Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [80,16,Mod(49,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 16, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("80.49");
S:= CuspForms(chi, 16);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 16 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.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: | \(114.154804080\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 29397x^{4} + 153469728x^{2} + 65015354624 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{19}\cdot 3^{4}\cdot 5^{6} \) |
Twist minimal: | no (minimal twist has level 5) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(21.5470i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 80.49 |
Dual form | 80.16.c.a.49.6 |
$q$-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 \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(21\) | \(31\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − | 6725.99i | − | 1.77561i | −0.460223 | − | 0.887803i | \(-0.652230\pi\) | ||
0.460223 | − | 0.887803i | \(-0.347770\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −160365. | − | 69286.1i | −0.917984 | − | 0.396617i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.29717e6i | − | 0.595333i | −0.954670 | − | 0.297667i | \(-0.903792\pi\) | ||
0.954670 | − | 0.297667i | \(-0.0962084\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.08900e7 | −2.15278 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.48560e7 | 0.384579 | 0.192290 | − | 0.981338i | \(-0.438409\pi\) | ||||
0.192290 | + | 0.981338i | \(0.438409\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.64842e8i | − | 0.728606i | −0.931281 | − | 0.364303i | \(-0.881307\pi\) | ||
0.931281 | − | 0.364303i | \(-0.118693\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.66018e8 | + | 1.07862e9i | −0.704235 | + | 1.62998i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.49651e9i | 1.47559i | 0.675024 | + | 0.737795i | \(0.264133\pi\) | ||||
−0.675024 | + | 0.737795i | \(0.735867\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.47974e9 | −0.893088 | −0.446544 | − | 0.894762i | \(-0.647345\pi\) | ||||
−0.446544 | + | 0.894762i | \(0.647345\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.72472e9 | −1.05708 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.39929e10i | − | 0.856934i | −0.903557 | − | 0.428467i | \(-0.859054\pi\) | ||
0.903557 | − | 0.428467i | \(-0.140946\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.09165e10 | + | 2.22222e10i | 0.685390 | + | 0.728176i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.11256e11i | 2.04688i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.33587e10 | 0.789709 | 0.394854 | − | 0.918744i | \(-0.370795\pi\) | ||||
0.394854 | + | 0.918744i | \(0.370795\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.63708e9 | −0.0433276 | −0.0216638 | − | 0.999765i | \(-0.506896\pi\) | ||||
−0.0216638 | + | 0.999765i | \(0.506896\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 1.67181e11i | − | 0.682862i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.98755e10 | + | 2.08020e11i | −0.236119 | + | 0.546506i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.47925e11i | 1.46840i | 0.678933 | + | 0.734201i | \(0.262443\pi\) | ||||
−0.678933 | + | 0.734201i | \(0.737557\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.10873e12 | −1.29372 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.77655e11 | −0.623603 | −0.311801 | − | 0.950147i | \(-0.600932\pi\) | ||||
−0.311801 | + | 0.950147i | \(0.600932\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.03959e12i | 1.14427i | 0.820158 | + | 0.572137i | \(0.193885\pi\) | ||||
−0.820158 | + | 0.572137i | \(0.806115\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.95369e12 | + | 2.14025e12i | 1.97622 | + | 0.853828i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.83108e12i | 1.10303i | 0.834165 | + | 0.551514i | \(0.185950\pi\) | ||||
−0.834165 | + | 0.551514i | \(0.814050\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.06492e12 | 0.645578 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.67915e13 | 2.62007 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 2.49472e12i | − | 0.291711i | −0.989306 | − | 0.145856i | \(-0.953407\pi\) | ||
0.989306 | − | 0.145856i | \(-0.0465935\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.98604e12 | − | 1.72217e12i | −0.353038 | − | 0.152531i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.34047e13i | 1.58577i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.33880e12 | −0.0700365 | −0.0350183 | − | 0.999387i | \(-0.511149\pi\) | ||||
−0.0350183 | + | 0.999387i | \(0.511149\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.16455e12 | 0.291887 | 0.145944 | − | 0.989293i | \(-0.453378\pi\) | ||||
0.145944 | + | 0.989293i | \(0.453378\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.00695e13i | 1.28162i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.14213e13 | + | 2.64349e13i | −0.288977 | + | 0.668849i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 6.61388e12i | − | 0.133320i | −0.997776 | − | 0.0666600i | \(-0.978766\pi\) | ||
0.997776 | − | 0.0666600i | \(-0.0212343\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.41158e13 | −1.52158 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.42046e13 | −0.185349 | −0.0926746 | − | 0.995696i | \(-0.529542\pi\) | ||||
−0.0926746 | + | 0.995696i | \(0.529542\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 5.85350e13i | − | 0.620147i | −0.950713 | − | 0.310073i | \(-0.899646\pi\) | ||
0.950713 | − | 0.310073i | \(-0.100354\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.49466e14 | − | 1.40684e14i | 1.29295 | − | 1.21698i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 3.22423e13i | − | 0.228953i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.48505e14 | −1.45590 | −0.727950 | − | 0.685630i | \(-0.759527\pi\) | ||||
−0.727950 | + | 0.685630i | \(0.759527\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.05065e14 | 1.48168 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.66100e13i | 0.269435i | 0.990884 | + | 0.134717i | \(0.0430127\pi\) | ||||
−0.990884 | + | 0.134717i | \(0.956987\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.72973e14 | − | 4.00353e14i | 0.585244 | − | 1.35457i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 4.93410e14i | − | 1.40221i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.07426e14 | −1.21604 | −0.608020 | − | 0.793922i | \(-0.708036\pi\) | ||||
−0.608020 | + | 0.793922i | \(0.708036\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.13827e14 | −0.433763 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.46409e13i | 0.0769327i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.58029e14 | + | 2.41097e14i | 0.819841 | + | 0.354214i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.18734e15i | − | 1.49206i | −0.665912 | − | 0.746030i | \(-0.731957\pi\) | ||
0.665912 | − | 0.746030i | \(-0.268043\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.67802e14 | −0.827915 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.97970e14 | 0.183734 | 0.0918671 | − | 0.995771i | \(-0.470717\pi\) | ||||
0.0918671 | + | 0.995771i | \(0.470717\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.50015e15i | − | 1.20186i | −0.799301 | − | 0.600931i | \(-0.794797\pi\) | ||
0.799301 | − | 0.600931i | \(-0.205203\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.39914e15 | + | 6.04502e14i | 0.970381 | + | 0.419255i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.89575e14i | 0.415148i | 0.978219 | + | 0.207574i | \(0.0665568\pi\) | ||||
−0.978219 | + | 0.207574i | \(0.933443\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.35369e15 | 0.709287 | 0.354644 | − | 0.935002i | \(-0.384602\pi\) | ||||
0.354644 | + | 0.935002i | \(0.384602\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.70314e15 | 2.60730 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.28009e15i | 0.911726i | 0.890050 | + | 0.455863i | \(0.150669\pi\) | ||||
−0.890050 | + | 0.455863i | \(0.849331\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.69510e14 | + | 2.24397e15i | −0.339874 | + | 0.786652i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.09197e15i | 1.56853i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.23838e15 | 0.878468 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.55943e15 | −0.852099 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.23050e15i | 1.10727i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.81459e15 | − | 5.01288e15i | −0.340371 | − | 0.940291i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.82207e15i | 0.469938i | 0.972003 | + | 0.234969i | \(0.0754988\pi\) | ||||
−0.972003 | + | 0.234969i | \(0.924501\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.37183e16 | 2.03178 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.54539e15 | −0.863775 | −0.431888 | − | 0.901927i | \(-0.642152\pi\) | ||||
−0.431888 | + | 0.901927i | \(0.642152\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.51379e15i | 0.531685i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.70846e15 | − | 1.78415e16i | 0.811828 | − | 1.87901i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 1.17625e16i | − | 1.10941i | −0.832046 | − | 0.554707i | \(-0.812830\pi\) | ||
0.832046 | − | 0.554707i | \(-0.187170\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.03768e16 | 1.72395 | 0.861976 | − | 0.506949i | \(-0.169227\pi\) | ||||
0.861976 | + | 0.506949i | \(0.169227\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.57678e16 | 1.95855 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 4.09731e15i | − | 0.280207i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.17642e16 | − | 5.08274e15i | −0.724940 | − | 0.313212i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 2.06146e16i | − | 1.14629i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.89572e16 | 1.45499 | 0.727493 | − | 0.686115i | \(-0.240685\pi\) | ||||
0.727493 | + | 0.686115i | \(0.240685\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.77226e13 | −0.000805748 | −0.000402874 | − | 1.00000i | \(-0.500128\pi\) | ||||
−0.000402874 | 1.00000i | \(0.500128\pi\) | ||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 7.71172e16i | − | 3.17662i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.06436e15 | + | 4.59857e14i | 0.0397740 | + | 0.0171844i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.04137e16i | 0.353475i | 0.984258 | + | 0.176737i | \(0.0565543\pi\) | ||||
−0.984258 | + | 0.176737i | \(0.943446\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.67795e16 | −0.517964 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.81510e16 | −0.510161 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 4.70622e16i | − | 1.20577i | −0.797827 | − | 0.602886i | \(-0.794017\pi\) | ||
0.797827 | − | 0.602886i | \(-0.205983\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.15833e16 | + | 2.68100e16i | −0.270834 | + | 0.626856i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.97751e16i | 0.849646i | 0.905276 | + | 0.424823i | \(0.139664\pi\) | ||||
−0.905276 | + | 0.424823i | \(0.860336\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.40130e16 | 0.469134 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.07489e17 | 1.92262 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.30223e16i | 1.03311i | 0.856253 | + | 0.516557i | \(0.172787\pi\) | ||||
−0.856253 | + | 0.516557i | \(0.827213\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.88258e16 | − | 2.71321e16i | 0.433507 | − | 0.408036i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.00474e15i | 0.124357i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.10684e16 | −0.267445 | −0.133722 | − | 0.991019i | \(-0.542693\pi\) | ||||
−0.133722 | + | 0.991019i | \(0.542693\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.74536e16 | 0.203843 | 0.101922 | − | 0.994792i | \(-0.467501\pi\) | ||||
0.101922 | + | 0.994792i | \(0.467501\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 4.81887e16i | − | 0.518277i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.87494e16 | − | 1.35978e17i | 0.582392 | − | 1.34797i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.20531e16i | 0.567482i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.44317e17 | 1.21858 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.82919e17 | 1.42728 | 0.713639 | − | 0.700514i | \(-0.247046\pi\) | ||||
0.713639 | + | 0.700514i | \(0.247046\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 4.54299e16i | − | 0.327840i | −0.986474 | − | 0.163920i | \(-0.947586\pi\) | ||
0.986474 | − | 0.163920i | \(-0.0524139\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.77801e17 | + | 7.68192e16i | 1.18761 | + | 0.513110i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.54430e17i | 1.57425i | 0.616797 | + | 0.787123i | \(0.288430\pi\) | ||||
−0.616797 | + | 0.787123i | \(0.711570\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.75148e17 | −1.00463 | −0.502316 | − | 0.864684i | \(-0.667518\pi\) | ||||
−0.502316 | + | 0.864684i | \(0.667518\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.44849e16 | −0.236724 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 9.51584e16i | − | 0.470140i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.24709e17 | + | 5.38807e16i | 0.572457 | + | 0.247331i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.32240e17i | 1.84479i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.64923e16 | −0.343463 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.58937e17 | −1.32709 | −0.663545 | − | 0.748137i | \(-0.730949\pi\) | ||||
−0.663545 | + | 0.748137i | \(0.730949\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.55399e16i | 0.329107i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.41315e17 | − | 3.27080e17i | 0.453838 | − | 1.05043i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.60939e15i | 0.0257943i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.93706e17 | −1.10114 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.11529e17 | 1.07512 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.51111e16i | 0.207826i | 0.994586 | + | 0.103913i | \(0.0331364\pi\) | ||||
−0.994586 | + | 0.103913i | \(0.966864\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.46110e17 | − | 6.86443e17i | −1.47549 | − | 1.56760i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.22273e16i | 0.175720i | 0.996133 | + | 0.0878602i | \(0.0280029\pi\) | ||||
−0.996133 | + | 0.0878602i | \(0.971997\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.91258e17 | −0.782884 | −0.391442 | − | 0.920203i | \(-0.628024\pi\) | ||||
−0.391442 | + | 0.920203i | \(0.628024\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.16862e17 | −0.406530 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 9.50055e17i | − | 1.66947i | −0.550650 | − | 0.834736i | \(-0.685620\pi\) | ||
0.550650 | − | 0.834736i | \(-0.314380\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.65440e17 | − | 6.14371e17i | 0.437480 | − | 1.01256i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.67144e18i | 2.58511i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.05534e17 | −0.443685 | −0.221843 | − | 0.975082i | \(-0.571207\pi\) | ||||
−0.221843 | + | 0.975082i | \(0.571207\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.24585e18 | −1.69956 | −0.849780 | − | 0.527137i | \(-0.823266\pi\) | ||||
−0.849780 | + | 0.527137i | \(0.823266\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 4.55471e17i | − | 0.584001i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.91507e17 | − | 2.12357e17i | −0.592631 | − | 0.256047i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.73606e17i | 0.650709i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.48018e17 | 0.478411 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.78704e17 | −0.380844 | −0.190422 | − | 0.981702i | \(-0.560986\pi\) | ||||
−0.190422 | + | 0.981702i | \(0.560986\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 3.47806e17i | − | 0.329559i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.69277e18 | − | 1.16342e18i | −2.40518 | − | 1.03916i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.98680e16i | 0.0588545i | 0.999567 | + | 0.0294273i | \(0.00936834\pi\) | ||||
−0.999567 | + | 0.0294273i | \(0.990632\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.09990e18 | 0.874188 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.26605e18 | −1.70007 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.94838e17i | 0.492284i | 0.969234 | + | 0.246142i | \(0.0791629\pi\) | ||||
−0.969234 | + | 0.246142i | \(0.920837\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.72849e17 | + | 4.00067e17i | −0.115698 | + | 0.267786i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.41294e18i | 2.15921i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.75703e18 | 1.05108 | 0.525542 | − | 0.850768i | \(-0.323863\pi\) | ||||
0.525542 | + | 0.850768i | \(0.323863\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.86384e18 | 1.05472 | 0.527362 | − | 0.849641i | \(-0.323181\pi\) | ||||
0.527362 | + | 0.849641i | \(0.323181\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.43820e18i | 0.770193i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.19899e17 | + | 5.52354e17i | 0.263587 | + | 0.280041i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.28806e18i | 1.57885i | 0.613846 | + | 0.789425i | \(0.289621\pi\) | ||||
−0.613846 | + | 0.789425i | \(0.710379\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.05020e17 | 0.0932747 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.41481e18 | 1.04132 | 0.520662 | − | 0.853763i | \(-0.325685\pi\) | ||||
0.520662 | + | 0.853763i | \(0.325685\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 1.11571e17i | − | 0.0456199i | −0.999740 | − | 0.0228099i | \(-0.992739\pi\) | ||
0.999740 | − | 0.0228099i | \(-0.00726126\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.62162e18 | − | 3.75330e18i | 0.628944 | − | 1.45571i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.00875e18i | 0.371251i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.37012e18 | −1.17737 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.98602e18 | −2.64931 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.59868e18i | 0.818927i | 0.912327 | + | 0.409463i | \(0.134284\pi\) | ||||
−0.912327 | + | 0.409463i | \(0.865716\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.14697e17 | + | 9.27600e16i | 0.0642924 | + | 0.0277777i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.76537e18i | 0.787189i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.30661e18 | −0.624367 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.64569e18 | 0.681224 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 1.33155e18i | − | 0.326240i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.14895e18 | − | 4.96404e17i | −0.267948 | − | 0.115767i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.96608e18i | 1.76892i | 0.466621 | + | 0.884458i | \(0.345471\pi\) | ||||
−0.466621 | + | 0.884458i | \(0.654529\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.00900e19 | −2.13403 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.72923e18 | 1.75903 | 0.879515 | − | 0.475872i | \(-0.157867\pi\) | ||||
0.879515 | + | 0.475872i | \(0.157867\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 3.04567e17i | − | 0.0584926i | −0.999572 | − | 0.0292463i | \(-0.990689\pi\) | ||
0.999572 | − | 0.0292463i | \(-0.00931071\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.77626e18 | − | 6.42575e18i | 0.508312 | − | 1.17651i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 5.64109e18i | − | 0.984961i | −0.870324 | − | 0.492480i | \(-0.836090\pi\) | ||
0.870324 | − | 0.492480i | \(-0.163910\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.82340e18 | 0.303706 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.63807e18 | 0.737140 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 8.68718e18i | − | 1.31783i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.66314e18 | − | 3.44791e18i | 0.530553 | − | 0.499379i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 9.10494e18i | − | 1.25941i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.96954e18 | 0.656670 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.05049e18 | −0.763978 | −0.381989 | − | 0.924167i | \(-0.624761\pi\) | ||||
−0.381989 | + | 0.924167i | \(0.624761\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 2.61925e19i | − | 3.16114i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.58250e17 | + | 1.06064e18i | −0.0528770 | + | 0.122386i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.58672e19i | 1.75096i | 0.483254 | + | 0.875480i | \(0.339455\pi\) | ||||
−0.483254 | + | 0.875480i | \(0.660545\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.53359e19 | 1.61887 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.64971e17 | −0.0166629 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.01341e19i | − | 0.979667i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.50929e19 | + | 6.52092e18i | 1.39679 | + | 0.603484i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 5.47026e18i | − | 0.484771i | −0.970180 | − | 0.242386i | \(-0.922070\pi\) | ||
0.970180 | − | 0.242386i | \(-0.0779299\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.51980e18 | −0.638287 | −0.319143 | − | 0.947706i | \(-0.603395\pi\) | ||||
−0.319143 | + | 0.947706i | \(0.603395\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.83396e19 | 1.49137 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.96219e18i | 0.308763i | 0.988011 | + | 0.154382i | \(0.0493385\pi\) | ||||
−0.988011 | + | 0.154382i | \(0.950662\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.27792e18 | + | 9.84179e17i | 0.170148 | + | 0.0735126i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 2.17813e19i | − | 1.55981i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.88540e19 | −1.29478 | −0.647390 | − | 0.762159i | \(-0.724140\pi\) | ||||
−0.647390 | + | 0.762159i | \(0.724140\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.07257e18 | −0.202394 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.39407e19i | 1.51299i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.05566e18 | + | 9.38699e18i | −0.245961 | + | 0.569285i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.02228e19i | 0.595077i | 0.954710 | + | 0.297538i | \(0.0961656\pi\) | ||||
−0.954710 | + | 0.297538i | \(0.903834\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.40218e19 | 1.34248 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.23607e18 | −0.173665 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.86547e19i | 0.961550i | 0.876844 | + | 0.480775i | \(0.159645\pi\) | ||||
−0.876844 | + | 0.480775i | \(0.840355\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.37166e19 | + | 1.22049e19i | −1.66959 | + | 0.604365i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 1.20926e19i | − | 0.575386i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.62923e19 | 1.65967 | 0.829833 | − | 0.558012i | \(-0.188436\pi\) | ||||
0.829833 | + | 0.558012i | \(0.188436\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.89812e19 | 0.834425 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.39832e19i | 1.43640i | 0.695839 | + | 0.718198i | \(0.255033\pi\) | ||||
−0.695839 | + | 0.718198i | \(0.744967\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.23394e18 | + | 5.17055e18i | −0.0908065 | + | 0.210175i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 6.30031e19i | − | 2.46337i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.43693e19 | 1.66902 | 0.834508 | − | 0.550996i | \(-0.185752\pi\) | ||||
0.834508 | + | 0.550996i | \(0.185752\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.49333e19 | 1.26448 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.40242e19i | 1.53373i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.98516e19 | + | 1.72179e19i | 1.33649 | + | 0.577434i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.44302e19i | 0.465953i | 0.972482 | + | 0.232977i | \(0.0748466\pi\) | ||||
−0.972482 | + | 0.232977i | \(0.925153\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.03597e19 | 0.944063 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.34827e19 | 0.703339 | 0.351669 | − | 0.936124i | \(-0.385614\pi\) | ||||
0.351669 | + | 0.936124i | \(0.385614\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.09407e18i | 0.0315687i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.89219e19 | − | 2.11368e19i | −1.36016 | − | 0.587660i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.10760e19i | 0.564717i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.99167e19 | −1.03093 | −0.515466 | − | 0.856910i | \(-0.672381\pi\) | ||||
−0.515466 | + | 0.856910i | \(0.672381\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.91142e19 | −1.96988 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.73664e18i | 0.0416951i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.61515e18 | − | 1.06819e19i | 0.106862 | − | 0.247337i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 1.37054e20i | − | 3.06106i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.16449e19 | −1.54376 | −0.771881 | − | 0.635767i | \(-0.780684\pi\) | ||||
−0.771881 | + | 0.635767i | \(0.780684\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.22202e18 | −0.129365 | −0.0646823 | − | 0.997906i | \(-0.520603\pi\) | ||||
−0.0646823 | + | 0.997906i | \(0.520603\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 1.18342e20i | − | 2.37458i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.54778e19 | + | 5.22181e19i | −1.07449 | + | 1.01136i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 9.29361e18i | − | 0.173770i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.75585e19 | −0.497537 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.93032e19 | 0.859598 | 0.429799 | − | 0.902925i | \(-0.358584\pi\) | ||||
0.429799 | + | 0.902925i | \(0.358584\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1.59414e19i | − | 0.268453i | −0.990951 | − | 0.134226i | \(-0.957145\pi\) | ||
0.990951 | − | 0.134226i | \(-0.0428549\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.41865e19 | + | 7.91259e19i | −0.556141 | + | 1.28721i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.86914e19i | 0.765318i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.26174e19 | 0.191640 | 0.0958201 | − | 0.995399i | \(-0.469453\pi\) | ||||
0.0958201 | + | 0.995399i | \(0.469453\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.46756e19 | −1.38979 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.89961e19i | 1.12093i | 0.828179 | + | 0.560464i | \(0.189377\pi\) | ||||
−0.828179 | + | 0.560464i | \(0.810623\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.13735e19 | + | 3.51576e19i | 1.11630 | + | 0.482301i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 1.94766e20i | − | 2.58348i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.36438e19 | 0.559854 | 0.279927 | − | 0.960021i | \(-0.409690\pi\) | ||||
0.279927 | + | 0.960021i | \(0.409690\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.93294e19 | −0.239825 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.19202e17i | 0.00143069i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.42905e19 | + | 1.48153e19i | 0.398188 | + | 0.172038i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 1.00520e20i | − | 1.12949i | −0.825266 | − | 0.564744i | \(-0.808975\pi\) | ||
0.825266 | − | 0.564744i | \(-0.191025\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.77750e20 | −3.02036 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.09258e20 | −1.15000 | −0.574999 | − | 0.818154i | \(-0.694998\pi\) | ||||
−0.574999 | + | 0.818154i | \(0.694998\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.81520e20i | 1.84955i | 0.380510 | + | 0.924777i | \(0.375748\pi\) | ||||
−0.380510 | + | 0.924777i | \(0.624252\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.09299e18 | − | 7.15885e18i | 0.0305128 | − | 0.0706230i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.14048e20i | 1.08946i | 0.838611 | + | 0.544731i | \(0.183368\pi\) | ||||
−0.838611 | + | 0.544731i | \(0.816632\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.57930e18 | −0.0793699 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.00425e19 | 0.627632 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.06961e19i | 0.440064i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.27837e19 | − | 7.73272e19i | −0.612114 | − | 0.650325i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.70621e19i | 0.627990i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.21110e20 | −0.956451 | −0.478226 | − | 0.878237i | \(-0.658720\pi\) | ||||
−0.478226 | + | 0.878237i | \(0.658720\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.39774e20 | 1.06989 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.22084e20i | 0.905846i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.22660e19 | + | 1.90408e20i | −0.591776 | + | 1.36969i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.00069e20i | 0.697963i | 0.937130 | + | 0.348982i | \(0.113472\pi\) | ||||
−0.937130 | + | 0.348982i | \(0.886528\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.16540e20 | −2.14098 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.32724e20 | 0.870641 | 0.435321 | − | 0.900276i | \(-0.356635\pi\) | ||||
0.435321 | + | 0.900276i | \(0.356635\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.83141e20i | 1.16529i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.23129e20 | + | 5.31980e19i | 0.760013 | + | 0.328365i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.84257e19i | 0.110345i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.34938e18 | 0.0543286 | 0.0271643 | − | 0.999631i | \(-0.491352\pi\) | ||||
0.0271643 | + | 0.999631i | \(0.491352\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.67527e20 | 1.50864 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 1.56622e20i | − | 0.857223i | −0.903489 | − | 0.428612i | \(-0.859003\pi\) | ||
0.903489 | − | 0.428612i | \(-0.140997\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.17476e19 | − | 1.37166e19i | −0.168665 | − | 0.0728720i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 1.61511e20i | − | 0.832997i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.94050e20 | 0.971698 | 0.485849 | − | 0.874043i | \(-0.338511\pi\) | ||||
0.485849 | + | 0.874043i | \(0.338511\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.59296e19 | −0.369194 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 3.87140e20i | − | 1.82805i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.03939e20 | + | 2.40571e20i | −0.476678 | + | 1.10329i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.52252e19i | 0.424202i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.23887e20 | 1.83441 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.43719e19 | −0.270653 | −0.135327 | − | 0.990801i | \(-0.543208\pi\) | ||||
−0.135327 | + | 0.990801i | \(0.543208\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 1.94571e20i | − | 0.794904i | −0.917623 | − | 0.397452i | \(-0.869895\pi\) | ||
0.917623 | − | 0.397452i | \(-0.130105\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.82490e20 | − | 1.93882e20i | −0.724511 | − | 0.769738i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1.65695e19i | − | 0.0639337i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.08352e19 | 0.265663 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.13555e19 | 0.150773 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.28190e20i | 0.454360i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.77779e19 | − | 1.10584e20i | 0.164655 | − | 0.381099i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.41706e20i | 0.474877i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.61817e19 | 0.248276 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.81403e19 | 0.0574996 | 0.0287498 | − | 0.999587i | \(-0.490847\pi\) | ||||
0.0287498 | + | 0.999587i | \(0.490847\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 1.17393e20i | − | 0.361945i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.17086e20 | − | 9.37922e19i | −0.651114 | − | 0.281315i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.00592e20i | 1.75257i | 0.481796 | + | 0.876283i | \(0.339985\pi\) | ||||
−0.481796 | + | 0.876283i | \(0.660015\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.21313e20 | −0.628369 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.55269e20 | −0.705279 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.22352e20i | 0.866746i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.14585e20 | − | 3.95148e20i | −2.39346 | − | 1.03410i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 2.29611e20i | − | 0.584895i | −0.956282 | − | 0.292447i | \(-0.905530\pi\) | ||
0.956282 | − | 0.292447i | \(-0.0944697\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.36210e20 | 0.833725 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.17369e20 | 1.00762 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 5.26651e20i | − | 1.23797i | −0.785403 | − | 0.618985i | \(-0.787544\pi\) | ||
0.785403 | − | 0.618985i | \(-0.212456\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.57979e20 | − | 3.65648e20i | 0.361606 | − | 0.836950i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 3.95720e20i | − | 0.882095i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.86825e20 | 1.27399 | 0.636996 | − | 0.770868i | \(-0.280177\pi\) | ||||
0.636996 | + | 0.770868i | \(0.280177\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.76080e20 | 0.583800 | 0.291900 | − | 0.956449i | \(-0.405713\pi\) | ||||
0.291900 | + | 0.956449i | \(0.405713\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 1.23031e21i | − | 2.53428i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.10952e20 | − | 2.92681e20i | 0.623999 | − | 0.587335i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.42599e20i | 0.278804i | 0.990236 | + | 0.139402i | \(0.0445180\pi\) | ||||
−0.990236 | + | 0.139402i | \(0.955482\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.05561e20 | −0.582115 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.64042e19 | 0.160404 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 6.20088e19i | − | 0.112186i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.52803e20 | − | 8.16576e20i | 0.622104 | − | 1.43988i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.48323e20i | 1.28618i | 0.765789 | + | 0.643092i | \(0.222349\pi\) | ||||
−0.765789 | + | 0.643092i | \(0.777651\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.30953e19 | 0.0386953 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.71130e21 | 2.79524 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.21784e20i | 0.512454i | 0.966617 | + | 0.256227i | \(0.0824794\pi\) | ||||
−0.966617 | + | 0.256227i | \(0.917521\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.19324e20 | − | 2.24375e20i | −0.806420 | − | 0.348415i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.17804e21i | 1.78383i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.08146e21 | 1.59702 | 0.798509 | − | 0.601983i | \(-0.205623\pi\) | ||||
0.798509 | + | 0.601983i | \(0.205623\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.36803e20 | 0.773136 | 0.386568 | − | 0.922261i | \(-0.373660\pi\) | ||||
0.386568 | + | 0.922261i | \(0.373660\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.04303e20i | 0.287009i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.70809e20 | + | 2.46619e20i | 0.782213 | + | 0.337957i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.11434e20i | 0.550029i | 0.961440 | + | 0.275014i | \(0.0886826\pi\) | ||||
−0.961440 | + | 0.275014i | \(0.911317\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.40035e20 | −0.834783 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.31522e20 | 0.803673 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 5.44101e20i | − | 0.675656i | −0.941208 | − | 0.337828i | \(-0.890308\pi\) | ||
0.941208 | − | 0.337828i | \(-0.109692\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.62401e20 | − | 8.38790e20i | 0.439163 | − | 1.01646i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.65828e20i | 0.550918i | 0.961313 | + | 0.275459i | \(0.0888298\pi\) | ||||
−0.961313 | + | 0.275459i | \(0.911170\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.51736e21 | −1.75150 | −0.875749 | − | 0.482767i | \(-0.839632\pi\) | ||||
−0.875749 | + | 0.482767i | \(0.839632\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.55678e21 | 1.75405 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.58215e20i | 0.723948i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.63262e19 | + | 9.29618e20i | −0.0604798 | + | 0.998169i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.81746e20i | 0.609855i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.11685e21 | −2.16676 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.94310e20 | −0.594009 | −0.297004 | − | 0.954876i | \(-0.595988\pi\) | ||||
−0.297004 | + | 0.954876i | \(0.595988\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.41421e21i | 2.35639i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.95530e20 | − | 4.52563e20i | 0.186385 | − | 0.431396i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 5.05228e20i | − | 0.470372i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.38780e20 | 0.399016 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.48383e20 | 0.842458 | 0.421229 | − | 0.906954i | \(-0.361599\pi\) | ||||
0.421229 | + | 0.906954i | \(0.361599\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.15909e21i | 1.87365i | 0.349800 | + | 0.936824i | \(0.386250\pi\) | ||||
−0.349800 | + | 0.936824i | \(0.613750\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.19994e21 | − | 9.50486e20i | −1.86514 | − | 0.805838i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 2.26989e20i | − | 0.188028i | −0.995571 | − | 0.0940139i | \(-0.970030\pi\) | ||
0.995571 | − | 0.0940139i | \(-0.0299698\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.32771e19 | −0.0269346 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.79067e19 | 0.0458006 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 2.12810e21i | − | 1.64491i | −0.568830 | − | 0.822455i | \(-0.692604\pi\) | ||
0.568830 | − | 0.822455i | \(-0.307396\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.04965e21 | + | 4.53504e20i | 0.792932 | + | 0.342588i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.80815e21i | 1.33504i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.97715e20 | −0.287032 | −0.143516 | − | 0.989648i | \(-0.545841\pi\) | ||||
−0.143516 | + | 0.989648i | \(0.545841\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.97089e20 | 0.139044 | 0.0695218 | − | 0.997580i | \(-0.477853\pi\) | ||||
0.0695218 | + | 0.997580i | \(0.477853\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 2.76794e21i | − | 1.90900i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.12743e20 | − | 7.23855e20i | 0.210875 | − | 0.488078i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1.02650e21i | − | 0.676729i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.72457e20 | 0.369017 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.78082e20 | 0.112254 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1.12563e21i | − | 0.693876i | −0.937888 | − | 0.346938i | \(-0.887221\pi\) | ||
0.937888 | − | 0.346938i | \(-0.112779\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.47234e21 | + | 2.32707e21i | −1.49049 | + | 1.40292i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 2.01414e21i | − | 1.18761i | −0.804608 | − | 0.593806i | \(-0.797625\pi\) | ||
0.804608 | − | 0.593806i | \(-0.202375\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.54017e21 | −0.888273 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.53060e20 | 0.312010 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 2.93860e21i | − | 1.62176i | −0.585215 | − | 0.810878i | \(-0.698990\pi\) | ||
0.585215 | − | 0.810878i | \(-0.301010\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.14974e20 | + | 1.88629e21i | −0.440012 | + | 1.01842i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.63160e21i | 1.39009i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.11235e20 | −0.212542 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.85211e20 | 0.0936661 | 0.0468330 | − | 0.998903i | \(-0.485087\pi\) | ||||
0.0468330 | + | 0.998903i | \(0.485087\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.95967e20i | 0.492885i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.26773e21 | − | 1.41183e21i | −1.58256 | − | 0.683748i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1.94142e21i | − | 0.920182i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.39006e21 | −2.96433 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.53115e21 | −0.695236 | −0.347618 | − | 0.937636i | \(-0.613009\pi\) | ||||
−0.347618 | + | 0.937636i | \(0.613009\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 2.95056e21i | − | 1.31141i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.13226e21 | − | 1.78535e21i | −1.79791 | − | 0.776792i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 2.56800e20i | − | 0.109383i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.28361e19 | −0.00535287 | −0.00267643 | − | 0.999996i | \(-0.500852\pi\) | ||||
−0.00267643 | + | 0.999996i | \(0.500852\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.67633e21 | 3.13423 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.28717e19i | 0.0371289i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.83886e20 | + | 6.57066e20i | −0.111135 | + | 0.257225i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.05502e21i | 0.787811i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.14657e21 | 1.18133 | 0.590665 | − | 0.806917i | \(-0.298866\pi\) | ||||
0.590665 | + | 0.806917i | \(0.298866\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.94594e21 | −0.715508 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.37955e21i | 3.01775i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.53440e21 | + | 1.63019e21i | 0.541259 | + | 0.575047i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 4.52609e21i | − | 1.56392i | −0.623327 | − | 0.781962i | \(-0.714219\pi\) | ||
0.623327 | − | 0.781962i | \(-0.285781\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.31386e21 | 0.444726 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.09186e21 | −1.68848 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.68116e21i | 0.871048i | 0.900177 | + | 0.435524i | \(0.143437\pi\) | ||||
−0.900177 | + | 0.435524i | \(0.856563\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.42831e21 | + | 3.30587e21i | −0.454639 | + | 1.05228i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.64395e20i | − | 0.0512721i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.15277e21 | 0.352298 | 0.176149 | − | 0.984364i | \(-0.443636\pi\) | ||||
0.176149 | + | 0.984364i | \(0.443636\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.85807e21 | 1.15540 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.64683e21i | 0.776801i | 0.921491 | + | 0.388400i | \(0.126972\pi\) | ||||
−0.921491 | + | 0.388400i | \(0.873028\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.64372e21 | − | 2.00633e21i | −1.33565 | − | 0.577072i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 2.05759e21i | − | 0.580034i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.94493e20 | 0.247151 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.36972e21 | 1.18346 | 0.591730 | − | 0.806136i | \(-0.298445\pi\) | ||||
0.591730 | + | 0.806136i | \(0.298445\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.54716e21i | 0.676229i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.84208e18 | + | 1.22793e18i | 0.000739664 | + | 0.000319573i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 7.25274e20i | − | 0.185047i | −0.995710 | − | 0.0925237i | \(-0.970507\pi\) | ||
0.995710 | − | 0.0925237i | \(-0.0294934\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.33934e21 | −0.585168 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.04957e21 | 0.502665 | 0.251333 | − | 0.967901i | \(-0.419131\pi\) | ||||
0.251333 | + | 0.967901i | \(0.419131\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1.75597e21i | − | 0.422262i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.34315e21 | + | 1.23669e22i | −1.25990 | + | 2.91609i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.20690e20i | 0.0510290i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.52209e21 | −0.571891 | −0.285945 | − | 0.958246i | \(-0.592308\pi\) | ||||
−0.285945 | + | 0.958246i | \(0.592308\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.69931e20 | 0.104503 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.53203e21i | 0.552233i | 0.961124 | + | 0.276117i | \(0.0890476\pi\) | ||||
−0.961124 | + | 0.276117i | \(0.910952\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.38824e20 | − | 1.47490e20i | −0.0296963 | − | 0.0315501i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 7.39791e21i | − | 1.55221i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.70603e21 | 0.556932 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.53069e20 | −0.0712815 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.16157e21i | 1.61644i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.21525e20 | − | 1.67000e21i | 0.140194 | − | 0.324484i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.39343e21i | 0.265629i | 0.991141 | + | 0.132814i | \(0.0424014\pi\) | ||||
−0.991141 | + | 0.132814i | \(0.957599\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.67347e21 | 0.874102 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.95766e21 | 0.542781 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1.18102e21i | − | 0.212671i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.69085e21 | + | 1.16258e21i | 0.475483 | + | 0.205433i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 9.55241e20i | − | 0.165644i | −0.996564 | − | 0.0828220i | \(-0.973607\pi\) | ||
0.996564 | − | 0.0828220i | \(-0.0263933\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.56431e21 | −1.62762 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.56744e22 | 2.61787 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 1.45495e21i | − | 0.238496i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.91080e21 | + | 1.25762e21i | 0.468320 | + | 0.202339i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 1.18178e22i | − | 1.86631i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.73892e21 | −1.50972 | −0.754861 | − | 0.655885i | \(-0.772296\pi\) | ||||
−0.754861 | + | 0.655885i | \(0.772296\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.03949e20 | −0.0614711 | −0.0307355 | − | 0.999528i | \(-0.509785\pi\) | ||||
−0.0307355 | + | 0.999528i | \(0.509785\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 1.25362e22i | − | 1.87277i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.26076e21 | + | 7.54715e21i | −0.478230 | + | 1.10688i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 7.09724e21i | − | 1.02194i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.60513e21 | 0.933797 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.42068e22 | 1.97207 | 0.986034 | − | 0.166541i | \(-0.0532599\pi\) | ||||
0.986034 | + | 0.166541i | \(0.0532599\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 6.03911e21i | − | 0.823141i | −0.911378 | − | 0.411570i | \(-0.864980\pi\) | ||
0.911378 | − | 0.411570i | \(-0.135020\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.71513e21 | − | 3.49684e21i | 0.497243 | − | 0.468027i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1.20995e22i | − | 1.59029i | −0.606421 | − | 0.795144i | \(-0.707395\pi\) | ||
0.606421 | − | 0.795144i | \(-0.292605\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.90195e21 | −0.761792 | −0.380896 | − | 0.924618i | \(-0.624384\pi\) | ||||
−0.380896 | + | 0.924618i | \(0.624384\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.21154e22 | 2.80342 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.65160e21i | 0.952610i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.75586e21 | − | 6.37855e21i | 0.336984 | − | 0.779962i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 7.38412e20i | − | 0.0886865i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.29661e22 | −1.52966 | −0.764831 | − | 0.644231i | \(-0.777178\pi\) | ||||
−0.764831 | + | 0.644231i | \(0.777178\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.24768e21 | −0.376360 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 1.62420e22i | − | 1.84898i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.85086e21 | − | 1.66377e21i | −0.430657 | − | 0.186066i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.61717e21i | 0.507283i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.50427e20 | −0.0810029 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.18649e22 | 1.25832 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 9.05799e21i | − | 0.943874i | −0.881632 | − | 0.471937i | \(-0.843555\pi\) | ||
0.881632 | − | 0.471937i | \(-0.156445\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.72375e22 | − | 7.44750e21i | −1.76494 | − | 0.762544i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.80435e22i | − | 1.81536i | −0.419660 | − | 0.907682i | \(-0.637851\pi\) | ||
0.419660 | − | 0.907682i | \(-0.362149\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.44689e21 | 0.241916 | 0.120958 | − | 0.992658i | \(-0.461403\pi\) | ||||
0.120958 | + | 0.992658i | \(0.461403\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.78482e21 | 0.659196 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.95152e21i | 0.950185i | 0.879936 | + | 0.475093i | \(0.157585\pi\) | ||||
−0.879936 | + | 0.475093i | \(0.842415\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.36657e21 | − | 1.01066e22i | 0.409750 | − | 0.948383i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.26674e22i | 2.09054i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.17683e21 | −0.559909 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.09025e21 | −0.0971378 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.66769e22i | 3.21208i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.50254e21 | + | 2.35382e21i | −0.559786 | + | 0.202634i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.75476e22i | 1.48498i | 0.669855 | + | 0.742492i | \(0.266356\pi\) | ||||
−0.669855 | + | 0.742492i | \(0.733644\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.74787e22 | 1.45409 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.45628e22 | −1.19104 | −0.595520 | − | 0.803341i | \(-0.703054\pi\) | ||||
−0.595520 | + | 0.803341i | \(0.703054\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.28619e22i | 1.03419i | 0.855928 | + | 0.517095i | \(0.172987\pi\) | ||||
−0.855928 | + | 0.517095i | \(0.827013\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.23903e20 | − | 1.44405e21i | 0.0493222 | − | 0.114158i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1.46337e22i | − | 1.13743i | −0.822534 | − | 0.568716i | \(-0.807440\pi\) | ||
0.822534 | − | 0.568716i | \(-0.192560\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.66070e21 | 0.279770 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.58270e21 | 0.569824 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 1.33311e22i | − | 0.985102i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.37864e21 | + | 1.45975e21i | 0.245510 | + | 0.106073i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.55142e22i | 1.10863i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.86888e20 | −0.0342162 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.22809e21 | 0.430446 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 1.77949e22i | − | 1.20959i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.79895e21 | − | 1.20929e21i | −0.187125 | − | 0.0808476i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 4.06427e21i | − | 0.267256i | −0.991032 | − | 0.133628i | \(-0.957337\pi\) | ||
0.991032 | − | 0.133628i | \(-0.0426627\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.11531e21 | −0.395539 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.36749e21 | −0.405117 | −0.202558 | − | 0.979270i | \(-0.564926\pi\) | ||||
−0.202558 | + | 0.979270i | \(0.564926\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.65566e21i | 0.103619i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.33881e21 | + | 7.72780e21i | −0.205557 | + | 0.475770i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.49045e21i | 0.514234i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.93596e22 | 1.74938 | 0.874690 | − | 0.484682i | \(-0.161065\pi\) | ||||
0.874690 | + | 0.484682i | \(0.161065\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.35798e22 | 3.14090 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.34151e21i | 0.135046i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.88427e22 | + | 1.77356e22i | −1.06925 | + | 1.00643i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.63396e22i | 2.58734i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.30652e22 | 1.81658 | 0.908288 | − | 0.418347i | \(-0.137390\pi\) | ||||
0.908288 | + | 0.418347i | \(0.137390\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.06651e22 | −0.576558 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 5.87127e22i | − | 3.12334i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.29942e21 | − | 9.95117e21i | 0.225073 | − | 0.520939i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.47429e22i | 1.78986i | 0.446205 | + | 0.894931i | \(0.352775\pi\) | ||||
−0.446205 | + | 0.894931i | \(0.647225\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.04852e21 | −0.103860 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.80935e21 | −0.140179 | −0.0700897 | − | 0.997541i | \(-0.522329\pi\) | ||||
−0.0700897 | + | 0.997541i | \(0.522329\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.08816e22i | 0.534387i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.31434e22 | − | 9.99915e21i | −1.11864 | − | 0.483308i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.11666e21i | 0.433722i | 0.976203 | + | 0.216861i | \(0.0695818\pi\) | ||||
−0.976203 | + | 0.216861i | \(0.930418\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.64903e21 | −0.451842 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.79419e22 | −1.74890 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.41863e22i | 0.643682i | 0.946794 | + | 0.321841i | \(0.104302\pi\) | ||||
−0.946794 | + | 0.321841i | \(0.895698\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.93338e22 | − | 1.26737e22i | −1.31022 | − | 0.566082i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 1.22642e22i | − | 0.539262i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.52578e22 | −0.660471 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.34212e22 | −0.998123 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 2.13010e22i | − | 0.893723i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.14766e21 | + | 7.28538e21i | −0.130027 | + | 0.300952i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.40091e22i | 0.569785i | 0.958560 | + | 0.284892i | \(0.0919578\pi\) | ||||
−0.958560 | + | 0.284892i | \(0.908042\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.84299e22 | −2.33995 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.55233e22 | 1.40078 | 0.700388 | − | 0.713762i | \(-0.253010\pi\) | ||||
0.700388 | + | 0.713762i | \(0.253010\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 2.64321e22i | − | 1.02633i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.31906e22 | − | 2.46383e22i | −0.886702 | − | 0.942054i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.18841e22i | 0.823985i | 0.911187 | + | 0.411993i | \(0.135167\pi\) | ||||
−0.911187 | + | 0.411993i | \(0.864833\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.26126e22 | −0.467663 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.18157e22 | −1.52694 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.12627e21i | 0.220315i | 0.993914 | + | 0.110158i | \(0.0351356\pi\) | ||||
−0.993914 | + | 0.110158i | \(0.964864\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.76285e22 | − | 4.08018e22i | 0.624372 | − | 1.44513i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 3.34251e22i | − | 1.16599i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.85397e22 | 0.980568 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.50331e22 | −1.18557 | −0.592784 | − | 0.805361i | \(-0.701971\pi\) | ||||
−0.592784 | + | 0.805361i | \(0.701971\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.06956e22i | 1.35652i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.80876e22 | + | 1.21353e22i | 0.922236 | + | 0.398453i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.84796e22i | 1.24456i | 0.782793 | + | 0.622282i | \(0.213794\pi\) | ||||
−0.782793 | + | 0.622282i | \(0.786206\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.43364e22 | −3.00565 |
(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 | 80.16.c.a.49.1 | 6 | ||
4.3 | odd | 2 | 5.16.b.a.4.4 | yes | 6 | ||
5.4 | even | 2 | inner | 80.16.c.a.49.6 | 6 | ||
12.11 | even | 2 | 45.16.b.b.19.3 | 6 | |||
20.3 | even | 4 | 25.16.a.f.1.4 | 6 | |||
20.7 | even | 4 | 25.16.a.f.1.3 | 6 | |||
20.19 | odd | 2 | 5.16.b.a.4.3 | ✓ | 6 | ||
60.59 | even | 2 | 45.16.b.b.19.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.16.b.a.4.3 | ✓ | 6 | 20.19 | odd | 2 | ||
5.16.b.a.4.4 | yes | 6 | 4.3 | odd | 2 | ||
25.16.a.f.1.3 | 6 | 20.7 | even | 4 | |||
25.16.a.f.1.4 | 6 | 20.3 | even | 4 | |||
45.16.b.b.19.3 | 6 | 12.11 | even | 2 | |||
45.16.b.b.19.4 | 6 | 60.59 | even | 2 | |||
80.16.c.a.49.1 | 6 | 1.1 | even | 1 | trivial | ||
80.16.c.a.49.6 | 6 | 5.4 | even | 2 | inner |