Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,15,Mod(127,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 15, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("144.127");
S:= CuspForms(chi, 15);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 15 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.g (of order \(2\), degree \(1\), 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: | \(179.033714139\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 16897x^{2} + 16896x + 285474816 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{9} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.1 | ||
Root | \(-64.7428 - 112.138i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.127 |
Dual form | 144.15.g.e.127.2 |
$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −48265.2 | −0.617794 | −0.308897 | − | 0.951096i | \(-0.599960\pi\) | ||||
−0.308897 | + | 0.951096i | \(0.599960\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 988060.i | − 1.19977i | −0.800087 | − | 0.599884i | \(-0.795214\pi\) | ||||
0.800087 | − | 0.599884i | \(-0.204786\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 2.32961e7i | − 1.19546i | −0.801698 | − | 0.597729i | \(-0.796070\pi\) | ||||
0.801698 | − | 0.597729i | \(-0.203930\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.22817e8 | −1.95729 | −0.978644 | − | 0.205562i | \(-0.934098\pi\) | ||||
−0.978644 | + | 0.205562i | \(0.934098\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.67127e8 | −1.38210 | −0.691048 | − | 0.722809i | \(-0.742851\pi\) | ||||
−0.691048 | + | 0.722809i | \(0.742851\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.44150e9i | 1.61265i | 0.591476 | + | 0.806323i | \(0.298545\pi\) | ||||
−0.591476 | + | 0.806323i | \(0.701455\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.82619e9i | 1.41746i | 0.705482 | + | 0.708728i | \(0.250731\pi\) | ||||
−0.705482 | + | 0.708728i | \(0.749269\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.77399e9 | −0.618331 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.25157e10 | 1.30526 | 0.652632 | − | 0.757675i | \(-0.273665\pi\) | ||||
0.652632 | + | 0.757675i | \(0.273665\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.74889e9i | 0.354343i | 0.984180 | + | 0.177171i | \(0.0566947\pi\) | ||||
−0.984180 | + | 0.177171i | \(0.943305\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.76889e10i | 0.741209i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.31253e10 | −0.454277 | −0.227138 | − | 0.973862i | \(-0.572937\pi\) | ||||
−0.227138 | + | 0.973862i | \(0.572937\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.29915e11 | −1.18054 | −0.590270 | − | 0.807206i | \(-0.700979\pi\) | ||||
−0.590270 | + | 0.807206i | \(0.700979\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.08622e11i | 0.399611i | 0.979836 | + | 0.199805i | \(0.0640310\pi\) | ||||
−0.979836 | + | 0.199805i | \(0.935969\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 1.42608e11i | − 0.281488i | −0.990046 | − | 0.140744i | \(-0.955051\pi\) | ||||
0.990046 | − | 0.140744i | \(-0.0449494\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.98039e11 | −0.439442 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.07891e11 | −0.432354 | −0.216177 | − | 0.976354i | \(-0.569359\pi\) | ||||
−0.216177 | + | 0.976354i | \(0.569359\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.12439e12i | 0.738547i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 4.16206e12i | − 1.67241i | −0.548413 | − | 0.836207i | \(-0.684768\pi\) | ||||
0.548413 | − | 0.836207i | \(-0.315232\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.20121e12 | −0.382218 | −0.191109 | − | 0.981569i | \(-0.561208\pi\) | ||||
−0.191109 | + | 0.981569i | \(0.561208\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.92778e12 | 1.20920 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.78597e12i | 0.624674i | 0.949971 | + | 0.312337i | \(0.101112\pi\) | ||||
−0.949971 | + | 0.312337i | \(0.898888\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 1.50156e13i | − 1.65095i | −0.564435 | − | 0.825477i | \(-0.690906\pi\) | ||||
0.564435 | − | 0.825477i | \(-0.309094\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.11912e12 | 0.101302 | 0.0506510 | − | 0.998716i | \(-0.483870\pi\) | ||||
0.0506510 | + | 0.998716i | \(0.483870\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.30179e13 | −1.43427 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.64523e13i | 1.37744i | 0.725025 | + | 0.688722i | \(0.241828\pi\) | ||||
−0.725025 | + | 0.688722i | \(0.758172\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.32326e12i | 0.196169i | 0.995178 | + | 0.0980846i | \(0.0312716\pi\) | ||||
−0.995178 | + | 0.0980846i | \(0.968728\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.73725e13 | 0.853850 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.78257e13 | 1.53343 | 0.766715 | − | 0.641988i | \(-0.221890\pi\) | ||||
0.766715 | + | 0.641988i | \(0.221890\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.21350e14i | 2.34829i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 6.95741e13i | − 0.996283i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.20889e13 | 0.397149 | 0.198574 | − | 0.980086i | \(-0.436369\pi\) | ||||
0.198574 | + | 0.980086i | \(0.436369\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.40282e13 | −0.410659 | −0.205329 | − | 0.978693i | \(-0.565827\pi\) | ||||
−0.205329 | + | 0.978693i | \(0.565827\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 1.27057e14i | − 1.03309i | −0.856260 | − | 0.516545i | \(-0.827218\pi\) | ||||
0.856260 | − | 0.516545i | \(-0.172782\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 2.57222e14i | − 1.60185i | −0.598767 | − | 0.800924i | \(-0.704342\pi\) | ||||
0.598767 | − | 0.800924i | \(-0.295658\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.19172e14 | −1.19895 | −0.599473 | − | 0.800395i | \(-0.704623\pi\) | ||||
−0.599473 | + | 0.800395i | \(0.704623\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.23218e14 | −0.523751 | −0.261876 | − | 0.965102i | \(-0.584341\pi\) | ||||
−0.261876 | + | 0.965102i | \(0.584341\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 2.32937e14i | − 0.875696i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.60356e14i | 1.65819i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.62958e14 | −0.429120 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.76739e14 | 0.999795 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.78796e14i | 0.710851i | 0.934705 | + | 0.355426i | \(0.115664\pi\) | ||||
−0.934705 | + | 0.355426i | \(0.884336\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.99337e14i | 0.301085i | 0.988604 | + | 0.150542i | \(0.0481020\pi\) | ||||
−0.988604 | + | 0.150542i | \(0.951898\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.42429e15 | 1.93480 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.95247e13 | −0.0877926 | −0.0438963 | − | 0.999036i | \(-0.513977\pi\) | ||||
−0.0438963 | + | 0.999036i | \(0.513977\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 1.68115e15i | − 1.67688i | −0.544992 | − | 0.838441i | \(-0.683467\pi\) | ||||
0.544992 | − | 0.838441i | \(-0.316533\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.86116e15i | 2.33986i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.08672e15 | −0.806385 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.69734e13 | −0.0226770 | −0.0113385 | − | 0.999936i | \(-0.503609\pi\) | ||||
−0.0113385 | + | 0.999936i | \(0.503609\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 6.80534e14i | − 0.380199i | −0.981765 | − | 0.190100i | \(-0.939119\pi\) | ||||
0.981765 | − | 0.190100i | \(-0.0608811\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 4.70532e14i | − 0.218911i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.15795e14 | −0.389494 | −0.194747 | − | 0.980854i | \(-0.562389\pi\) | ||||
−0.194747 | + | 0.980854i | \(0.562389\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.76856e15 | 1.70062 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 1.59110e15i | − 0.520456i | −0.965547 | − | 0.260228i | \(-0.916202\pi\) | ||||
0.965547 | − | 0.260228i | \(-0.0837977\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 5.05801e15i | − 1.39625i | −0.715974 | − | 0.698127i | \(-0.754017\pi\) | ||||
0.715974 | − | 0.698127i | \(-0.245983\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.11466e16 | 2.83098 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.84738e15 | 0.829549 | 0.414775 | − | 0.909924i | \(-0.363860\pi\) | ||||
0.414775 | + | 0.909924i | \(0.363860\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.72893e15i | 0.741853i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 3.62594e15i | − 0.615814i | −0.951416 | − | 0.307907i | \(-0.900371\pi\) | ||||
0.951416 | − | 0.307907i | \(-0.0996286\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.03797e16 | −1.63093 | −0.815465 | − | 0.578807i | \(-0.803519\pi\) | ||||
−0.815465 | + | 0.578807i | \(0.803519\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.08145e15 | 0.280649 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.32119e16i | 1.65224i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.34062e15i | 0.683751i | 0.939745 | + | 0.341875i | \(0.111062\pi\) | ||||
−0.939745 | + | 0.341875i | \(0.888938\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.42606e15 | 0.443727 | 0.221863 | − | 0.975078i | \(-0.428786\pi\) | ||||
0.221863 | + | 0.975078i | \(0.428786\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.06093e15 | −0.352665 | −0.176333 | − | 0.984331i | \(-0.556423\pi\) | ||||
−0.176333 | + | 0.984331i | \(0.556423\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 5.32846e15i | − 0.431152i | −0.976487 | − | 0.215576i | \(-0.930837\pi\) | ||||
0.976487 | − | 0.215576i | \(-0.0691629\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 2.22468e16i | − 1.56601i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.10969e16 | 0.729331 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.35813e16 | 1.92785 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.74049e16i | 0.934749i | 0.884060 | + | 0.467374i | \(0.154800\pi\) | ||||
−0.884060 | + | 0.467374i | \(0.845200\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 5.24264e15i | − 0.246877i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.63249e15 | 0.425129 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.96528e16 | 2.70516 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.68823e15i | 0.134488i | 0.997737 | + | 0.0672441i | \(0.0214206\pi\) | ||||
−0.997737 | + | 0.0672441i | \(0.978579\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.23682e16i | 1.36414i | 0.731286 | + | 0.682071i | \(0.238920\pi\) | ||||
−0.731286 | + | 0.682071i | \(0.761080\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.81851e16 | 0.853436 | 0.426718 | − | 0.904385i | \(-0.359670\pi\) | ||||
0.426718 | + | 0.904385i | \(0.359670\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.09104e15 | 0.136557 | 0.0682787 | − | 0.997666i | \(-0.478249\pi\) | ||||
0.0682787 | + | 0.997666i | \(0.478249\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.88300e15i | 0.173901i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 2.69545e16i | − 0.605126i | −0.953129 | − | 0.302563i | \(-0.902158\pi\) | ||||
0.953129 | − | 0.302563i | \(-0.0978423\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.01381e16 | 0.426480 | 0.213240 | − | 0.977000i | \(-0.431598\pi\) | ||||
0.213240 | + | 0.977000i | \(0.431598\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.43849e16 | 0.271484 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 1.77040e17i | − 3.15641i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.33496e15i | 0.0690667i | 0.999404 | + | 0.0345334i | \(0.0109945\pi\) | ||||
−0.999404 | + | 0.0345334i | \(0.989006\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.12431e17 | 1.69451 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.59521e16 | 1.29575 | 0.647877 | − | 0.761745i | \(-0.275657\pi\) | ||||
0.647877 | + | 0.761745i | \(0.275657\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.26104e16i | 0.545026i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.11253e17i | 1.27826i | 0.769097 | + | 0.639132i | \(0.220706\pi\) | ||||
−0.769097 | + | 0.639132i | \(0.779294\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.45134e16 | 0.267105 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.61075e17 | 1.58039 | 0.790193 | − | 0.612858i | \(-0.209980\pi\) | ||||
0.790193 | + | 0.612858i | \(0.209980\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.56194e16i | 0.424976i | 0.977164 | + | 0.212488i | \(0.0681566\pi\) | ||||
−0.977164 | + | 0.212488i | \(0.931843\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.79193e16i | 0.739188i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.63997e17 | −1.31062 | −0.655311 | − | 0.755359i | \(-0.727462\pi\) | ||||
−0.655311 | + | 0.755359i | \(0.727462\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.21492e17 | 1.60108 | 0.800541 | − | 0.599278i | \(-0.204545\pi\) | ||||
0.800541 | + | 0.599278i | \(0.204545\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 1.46578e17i | − 1.00824i | −0.863634 | − | 0.504120i | \(-0.831817\pi\) | ||||
0.863634 | − | 0.504120i | \(-0.168183\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.27170e17i | 1.41637i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.53256e17 | 0.910188 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.00771e17 | −1.08300 | −0.541498 | − | 0.840702i | \(-0.682143\pi\) | ||||
−0.541498 | + | 0.840702i | \(0.682143\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.00882e17i | 1.03321i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 5.92738e17i | − 2.77437i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.07325e17 | 0.479440 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.79768e16 | 0.236132 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.87213e17i | 1.50654i | 0.657709 | + | 0.753272i | \(0.271526\pi\) | ||||
−0.657709 | + | 0.753272i | \(0.728474\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.39856e17i | 0.497002i | 0.968632 | + | 0.248501i | \(0.0799380\pi\) | ||||
−0.968632 | + | 0.248501i | \(0.920062\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.80451e17 | −0.613126 | −0.306563 | − | 0.951850i | \(-0.599179\pi\) | ||||
−0.306563 | + | 0.951850i | \(0.599179\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.01450e17 | 0.937130 | 0.468565 | − | 0.883429i | \(-0.344771\pi\) | ||||
0.468565 | + | 0.883429i | \(0.344771\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 5.24527e17i | − 1.56039i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 8.17513e17i | − 2.22883i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.63510e17 | 1.21025 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.40905e17 | −0.337720 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.22226e17i | 1.65912i | 0.558420 | + | 0.829558i | \(0.311408\pi\) | ||||
−0.558420 | + | 0.829558i | \(0.688592\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 1.82730e17i | − 0.385920i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.55312e17 | 0.314626 | 0.157313 | − | 0.987549i | \(-0.449717\pi\) | ||||
0.157313 | + | 0.987549i | \(0.449717\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.27111e17 | 0.423602 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 3.75644e17i | − 0.672540i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.64463e17i | 0.436575i | 0.975885 | + | 0.218287i | \(0.0700470\pi\) | ||||
−0.975885 | + | 0.218287i | \(0.929953\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.66338e16 | −0.0422333 | −0.0211167 | − | 0.999777i | \(-0.506722\pi\) | ||||
−0.0211167 | + | 0.999777i | \(0.506722\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.90609e17 | −0.571900 | −0.285950 | − | 0.958245i | \(-0.592309\pi\) | ||||
−0.285950 | + | 0.958245i | \(0.592309\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.24732e17i | 1.01995i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.03460e18i | 1.34621i | 0.739547 | + | 0.673105i | \(0.235040\pi\) | ||||
−0.739547 | + | 0.673105i | \(0.764960\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.27891e18 | −1.60063 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.40146e16 | −0.0625837 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.77333e17i | 0.532303i | 0.963931 | + | 0.266152i | \(0.0857521\pi\) | ||||
−0.963931 | + | 0.266152i | \(0.914248\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.01826e17i | 0.518724i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.73235e17 | −0.769750 | −0.384875 | − | 0.922969i | \(-0.625755\pi\) | ||||
−0.384875 | + | 0.922969i | \(0.625755\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.76530e18 | −2.55478 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 1.12169e18i | − 0.998617i | −0.866424 | − | 0.499308i | \(-0.833587\pi\) | ||||
0.866424 | − | 0.499308i | \(-0.166413\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.84075e17i | 0.648584i | 0.945957 | + | 0.324292i | \(0.105126\pi\) | ||||
−0.945957 | + | 0.324292i | \(0.894874\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.11096e18 | 0.886084 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.84400e17 | −0.507765 | −0.253883 | − | 0.967235i | \(-0.581708\pi\) | ||||
−0.253883 | + | 0.967235i | \(0.581708\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 2.73706e18i | − 1.95906i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 1.27673e18i | − 0.850977i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.94763e18 | −1.25306 | −0.626532 | − | 0.779396i | \(-0.715526\pi\) | ||||
−0.626532 | + | 0.779396i | \(0.715526\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.07795e17 | 0.304563 | 0.152282 | − | 0.988337i | \(-0.451338\pi\) | ||||
0.152282 | + | 0.988337i | \(0.451338\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 1.19733e18i | − 0.693551i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.00465e18i | 0.543069i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.02120e18 | −0.533392 | −0.266696 | − | 0.963781i | \(-0.585932\pi\) | ||||
−0.266696 | + | 0.963781i | \(0.585932\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.11236e18 | −2.00651 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 2.56928e17i | − 0.121192i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.76380e17i | 0.254220i | 0.991889 | + | 0.127110i | \(0.0405702\pi\) | ||||
−0.991889 | + | 0.127110i | \(0.959430\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.73770e18 | 0.741312 | 0.370656 | − | 0.928770i | \(-0.379133\pi\) | ||||
0.370656 | + | 0.928770i | \(0.379133\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.14033e18 | 0.854592 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.18687e18i | 0.458573i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.66339e17i | 0.204991i | 0.994733 | + | 0.102496i | \(0.0326828\pi\) | ||||
−0.994733 | + | 0.102496i | \(0.967317\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.30265e18 | −1.15730 | −0.578651 | − | 0.815575i | \(-0.696421\pi\) | ||||
−0.578651 | + | 0.815575i | \(0.696421\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.95694e18 | −2.28585 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.99529e18i | 0.634972i | 0.948263 | + | 0.317486i | \(0.102839\pi\) | ||||
−0.948263 | + | 0.317486i | \(0.897161\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.68211e17i | 0.109969i | 0.998487 | + | 0.0549846i | \(0.0175110\pi\) | ||||
−0.998487 | + | 0.0549846i | \(0.982489\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.27362e18 | −0.947344 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.79373e18 | −0.759382 | −0.379691 | − | 0.925113i | \(-0.623970\pi\) | ||||
−0.379691 | + | 0.925113i | \(0.623970\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.35613e18i | 1.41129i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 5.85700e18i | − 1.45076i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.74659e18 | 0.419544 | 0.209772 | − | 0.977750i | \(-0.432728\pi\) | ||||
0.209772 | + | 0.977750i | \(0.432728\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.93335e18 | 1.11490 | 0.557449 | − | 0.830211i | \(-0.311780\pi\) | ||||
0.557449 | + | 0.830211i | \(0.311780\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.53867e17i | 0.0556595i | 0.999613 | + | 0.0278298i | \(0.00885963\pi\) | ||||
−0.999613 | + | 0.0278298i | \(0.991140\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.03491e18i | 0.832944i | 0.909148 | + | 0.416472i | \(0.136734\pi\) | ||||
−0.909148 | + | 0.416472i | \(0.863266\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.74076e18 | 0.749463 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.53046e18 | 0.477718 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 5.44020e18i | − 0.997148i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 5.06724e18i | − 0.875837i | −0.899015 | − | 0.437918i | \(-0.855716\pi\) | ||||
0.899015 | − | 0.437918i | \(-0.144284\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.29652e18 | 0.889150 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.54878e18 | −0.245356 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.73830e18i | 1.03716i | 0.855028 | + | 0.518582i | \(0.173540\pi\) | ||||
−0.855028 | + | 0.518582i | \(0.826460\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 6.14735e18i | − 0.893547i | −0.894647 | − | 0.446773i | \(-0.852573\pi\) | ||||
0.894647 | − | 0.446773i | \(-0.147427\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.27692e19 | −1.80400 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.48363e19 | −1.98076 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.70589e18i | 1.25989i | 0.776641 | + | 0.629943i | \(0.216922\pi\) | ||||
−0.776641 | + | 0.629943i | \(0.783078\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 4.85404e18i | − 0.595838i | −0.954591 | − | 0.297919i | \(-0.903708\pi\) | ||||
0.954591 | − | 0.297919i | \(-0.0962925\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.12503e18 | 0.253702 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.60469e18 | −0.520207 | −0.260103 | − | 0.965581i | \(-0.583757\pi\) | ||||
−0.260103 | + | 0.965581i | \(0.583757\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 1.10576e18i | − 0.121539i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.13243e18i | 0.638237i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.32221e18 | −0.336507 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.66774e19 | 1.60054 | 0.800268 | − | 0.599643i | \(-0.204691\pi\) | ||||
0.800268 | + | 0.599643i | \(0.204691\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.97930e19i | − 1.84927i | −0.380859 | − | 0.924633i | \(-0.624372\pi\) | ||||
0.380859 | − | 0.924633i | \(-0.375628\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 5.52886e18i | − 0.489735i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.16993e19 | −1.00918 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.82375e19 | 2.31066 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.24148e19i | 0.989612i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.94316e18i | 0.525334i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.35383e19 | 1.73538 | 0.867689 | − | 0.497107i | \(-0.165604\pi\) | ||||
0.867689 | + | 0.497107i | \(0.165604\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.05784e19 | 0.740701 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 2.88009e19i | − 1.96560i | −0.184676 | − | 0.982800i | \(-0.559123\pi\) | ||||
0.184676 | − | 0.982800i | \(-0.440877\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.24563e19i | 2.10493i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.61365e19 | 1.65261 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.51606e18 | −0.511979 | −0.255990 | − | 0.966680i | \(-0.582401\pi\) | ||||
−0.255990 | + | 0.966680i | \(0.582401\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 1.33406e19i | − 0.782153i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.92502e19i | 1.63144i | 0.578449 | + | 0.815718i | \(0.303658\pi\) | ||||
−0.578449 | + | 0.815718i | \(0.696342\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.94714e18 | 0.323570 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.81906e19 | 0.942022 | 0.471011 | − | 0.882127i | \(-0.343889\pi\) | ||||
0.471011 | + | 0.882127i | \(0.343889\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.74800e19i | 0.883258i | 0.897198 | + | 0.441629i | \(0.145599\pi\) | ||||
−0.897198 | + | 0.441629i | \(0.854401\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 1.82140e19i | − 0.876456i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.14406e18 | 0.100695 | 0.0503473 | − | 0.998732i | \(-0.483967\pi\) | ||||
0.0503473 | + | 0.998732i | \(0.483967\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.25970e18 | 0.235357 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.18319e19i | 0.516861i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 2.27567e19i | − 0.947637i | −0.880623 | − | 0.473818i | \(-0.842875\pi\) | ||||
0.880623 | − | 0.473818i | \(-0.157125\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.40530e19 | −0.571429 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.61609e19 | 0.626734 | 0.313367 | − | 0.949632i | \(-0.398543\pi\) | ||||
0.313367 | + | 0.949632i | \(0.398543\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 2.70457e19i | − 1.02442i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.29804e19i | 0.469139i | 0.972099 | + | 0.234569i | \(0.0753680\pi\) | ||||
−0.972099 | + | 0.234569i | \(0.924632\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.14780e19 | 0.758353 | 0.379177 | − | 0.925324i | \(-0.376207\pi\) | ||||
0.379177 | + | 0.925324i | \(0.376207\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.86521e18 | 0.265108 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.67305e19i | 0.551048i | 0.961294 | + | 0.275524i | \(0.0888513\pi\) | ||||
−0.961294 | + | 0.275524i | \(0.911149\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.75147e19i | 0.550952i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.11132e19 | 0.649129 | 0.324565 | − | 0.945864i | \(-0.394782\pi\) | ||||
0.324565 | + | 0.945864i | \(0.394782\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.84940e19 | 1.71836 | 0.859181 | − | 0.511671i | \(-0.170973\pi\) | ||||
0.859181 | + | 0.511671i | \(0.170973\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 3.86175e18i | − 0.110905i | −0.998461 | − | 0.0554523i | \(-0.982340\pi\) | ||||
0.998461 | − | 0.0554523i | \(-0.0176601\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 6.70158e19i | − 1.83976i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.47123e16 | 0.000663366 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.44576e19 | 0.627854 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.88197e19i | 1.47678i | 0.674371 | + | 0.738392i | \(0.264415\pi\) | ||||
−0.674371 | + | 0.738392i | \(0.735585\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1.82826e19i | − 0.439160i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.66043e19 | 0.860114 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.21396e19 | 0.497925 | 0.248963 | − | 0.968513i | \(-0.419910\pi\) | ||||
0.248963 | + | 0.968513i | \(0.419910\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 2.96363e19i | − 0.652149i | −0.945344 | − | 0.326075i | \(-0.894274\pi\) | ||||
0.945344 | − | 0.326075i | \(-0.105726\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 4.28835e19i | − 0.903566i | −0.892128 | − | 0.451783i | \(-0.850788\pi\) | ||||
0.892128 | − | 0.451783i | \(-0.149212\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.69597e19 | −1.99930 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.57770e19 | −0.509142 | −0.254571 | − | 0.967054i | \(-0.581934\pi\) | ||||
−0.254571 | + | 0.967054i | \(0.581934\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 9.62104e18i | − 0.186008i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 6.04554e19i | − 1.12005i | −0.828476 | − | 0.560025i | \(-0.810791\pi\) | ||||
0.828476 | − | 0.560025i | \(-0.189209\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.86845e19 | −0.701661 | −0.350830 | − | 0.936439i | \(-0.614101\pi\) | ||||
−0.350830 | + | 0.936439i | \(0.614101\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.87434e19 | −1.19531 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.08665e20i | 1.85015i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.79836e19i | 0.456926i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.62671e19 | 1.05972 | 0.529862 | − | 0.848084i | \(-0.322244\pi\) | ||||
0.529862 | + | 0.848084i | \(0.322244\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.37507e19 | −1.43831 | −0.719157 | − | 0.694847i | \(-0.755472\pi\) | ||||
−0.719157 | + | 0.694847i | \(0.755472\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 3.17058e19i | − 0.476486i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.11901e20i | 1.61394i | 0.590591 | + | 0.806971i | \(0.298895\pi\) | ||||
−0.590591 | + | 0.806971i | \(0.701105\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.83827e18 | 0.0542378 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.23776e19 | 0.846241 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.28716e20i | 1.71114i | 0.517687 | + | 0.855570i | \(0.326793\pi\) | ||||
−0.517687 | + | 0.855570i | \(0.673207\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.11409e19i | 1.03597i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.30391e20 | 1.63162 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.39963e19 | 0.889577 | 0.444789 | − | 0.895636i | \(-0.353279\pi\) | ||||
0.444789 | + | 0.895636i | \(0.353279\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 6.21651e19i | − 0.732587i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.35025e19i | 0.492695i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.08505e19 | −0.120483 | −0.0602416 | − | 0.998184i | \(-0.519187\pi\) | ||||
−0.0602416 | + | 0.998184i | \(0.519187\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.70500e19 | −0.502265 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 1.38094e20i | − 1.44555i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 1.30501e20i | − 1.31375i | −0.753999 | − | 0.656875i | \(-0.771878\pi\) | ||||
0.753999 | − | 0.656875i | \(-0.228122\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.25540e20 | −1.23947 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.49739e19 | −0.807085 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 1.19103e20i | − 1.10964i | −0.831971 | − | 0.554820i | \(-0.812787\pi\) | ||||
0.831971 | − | 0.554820i | \(-0.187213\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 6.16023e19i | − 0.552300i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.04057e20 | −1.79483 | −0.897415 | − | 0.441187i | \(-0.854558\pi\) | ||||
−0.897415 | + | 0.441187i | \(0.854558\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.81982e19 | 0.746771 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 9.96867e19i | − 0.828183i | −0.910235 | − | 0.414091i | \(-0.864099\pi\) | ||||
0.910235 | − | 0.414091i | \(-0.135901\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.48171e18i | 0.0358527i | 0.999839 | + | 0.0179263i | \(0.00570644\pi\) | ||||
−0.999839 | + | 0.0179263i | \(0.994294\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.78452e18 | 0.0140097 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.54150e20 | −1.92184 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 1.75149e20i | − 1.29996i | −0.759953 | − | 0.649978i | \(-0.774778\pi\) | ||||
0.759953 | − | 0.649978i | \(-0.225222\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.28461e19i | 0.234885i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.03204e19 | 0.423441 | 0.211721 | − | 0.977330i | \(-0.432093\pi\) | ||||
0.211721 | + | 0.977330i | \(0.432093\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.90495e20 | −1.96538 | −0.982688 | − | 0.185266i | \(-0.940685\pi\) | ||||
−0.982688 | + | 0.185266i | \(0.940685\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.16555e20i | 1.43846i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.11171e20i | 3.27340i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.31873e19 | 0.523086 | 0.261543 | − | 0.965192i | \(-0.415769\pi\) | ||||
0.261543 | + | 0.965192i | \(0.415769\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.51800e20 | −0.920481 | −0.460241 | − | 0.887794i | \(-0.652237\pi\) | ||||
−0.460241 | + | 0.887794i | \(0.652237\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 3.67922e19i | − 0.219101i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 3.31422e20i | − 1.90379i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.49806e20 | −1.97365 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.42010e19 | 0.240627 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.16371e19i | 0.276146i | 0.990422 | + | 0.138073i | \(0.0440908\pi\) | ||||
−0.990422 | + | 0.138073i | \(0.955909\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.21747e20i | 0.628380i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.47529e20 | 0.748111 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.17303e20 | −1.06380 | −0.531898 | − | 0.846809i | \(-0.678521\pi\) | ||||
−0.531898 | + | 0.846809i | \(0.678521\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.08769e19i | 0.389043i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 2.60712e19i | − 0.121102i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.30155e20 | −1.05063 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.96253e20 | 1.74716 | 0.873581 | − | 0.486679i | \(-0.161792\pi\) | ||||
0.873581 | + | 0.486679i | \(0.161792\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 5.62010e19i | − 0.243556i | −0.992557 | − | 0.121778i | \(-0.961140\pi\) | ||||
0.992557 | − | 0.121778i | \(-0.0388596\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.67946e19i | 0.321534i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.56578e20 | −0.644430 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.46915e20 | −1.77755 | −0.888776 | − | 0.458341i | \(-0.848444\pi\) | ||||
−0.888776 | + | 0.458341i | \(0.848444\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.52023e20i | 1.37649i | 0.725479 | + | 0.688245i | \(0.241618\pi\) | ||||
−0.725479 | + | 0.688245i | \(0.758382\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 2.57157e20i | − 0.971987i | −0.873962 | − | 0.485993i | \(-0.838458\pi\) | ||||
0.873962 | − | 0.485993i | \(-0.161542\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.04550e20 | 0.760182 | 0.380091 | − | 0.924949i | \(-0.375893\pi\) | ||||
0.380091 | + | 0.924949i | \(0.375893\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.69026e20 | 0.607350 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.44126e20i | 0.862598i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 4.46857e20i | − 1.52699i | −0.645816 | − | 0.763493i | \(-0.723483\pi\) | ||||
0.645816 | − | 0.763493i | \(-0.276517\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.09396e20 | 0.703715 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.37993e20 | −1.74896 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.61013e20i | 0.514844i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 2.08131e20i | − 0.643917i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.43984e20 | −0.742538 | −0.371269 | − | 0.928525i | \(-0.621077\pi\) | ||||
−0.371269 | + | 0.928525i | \(0.621077\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.30060e20 | 0.972137 | 0.486068 | − | 0.873921i | \(-0.338431\pi\) | ||||
0.486068 | + | 0.873921i | \(0.338431\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 3.07504e20i | − 0.891043i | −0.895271 | − | 0.445522i | \(-0.853018\pi\) | ||||
0.895271 | − | 0.445522i | \(-0.146982\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.92528e20i | 0.820525i | 0.911967 | + | 0.410262i | \(0.134563\pi\) | ||||
−0.911967 | + | 0.410262i | \(0.865437\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.85694e20 | −0.512490 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.16236e20 | 1.64668 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 4.64981e20i | − 1.22267i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 4.71047e20i | − 1.19952i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.73744e20 | 0.686038 | 0.343019 | − | 0.939329i | \(-0.388551\pi\) | ||||
0.343019 | + | 0.939329i | \(0.388551\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.72617e20 | −0.904547 | −0.452274 | − | 0.891879i | \(-0.649387\pi\) | ||||
−0.452274 | + | 0.891879i | \(0.649387\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.43070e20i | 0.819705i | 0.912152 | + | 0.409853i | \(0.134420\pi\) | ||||
−0.912152 | + | 0.409853i | \(0.865580\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 4.98820e20i | − 1.15473i | −0.816488 | − | 0.577363i | \(-0.804082\pi\) | ||||
0.816488 | − | 0.577363i | \(-0.195918\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.74273e20 | 0.852856 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.05569e20 | 0.453940 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.75007e20i | 0.380446i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.19503e20i | 0.462511i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.88039e20 | 0.597554 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.00978e20 | 1.00758 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.49105e20i | 0.889399i | 0.895680 | + | 0.444700i | \(0.146690\pi\) | ||||
−0.895680 | + | 0.444700i | \(0.853310\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.87755e20i | 0.936641i | 0.883559 | + | 0.468320i | \(0.155141\pi\) | ||||
−0.883559 | + | 0.468320i | \(0.844859\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.24011e20 | 0.234512 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.96957e20 | 0.361232 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 4.16251e19i | − 0.0751877i | −0.999293 | − | 0.0375938i | \(-0.988031\pi\) | ||||
0.999293 | − | 0.0375938i | \(-0.0119693\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.84417e21i | 3.23139i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.62755e20 | 0.280893 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.12297e20 | 0.522947 | 0.261473 | − | 0.965211i | \(-0.415792\pi\) | ||||
0.261473 | + | 0.965211i | \(0.415792\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 4.29623e20i | − 0.708663i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 6.37672e20i | − 1.02074i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.84262e20 | −0.290575 | −0.145288 | − | 0.989389i | \(-0.546411\pi\) | ||||
−0.145288 | + | 0.989389i | \(0.546411\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.97291e20 | −0.608109 | −0.304054 | − | 0.952655i | \(-0.598340\pi\) | ||||
−0.304054 | + | 0.952655i | \(0.598340\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1.10961e21i | − 1.67336i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.96271e20i | 0.287347i | 0.989625 | + | 0.143674i | \(0.0458915\pi\) | ||||
−0.989625 | + | 0.143674i | \(0.954108\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.37447e20 | −0.198277 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.41143e21 | 1.97701 | 0.988507 | − | 0.151177i | \(-0.0483063\pi\) | ||||
0.988507 | + | 0.151177i | \(0.0483063\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 3.06031e20i | − 0.422417i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.85752e19i | 0.105331i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.61903e20 | 0.874441 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.13624e20 | −0.274132 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 4.30311e19i | − 0.0544249i | −0.999630 | − | 0.0272124i | \(-0.991337\pi\) | ||||
0.999630 | − | 0.0272124i | \(-0.00866306\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.43559e20i | 0.667901i | 0.942591 | + | 0.333951i | \(0.108382\pi\) | ||||
−0.942591 | + | 0.333951i | \(0.891618\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.66108e21 | −2.01187 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.68715e20 | 0.787008 | 0.393504 | − | 0.919323i | \(-0.371263\pi\) | ||||
0.393504 | + | 0.919323i | \(0.371263\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1.58007e21i | − 1.83315i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.25760e20i | 0.141798i | 0.997484 | + | 0.0708988i | \(0.0225868\pi\) | ||||
−0.997484 | + | 0.0708988i | \(0.977413\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.96002e20 | 0.217874 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.24228e20 | −0.566430 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.59246e20i | 0.595782i | 0.954600 | + | 0.297891i | \(0.0962832\pi\) | ||||
−0.954600 | + | 0.297891i | \(0.903717\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.57179e20i | 0.266363i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.53050e21 | 1.56303 | 0.781514 | − | 0.623888i | \(-0.214448\pi\) | ||||
0.781514 | + | 0.623888i | \(0.214448\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 144.15.g.e.127.1 | 4 | ||
3.2 | odd | 2 | 48.15.g.a.31.2 | ✓ | 4 | ||
4.3 | odd | 2 | inner | 144.15.g.e.127.2 | 4 | ||
12.11 | even | 2 | 48.15.g.a.31.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.15.g.a.31.2 | ✓ | 4 | 3.2 | odd | 2 | ||
48.15.g.a.31.4 | yes | 4 | 12.11 | even | 2 | ||
144.15.g.e.127.1 | 4 | 1.1 | even | 1 | trivial | ||
144.15.g.e.127.2 | 4 | 4.3 | odd | 2 | inner |