i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.49618e11 | 0.260782 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.33488e12i | 1.33991i | 0.742402 | + | 0.669954i | \(0.233686\pi\) | ||||
−0.742402 | + | 0.669954i | \(0.766314\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.05888e11 | 0.198622 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 8.65558e11i | − 0.802778i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.86756e11 | −0.880125 | −0.440062 | − | 0.897967i | \(-0.645044\pi\) | ||||
−0.440062 | + | 0.897967i | \(0.645044\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 2.01354e12i | − 1.72768i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.42841e12 | 1.17937 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 1.68123e12i | − 1.33613i | −0.744103 | − | 0.668065i | \(-0.767123\pi\) | ||||
0.744103 | − | 0.668065i | \(-0.232877\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.60287e11 | −0.275689 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 8.01756e11i | − 0.590862i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.11806e10 | 0.0292369 | 0.0146185 | − | 0.999893i | \(-0.495347\pi\) | ||||
0.0146185 | + | 0.999893i | \(0.495347\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.68592e11i | 0.183758i | 0.995770 | + | 0.0918791i | \(0.0292873\pi\) | ||||
−0.995770 | + | 0.0918791i | \(0.970713\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.87922e12 | −1.23927 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 8.39468e10i | − 0.0533754i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.53091e11 | −0.461794 | −0.230897 | − | 0.972978i | \(-0.574166\pi\) | ||||
−0.230897 | + | 0.972978i | \(0.574166\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.52912e11i | 0.327066i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.09457e12 | −0.624760 | −0.312380 | − | 0.949957i | \(-0.601126\pi\) | ||||
−0.312380 | + | 0.949957i | \(0.601126\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 2.91466e12i | − 1.60567i | −0.596202 | − | 0.802834i | \(-0.703324\pi\) | ||||
0.596202 | − | 0.802834i | \(-0.296676\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.23499e12 | 0.656807 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 3.01889e11i | − 0.155038i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.98214e12 | 2.47131 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.87416e11i | 0.0898137i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.36019e12 | 1.09297 | 0.546485 | − | 0.837469i | \(-0.315965\pi\) | ||||
0.546485 | + | 0.837469i | \(0.315965\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 2.29189e12i | − 1.02585i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.16177e11 | 0.180093 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.17288e12i | 1.32769i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.01643e12 | 2.83977 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.06771e12i | 0.418063i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.10304e12 | −0.417918 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.55346e12i | 0.569649i | 0.958580 | + | 0.284825i | \(0.0919354\pi\) | ||||
−0.958580 | + | 0.284825i | \(0.908065\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.12576e12 | 0.399627 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 5.98675e10i | − 0.0205773i | −0.999947 | − | 0.0102887i | \(-0.996725\pi\) | ||||
0.999947 | − | 0.0102887i | \(-0.00327504\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.16246e12 | 1.38557 | 0.692785 | − | 0.721144i | \(-0.256383\pi\) | ||||
0.692785 | + | 0.721144i | \(0.256383\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 3.60051e12i | − 1.16094i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.31147e12 | −0.409698 | −0.204849 | − | 0.978794i | \(-0.565670\pi\) | ||||
−0.204849 | + | 0.978794i | \(0.565670\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.06906e12i | 0.323629i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.73550e12 | −0.509214 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.98500e12i | 2.84011i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.29368e12 | 0.356789 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 1.42628e11i | − 0.0381475i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.47305e12 | 0.382153 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.23994e11i | 0.131882i | 0.997824 | + | 0.0659411i | \(0.0210049\pi\) | ||||
−0.997824 | + | 0.0659411i | \(0.978995\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.94348e12 | −0.718852 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 3.43389e12i | − 0.813884i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.91746e12 | 0.671205 | 0.335602 | − | 0.942004i | \(-0.391060\pi\) | ||||
0.335602 | + | 0.942004i | \(0.391060\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 1.41831e12i | − 0.316790i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.13813e11 | −0.0897496 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.06237e13i | − 2.23772i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.03445e12 | 0.416247 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 1.67790e11i | − 0.0333518i | −0.999861 | − | 0.0166759i | \(-0.994692\pi\) | ||||
0.999861 | − | 0.0166759i | \(-0.00530835\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.90701e12 | −0.947742 | −0.473871 | − | 0.880594i | \(-0.657144\pi\) | ||||
−0.473871 | + | 0.880594i | \(0.657144\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.41360e12i | 1.20383i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.40830e12 | −0.986705 | −0.493353 | − | 0.869829i | \(-0.664229\pi\) | ||||
−0.493353 | + | 0.869829i | \(0.664229\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 2.85435e11i | − 0.0506250i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.74218e12 | −1.68002 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 4.03290e11i | − 0.0676309i | −0.999428 | − | 0.0338155i | \(-0.989234\pi\) | ||||
0.999428 | − | 0.0338155i | \(-0.0107658\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.11562e12 | −1.32369 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 3.02269e12i | − 0.479579i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.68925e11 | 0.149564 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.04392e13i | 1.56796i | 0.620786 | + | 0.783980i | \(0.286813\pi\) | ||||
−0.620786 | + | 0.783980i | \(0.713187\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.41314e11 | −0.0645083 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.05517e12i | 0.576952i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.02668e12 | 1.25021 | 0.625106 | − | 0.780540i | \(-0.285056\pi\) | ||||
0.625106 | + | 0.780540i | \(0.285056\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 4.02476e12i | − 0.542730i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.64749e13 | −2.16330 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 1.03303e13i | − 1.32105i | −0.750806 | − | 0.660523i | \(-0.770334\pi\) | ||||
0.750806 | − | 0.660523i | \(-0.229666\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.41928e12 | 0.799579 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.20386e12i | 0.631439i | 0.948853 | + | 0.315720i | \(0.102246\pi\) | ||||
−0.948853 | + | 0.315720i | \(0.897754\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.69471e12 | 0.318572 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 1.02569e13i | − 1.18157i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.47926e12 | −0.727407 | −0.363704 | − | 0.931515i | \(-0.618488\pi\) | ||||
−0.363704 | + | 0.931515i | \(0.618488\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.64487e13i | 1.79990i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.48812e12 | 0.798749 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 6.48317e12i | − 0.674220i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.67280e12 | −0.676636 | −0.338318 | − | 0.941032i | \(-0.609858\pi\) | ||||
−0.338318 | + | 0.941032i | \(0.609858\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 1.39002e13i | − 1.37454i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.31383e12 | 0.416046 | 0.208023 | − | 0.978124i | \(-0.433297\pi\) | ||||
0.208023 | + | 0.978124i | \(0.433297\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 6.37716e12i | − 0.599932i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.91243e12 | −0.267288 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 2.20297e12i | − 0.197259i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.82143e13 | 1.59146 | 0.795731 | − | 0.605650i | \(-0.207087\pi\) | ||||
0.795731 | + | 0.605650i | \(0.207087\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.72802e12i | 0.317884i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.57960e13 | −2.14685 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 5.51611e12i | − 0.448118i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.00032e12 | −0.158642 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.44732e12i | 0.654107i | 0.945006 | + | 0.327054i | \(0.106056\pi\) | ||||
−0.945006 | + | 0.327054i | \(0.893944\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.27063e12 | −0.322910 | −0.161455 | − | 0.986880i | \(-0.551619\pi\) | ||||
−0.161455 | + | 0.986880i | \(0.551619\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 2.15336e12i | − 0.159007i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.70666e12 | 0.483684 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.24151e13i | 0.874603i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.05601e12 | −0.141494 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.53083e12i | 0.506356i | 0.967420 | + | 0.253178i | \(0.0814759\pi\) | ||||
−0.967420 | + | 0.253178i | \(0.918524\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.89649e13 | −1.24598 | −0.622989 | − | 0.782231i | \(-0.714082\pi\) | ||||
−0.622989 | + | 0.782231i | \(0.714082\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.05637e13i | 0.678220i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.34692e13 | −1.47262 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.59980e12i | 0.466100i | 0.972465 | + | 0.233050i | \(0.0748707\pi\) | ||||
−0.972465 | + | 0.233050i | \(0.925129\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.80276e13 | −1.68032 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.74464e13i | 1.02256i | 0.859414 | + | 0.511280i | \(0.170828\pi\) | ||||
−0.859414 | + | 0.511280i | \(0.829172\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.77174e13 | −1.01531 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.63145e12i | 0.147454i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.92870e13 | 1.05690 | 0.528448 | − | 0.848965i | \(-0.322774\pi\) | ||||
0.528448 | + | 0.848965i | \(0.322774\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 3.30290e11i | − 0.0177016i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.42315e13 | −0.746037 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.15274e13i | 2.12950i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.97035e13 | 0.988468 | 0.494234 | − | 0.869329i | \(-0.335449\pi\) | ||||
0.494234 | + | 0.869329i | \(0.335449\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.32491e13i | 1.63199i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.70800e13 | 0.820321 | 0.410161 | − | 0.912013i | \(-0.365473\pi\) | ||||
0.410161 | + | 0.912013i | \(0.365473\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 2.03199e13i | − 0.955029i | −0.878624 | − | 0.477514i | \(-0.841538\pi\) | ||||
0.878624 | − | 0.477514i | \(-0.158462\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.08903e12 | −0.188086 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 3.06149e13i | − 1.37831i | −0.724612 | − | 0.689157i | \(-0.757981\pi\) | ||||
0.724612 | − | 0.689157i | \(-0.242019\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.86497e13 | −1.70326 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 8.67948e12i | − 0.374446i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.67651e12 | 0.324234 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.56913e12i | 0.395735i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.92801e12 | 0.240058 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 2.59599e13i | − 1.02950i | −0.857341 | − | 0.514749i | \(-0.827885\pi\) | ||||
0.857341 | − | 0.514749i | \(-0.172115\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.39494e13 | 1.31858 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 2.28985e13i | − 0.871106i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.14157e12 | 0.154332 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 4.57345e13i | − 1.66955i | −0.550592 | − | 0.834774i | \(-0.685598\pi\) | ||||
0.550592 | − | 0.834774i | \(-0.314402\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.25666e12 | −0.116474 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 4.82141e12i | − 0.168953i | −0.996425 | − | 0.0844766i | \(-0.973078\pi\) | ||||
0.996425 | − | 0.0844766i | \(-0.0269218\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.54088e13 | −2.93270 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 3.93923e12i | − 0.132552i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.21267e12 | −0.105946 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 1.54166e13i | − 0.498295i | −0.968466 | − | 0.249148i | \(-0.919850\pi\) | ||||
0.968466 | − | 0.249148i | \(-0.0801504\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.18053e12 | 0.0374016 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.50859e13i | 1.71080i | 0.517965 | + | 0.855402i | \(0.326690\pi\) | ||||
−0.517965 | + | 0.855402i | \(0.673310\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.35946e13 | 0.718381 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 1.49098e13i | − 0.445075i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.04337e12 | −0.264692 | −0.132346 | − | 0.991204i | \(-0.542251\pi\) | ||||
−0.132346 | + | 0.991204i | \(0.542251\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 1.09056e13i | − 0.313001i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.74402e13 | −1.33524 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 2.48774e13i | − 0.686702i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.61163e12 | 0.0436327 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 2.89140e12i | − 0.0767842i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.29993e13 | −0.599136 | −0.299568 | − | 0.954075i | \(-0.596843\pi\) | ||||
−0.299568 | + | 0.954075i | \(0.596843\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 2.96086e13i | − 0.756676i | −0.925667 | − | 0.378338i | \(-0.876496\pi\) | ||||
0.925667 | − | 0.378338i | \(-0.123504\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.33642e12 | −0.234091 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 3.30603e13i | − 0.813305i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.76467e12 | 0.0667367 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.77097e13i | 0.893265i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.09001e12 | 0.118327 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.83516e13i | 0.875013i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.19755e13 | −0.716054 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 2.09765e13i | − 0.461095i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.97902e13 | 1.07438 | 0.537189 | − | 0.843462i | \(-0.319486\pi\) | ||||
0.537189 | + | 0.843462i | \(0.319486\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 3.71562e13i | − 0.787104i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.15183e12 | −0.0655511 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.59283e13i | 0.325261i | 0.986687 | + | 0.162631i | \(0.0519979\pi\) | ||||
−0.986687 | + | 0.162631i | \(0.948002\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.81489e13 | 0.363906 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 1.21862e14i | − 2.39944i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.29705e13 | −1.41098 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 2.17683e13i | − 0.413390i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.45122e13 | −0.270682 | −0.135341 | − | 0.990799i | \(-0.543213\pi\) | ||||
−0.135341 | + | 0.990799i | \(0.543213\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.18301e14i | 2.16734i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.06587e13 | −0.191818 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 5.60100e13i | − 0.990202i | −0.868835 | − | 0.495101i | \(-0.835131\pi\) | ||||
0.868835 | − | 0.495101i | \(-0.164869\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.13421e13 | −0.544359 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.27805e13i | 0.559371i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.30086e12 | 0.0721097 | 0.0360549 | − | 0.999350i | \(-0.488521\pi\) | ||||
0.0360549 | + | 0.999350i | \(0.488521\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.05773e14i | 1.74258i | 0.490770 | + | 0.871289i | \(0.336716\pi\) | ||||
−0.490770 | + | 0.871289i | \(0.663284\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.00861e13 | 0.325179 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.57636e13i | 0.250794i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.44373e13 | 1.00753 | 0.503766 | − | 0.863840i | \(-0.331948\pi\) | ||||
0.503766 | + | 0.863840i | \(0.331948\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.66012e13i | 0.562474i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.20858e13 | −0.937804 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.43667e12i | 0.0658740i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.07065e13 | 0.886045 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 5.38824e13i | − 0.773136i | −0.922261 | − | 0.386568i | \(-0.873660\pi\) | ||||
0.922261 | − | 0.386568i | \(-0.126340\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.71707e13 | 0.665420 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 4.48575e13i | − 0.622154i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.11219e14 | −1.51672 | −0.758361 | − | 0.651834i | \(-0.774000\pi\) | ||||
−0.758361 | + | 0.651834i | \(0.774000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.15285e14i | 2.88688i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.42810e13 | 0.452046 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 1.16949e14i | − 1.51657i | −0.651921 | − | 0.758287i | \(-0.726037\pi\) | ||||
0.651921 | − | 0.758287i | \(-0.273963\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.83099e13 | 0.488583 | 0.244292 | − | 0.969702i | \(-0.421445\pi\) | ||||
0.244292 | + | 0.969702i | \(0.421445\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.64997e13i | 0.708695i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.67960e13 | −0.824088 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.08595e14i | 1.31785i | 0.752208 | + | 0.658926i | \(0.228989\pi\) | ||||
−0.752208 | + | 0.658926i | \(0.771011\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.18899e14 | 1.41935 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.48364e13i | 0.291663i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.85493e13 | 0.445363 | 0.222681 | − | 0.974891i | \(-0.428519\pi\) | ||||
0.222681 | + | 0.974891i | \(0.428519\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 3.26371e12i | − 0.0370968i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.55996e14 | 1.74457 | 0.872283 | − | 0.489002i | \(-0.162639\pi\) | ||||
0.872283 | + | 0.489002i | \(0.162639\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 1.16264e14i | − 1.27936i | −0.768643 | − | 0.639678i | \(-0.779068\pi\) | ||||
0.768643 | − | 0.639678i | \(-0.220932\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.81503e13 | −0.846199 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.99416e14i | 2.12481i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.41821e13 | −0.672998 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 1.52079e13i | − 0.156939i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.75999e14 | 1.78755 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.58442e12i | 0.0558253i | 0.999610 | + | 0.0279127i | \(0.00888603\pi\) | ||||
−0.999610 | + | 0.0279127i | \(0.991114\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.05586e12 | 0.0595878 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1.41855e14i | − 1.37396i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.23264e14 | 3.08220 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.69642e12i | 0.0440821i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.89575e13 | 0.359999 | 0.179999 | − | 0.983667i | \(-0.442390\pi\) | ||||
0.179999 | + | 0.983667i | \(0.442390\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.61241e13i | 0.328656i | 0.986406 | + | 0.164328i | \(0.0525456\pi\) | ||||
−0.986406 | + | 0.164328i | \(0.947454\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.58542e13 | 0.679487 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.66446e14i | 1.46809i | 0.679100 | + | 0.734046i | \(0.262370\pi\) | ||||
−0.679100 | + | 0.734046i | \(0.737630\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.82228e13 | −0.245119 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.60236e13i | 0.393618i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.13416e14 | 1.79747 | 0.898734 | − | 0.438493i | \(-0.144488\pi\) | ||||
0.898734 | + | 0.438493i | \(0.144488\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 1.65474e14i | − 1.37254i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.59423e13 | −0.130234 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 1.80608e14i | − 1.45315i | −0.687088 | − | 0.726574i | \(-0.741111\pi\) | ||||
0.687088 | − | 0.726574i | \(-0.258889\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.76768e13 | 0.140086 | 0.0700431 | − | 0.997544i | \(-0.477686\pi\) | ||||
0.0700431 | + | 0.997544i | \(0.477686\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 1.64258e14i | − 1.28221i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.07171e14 | −2.36195 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 2.00749e14i | − 1.52063i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.16321e13 | −0.683781 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.35831e13i | 0.0998587i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.60902e14 | 1.16543 | 0.582715 | − | 0.812676i | \(-0.301990\pi\) | ||||
0.582715 | + | 0.812676i | \(0.301990\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.18643e13i | 0.227397i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.09256e14 | 0.768248 | 0.384124 | − | 0.923282i | \(-0.374504\pi\) | ||||
0.384124 | + | 0.923282i | \(0.374504\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 4.66149e13i | − 0.322980i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.81780e13 | 0.397213 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1.57116e13i | − 0.105710i | −0.998602 | − | 0.0528552i | \(-0.983168\pi\) | ||||
0.998602 | − | 0.0528552i | \(-0.0168322\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.23826e13 | 0.546239 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 4.78623e13i | − 0.312759i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.83723e13 | −0.440336 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.42414e14i | 0.903986i | 0.892022 | + | 0.451993i | \(0.149287\pi\) | ||||
−0.892022 | + | 0.451993i | \(0.850713\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.43375e13 | −0.277399 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.42035e13i | 0.272604i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.63875e13 | 0.160411 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.19952e13i | 0.191734i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.44711e13 | −0.439944 | −0.219972 | − | 0.975506i | \(-0.570597\pi\) | ||||
−0.219972 | + | 0.975506i | \(0.570597\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.51117e14i | 1.46251i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.59251e13 | 0.0914398 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 2.65566e14i | − 1.50340i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.39122e14 | 1.33472 | 0.667358 | − | 0.744737i | \(-0.267425\pi\) | ||||
0.667358 | + | 0.744737i | \(0.267425\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.06671e14i | 0.587083i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.77063e13 | 0.421705 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.54342e13i | 0.243138i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.51381e13 | 0.343747 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 5.65489e13i | − 0.294293i | −0.989115 | − | 0.147146i | \(-0.952991\pi\) | ||||
0.989115 | − | 0.147146i | \(-0.0470089\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.80004e14 | −1.43710 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 6.47486e13i | − 0.327747i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.18516e13 | −0.408636 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 1.80601e14i | − 0.889298i | −0.895705 | − | 0.444649i | \(-0.853328\pi\) | ||||
0.895705 | − | 0.444649i | \(-0.146672\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.23881e13 | −0.205876 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.13290e14i | 2.93818i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.92425e14 | −0.909373 | −0.454686 | − | 0.890652i | \(-0.650249\pi\) | ||||
−0.454686 | + | 0.890652i | \(0.650249\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 2.07277e14i | − 0.966304i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.22857e13 | −0.194472 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 4.62941e13i | − 0.210041i | −0.994470 | − | 0.105020i | \(-0.966509\pi\) | ||||
0.994470 | − | 0.105020i | \(-0.0334908\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.34365e14 | 1.04906 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.11220e14i | 1.37443i | 0.726452 | + | 0.687217i | \(0.241168\pi\) | ||||
−0.726452 | + | 0.687217i | \(0.758832\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.81503e13 | 0.253379 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.07596e13i | 0.390202i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.31661e14 | 1.83119 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 1.61606e14i | − 0.676484i | −0.941059 | − | 0.338242i | \(-0.890168\pi\) | ||||
0.941059 | − | 0.338242i | \(-0.109832\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.62431e14 | 0.670954 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.14492e14i | 1.28196i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.17141e14 | 1.67804 | 0.839022 | − | 0.544097i | \(-0.183128\pi\) | ||||
0.839022 | + | 0.544097i | \(0.183128\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 2.50527e13i | − 0.0994593i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.50768e13 | 0.176616 | 0.0883080 | − | 0.996093i | \(-0.471854\pi\) | ||||
0.0883080 | + | 0.996093i | \(0.471854\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.54750e13i | 0.137183i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.14712e14 | 1.20118 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 4.34935e14i | − 1.63850i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.82550e13 | 0.0678812 | 0.0339406 | − | 0.999424i | \(-0.489194\pi\) | ||||
0.0339406 | + | 0.999424i | \(0.489194\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.20070e14i | 0.440719i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.36967e14 | −1.58326 | −0.791628 | − | 0.611003i | \(-0.790766\pi\) | ||||
−0.791628 | + | 0.611003i | \(0.790766\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 3.16833e13i | − 0.113324i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.45011e14 | −0.865127 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.76499e13i | 0.131243i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.51491e12 | −0.0120965 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 4.05789e14i | − 1.37877i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.91801e14 | −0.643432 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 4.98660e14i | − 1.65170i | −0.563891 | − | 0.825849i | \(-0.690696\pi\) | ||||
0.563891 | − | 0.825849i | \(-0.309304\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.04574e14 | −0.669062 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.52767e14i | 1.13921i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.09325e14 | −0.667507 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.38402e13i | 0.138050i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.93513e12 | −0.0277849 | −0.0138925 | − | 0.999903i | \(-0.504422\pi\) | ||||
−0.0138925 | + | 0.999903i | \(0.504422\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.28756e14i | 0.395397i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.91514e14 | 0.884091 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 1.19316e13i | − 0.0357372i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.06016e14 | −1.49687 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 5.01091e12i | − 0.0146403i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.61148e14 | 1.04218 | 0.521090 | − | 0.853502i | \(-0.325526\pi\) | ||||
0.521090 | + | 0.853502i | \(0.325526\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.05369e12i | 0.0229557i | 0.999934 | + | 0.0114779i | \(0.00365359\pi\) | ||||
−0.999934 | + | 0.0114779i | \(0.996346\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.26826e13 | 0.0920162 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.19665e13i | 0.200144i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.75047e14 | −2.40393 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 6.83274e14i | − 1.85428i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.81853e14 | 1.82799 | 0.913997 | − | 0.405721i | \(-0.132980\pi\) | ||||
0.913997 | + | 0.405721i | \(0.132980\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 2.85674e12i | − 0.00756610i | −0.999993 | − | 0.00378305i | \(-0.998796\pi\) | ||||
0.999993 | − | 0.00378305i | \(-0.00120418\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.02148e13 | −0.0267275 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 4.38934e14i | − 1.13468i | −0.823485 | − | 0.567338i | \(-0.807973\pi\) | ||||
0.823485 | − | 0.567338i | \(-0.192027\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.60079e14 | −1.17506 | −0.587530 | − | 0.809203i | \(-0.699900\pi\) | ||||
−0.587530 | + | 0.809203i | \(0.699900\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.16371e13i | 0.231242i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.67585e15 | 4.17841 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 2.60877e13i | − 0.0642693i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.57074e14 | 0.382364 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.05802e13i | 0.0254499i | 0.999919 | + | 0.0127249i | \(0.00405058\pi\) | ||||
−0.999919 | + | 0.0127249i | \(0.995949\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.21666e14 | 1.47767 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.33189e14i | 0.312846i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.29481e14 | −0.764798 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.51814e14i | 1.72462i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.54660e14 | −0.804032 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.13677e14i | 0.926858i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.94235e14 | −0.651552 | −0.325776 | − | 0.945447i | \(-0.605625\pi\) | ||||
−0.325776 | + | 0.945447i | \(0.605625\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.49034e14i | 0.982763i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.02180e14 | 1.30263 | 0.651316 | − | 0.758806i | \(-0.274217\pi\) | ||||
0.651316 | + | 0.758806i | \(0.274217\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 5.52016e14i | − 1.18028i | −0.807300 | − | 0.590141i | \(-0.799072\pi\) | ||||
0.807300 | − | 0.590141i | \(-0.200928\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.67343e13 | −0.0776347 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 6.88007e14i | − 1.43727i | −0.695387 | − | 0.718636i | \(-0.744767\pi\) | ||||
0.695387 | − | 0.718636i | \(-0.255233\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.38949e13 | −0.131943 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 6.06233e14i | − 1.23750i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.98353e13 | −0.161100 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 6.51654e14i | − 1.29995i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.81436e13 | −0.134386 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00105e15i | 1.95172i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.78717e14 | −1.11550 | −0.557748 | − | 0.830010i | \(-0.688335\pi\) | ||||
−0.557748 | + | 0.830010i | \(0.688335\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 2.87191e14i | − 0.547301i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.04795e14 | −1.13954 | −0.569768 | − | 0.821805i | \(-0.692967\pi\) | ||||
−0.569768 | + | 0.821805i | \(0.692967\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.86926e14i | 0.534522i | 0.963624 | + | 0.267261i | \(0.0861187\pi\) | ||||
−0.963624 | + | 0.267261i | \(0.913881\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.78880e14 | −0.513689 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.21370e14i | 0.221051i | 0.993873 | + | 0.110525i | \(0.0352534\pi\) | ||||
−0.993873 | + | 0.110525i | \(0.964747\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.59663e15 | −2.87538 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.58643e13i | 0.0638667i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.83710e14 | −0.323501 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.06601e14i | 1.23044i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.86080e14 | 0.664837 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.03484e14i | 0.687113i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.54453e14 | −0.596946 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 8.53768e14i | − 1.42200i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.21086e14 | −1.35253 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 8.79272e14i | − 1.43247i | −0.697857 | − | 0.716237i | \(-0.745863\pi\) | ||||
0.697857 | − | 0.716237i | \(-0.254137\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.88214e14 | −0.625536 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.15401e15i | 1.83915i | 0.392915 | + | 0.919575i | \(0.371467\pi\) | ||||
−0.392915 | + | 0.919575i | \(0.628533\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.79267e13 | −0.107075 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.34219e14i | 0.209271i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.86247e15 | −2.87239 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.02115e14i | 0.918548i | 0.888295 | + | 0.459274i | \(0.151890\pi\) | ||||
−0.888295 | + | 0.459274i | \(0.848110\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.89027e14 | 0.285250 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 5.41674e13i | − 0.0808592i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.68669e14 | 0.249073 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.09321e14i | 0.597951i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.38405e13 | 0.0922609 | 0.0461305 | − | 0.998935i | \(-0.485311\pi\) | ||||
0.0461305 | + | 0.998935i | \(0.485311\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.39112e15i | 3.41864i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.28476e12 | −0.0103040 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.35538e14i | 0.329612i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.16317e14 | 0.576402 | 0.288201 | − | 0.957570i | \(-0.406943\pi\) | ||||
0.288201 | + | 0.957570i | \(0.406943\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 5.06494e14i | − 0.693819i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.14113e14 | −1.23894 | −0.619472 | − | 0.785018i | \(-0.712653\pi\) | ||||
−0.619472 | + | 0.785018i | \(0.712653\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.20223e13i | 0.0831743i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.02285e15 | −1.35723 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.75991e14i | 0.624955i | 0.949925 | + | 0.312478i | \(0.101159\pi\) | ||||
−0.949925 | + | 0.312478i | \(0.898841\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.83874e14 | 0.238886 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.59582e14i | 0.205155i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.25881e14 | 0.414566 | 0.207283 | − | 0.978281i | \(-0.433538\pi\) | ||||
0.207283 | + | 0.978281i | \(0.433538\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 4.43867e14i | − 0.558774i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.30084e14 | 0.162056 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 9.27247e14i | − 1.14315i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.63446e14 | 0.809448 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 6.31020e14i | − 0.761924i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.08822e14 | 0.966532 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1.32849e15i | − 1.57117i | −0.618751 | − | 0.785587i | \(-0.712361\pi\) | ||||
0.618751 | − | 0.785587i | \(-0.287639\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.21499e15 | 1.42218 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.33037e15i | 1.54126i | 0.637285 | + | 0.770628i | \(0.280057\pi\) | ||||
−0.637285 | + | 0.770628i | \(0.719943\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.97526e14 | 0.570495 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 1.57417e14i | − 0.178660i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.00671e15 | −1.13092 | −0.565462 | − | 0.824774i | \(-0.691302\pi\) | ||||
−0.565462 | + | 0.824774i | \(0.691302\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.18176e14i | 0.242602i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.18588e13 | 0.0570792 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 6.92063e14i | − 0.754011i | −0.926211 | − | 0.377006i | \(-0.876954\pi\) | ||||
0.926211 | − | 0.377006i | \(-0.123046\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.91272e14 | −1.06908 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 1.79242e14i | − 0.191362i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.44150e15 | −1.52347 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.78144e15i | 1.86381i | 0.362700 | + | 0.931906i | \(0.381855\pi\) | ||||
−0.362700 | + | 0.931906i | \(0.618145\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.37603e13 | 0.0660395 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 7.57550e14i | − 0.776776i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.40996e14 | −0.853726 | −0.426863 | − | 0.904316i | \(-0.640381\pi\) | ||||
−0.426863 | + | 0.904316i | \(0.640381\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.36197e14i | 0.840391i |
(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 | 256.11.c.j.255.5 | 10 | ||
4.3 | odd | 2 | inner | 256.11.c.j.255.6 | 10 | ||
8.3 | odd | 2 | 256.11.c.k.255.5 | 10 | |||
8.5 | even | 2 | 256.11.c.k.255.6 | 10 | |||
16.3 | odd | 4 | 128.11.d.f.63.10 | yes | 20 | ||
16.5 | even | 4 | 128.11.d.f.63.9 | ✓ | 20 | ||
16.11 | odd | 4 | 128.11.d.f.63.11 | yes | 20 | ||
16.13 | even | 4 | 128.11.d.f.63.12 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
128.11.d.f.63.9 | ✓ | 20 | 16.5 | even | 4 | ||
128.11.d.f.63.10 | yes | 20 | 16.3 | odd | 4 | ||
128.11.d.f.63.11 | yes | 20 | 16.11 | odd | 4 | ||
128.11.d.f.63.12 | yes | 20 | 16.13 | even | 4 | ||
256.11.c.j.255.5 | 10 | 1.1 | even | 1 | trivial | ||
256.11.c.j.255.6 | 10 | 4.3 | odd | 2 | inner | ||
256.11.c.k.255.5 | 10 | 8.3 | odd | 2 | |||
256.11.c.k.255.6 | 10 | 8.5 | even | 2 |