Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,34,Mod(24,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 34, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.24");
S:= CuspForms(chi, 34);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 34 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.b (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: | \(172.457072203\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 20265063301 x^{10} + \cdots + 39\!\cdots\!96 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{47}\cdot 3^{10}\cdot 5^{36}\cdot 7^{2}\cdot 11^{4} \) |
Twist minimal: | no (minimal twist has level 5) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 24.6 | ||
Root | \(-9129.22i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.24 |
Dual form | 25.34.b.c.24.7 |
$q$-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 \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 18258.4i | − 0.197001i | −0.995137 | − | 0.0985006i | \(-0.968595\pi\) | ||||
0.995137 | − | 0.0985006i | \(-0.0314046\pi\) | |||||||
\(3\) | 3.67420e7i | 0.492791i | 0.969169 | + | 0.246395i | \(0.0792462\pi\) | ||||
−0.969169 | + | 0.246395i | \(0.920754\pi\) | |||||||
\(4\) | 8.25656e9 | 0.961191 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 6.70852e11 | 0.0970803 | ||||||||
\(7\) | − 1.51681e13i | − 0.172510i | −0.996273 | − | 0.0862550i | \(-0.972510\pi\) | ||||
0.996273 | − | 0.0862550i | \(-0.0274900\pi\) | |||||||
\(8\) | − 3.07591e14i | − 0.386357i | ||||||||
\(9\) | 4.20908e15 | 0.757157 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.61480e17 | −1.71577 | −0.857887 | − | 0.513839i | \(-0.828223\pi\) | ||||
−0.857887 | + | 0.513839i | \(0.828223\pi\) | |||||||
\(12\) | 3.03363e17i | 0.473666i | ||||||||
\(13\) | 3.70714e17i | 0.154516i | 0.997011 | + | 0.0772580i | \(0.0246165\pi\) | ||||
−0.997011 | + | 0.0772580i | \(0.975383\pi\) | |||||||
\(14\) | −2.76946e17 | −0.0339847 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 6.53072e19 | 0.885078 | ||||||||
\(17\) | − 3.71730e20i | − 1.85276i | −0.376585 | − | 0.926382i | \(-0.622902\pi\) | ||||
0.376585 | − | 0.926382i | \(-0.377098\pi\) | |||||||
\(18\) | − 7.68513e19i | − 0.149161i | ||||||||
\(19\) | −1.42255e21 | −1.13145 | −0.565723 | − | 0.824595i | \(-0.691403\pi\) | ||||
−0.565723 | + | 0.824595i | \(0.691403\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.57308e20 | 0.0850113 | ||||||||
\(22\) | 4.77422e21i | 0.338009i | ||||||||
\(23\) | 3.26990e22i | 1.11180i | 0.831250 | + | 0.555898i | \(0.187626\pi\) | ||||
−0.831250 | + | 0.555898i | \(0.812374\pi\) | |||||||
\(24\) | 1.13015e22 | 0.190393 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.76865e21 | 0.0304398 | ||||||||
\(27\) | 3.58901e23i | 0.865911i | ||||||||
\(28\) | − 1.25237e23i | − 0.165815i | ||||||||
\(29\) | −6.41343e23 | −0.475909 | −0.237954 | − | 0.971276i | \(-0.576477\pi\) | ||||
−0.237954 | + | 0.971276i | \(0.576477\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.44554e23 | −0.0356914 | −0.0178457 | − | 0.999841i | \(-0.505681\pi\) | ||||
−0.0178457 | + | 0.999841i | \(0.505681\pi\) | |||||||
\(32\) | − 3.83459e24i | − 0.560718i | ||||||||
\(33\) | − 9.60732e24i | − 0.845517i | ||||||||
\(34\) | −6.78720e24 | −0.364997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.47526e25 | 0.727772 | ||||||||
\(37\) | 1.34909e26i | 1.79768i | 0.438273 | + | 0.898842i | \(0.355590\pi\) | ||||
−0.438273 | + | 0.898842i | \(0.644410\pi\) | |||||||
\(38\) | 2.59736e25i | 0.222896i | ||||||||
\(39\) | −1.36208e25 | −0.0761440 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.37865e26 | 1.56241 | 0.781205 | − | 0.624275i | \(-0.214605\pi\) | ||||
0.781205 | + | 0.624275i | \(0.214605\pi\) | |||||||
\(42\) | − 1.01756e25i | − 0.0167473i | ||||||||
\(43\) | − 3.37044e26i | − 0.376233i | −0.982147 | − | 0.188117i | \(-0.939762\pi\) | ||||
0.982147 | − | 0.188117i | \(-0.0602383\pi\) | |||||||
\(44\) | −2.15893e27 | −1.64919 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.97033e26 | 0.219025 | ||||||||
\(47\) | 3.12828e27i | 0.804807i | 0.915462 | + | 0.402403i | \(0.131825\pi\) | ||||
−0.915462 | + | 0.402403i | \(0.868175\pi\) | |||||||
\(48\) | 2.39952e27i | 0.436158i | ||||||||
\(49\) | 7.50092e27 | 0.970240 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.36581e28 | 0.913025 | ||||||||
\(52\) | 3.06082e27i | 0.148519i | ||||||||
\(53\) | 4.06250e28i | 1.43960i | 0.694182 | + | 0.719799i | \(0.255766\pi\) | ||||
−0.694182 | + | 0.719799i | \(0.744234\pi\) | |||||||
\(54\) | 6.55298e27 | 0.170585 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.66557e27 | −0.0666504 | ||||||||
\(57\) | − 5.22675e28i | − 0.557566i | ||||||||
\(58\) | 1.17099e28i | 0.0937545i | ||||||||
\(59\) | 8.77955e28 | 0.530169 | 0.265084 | − | 0.964225i | \(-0.414600\pi\) | ||||
0.265084 | + | 0.964225i | \(0.414600\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.84902e28 | −0.0644168 | −0.0322084 | − | 0.999481i | \(-0.510254\pi\) | ||||
−0.0322084 | + | 0.999481i | \(0.510254\pi\) | |||||||
\(62\) | 2.63933e27i | 0.00703124i | ||||||||
\(63\) | − 6.38439e28i | − 0.130617i | ||||||||
\(64\) | 4.90971e29 | 0.774616 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.75415e29 | −0.166568 | ||||||||
\(67\) | 7.69531e29i | 0.570154i | 0.958505 | + | 0.285077i | \(0.0920192\pi\) | ||||
−0.958505 | + | 0.285077i | \(0.907981\pi\) | |||||||
\(68\) | − 3.06921e30i | − 1.78086i | ||||||||
\(69\) | −1.20143e30 | −0.547883 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.72988e30 | 0.776929 | 0.388464 | − | 0.921464i | \(-0.373006\pi\) | ||||
0.388464 | + | 0.921464i | \(0.373006\pi\) | |||||||
\(72\) | − 1.29468e30i | − 0.292533i | ||||||||
\(73\) | − 4.44452e30i | − 0.799831i | −0.916552 | − | 0.399915i | \(-0.869040\pi\) | ||||
0.916552 | − | 0.399915i | \(-0.130960\pi\) | |||||||
\(74\) | 2.46323e30 | 0.354146 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.17454e31 | −1.08754 | ||||||||
\(77\) | 3.96617e30i | 0.295988i | ||||||||
\(78\) | 2.48694e29i | 0.0150005i | ||||||||
\(79\) | 1.16758e31 | 0.570743 | 0.285371 | − | 0.958417i | \(-0.407883\pi\) | ||||
0.285371 | + | 0.958417i | \(0.407883\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.02118e31 | 0.330445 | ||||||||
\(82\) | − 1.16464e31i | − 0.307796i | ||||||||
\(83\) | 4.84088e31i | 1.04746i | 0.851886 | + | 0.523728i | \(0.175459\pi\) | ||||
−0.851886 | + | 0.523728i | \(0.824541\pi\) | |||||||
\(84\) | 4.60145e30 | 0.0817121 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.15390e30 | −0.0741184 | ||||||||
\(87\) | − 2.35643e31i | − 0.234523i | ||||||||
\(88\) | 8.04290e31i | 0.662901i | ||||||||
\(89\) | −1.18101e32 | −0.807831 | −0.403915 | − | 0.914796i | \(-0.632351\pi\) | ||||
−0.403915 | + | 0.914796i | \(0.632351\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.62303e30 | 0.0266555 | ||||||||
\(92\) | 2.69981e32i | 1.06865i | ||||||||
\(93\) | − 5.31122e30i | − 0.0175884i | ||||||||
\(94\) | 5.71176e31 | 0.158548 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.40891e32 | 0.276317 | ||||||||
\(97\) | − 2.71846e31i | − 0.0449355i | −0.999748 | − | 0.0224678i | \(-0.992848\pi\) | ||||
0.999748 | − | 0.0224678i | \(-0.00715231\pi\) | |||||||
\(98\) | − 1.36955e32i | − 0.191138i | ||||||||
\(99\) | −1.10059e33 | −1.29911 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.30031e33 | −1.10343 | −0.551714 | − | 0.834033i | \(-0.686026\pi\) | ||||
−0.551714 | + | 0.834033i | \(0.686026\pi\) | |||||||
\(102\) | − 2.49376e32i | − 0.179867i | ||||||||
\(103\) | − 1.73233e33i | − 1.06369i | −0.846841 | − | 0.531846i | \(-0.821498\pi\) | ||||
0.846841 | − | 0.531846i | \(-0.178502\pi\) | |||||||
\(104\) | 1.14028e32 | 0.0596983 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.41749e32 | 0.283603 | ||||||||
\(107\) | 3.72062e32i | 0.121838i | 0.998143 | + | 0.0609191i | \(0.0194032\pi\) | ||||
−0.998143 | + | 0.0609191i | \(0.980597\pi\) | |||||||
\(108\) | 2.96329e33i | 0.832305i | ||||||||
\(109\) | 5.92448e33 | 1.42927 | 0.714633 | − | 0.699500i | \(-0.246594\pi\) | ||||
0.714633 | + | 0.699500i | \(0.246594\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.95684e33 | −0.885882 | ||||||||
\(112\) | − 9.90588e32i | − 0.152685i | ||||||||
\(113\) | − 2.74196e33i | − 0.364978i | −0.983208 | − | 0.182489i | \(-0.941585\pi\) | ||||
0.983208 | − | 0.182489i | \(-0.0584154\pi\) | |||||||
\(114\) | −9.54322e32 | −0.109841 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.29529e33 | −0.457439 | ||||||||
\(117\) | 1.56036e33i | 0.116993i | ||||||||
\(118\) | − 1.60301e33i | − 0.104444i | ||||||||
\(119\) | −5.63844e33 | −0.319620 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.51469e34 | 1.94388 | ||||||||
\(122\) | 3.37602e32i | 0.0126902i | ||||||||
\(123\) | 2.34364e34i | 0.769941i | ||||||||
\(124\) | −1.19352e33 | −0.0343062 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.16569e33 | −0.0257317 | ||||||||
\(127\) | 7.72774e34i | 1.49724i | 0.663000 | + | 0.748619i | \(0.269283\pi\) | ||||
−0.663000 | + | 0.748619i | \(0.730717\pi\) | |||||||
\(128\) | − 4.19033e34i | − 0.713318i | ||||||||
\(129\) | 1.23837e34 | 0.185404 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.77088e34 | −0.205690 | −0.102845 | − | 0.994697i | \(-0.532795\pi\) | ||||
−0.102845 | + | 0.994697i | \(0.532795\pi\) | |||||||
\(132\) | − 7.93235e34i | − 0.812703i | ||||||||
\(133\) | 2.15774e34i | 0.195186i | ||||||||
\(134\) | 1.40504e34 | 0.112321 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.14341e35 | −0.715828 | ||||||||
\(137\) | − 1.26744e35i | − 0.703133i | −0.936163 | − | 0.351567i | \(-0.885649\pi\) | ||||
0.936163 | − | 0.351567i | \(-0.114351\pi\) | |||||||
\(138\) | 2.19362e34i | 0.107934i | ||||||||
\(139\) | −1.04160e35 | −0.454941 | −0.227471 | − | 0.973785i | \(-0.573046\pi\) | ||||
−0.227471 | + | 0.973785i | \(0.573046\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.14940e35 | −0.396601 | ||||||||
\(142\) | − 4.98434e34i | − 0.153056i | ||||||||
\(143\) | − 9.69344e34i | − 0.265114i | ||||||||
\(144\) | 2.74884e35 | 0.670143 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.11501e34 | −0.157568 | ||||||||
\(147\) | 2.75599e35i | 0.478125i | ||||||||
\(148\) | 1.11389e36i | 1.72792i | ||||||||
\(149\) | 3.09463e35 | 0.429572 | 0.214786 | − | 0.976661i | \(-0.431095\pi\) | ||||
0.214786 | + | 0.976661i | \(0.431095\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.12720e36 | 1.25569 | 0.627844 | − | 0.778340i | \(-0.283938\pi\) | ||||
0.627844 | + | 0.778340i | \(0.283938\pi\) | |||||||
\(152\) | 4.37564e35i | 0.437142i | ||||||||
\(153\) | − 1.56464e36i | − 1.40283i | ||||||||
\(154\) | 7.24160e34 | 0.0583100 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.12461e35 | −0.0731889 | ||||||||
\(157\) | 1.58631e36i | 0.929061i | 0.885557 | + | 0.464530i | \(0.153777\pi\) | ||||
−0.885557 | + | 0.464530i | \(0.846223\pi\) | |||||||
\(158\) | − 2.13182e35i | − 0.112437i | ||||||||
\(159\) | −1.49264e36 | −0.709421 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.95982e35 | 0.191796 | ||||||||
\(162\) | − 1.86451e35i | − 0.0650979i | ||||||||
\(163\) | 3.56599e36i | 1.12483i | 0.826857 | + | 0.562413i | \(0.190127\pi\) | ||||
−0.826857 | + | 0.562413i | \(0.809873\pi\) | |||||||
\(164\) | 5.26657e36 | 1.50177 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.83869e35 | 0.206350 | ||||||||
\(167\) | 6.77798e36i | 1.43311i | 0.697532 | + | 0.716553i | \(0.254281\pi\) | ||||
−0.697532 | + | 0.716553i | \(0.745719\pi\) | |||||||
\(168\) | − 1.71423e35i | − 0.0328447i | ||||||||
\(169\) | 5.61870e36 | 0.976125 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.98764e36 | −0.856683 | ||||||||
\(172\) | − 2.78283e36i | − 0.361632i | ||||||||
\(173\) | − 1.72200e36i | − 0.203364i | −0.994817 | − | 0.101682i | \(-0.967578\pi\) | ||||
0.994817 | − | 0.101682i | \(-0.0324224\pi\) | |||||||
\(174\) | −4.30247e35 | −0.0462014 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.70766e37 | −1.51859 | ||||||||
\(177\) | 3.22578e36i | 0.261262i | ||||||||
\(178\) | 2.15635e36i | 0.159144i | ||||||||
\(179\) | 6.69163e36 | 0.450253 | 0.225127 | − | 0.974330i | \(-0.427720\pi\) | ||||
0.225127 | + | 0.974330i | \(0.427720\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.34636e37 | 0.754163 | 0.377082 | − | 0.926180i | \(-0.376928\pi\) | ||||
0.377082 | + | 0.926180i | \(0.376928\pi\) | |||||||
\(182\) | − 1.02668e35i | − 0.00525117i | ||||||||
\(183\) | − 6.79367e35i | − 0.0317440i | ||||||||
\(184\) | 1.00579e37 | 0.429550 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −9.69745e34 | −0.00346493 | ||||||||
\(187\) | 9.72001e37i | 3.17892i | ||||||||
\(188\) | 2.58289e37i | 0.773573i | ||||||||
\(189\) | 5.44386e36 | 0.149378 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.65942e36 | −0.153598 | −0.0767990 | − | 0.997047i | \(-0.524470\pi\) | ||||
−0.0767990 | + | 0.997047i | \(0.524470\pi\) | |||||||
\(192\) | 1.80393e37i | 0.381723i | ||||||||
\(193\) | 5.05982e37i | 0.982742i | 0.870950 | + | 0.491371i | \(0.163504\pi\) | ||||
−0.870950 | + | 0.491371i | \(0.836496\pi\) | |||||||
\(194\) | −4.96349e35 | −0.00885235 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.19318e37 | 0.932586 | ||||||||
\(197\) | 2.33016e37i | 0.322621i | 0.986904 | + | 0.161311i | \(0.0515721\pi\) | ||||
−0.986904 | + | 0.161311i | \(0.948428\pi\) | |||||||
\(198\) | 2.00951e37i | 0.255926i | ||||||||
\(199\) | 1.24079e38 | 1.45420 | 0.727100 | − | 0.686531i | \(-0.240868\pi\) | ||||
0.727100 | + | 0.686531i | \(0.240868\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.82742e37 | −0.280967 | ||||||||
\(202\) | 2.37416e37i | 0.217377i | ||||||||
\(203\) | 9.72798e36i | 0.0820990i | ||||||||
\(204\) | 1.12769e38 | 0.877591 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.16296e37 | −0.209549 | ||||||||
\(207\) | 1.37633e38i | 0.841805i | ||||||||
\(208\) | 2.42103e37i | 0.136759i | ||||||||
\(209\) | 3.71970e38 | 1.94130 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.15498e38 | −0.961133 | −0.480567 | − | 0.876958i | \(-0.659569\pi\) | ||||
−0.480567 | + | 0.876958i | \(0.659569\pi\) | |||||||
\(212\) | 3.35423e38i | 1.38373i | ||||||||
\(213\) | 1.00301e38i | 0.382863i | ||||||||
\(214\) | 6.79328e36 | 0.0240023 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.10395e38 | 0.334550 | ||||||||
\(217\) | 2.19262e36i | 0.00615711i | ||||||||
\(218\) | − 1.08172e38i | − 0.281567i | ||||||||
\(219\) | 1.63301e38 | 0.394149 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.37805e38 | 0.286282 | ||||||||
\(222\) | 9.05042e37i | 0.174520i | ||||||||
\(223\) | 1.94520e37i | 0.0348285i | 0.999848 | + | 0.0174142i | \(0.00554340\pi\) | ||||
−0.999848 | + | 0.0174142i | \(0.994457\pi\) | |||||||
\(224\) | −5.81636e37 | −0.0967294 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.00639e37 | −0.0719011 | ||||||||
\(227\) | 1.37345e39i | 1.83395i | 0.398947 | + | 0.916974i | \(0.369376\pi\) | ||||
−0.398947 | + | 0.916974i | \(0.630624\pi\) | |||||||
\(228\) | − 4.31550e38i | − 0.535927i | ||||||||
\(229\) | 3.69693e38 | 0.427126 | 0.213563 | − | 0.976929i | \(-0.431493\pi\) | ||||
0.213563 | + | 0.976929i | \(0.431493\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.45725e38 | −0.145860 | ||||||||
\(232\) | 1.97271e38i | 0.183871i | ||||||||
\(233\) | 2.02428e39i | 1.75751i | 0.477275 | + | 0.878754i | \(0.341625\pi\) | ||||
−0.477275 | + | 0.878754i | \(0.658375\pi\) | |||||||
\(234\) | 2.84898e37 | 0.0230477 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.24889e38 | 0.509593 | ||||||||
\(237\) | 4.28994e38i | 0.281257i | ||||||||
\(238\) | 1.02949e38i | 0.0629655i | ||||||||
\(239\) | 6.31944e38 | 0.360673 | 0.180336 | − | 0.983605i | \(-0.442281\pi\) | ||||
0.180336 | + | 0.983605i | \(0.442281\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.82829e39 | −0.909420 | −0.454710 | − | 0.890640i | \(-0.650257\pi\) | ||||
−0.454710 | + | 0.890640i | \(0.650257\pi\) | |||||||
\(242\) | − 8.24311e38i | − 0.382946i | ||||||||
\(243\) | 2.37036e39i | 1.02875i | ||||||||
\(244\) | −1.52665e38 | −0.0619168 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.27913e38 | 0.151679 | ||||||||
\(247\) | − 5.27360e38i | − 0.174826i | ||||||||
\(248\) | 4.44636e37i | 0.0137896i | ||||||||
\(249\) | −1.77864e39 | −0.516177 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.17903e39 | −0.554174 | −0.277087 | − | 0.960845i | \(-0.589369\pi\) | ||||
−0.277087 | + | 0.960845i | \(0.589369\pi\) | |||||||
\(252\) | − 5.27131e38i | − 0.125548i | ||||||||
\(253\) | − 8.55015e39i | − 1.90759i | ||||||||
\(254\) | 1.41096e39 | 0.294958 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.45232e39 | 0.634091 | ||||||||
\(257\) | − 1.48926e39i | − 0.256492i | −0.991742 | − | 0.128246i | \(-0.959065\pi\) | ||||
0.991742 | − | 0.128246i | \(-0.0409348\pi\) | |||||||
\(258\) | − 2.26107e38i | − 0.0365249i | ||||||||
\(259\) | 2.04632e39 | 0.310118 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.69947e39 | −0.360338 | ||||||||
\(262\) | 3.23335e38i | 0.0405211i | ||||||||
\(263\) | − 1.17319e40i | − 1.38069i | −0.723479 | − | 0.690346i | \(-0.757458\pi\) | ||||
0.723479 | − | 0.690346i | \(-0.242542\pi\) | |||||||
\(264\) | −2.95512e39 | −0.326671 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.93970e38 | 0.0384518 | ||||||||
\(267\) | − 4.33929e39i | − 0.398091i | ||||||||
\(268\) | 6.35369e39i | 0.548027i | ||||||||
\(269\) | −2.30936e40 | −1.87318 | −0.936590 | − | 0.350428i | \(-0.886036\pi\) | ||||
−0.936590 | + | 0.350428i | \(0.886036\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.16176e40 | 1.55172 | 0.775861 | − | 0.630903i | \(-0.217316\pi\) | ||||
0.775861 | + | 0.630903i | \(0.217316\pi\) | |||||||
\(272\) | − 2.42766e40i | − 1.63984i | ||||||||
\(273\) | 2.06602e38i | 0.0131356i | ||||||||
\(274\) | −2.31414e39 | −0.138518 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −9.91967e39 | −0.526620 | ||||||||
\(277\) | − 1.86721e40i | − 0.933847i | −0.884298 | − | 0.466924i | \(-0.845362\pi\) | ||||
0.884298 | − | 0.466924i | \(-0.154638\pi\) | |||||||
\(278\) | 1.90179e39i | 0.0896239i | ||||||||
\(279\) | −6.08441e38 | −0.0270240 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.80173e39 | −0.268513 | −0.134256 | − | 0.990947i | \(-0.542865\pi\) | ||||
−0.134256 | + | 0.990947i | \(0.542865\pi\) | |||||||
\(282\) | 2.09862e39i | 0.0781309i | ||||||||
\(283\) | 3.60211e40i | 1.26497i | 0.774573 | + | 0.632485i | \(0.217965\pi\) | ||||
−0.774573 | + | 0.632485i | \(0.782035\pi\) | |||||||
\(284\) | 2.25395e40 | 0.746777 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.76987e39 | −0.0522278 | ||||||||
\(287\) | − 9.67521e39i | − 0.269531i | ||||||||
\(288\) | − 1.61401e40i | − 0.424552i | ||||||||
\(289\) | −9.79285e40 | −2.43274 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.98819e38 | 0.0221438 | ||||||||
\(292\) | − 3.66965e40i | − 0.768790i | ||||||||
\(293\) | − 6.02024e40i | − 1.19206i | −0.802962 | − | 0.596030i | \(-0.796744\pi\) | ||||
0.802962 | − | 0.596030i | \(-0.203256\pi\) | |||||||
\(294\) | 5.03201e39 | 0.0941912 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.14968e40 | 0.694547 | ||||||||
\(297\) | − 9.38457e40i | − 1.48571i | ||||||||
\(298\) | − 5.65032e39i | − 0.0846261i | ||||||||
\(299\) | −1.21220e40 | −0.171790 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.11233e39 | −0.0649040 | ||||||||
\(302\) | − 2.05809e40i | − 0.247372i | ||||||||
\(303\) | − 4.77760e40i | − 0.543759i | ||||||||
\(304\) | −9.29029e40 | −1.00142 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.85679e40 | −0.276360 | ||||||||
\(307\) | 2.05983e41i | 1.88820i | 0.329664 | + | 0.944098i | \(0.393064\pi\) | ||||
−0.329664 | + | 0.944098i | \(0.606936\pi\) | |||||||
\(308\) | 3.27469e40i | 0.284501i | ||||||||
\(309\) | 6.36493e40 | 0.524178 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.19843e41 | −0.887294 | −0.443647 | − | 0.896202i | \(-0.646316\pi\) | ||||
−0.443647 | + | 0.896202i | \(0.646316\pi\) | |||||||
\(312\) | 4.18962e39i | 0.0294188i | ||||||||
\(313\) | − 2.13282e41i | − 1.42060i | −0.703897 | − | 0.710302i | \(-0.748558\pi\) | ||||
0.703897 | − | 0.710302i | \(-0.251442\pi\) | |||||||
\(314\) | 2.89636e40 | 0.183026 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.64022e40 | 0.548593 | ||||||||
\(317\) | − 2.31538e41i | − 1.25068i | −0.780354 | − | 0.625338i | \(-0.784961\pi\) | ||||
0.780354 | − | 0.625338i | \(-0.215039\pi\) | |||||||
\(318\) | 2.72534e40i | 0.139757i | ||||||||
\(319\) | 1.67699e41 | 0.816552 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.36703e40 | −0.0600407 | ||||||||
\(322\) | − 9.05586e39i | − 0.0377840i | ||||||||
\(323\) | 5.28805e41i | 2.09630i | ||||||||
\(324\) | 8.43142e40 | 0.317620 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.51094e40 | 0.221592 | ||||||||
\(327\) | 2.17677e41i | 0.704329i | ||||||||
\(328\) | − 1.96201e41i | − 0.603647i | ||||||||
\(329\) | 4.74502e40 | 0.138837 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.27790e40 | −0.0867830 | −0.0433915 | − | 0.999058i | \(-0.513816\pi\) | ||||
−0.0433915 | + | 0.999058i | \(0.513816\pi\) | |||||||
\(332\) | 3.99690e41i | 1.00680i | ||||||||
\(333\) | 5.67844e41i | 1.36113i | ||||||||
\(334\) | 1.23755e41 | 0.282324 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.63962e40 | 0.0752416 | ||||||||
\(337\) | 5.05149e41i | 0.994321i | 0.867659 | + | 0.497160i | \(0.165624\pi\) | ||||
−0.867659 | + | 0.497160i | \(0.834376\pi\) | |||||||
\(338\) | − 1.02589e41i | − 0.192298i | ||||||||
\(339\) | 1.00745e41 | 0.179858 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.77981e40 | 0.0612383 | ||||||||
\(342\) | 1.09325e41i | 0.168767i | ||||||||
\(343\) | − 2.31040e41i | − 0.339886i | ||||||||
\(344\) | −1.03672e41 | −0.145360 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.14411e40 | −0.0400629 | ||||||||
\(347\) | 5.54748e40i | 0.0673999i | 0.999432 | + | 0.0337000i | \(0.0107291\pi\) | ||||
−0.999432 | + | 0.0337000i | \(0.989271\pi\) | |||||||
\(348\) | − 1.94560e41i | − 0.225422i | ||||||||
\(349\) | 4.36140e41 | 0.481955 | 0.240978 | − | 0.970531i | \(-0.422532\pi\) | ||||
0.240978 | + | 0.970531i | \(0.422532\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.33050e41 | −0.133797 | ||||||||
\(352\) | 1.00267e42i | 0.962065i | ||||||||
\(353\) | − 2.19124e41i | − 0.200635i | −0.994955 | − | 0.100318i | \(-0.968014\pi\) | ||||
0.994955 | − | 0.100318i | \(-0.0319859\pi\) | |||||||
\(354\) | 5.88978e40 | 0.0514689 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −9.75113e41 | −0.776479 | ||||||||
\(357\) | − 2.07168e41i | − 0.157506i | ||||||||
\(358\) | − 1.22179e41i | − 0.0887004i | ||||||||
\(359\) | 1.83249e42 | 1.27053 | 0.635264 | − | 0.772295i | \(-0.280891\pi\) | ||||
0.635264 | + | 0.772295i | \(0.280891\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.42885e41 | 0.280170 | ||||||||
\(362\) | − 2.45825e41i | − 0.148571i | ||||||||
\(363\) | 1.65879e42i | 0.957925i | ||||||||
\(364\) | 4.64269e40 | 0.0256211 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.24042e40 | −0.00625360 | ||||||||
\(367\) | 2.46022e42i | 1.18572i | 0.805304 | + | 0.592862i | \(0.202002\pi\) | ||||
−0.805304 | + | 0.592862i | \(0.797998\pi\) | |||||||
\(368\) | 2.13548e42i | 0.984026i | ||||||||
\(369\) | 2.68483e42 | 1.18299 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.16205e41 | 0.248345 | ||||||||
\(372\) | − 4.38524e40i | − 0.0169058i | ||||||||
\(373\) | − 9.17264e41i | − 0.338297i | −0.985591 | − | 0.169149i | \(-0.945898\pi\) | ||||
0.985591 | − | 0.169149i | \(-0.0541018\pi\) | |||||||
\(374\) | 1.77472e42 | 0.626251 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.62231e41 | 0.310942 | ||||||||
\(377\) | − 2.37755e41i | − 0.0735355i | ||||||||
\(378\) | − 9.93964e40i | − 0.0294277i | ||||||||
\(379\) | −5.49346e42 | −1.55704 | −0.778518 | − | 0.627622i | \(-0.784028\pi\) | ||||
−0.778518 | + | 0.627622i | \(0.784028\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.83933e42 | −0.737825 | ||||||||
\(382\) | 1.21591e41i | 0.0302590i | ||||||||
\(383\) | − 2.70725e42i | − 0.645281i | −0.946522 | − | 0.322640i | \(-0.895430\pi\) | ||||
0.946522 | − | 0.322640i | \(-0.104570\pi\) | |||||||
\(384\) | 1.53961e42 | 0.351517 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.23844e41 | 0.193601 | ||||||||
\(387\) | − 1.41865e42i | − 0.284868i | ||||||||
\(388\) | − 2.24452e41i | − 0.0431916i | ||||||||
\(389\) | −5.33079e42 | −0.983157 | −0.491579 | − | 0.870833i | \(-0.663580\pi\) | ||||
−0.491579 | + | 0.870833i | \(0.663580\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.21552e43 | 2.05990 | ||||||||
\(392\) | − 2.30721e42i | − 0.374859i | ||||||||
\(393\) | − 6.50657e41i | − 0.101362i | ||||||||
\(394\) | 4.25451e41 | 0.0635568 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −9.08712e42 | −1.24869 | ||||||||
\(397\) | 8.08784e42i | 1.06608i | 0.846091 | + | 0.533039i | \(0.178950\pi\) | ||||
−0.846091 | + | 0.533039i | \(0.821050\pi\) | |||||||
\(398\) | − 2.26550e42i | − 0.286479i | ||||||||
\(399\) | −7.92799e41 | −0.0961857 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.16113e43 | −1.29717 | −0.648587 | − | 0.761140i | \(-0.724640\pi\) | ||||
−0.648587 | + | 0.761140i | \(0.724640\pi\) | |||||||
\(402\) | 5.16242e41i | 0.0553507i | ||||||||
\(403\) | − 5.35882e40i | − 0.00551488i | ||||||||
\(404\) | −1.07361e43 | −1.06061 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.77618e41 | 0.0161736 | ||||||||
\(407\) | − 3.52761e43i | − 3.08442i | ||||||||
\(408\) | − 4.20111e42i | − 0.352753i | ||||||||
\(409\) | −4.40488e42 | −0.355222 | −0.177611 | − | 0.984101i | \(-0.556837\pi\) | ||||
−0.177611 | + | 0.984101i | \(0.556837\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.65683e42 | 0.346498 | ||||||||
\(412\) | − 1.43031e43i | − 1.02241i | ||||||||
\(413\) | − 1.33169e42i | − 0.0914594i | ||||||||
\(414\) | 2.51296e42 | 0.165836 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.42154e42 | 0.0866399 | ||||||||
\(417\) | − 3.82704e42i | − 0.224191i | ||||||||
\(418\) | − 6.79158e42i | − 0.382439i | ||||||||
\(419\) | −2.34926e43 | −1.27174 | −0.635871 | − | 0.771796i | \(-0.719359\pi\) | ||||
−0.635871 | + | 0.771796i | \(0.719359\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.10149e42 | −0.205252 | −0.102626 | − | 0.994720i | \(-0.532724\pi\) | ||||
−0.102626 | + | 0.994720i | \(0.532724\pi\) | |||||||
\(422\) | 3.93466e42i | 0.189344i | ||||||||
\(423\) | 1.31672e43i | 0.609365i | ||||||||
\(424\) | 1.24959e43 | 0.556199 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.83135e42 | 0.0754245 | ||||||||
\(427\) | 2.80461e41i | 0.0111125i | ||||||||
\(428\) | 3.07196e42i | 0.117110i | ||||||||
\(429\) | 3.56157e42 | 0.130646 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.92923e43 | 0.655404 | 0.327702 | − | 0.944781i | \(-0.393726\pi\) | ||||
0.327702 | + | 0.944781i | \(0.393726\pi\) | |||||||
\(432\) | 2.34389e43i | 0.766398i | ||||||||
\(433\) | − 1.20050e43i | − 0.377843i | −0.981992 | − | 0.188922i | \(-0.939501\pi\) | ||||
0.981992 | − | 0.188922i | \(-0.0604992\pi\) | |||||||
\(434\) | 4.00338e40 | 0.00121296 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.89159e43 | 1.37380 | ||||||||
\(437\) | − 4.65160e43i | − 1.25794i | ||||||||
\(438\) | − 2.98162e42i | − 0.0776478i | ||||||||
\(439\) | −3.55254e43 | −0.890993 | −0.445496 | − | 0.895284i | \(-0.646973\pi\) | ||||
−0.445496 | + | 0.895284i | \(0.646973\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.15720e43 | 0.734625 | ||||||||
\(442\) | − 2.51611e42i | − 0.0563978i | ||||||||
\(443\) | − 4.50074e43i | − 0.971901i | −0.873986 | − | 0.485951i | \(-0.838474\pi\) | ||||
0.873986 | − | 0.485951i | \(-0.161526\pi\) | |||||||
\(444\) | −4.09265e43 | −0.851501 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.55163e41 | 0.00686124 | ||||||||
\(447\) | 1.13703e43i | 0.211689i | ||||||||
\(448\) | − 7.44711e42i | − 0.133629i | ||||||||
\(449\) | 4.48522e43 | 0.775745 | 0.387872 | − | 0.921713i | \(-0.373210\pi\) | ||||
0.387872 | + | 0.921713i | \(0.373210\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.66789e44 | −2.68074 | ||||||||
\(452\) | − 2.26392e43i | − 0.350814i | ||||||||
\(453\) | 4.14156e43i | 0.618791i | ||||||||
\(454\) | 2.50771e43 | 0.361290 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.60770e43 | −0.215419 | ||||||||
\(457\) | 5.99465e43i | 0.774723i | 0.921928 | + | 0.387362i | \(0.126614\pi\) | ||||
−0.921928 | + | 0.387362i | \(0.873386\pi\) | |||||||
\(458\) | − 6.75002e42i | − 0.0841442i | ||||||||
\(459\) | 1.33414e44 | 1.60433 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.64117e43 | 0.407546 | 0.203773 | − | 0.979018i | \(-0.434680\pi\) | ||||
0.203773 | + | 0.979018i | \(0.434680\pi\) | |||||||
\(462\) | 2.66071e42i | 0.0287346i | ||||||||
\(463\) | 4.93497e43i | 0.514278i | 0.966374 | + | 0.257139i | \(0.0827798\pi\) | ||||
−0.966374 | + | 0.257139i | \(0.917220\pi\) | |||||||
\(464\) | −4.18844e43 | −0.421216 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.69601e43 | 0.346231 | ||||||||
\(467\) | 6.19636e43i | 0.560284i | 0.959959 | + | 0.280142i | \(0.0903815\pi\) | ||||
−0.959959 | + | 0.280142i | \(0.909619\pi\) | |||||||
\(468\) | 1.28833e43i | 0.112452i | ||||||||
\(469\) | 1.16723e43 | 0.0983572 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.82843e43 | −0.457832 | ||||||||
\(472\) | − 2.70051e43i | − 0.204834i | ||||||||
\(473\) | 8.81305e43i | 0.645531i | ||||||||
\(474\) | 7.83275e42 | 0.0554079 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.65542e43 | −0.307216 | ||||||||
\(477\) | 1.70994e44i | 1.09000i | ||||||||
\(478\) | − 1.15383e43i | − 0.0710530i | ||||||||
\(479\) | −1.65648e44 | −0.985483 | −0.492741 | − | 0.870176i | \(-0.664005\pi\) | ||||
−0.492741 | + | 0.870176i | \(0.664005\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.00127e43 | −0.277771 | ||||||||
\(482\) | 3.33818e43i | 0.179157i | ||||||||
\(483\) | 1.82234e43i | 0.0945152i | ||||||||
\(484\) | 3.72758e44 | 1.86844 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 4.32790e43 | 0.202665 | ||||||||
\(487\) | 3.41088e44i | 1.54397i | 0.635642 | + | 0.771984i | \(0.280736\pi\) | ||||
−0.635642 | + | 0.771984i | \(0.719264\pi\) | |||||||
\(488\) | 5.68741e42i | 0.0248879i | ||||||||
\(489\) | −1.31022e44 | −0.554303 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.35160e44 | 1.72109 | 0.860547 | − | 0.509371i | \(-0.170122\pi\) | ||||
0.860547 | + | 0.509371i | \(0.170122\pi\) | |||||||
\(492\) | 1.93505e44i | 0.740060i | ||||||||
\(493\) | 2.38406e44i | 0.881747i | ||||||||
\(494\) | −9.62876e42 | −0.0344410 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.44044e42 | −0.0315896 | ||||||||
\(497\) | − 4.14072e43i | − 0.134028i | ||||||||
\(498\) | 3.24751e43i | 0.101687i | ||||||||
\(499\) | 6.19626e44 | 1.87703 | 0.938514 | − | 0.345242i | \(-0.112203\pi\) | ||||
0.938514 | + | 0.345242i | \(0.112203\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.49037e44 | −0.706222 | ||||||||
\(502\) | 3.97856e43i | 0.109173i | ||||||||
\(503\) | − 5.28443e44i | − 1.40322i | −0.712560 | − | 0.701611i | \(-0.752464\pi\) | ||||
0.712560 | − | 0.701611i | \(-0.247536\pi\) | |||||||
\(504\) | −1.96378e43 | −0.0504648 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.56112e44 | −0.375797 | ||||||||
\(507\) | 2.06443e44i | 0.481025i | ||||||||
\(508\) | 6.38046e44i | 1.43913i | ||||||||
\(509\) | 4.72823e43 | 0.103242 | 0.0516209 | − | 0.998667i | \(-0.483561\pi\) | ||||
0.0516209 | + | 0.998667i | \(0.483561\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.74151e43 | −0.137979 | ||||||||
\(512\) | − 4.22980e44i | − 0.838235i | ||||||||
\(513\) | − 5.10556e44i | − 0.979731i | ||||||||
\(514\) | −2.71916e43 | −0.0505293 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.02247e44 | 0.178209 | ||||||||
\(517\) | − 8.17985e44i | − 1.38087i | ||||||||
\(518\) | − 3.73626e43i | − 0.0610937i | ||||||||
\(519\) | 6.32699e43 | 0.100216 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.38738e44 | −0.652203 | −0.326102 | − | 0.945335i | \(-0.605735\pi\) | ||||
−0.326102 | + | 0.945335i | \(0.605735\pi\) | |||||||
\(522\) | 4.92881e43i | 0.0709869i | ||||||||
\(523\) | 1.40016e44i | 0.195389i | 0.995216 | + | 0.0976944i | \(0.0311468\pi\) | ||||
−0.995216 | + | 0.0976944i | \(0.968853\pi\) | |||||||
\(524\) | −1.46214e44 | −0.197707 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.14205e44 | −0.271998 | ||||||||
\(527\) | 5.37351e43i | 0.0661277i | ||||||||
\(528\) | − 6.27428e44i | − 0.748349i | ||||||||
\(529\) | −2.04220e44 | −0.236091 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.69539e44 | 0.401421 | ||||||||
\(532\) | 1.78156e44i | 0.187611i | ||||||||
\(533\) | 2.36465e44i | 0.241417i | ||||||||
\(534\) | −7.92286e43 | −0.0784244 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.36701e44 | 0.220283 | ||||||||
\(537\) | 2.45864e44i | 0.221881i | ||||||||
\(538\) | 4.21653e44i | 0.369018i | ||||||||
\(539\) | −1.96134e45 | −1.66471 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.56960e45 | 1.25324 | 0.626622 | − | 0.779324i | \(-0.284437\pi\) | ||||
0.626622 | + | 0.779324i | \(0.284437\pi\) | |||||||
\(542\) | − 3.94704e44i | − 0.305691i | ||||||||
\(543\) | 4.94681e44i | 0.371645i | ||||||||
\(544\) | −1.42543e45 | −1.03888 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.77222e42 | 0.00258773 | ||||||||
\(547\) | − 2.11683e45i | − 1.40895i | −0.709730 | − | 0.704474i | \(-0.751183\pi\) | ||||
0.709730 | − | 0.704474i | \(-0.248817\pi\) | |||||||
\(548\) | − 1.04647e45i | − 0.675845i | ||||||||
\(549\) | −7.78267e43 | −0.0487736 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.12345e44 | 0.538465 | ||||||||
\(552\) | 3.69548e44i | 0.211678i | ||||||||
\(553\) | − 1.77100e44i | − 0.0984588i | ||||||||
\(554\) | −3.40922e44 | −0.183969 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.60001e44 | −0.437285 | ||||||||
\(557\) | − 1.56733e45i | − 0.773661i | −0.922151 | − | 0.386830i | \(-0.873570\pi\) | ||||
0.922151 | − | 0.386830i | \(-0.126430\pi\) | |||||||
\(558\) | 1.11092e43i | 0.00532375i | ||||||||
\(559\) | 1.24947e44 | 0.0581341 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.57133e45 | −1.56654 | ||||||||
\(562\) | 1.24189e44i | 0.0528974i | ||||||||
\(563\) | − 1.29413e44i | − 0.0535291i | −0.999642 | − | 0.0267646i | \(-0.991480\pi\) | ||||
0.999642 | − | 0.0267646i | \(-0.00852044\pi\) | |||||||
\(564\) | −9.49006e44 | −0.381209 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.57688e44 | 0.249200 | ||||||||
\(567\) | − 1.54894e44i | − 0.0570050i | ||||||||
\(568\) | − 8.39687e44i | − 0.300172i | ||||||||
\(569\) | 2.93499e45 | 1.01919 | 0.509593 | − | 0.860415i | \(-0.329796\pi\) | ||||
0.509593 | + | 0.860415i | \(0.329796\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.20277e44 | −0.301594 | −0.150797 | − | 0.988565i | \(-0.548184\pi\) | ||||
−0.150797 | + | 0.988565i | \(0.548184\pi\) | |||||||
\(572\) | − 8.00345e44i | − 0.254825i | ||||||||
\(573\) | − 2.44681e44i | − 0.0756917i | ||||||||
\(574\) | −1.76654e44 | −0.0530979 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.06654e45 | 0.586506 | ||||||||
\(577\) | − 6.78370e45i | − 1.87097i | −0.353371 | − | 0.935483i | \(-0.614965\pi\) | ||||
0.353371 | − | 0.935483i | \(-0.385035\pi\) | |||||||
\(578\) | 1.78802e45i | 0.479251i | ||||||||
\(579\) | −1.85908e45 | −0.484286 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.34270e44 | 0.180697 | ||||||||
\(582\) | − 1.82369e43i | − 0.00436236i | ||||||||
\(583\) | − 1.06226e46i | − 2.47003i | ||||||||
\(584\) | −1.36709e45 | −0.309020 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.09920e45 | −0.234837 | ||||||||
\(587\) | 1.92291e45i | 0.399421i | 0.979855 | + | 0.199710i | \(0.0640001\pi\) | ||||
−0.979855 | + | 0.199710i | \(0.936000\pi\) | |||||||
\(588\) | 2.27550e45i | 0.459570i | ||||||||
\(589\) | 2.05636e44 | 0.0403828 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.56148e44 | −0.158985 | ||||||||
\(592\) | 8.81055e45i | 1.59109i | ||||||||
\(593\) | 3.84061e45i | 0.674524i | 0.941411 | + | 0.337262i | \(0.109501\pi\) | ||||
−0.941411 | + | 0.337262i | \(0.890499\pi\) | |||||||
\(594\) | −1.71348e45 | −0.292686 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.55510e45 | 0.412900 | ||||||||
\(597\) | 4.55893e45i | 0.716616i | ||||||||
\(598\) | 2.21328e44i | 0.0338429i | ||||||||
\(599\) | 1.48464e45 | 0.220840 | 0.110420 | − | 0.993885i | \(-0.464780\pi\) | ||||
0.110420 | + | 0.993885i | \(0.464780\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.01345e45 | 0.705843 | 0.352921 | − | 0.935653i | \(-0.385188\pi\) | ||||
0.352921 | + | 0.935653i | \(0.385188\pi\) | |||||||
\(602\) | 9.33431e43i | 0.0127862i | ||||||||
\(603\) | 3.23902e45i | 0.431696i | ||||||||
\(604\) | 9.30680e45 | 1.20695 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −8.72316e44 | −0.107121 | ||||||||
\(607\) | 3.29284e45i | 0.393511i | 0.980453 | + | 0.196756i | \(0.0630406\pi\) | ||||
−0.980453 | + | 0.196756i | \(0.936959\pi\) | |||||||
\(608\) | 5.45491e45i | 0.634422i | ||||||||
\(609\) | −3.57426e44 | −0.0404576 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.15970e45 | −0.124355 | ||||||||
\(612\) | − 1.29186e46i | − 1.34839i | ||||||||
\(613\) | 1.00399e46i | 1.02008i | 0.860152 | + | 0.510038i | \(0.170369\pi\) | ||||
−0.860152 | + | 0.510038i | \(0.829631\pi\) | |||||||
\(614\) | 3.76092e45 | 0.371977 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.21996e45 | 0.114357 | ||||||||
\(617\) | 1.43698e46i | 1.31144i | 0.755006 | + | 0.655718i | \(0.227634\pi\) | ||||
−0.755006 | + | 0.655718i | \(0.772366\pi\) | |||||||
\(618\) | − 1.16214e45i | − 0.103264i | ||||||||
\(619\) | −1.61224e46 | −1.39487 | −0.697435 | − | 0.716648i | \(-0.745675\pi\) | ||||
−0.697435 | + | 0.716648i | \(0.745675\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.17357e46 | −0.962716 | ||||||||
\(622\) | 2.18815e45i | 0.174798i | ||||||||
\(623\) | 1.79138e45i | 0.139359i | ||||||||
\(624\) | −8.89535e44 | −0.0673934 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3.89420e45 | −0.279861 | ||||||||
\(627\) | 1.36669e46i | 0.956657i | ||||||||
\(628\) | 1.30975e46i | 0.893004i | ||||||||
\(629\) | 5.01498e46 | 3.33068 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.47683e46 | 1.56103 | 0.780516 | − | 0.625136i | \(-0.214957\pi\) | ||||
0.780516 | + | 0.625136i | \(0.214957\pi\) | |||||||
\(632\) | − 3.59138e45i | − 0.220510i | ||||||||
\(633\) | − 7.91785e45i | − 0.473638i | ||||||||
\(634\) | −4.22752e45 | −0.246384 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.23241e46 | −0.681889 | ||||||||
\(637\) | 2.78069e45i | 0.149918i | ||||||||
\(638\) | − 3.06192e45i | − 0.160862i | ||||||||
\(639\) | 1.14903e46 | 0.588257 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.57575e46 | −1.73864 | −0.869321 | − | 0.494249i | \(-0.835443\pi\) | ||||
−0.869321 | + | 0.494249i | \(0.835443\pi\) | |||||||
\(642\) | 2.49599e44i | 0.0118281i | ||||||||
\(643\) | − 1.88292e46i | − 0.869663i | −0.900512 | − | 0.434831i | \(-0.856808\pi\) | ||||
0.900512 | − | 0.434831i | \(-0.143192\pi\) | |||||||
\(644\) | 4.09511e45 | 0.184352 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.65515e45 | 0.412974 | ||||||||
\(647\) | 2.33501e46i | 0.973573i | 0.873521 | + | 0.486787i | \(0.161831\pi\) | ||||
−0.873521 | + | 0.486787i | \(0.838169\pi\) | |||||||
\(648\) | − 3.14105e45i | − 0.127669i | ||||||||
\(649\) | −2.29568e46 | −0.909649 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.05612e43 | −0.00303417 | ||||||||
\(652\) | 2.94428e46i | 1.08117i | ||||||||
\(653\) | − 2.35876e46i | − 0.844531i | −0.906472 | − | 0.422266i | \(-0.861235\pi\) | ||||
0.906472 | − | 0.422266i | \(-0.138765\pi\) | |||||||
\(654\) | 3.97445e45 | 0.138754 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.16572e46 | 1.38285 | ||||||||
\(657\) | − 1.87074e46i | − 0.605598i | ||||||||
\(658\) | − 8.66366e44i | − 0.0273511i | ||||||||
\(659\) | −2.73242e46 | −0.841276 | −0.420638 | − | 0.907228i | \(-0.638194\pi\) | ||||
−0.420638 | + | 0.907228i | \(0.638194\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.72690e46 | −0.798629 | −0.399315 | − | 0.916814i | \(-0.630752\pi\) | ||||
−0.399315 | + | 0.916814i | \(0.630752\pi\) | |||||||
\(662\) | 5.98494e44i | 0.0170963i | ||||||||
\(663\) | 5.06325e45i | 0.141077i | ||||||||
\(664\) | 1.48901e46 | 0.404692 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.03679e46 | 0.268144 | ||||||||
\(667\) | − 2.09713e46i | − 0.529114i | ||||||||
\(668\) | 5.59628e46i | 1.37749i | ||||||||
\(669\) | −7.14706e44 | −0.0171631 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.83482e45 | 0.110525 | ||||||||
\(672\) | − 2.13705e45i | − 0.0476674i | ||||||||
\(673\) | 1.12643e46i | 0.245163i | 0.992458 | + | 0.122581i | \(0.0391173\pi\) | ||||
−0.992458 | + | 0.122581i | \(0.960883\pi\) | |||||||
\(674\) | 9.22324e45 | 0.195882 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.63912e46 | 0.938242 | ||||||||
\(677\) | − 4.69606e46i | − 0.926874i | −0.886130 | − | 0.463437i | \(-0.846616\pi\) | ||||
0.886130 | − | 0.463437i | \(-0.153384\pi\) | |||||||
\(678\) | − 1.83945e45i | − 0.0354322i | ||||||||
\(679\) | −4.12340e44 | −0.00775183 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.04634e46 | −0.903753 | ||||||||
\(682\) | − 6.90134e44i | − 0.0120640i | ||||||||
\(683\) | 1.23577e46i | 0.210860i | 0.994427 | + | 0.105430i | \(0.0336220\pi\) | ||||
−0.994427 | + | 0.105430i | \(0.966378\pi\) | |||||||
\(684\) | −4.94373e46 | −0.823435 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4.21842e45 | −0.0669579 | ||||||||
\(687\) | 1.35833e46i | 0.210484i | ||||||||
\(688\) | − 2.20114e46i | − 0.332996i | ||||||||
\(689\) | −1.50602e46 | −0.222441 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.45406e46 | −0.486342 | −0.243171 | − | 0.969983i | \(-0.578188\pi\) | ||||
−0.243171 | + | 0.969983i | \(0.578188\pi\) | |||||||
\(692\) | − 1.42178e46i | − 0.195471i | ||||||||
\(693\) | 1.66939e46i | 0.224109i | ||||||||
\(694\) | 1.01288e45 | 0.0132779 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7.24815e45 | −0.0906097 | ||||||||
\(697\) | − 2.37113e47i | − 2.89478i | ||||||||
\(698\) | − 7.96324e45i | − 0.0949457i | ||||||||
\(699\) | −7.43761e46 | −0.866084 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.58600e46 | 0.509433 | 0.254716 | − | 0.967016i | \(-0.418018\pi\) | ||||
0.254716 | + | 0.967016i | \(0.418018\pi\) | |||||||
\(702\) | 2.42928e45i | 0.0263582i | ||||||||
\(703\) | − 1.91915e47i | − 2.03398i | ||||||||
\(704\) | −1.28379e47 | −1.32907 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.00086e45 | −0.0395254 | ||||||||
\(707\) | 1.97233e46i | 0.190352i | ||||||||
\(708\) | 2.66339e46i | 0.251123i | ||||||||
\(709\) | −1.01825e46 | −0.0937978 | −0.0468989 | − | 0.998900i | \(-0.514934\pi\) | ||||
−0.0468989 | + | 0.998900i | \(0.514934\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.91445e46 | 0.432142 | ||||||||
\(712\) | 3.63269e46i | 0.312111i | ||||||||
\(713\) | − 4.72678e45i | − 0.0396815i | ||||||||
\(714\) | −3.78256e45 | −0.0310288 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.52498e46 | 0.432779 | ||||||||
\(717\) | 2.32189e46i | 0.177736i | ||||||||
\(718\) | − 3.34585e46i | − 0.250295i | ||||||||
\(719\) | 2.37751e46 | 0.173818 | 0.0869092 | − | 0.996216i | \(-0.472301\pi\) | ||||
0.0869092 | + | 0.996216i | \(0.472301\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.62762e46 | −0.183498 | ||||||||
\(722\) | − 8.08638e45i | − 0.0551938i | ||||||||
\(723\) | − 6.71752e46i | − 0.448154i | ||||||||
\(724\) | 1.11163e47 | 0.724895 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.02869e46 | 0.188712 | ||||||||
\(727\) | − 7.60235e46i | − 0.463053i | −0.972829 | − | 0.231526i | \(-0.925628\pi\) | ||||
0.972829 | − | 0.231526i | \(-0.0743719\pi\) | |||||||
\(728\) | − 1.72959e45i | − 0.0102985i | ||||||||
\(729\) | −3.03238e46 | −0.176514 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.25289e47 | −0.697072 | ||||||||
\(732\) | − 5.60924e45i | − 0.0305120i | ||||||||
\(733\) | 9.46431e46i | 0.503354i | 0.967811 | + | 0.251677i | \(0.0809820\pi\) | ||||
−0.967811 | + | 0.251677i | \(0.919018\pi\) | |||||||
\(734\) | 4.49197e46 | 0.233589 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.25387e47 | 0.623404 | ||||||||
\(737\) | − 2.01217e47i | − 0.978255i | ||||||||
\(738\) | − 4.90207e46i | − 0.233050i | ||||||||
\(739\) | −1.36554e46 | −0.0634851 | −0.0317425 | − | 0.999496i | \(-0.510106\pi\) | ||||
−0.0317425 | + | 0.999496i | \(0.510106\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.93763e46 | 0.0861529 | ||||||||
\(742\) | − 1.12509e46i | − 0.0489243i | ||||||||
\(743\) | − 2.14591e47i | − 0.912632i | −0.889818 | − | 0.456316i | \(-0.849169\pi\) | ||||
0.889818 | − | 0.456316i | \(-0.150831\pi\) | |||||||
\(744\) | −1.63368e45 | −0.00679538 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.67478e46 | −0.0666449 | ||||||||
\(747\) | 2.03757e47i | 0.793089i | ||||||||
\(748\) | 8.02539e47i | 3.05555i | ||||||||
\(749\) | 5.64349e45 | 0.0210183 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.00124e47 | −1.06965 | −0.534825 | − | 0.844963i | \(-0.679622\pi\) | ||||
−0.534825 | + | 0.844963i | \(0.679622\pi\) | |||||||
\(752\) | 2.04300e47i | 0.712317i | ||||||||
\(753\) | − 8.00619e46i | − 0.273092i | ||||||||
\(754\) | −4.34103e45 | −0.0144866 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.49476e46 | 0.143581 | ||||||||
\(757\) | 3.75997e47i | 1.17517i | 0.809161 | + | 0.587587i | \(0.199922\pi\) | ||||
−0.809161 | + | 0.587587i | \(0.800078\pi\) | |||||||
\(758\) | 1.00302e47i | 0.306738i | ||||||||
\(759\) | 3.14150e47 | 0.940043 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.05125e47 | 0.587723 | 0.293861 | − | 0.955848i | \(-0.405060\pi\) | ||||
0.293861 | + | 0.955848i | \(0.405060\pi\) | |||||||
\(762\) | 5.18417e46i | 0.145352i | ||||||||
\(763\) | − 8.98632e46i | − 0.246563i | ||||||||
\(764\) | −5.49839e46 | −0.147637 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.94302e46 | −0.127121 | ||||||||
\(767\) | 3.25470e46i | 0.0819195i | ||||||||
\(768\) | 1.26845e47i | 0.312474i | ||||||||
\(769\) | 3.91739e47 | 0.944522 | 0.472261 | − | 0.881459i | \(-0.343438\pi\) | ||||
0.472261 | + | 0.881459i | \(0.343438\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.47185e46 | 0.126397 | ||||||||
\(772\) | 4.17767e47i | 0.944602i | ||||||||
\(773\) | − 6.18683e47i | − 1.36933i | −0.728860 | − | 0.684663i | \(-0.759949\pi\) | ||||
0.728860 | − | 0.684663i | \(-0.240051\pi\) | |||||||
\(774\) | −2.59023e46 | −0.0561193 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.36174e45 | −0.0173611 | ||||||||
\(777\) | 7.51860e46i | 0.152823i | ||||||||
\(778\) | 9.73319e46i | 0.193683i | ||||||||
\(779\) | −9.07396e47 | −1.76778 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.13811e47 | −1.33303 | ||||||||
\(782\) | − 2.21935e47i | − 0.405802i | ||||||||
\(783\) | − 2.30179e47i | − 0.412095i | ||||||||
\(784\) | 4.89864e47 | 0.858738 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.18800e46 | −0.0199684 | ||||||||
\(787\) | 2.50651e45i | 0.00412559i | 0.999998 | + | 0.00206280i | \(0.000656609\pi\) | ||||
−0.999998 | + | 0.00206280i | \(0.999343\pi\) | |||||||
\(788\) | 1.92391e47i | 0.310101i | ||||||||
\(789\) | 4.31052e47 | 0.680392 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.15904e46 | −0.0629624 | ||||||||
\(792\) | 3.38532e47i | 0.501920i | ||||||||
\(793\) | − 6.85457e45i | − 0.00995342i | ||||||||
\(794\) | 1.47671e47 | 0.210019 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.02447e48 | 1.39776 | ||||||||
\(797\) | 7.37335e47i | 0.985378i | 0.870206 | + | 0.492689i | \(0.163986\pi\) | ||||
−0.870206 | + | 0.492689i | \(0.836014\pi\) | |||||||
\(798\) | 1.44753e46i | 0.0189487i | ||||||||
\(799\) | 1.16288e48 | 1.49112 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.97099e47 | −0.611655 | ||||||||
\(802\) | 2.12004e47i | 0.255545i | ||||||||
\(803\) | 1.16216e48i | 1.37233i | ||||||||
\(804\) | −2.33447e47 | −0.270062 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.78438e44 | −0.00108644 | ||||||||
\(807\) | − 8.48506e47i | − 0.923085i | ||||||||
\(808\) | 3.99963e47i | 0.426317i | ||||||||
\(809\) | 9.92771e47 | 1.03681 | 0.518404 | − | 0.855136i | \(-0.326526\pi\) | ||||
0.518404 | + | 0.855136i | \(0.326526\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.07185e47 | 0.107470 | 0.0537351 | − | 0.998555i | \(-0.482887\pi\) | ||||
0.0537351 | + | 0.998555i | \(0.482887\pi\) | |||||||
\(812\) | 8.03197e46i | 0.0789128i | ||||||||
\(813\) | 7.94274e47i | 0.764674i | ||||||||
\(814\) | −6.44087e47 | −0.607634 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 8.91973e47 | 0.808098 | ||||||||
\(817\) | 4.79463e47i | 0.425688i | ||||||||
\(818\) | 8.04262e46i | 0.0699791i | ||||||||
\(819\) | 2.36678e46 | 0.0201824 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.20939e48 | −0.990610 | −0.495305 | − | 0.868719i | \(-0.664944\pi\) | ||||
−0.495305 | + | 0.868719i | \(0.664944\pi\) | |||||||
\(822\) | − 8.50264e46i | − 0.0682604i | ||||||||
\(823\) | − 2.45743e48i | − 1.93367i | −0.255396 | − | 0.966837i | \(-0.582206\pi\) | ||||
0.255396 | − | 0.966837i | \(-0.417794\pi\) | |||||||
\(824\) | −5.32848e47 | −0.410965 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.43146e46 | −0.0180176 | ||||||||
\(827\) | − 1.80057e48i | − 1.30789i | −0.756544 | − | 0.653943i | \(-0.773114\pi\) | ||||
0.756544 | − | 0.653943i | \(-0.226886\pi\) | |||||||
\(828\) | 1.13637e48i | 0.809135i | ||||||||
\(829\) | −6.57735e47 | −0.459094 | −0.229547 | − | 0.973298i | \(-0.573724\pi\) | ||||
−0.229547 | + | 0.973298i | \(0.573724\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.86049e47 | 0.460191 | ||||||||
\(832\) | 1.82010e47i | 0.119691i | ||||||||
\(833\) | − 2.78832e48i | − 1.79763i | ||||||||
\(834\) | −6.98757e46 | −0.0441658 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.07119e48 | 1.86596 | ||||||||
\(837\) | − 5.18807e46i | − 0.0309055i | ||||||||
\(838\) | 4.28937e47i | 0.250534i | ||||||||
\(839\) | −6.26140e47 | −0.358591 | −0.179295 | − | 0.983795i | \(-0.557382\pi\) | ||||
−0.179295 | + | 0.983795i | \(0.557382\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.40475e48 | −0.773511 | ||||||||
\(842\) | 7.48868e46i | 0.0404348i | ||||||||
\(843\) | − 2.49910e47i | − 0.132321i | ||||||||
\(844\) | −1.77928e48 | −0.923832 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.40413e47 | 0.120046 | ||||||||
\(847\) | − 6.84793e47i | − 0.335338i | ||||||||
\(848\) | 2.65311e48i | 1.27416i | ||||||||
\(849\) | −1.32349e48 | −0.623365 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.41140e48 | −1.99866 | ||||||||
\(852\) | 8.28145e47i | 0.368005i | ||||||||
\(853\) | − 3.16331e48i | − 1.37874i | −0.724410 | − | 0.689370i | \(-0.757888\pi\) | ||||
0.724410 | − | 0.689370i | \(-0.242112\pi\) | |||||||
\(854\) | 5.12079e45 | 0.00218918 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.14443e47 | 0.0470730 | ||||||||
\(857\) | − 3.13666e48i | − 1.26556i | −0.774330 | − | 0.632782i | \(-0.781913\pi\) | ||||
0.774330 | − | 0.632782i | \(-0.218087\pi\) | |||||||
\(858\) | − 6.50286e46i | − 0.0257374i | ||||||||
\(859\) | −2.20270e48 | −0.855202 | −0.427601 | − | 0.903968i | \(-0.640641\pi\) | ||||
−0.427601 | + | 0.903968i | \(0.640641\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.55487e47 | 0.132822 | ||||||||
\(862\) | − 3.52247e47i | − 0.129115i | ||||||||
\(863\) | − 5.00806e47i | − 0.180091i | −0.995938 | − | 0.0900453i | \(-0.971299\pi\) | ||||
0.995938 | − | 0.0900453i | \(-0.0287012\pi\) | |||||||
\(864\) | 1.37624e48 | 0.485532 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.19192e47 | −0.0744356 | ||||||||
\(867\) | − 3.59809e48i | − 1.19883i | ||||||||
\(868\) | 1.81035e46i | 0.00591816i | ||||||||
\(869\) | −3.05300e48 | −0.979266 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.85276e47 | −0.0880979 | ||||||||
\(872\) | − 1.82232e48i | − 0.552207i | ||||||||
\(873\) | − 1.14422e47i | − 0.0340233i | ||||||||
\(874\) | −8.49310e47 | −0.247815 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.34830e48 | 0.378852 | ||||||||
\(877\) | − 1.77120e48i | − 0.488400i | −0.969725 | − | 0.244200i | \(-0.921475\pi\) | ||||
0.969725 | − | 0.244200i | \(-0.0785253\pi\) | |||||||
\(878\) | 6.48638e47i | 0.175527i | ||||||||
\(879\) | 2.21196e48 | 0.587436 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.59935e48 | 0.409111 | 0.204555 | − | 0.978855i | \(-0.434425\pi\) | ||||
0.204555 | + | 0.978855i | \(0.434425\pi\) | |||||||
\(882\) | − 5.76455e47i | − 0.144722i | ||||||||
\(883\) | 2.38704e48i | 0.588177i | 0.955778 | + | 0.294089i | \(0.0950161\pi\) | ||||
−0.955778 | + | 0.294089i | \(0.904984\pi\) | |||||||
\(884\) | 1.13780e48 | 0.275171 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.21764e47 | −0.191466 | ||||||||
\(887\) | 5.13361e48i | 1.17404i | 0.809572 | + | 0.587020i | \(0.199699\pi\) | ||||
−0.809572 | + | 0.587020i | \(0.800301\pi\) | |||||||
\(888\) | 1.52468e48i | 0.342266i | ||||||||
\(889\) | 1.17215e48 | 0.258289 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.67018e48 | −0.566968 | ||||||||
\(892\) | 1.60607e47i | 0.0334768i | ||||||||
\(893\) | − 4.45015e48i | − 0.910595i | ||||||||
\(894\) | 2.07604e47 | 0.0417030 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −6.35594e47 | −0.123054 | ||||||||
\(897\) | − 4.45386e47i | − 0.0846566i | ||||||||
\(898\) | − 8.18931e47i | − 0.152823i | ||||||||
\(899\) | 9.27089e46 | 0.0169858 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.51015e49 | 2.66724 | ||||||||
\(902\) | 3.04531e48i | 0.528109i | ||||||||
\(903\) | − 1.87837e47i | − 0.0319841i | ||||||||
\(904\) | −8.43402e47 | −0.141012 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7.56185e47 | 0.121903 | ||||||||
\(907\) | 5.18589e48i | 0.820924i | 0.911878 | + | 0.410462i | \(0.134632\pi\) | ||||
−0.911878 | + | 0.410462i | \(0.865368\pi\) | |||||||
\(908\) | 1.13400e49i | 1.76277i | ||||||||
\(909\) | −5.47311e48 | −0.835469 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.63747e48 | −0.977123 | −0.488562 | − | 0.872529i | \(-0.662478\pi\) | ||||
−0.488562 | + | 0.872529i | \(0.662478\pi\) | |||||||
\(912\) | − 3.41344e48i | − 0.493489i | ||||||||
\(913\) | − 1.26580e49i | − 1.79720i | ||||||||
\(914\) | 1.09453e48 | 0.152621 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.05239e48 | 0.410549 | ||||||||
\(917\) | 2.68609e47i | 0.0354835i | ||||||||
\(918\) | − 2.43594e48i | − 0.316054i | ||||||||
\(919\) | 7.10984e48 | 0.906054 | 0.453027 | − | 0.891497i | \(-0.350344\pi\) | ||||
0.453027 | + | 0.891497i | \(0.350344\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.56822e48 | −0.930486 | ||||||||
\(922\) | − 6.64821e47i | − 0.0802869i | ||||||||
\(923\) | 1.01200e48i | 0.120048i | ||||||||
\(924\) | −1.20319e48 | −0.140199 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9.01048e47 | 0.101313 | ||||||||
\(927\) | − 7.29151e48i | − 0.805382i | ||||||||
\(928\) | 2.45929e48i | 0.266851i | ||||||||
\(929\) | 1.17316e49 | 1.25054 | 0.625272 | − | 0.780407i | \(-0.284988\pi\) | ||||
0.625272 | + | 0.780407i | \(0.284988\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.06705e49 | −1.09777 | ||||||||
\(932\) | 1.67136e49i | 1.68930i | ||||||||
\(933\) | − 4.40329e48i | − 0.437250i | ||||||||
\(934\) | 1.13136e48 | 0.110376 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.79954e47 | 0.0452010 | ||||||||
\(937\) | 7.60807e48i | 0.703998i | 0.936000 | + | 0.351999i | \(0.114498\pi\) | ||||
−0.936000 | + | 0.351999i | \(0.885502\pi\) | |||||||
\(938\) | − 2.13119e47i | − 0.0193765i | ||||||||
\(939\) | 7.83643e48 | 0.700061 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.90432e48 | −0.509262 | −0.254631 | − | 0.967038i | \(-0.581954\pi\) | ||||
−0.254631 | + | 0.967038i | \(0.581954\pi\) | |||||||
\(942\) | 1.06418e48i | 0.0901935i | ||||||||
\(943\) | 2.08575e49i | 1.73708i | ||||||||
\(944\) | 5.73368e48 | 0.469241 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.60912e48 | 0.127170 | ||||||||
\(947\) | − 7.50195e47i | − 0.0582639i | −0.999576 | − | 0.0291319i | \(-0.990726\pi\) | ||||
0.999576 | − | 0.0291319i | \(-0.00927430\pi\) | |||||||
\(948\) | 3.54201e48i | 0.270341i | ||||||||
\(949\) | 1.64765e48 | 0.123587 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.50718e48 | 0.616321 | ||||||||
\(952\) | 1.73433e48i | 0.123487i | ||||||||
\(953\) | 1.06031e49i | 0.741993i | 0.928634 | + | 0.370997i | \(0.120984\pi\) | ||||
−0.928634 | + | 0.370997i | \(0.879016\pi\) | |||||||
\(954\) | 3.12208e48 | 0.214732 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.21769e48 | 0.346675 | ||||||||
\(957\) | 6.16159e48i | 0.402389i | ||||||||
\(958\) | 3.02447e48i | 0.194141i | ||||||||
\(959\) | −1.92247e48 | −0.121297 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.63826e49 | −0.998726 | ||||||||
\(962\) | 9.13154e47i | 0.0547212i | ||||||||
\(963\) | 1.56604e48i | 0.0922507i | ||||||||
\(964\) | −1.50954e49 | −0.874126 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.32731e47 | 0.0186196 | ||||||||
\(967\) | − 3.31961e48i | − 0.182621i | −0.995822 | − | 0.0913104i | \(-0.970894\pi\) | ||||
0.995822 | − | 0.0913104i | \(-0.0291056\pi\) | |||||||
\(968\) | − 1.38868e49i | − 0.751030i | ||||||||
\(969\) | −1.94294e49 | −1.03304 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.67736e49 | 0.862003 | 0.431001 | − | 0.902351i | \(-0.358160\pi\) | ||||
0.431001 | + | 0.902351i | \(0.358160\pi\) | |||||||
\(972\) | 1.95710e49i | 0.988826i | ||||||||
\(973\) | 1.57991e48i | 0.0784819i | ||||||||
\(974\) | 6.22773e48 | 0.304164 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.20754e48 | −0.0570139 | ||||||||
\(977\) | 2.50785e49i | 1.16424i | 0.813104 | + | 0.582118i | \(0.197776\pi\) | ||||
−0.813104 | + | 0.582118i | \(0.802224\pi\) | |||||||
\(978\) | 2.39225e48i | 0.109198i | ||||||||
\(979\) | 3.08812e49 | 1.38605 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.49366e49 | 1.08218 | ||||||||
\(982\) | − 7.94535e48i | − 0.339058i | ||||||||
\(983\) | − 1.24304e49i | − 0.521616i | −0.965391 | − | 0.260808i | \(-0.916011\pi\) | ||||
0.965391 | − | 0.260808i | \(-0.0839890\pi\) | |||||||
\(984\) | 7.20883e48 | 0.297472 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4.35293e48 | 0.173705 | ||||||||
\(987\) | 1.74342e48i | 0.0684177i | ||||||||
\(988\) | − 4.35418e48i | − 0.168042i | ||||||||
\(989\) | 1.10210e49 | 0.418295 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.48644e49 | −0.912774 | −0.456387 | − | 0.889781i | \(-0.650857\pi\) | ||||
−0.456387 | + | 0.889781i | \(0.650857\pi\) | |||||||
\(992\) | 5.54307e47i | 0.0200128i | ||||||||
\(993\) | − 1.20437e48i | − 0.0427658i | ||||||||
\(994\) | −7.56031e47 | −0.0264037 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.46854e49 | −0.496144 | ||||||||
\(997\) | − 2.01041e49i | − 0.668058i | −0.942563 | − | 0.334029i | \(-0.891592\pi\) | ||||
0.942563 | − | 0.334029i | \(-0.108408\pi\) | |||||||
\(998\) | − 1.13134e49i | − 0.369777i | ||||||||
\(999\) | −4.84191e49 | −1.55663 |
(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 | 25.34.b.c.24.6 | 12 | ||
5.2 | odd | 4 | 25.34.a.c.1.4 | 6 | |||
5.3 | odd | 4 | 5.34.a.b.1.3 | ✓ | 6 | ||
5.4 | even | 2 | inner | 25.34.b.c.24.7 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.34.a.b.1.3 | ✓ | 6 | 5.3 | odd | 4 | ||
25.34.a.c.1.4 | 6 | 5.2 | odd | 4 | |||
25.34.b.c.24.6 | 12 | 1.1 | even | 1 | trivial | ||
25.34.b.c.24.7 | 12 | 5.4 | even | 2 | inner |