Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,12,Mod(199,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.199");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.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: | \(172.877215626\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 3) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.199 |
Dual form | 225.12.b.a.199.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 78.0000i | − 1.72357i | −0.507271 | − | 0.861786i | \(-0.669346\pi\) | ||||
0.507271 | − | 0.861786i | \(-0.330654\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4036.00 | −1.97070 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 27760.0i | − 0.624281i | −0.950036 | − | 0.312141i | \(-0.898954\pi\) | ||||
0.950036 | − | 0.312141i | \(-0.101046\pi\) | |||||||
\(8\) | 155064.i | 1.67308i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −637836. | −1.19412 | −0.597062 | − | 0.802195i | \(-0.703665\pi\) | ||||
−0.597062 | + | 0.802195i | \(0.703665\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 766214.i | − 0.572350i | −0.958177 | − | 0.286175i | \(-0.907616\pi\) | ||||
0.958177 | − | 0.286175i | \(-0.0923839\pi\) | |||||||
\(14\) | −2.16528e6 | −1.07599 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.82926e6 | 0.912968 | ||||||||
\(17\) | − 3.08435e6i | − 0.526860i | −0.964679 | − | 0.263430i | \(-0.915146\pi\) | ||||
0.964679 | − | 0.263430i | \(-0.0848538\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.95114e7 | 1.80777 | 0.903886 | − | 0.427773i | \(-0.140702\pi\) | ||||
0.903886 | + | 0.427773i | \(0.140702\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.97512e7i | 2.05816i | ||||||||
\(23\) | 1.53124e7i | 0.496066i | 0.968752 | + | 0.248033i | \(0.0797841\pi\) | ||||
−0.968752 | + | 0.248033i | \(0.920216\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.97647e7 | −0.986487 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.12039e8i | 1.23027i | ||||||||
\(29\) | 1.07513e7 | 0.0973353 | 0.0486677 | − | 0.998815i | \(-0.484502\pi\) | ||||
0.0486677 | + | 0.998815i | \(0.484502\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.09374e7 | −0.319556 | −0.159778 | − | 0.987153i | \(-0.551078\pi\) | ||||
−0.159778 | + | 0.987153i | \(0.551078\pi\) | |||||||
\(32\) | 1.88885e7i | 0.0995112i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.40580e8 | −0.908081 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.64741e8i | 1.57595i | 0.615706 | + | 0.787976i | \(0.288871\pi\) | ||||
−0.615706 | + | 0.787976i | \(0.711129\pi\) | |||||||
\(38\) | − 1.52189e9i | − 3.11583i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.98833e8 | −1.21162 | −0.605812 | − | 0.795608i | \(-0.707152\pi\) | ||||
−0.605812 | + | 0.795608i | \(0.707152\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.57947e8i | 0.993722i | 0.867830 | + | 0.496861i | \(0.165514\pi\) | ||||
−0.867830 | + | 0.496861i | \(0.834486\pi\) | |||||||
\(44\) | 2.57431e9 | 2.35326 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.19436e9 | 0.855005 | ||||||||
\(47\) | 1.55574e9i | 0.989462i | 0.869046 | + | 0.494731i | \(0.164733\pi\) | ||||
−0.869046 | + | 0.494731i | \(0.835267\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.20671e9 | 0.610273 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.09244e9i | 1.12793i | ||||||||
\(53\) | 3.79242e9i | 1.24566i | 0.782358 | + | 0.622829i | \(0.214017\pi\) | ||||
−0.782358 | + | 0.622829i | \(0.785983\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.30458e9 | 1.04447 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 8.38598e8i | − 0.167765i | ||||||||
\(59\) | 5.55307e8 | 0.101122 | 0.0505612 | − | 0.998721i | \(-0.483899\pi\) | ||||
0.0505612 | + | 0.998721i | \(0.483899\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.95042e9 | 0.750461 | 0.375230 | − | 0.926932i | \(-0.377564\pi\) | ||||
0.375230 | + | 0.926932i | \(0.377564\pi\) | |||||||
\(62\) | 3.97312e9i | 0.550779i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 9.31563e9 | 1.08448 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.29240e9i | 0.478896i | 0.970909 | + | 0.239448i | \(0.0769665\pi\) | ||||
−0.970909 | + | 0.239448i | \(0.923034\pi\) | |||||||
\(68\) | 1.24485e10i | 1.03828i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.48311e10 | 0.975556 | 0.487778 | − | 0.872968i | \(-0.337808\pi\) | ||||
0.487778 | + | 0.872968i | \(0.337808\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 1.39710e10i | − 0.788773i | −0.918945 | − | 0.394386i | \(-0.870957\pi\) | ||||
0.918945 | − | 0.394386i | \(-0.129043\pi\) | |||||||
\(74\) | 5.18498e10 | 2.71627 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.87480e10 | −3.56258 | ||||||||
\(77\) | 1.77063e10i | 0.745469i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.72054e9 | −0.136037 | −0.0680185 | − | 0.997684i | \(-0.521668\pi\) | ||||
−0.0680185 | + | 0.997684i | \(0.521668\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.01090e10i | 2.08832i | ||||||||
\(83\) | 8.76845e9i | 0.244339i | 0.992509 | + | 0.122170i | \(0.0389852\pi\) | ||||
−0.992509 | + | 0.122170i | \(0.961015\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.47199e10 | 1.71275 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 9.89054e10i | − 1.99786i | ||||||||
\(89\) | −2.54728e10 | −0.483539 | −0.241769 | − | 0.970334i | \(-0.577728\pi\) | ||||
−0.241769 | + | 0.970334i | \(0.577728\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.12701e10 | −0.357307 | ||||||||
\(92\) | − 6.18007e10i | − 0.977598i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.21348e11 | 1.70541 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 3.90925e10i | − 0.462220i | −0.972928 | − | 0.231110i | \(-0.925764\pi\) | ||||
0.972928 | − | 0.231110i | \(-0.0742357\pi\) | |||||||
\(98\) | − 9.41233e10i | − 1.05185i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.31078e9 | −0.0881492 | −0.0440746 | − | 0.999028i | \(-0.514034\pi\) | ||||
−0.0440746 | + | 0.999028i | \(0.514034\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 4.85751e10i | − 0.412865i | −0.978461 | − | 0.206433i | \(-0.933815\pi\) | ||||
0.978461 | − | 0.206433i | \(-0.0661855\pi\) | |||||||
\(104\) | 1.18812e11 | 0.957586 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.95809e11 | 2.14698 | ||||||||
\(107\) | − 2.25596e11i | − 1.55496i | −0.628906 | − | 0.777482i | \(-0.716497\pi\) | ||||
0.628906 | − | 0.777482i | \(-0.283503\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.94512e10 | 0.432348 | 0.216174 | − | 0.976355i | \(-0.430642\pi\) | ||||
0.216174 | + | 0.976355i | \(0.430642\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 1.06300e11i | − 0.569949i | ||||||||
\(113\) | − 3.59665e11i | − 1.83640i | −0.396122 | − | 0.918198i | \(-0.629644\pi\) | ||||
0.396122 | − | 0.918198i | \(-0.370356\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.33921e10 | −0.191819 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 4.33139e10i | − 0.174292i | ||||||||
\(119\) | −8.56217e10 | −0.328909 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.21523e11 | 0.425931 | ||||||||
\(122\) | − 3.86133e11i | − 1.29347i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.05583e11 | 0.629751 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.50273e11i | 0.672192i | 0.941828 | + | 0.336096i | \(0.109107\pi\) | ||||
−0.941828 | + | 0.336096i | \(0.890893\pi\) | |||||||
\(128\) | − 6.87936e11i | − 1.76967i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.78918e10 | 0.221694 | 0.110847 | − | 0.993837i | \(-0.464644\pi\) | ||||
0.110847 | + | 0.993837i | \(0.464644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 5.41637e11i | − 1.12856i | ||||||||
\(134\) | 4.12807e11 | 0.825412 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.78272e11 | 0.881477 | ||||||||
\(137\) | 1.55015e11i | 0.274416i | 0.990542 | + | 0.137208i | \(0.0438129\pi\) | ||||
−0.990542 | + | 0.137208i | \(0.956187\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.12627e12 | 1.84102 | 0.920512 | − | 0.390715i | \(-0.127772\pi\) | ||||
0.920512 | + | 0.390715i | \(0.127772\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 1.15682e12i | − 1.68144i | ||||||||
\(143\) | 4.88719e11i | 0.683457i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.08974e12 | −1.35951 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 2.68289e12i | − 3.10573i | ||||||||
\(149\) | −1.38458e12 | −1.54452 | −0.772261 | − | 0.635306i | \(-0.780874\pi\) | ||||
−0.772261 | + | 0.635306i | \(0.780874\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.98601e11 | −0.724196 | −0.362098 | − | 0.932140i | \(-0.617939\pi\) | ||||
−0.362098 | + | 0.932140i | \(0.617939\pi\) | |||||||
\(152\) | 3.02552e12i | 3.02454i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.38109e12 | 1.28487 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.13127e12i | 1.78316i | 0.452863 | + | 0.891580i | \(0.350403\pi\) | ||||
−0.452863 | + | 0.891580i | \(0.649597\pi\) | |||||||
\(158\) | 2.90202e11i | 0.234470i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.25071e11 | 0.309684 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.63564e11i | 0.111342i | 0.998449 | + | 0.0556708i | \(0.0177297\pi\) | ||||
−0.998449 | + | 0.0556708i | \(0.982270\pi\) | |||||||
\(164\) | 3.62769e12 | 2.38775 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.83939e11 | 0.421137 | ||||||||
\(167\) | 8.80943e9i | 0.00524816i | 0.999997 | + | 0.00262408i | \(0.000835271\pi\) | ||||
−0.999997 | + | 0.00262408i | \(0.999165\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.20508e12 | 0.672416 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 3.86627e12i | − 1.95833i | ||||||||
\(173\) | − 7.30852e11i | − 0.358571i | −0.983797 | − | 0.179286i | \(-0.942621\pi\) | ||||
0.983797 | − | 0.179286i | \(-0.0573786\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.44244e12 | −1.09020 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.98688e12i | 0.833414i | ||||||||
\(179\) | 3.92371e12 | 1.59590 | 0.797950 | − | 0.602724i | \(-0.205918\pi\) | ||||
0.797950 | + | 0.602724i | \(0.205918\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.27931e12 | 0.872110 | 0.436055 | − | 0.899920i | \(-0.356375\pi\) | ||||
0.436055 | + | 0.899920i | \(0.356375\pi\) | |||||||
\(182\) | 1.65907e12i | 0.615845i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.37440e12 | −0.829956 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.96731e12i | 0.629136i | ||||||||
\(188\) | − 6.27897e12i | − 1.94994i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.38709e12 | −0.964147 | −0.482073 | − | 0.876131i | \(-0.660116\pi\) | ||||
−0.482073 | + | 0.876131i | \(0.660116\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.92921e12i | 1.32499i | 0.749067 | + | 0.662494i | \(0.230502\pi\) | ||||
−0.749067 | + | 0.662494i | \(0.769498\pi\) | |||||||
\(194\) | −3.04921e12 | −0.796670 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.87028e12 | −1.20267 | ||||||||
\(197\) | − 6.35785e12i | − 1.52667i | −0.646001 | − | 0.763337i | \(-0.723560\pi\) | ||||
0.646001 | − | 0.763337i | \(-0.276440\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.78554e12 | 0.859875 | 0.429938 | − | 0.902859i | \(-0.358536\pi\) | ||||
0.429938 | + | 0.902859i | \(0.358536\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.26241e11i | 0.151932i | ||||||||
\(203\) | − 2.98455e11i | − 0.0607646i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.78885e12 | −0.711604 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 2.93404e12i | − 0.522537i | ||||||||
\(209\) | −1.24451e13 | −2.15870 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.79494e11 | 0.0295458 | 0.0147729 | − | 0.999891i | \(-0.495297\pi\) | ||||
0.0147729 | + | 0.999891i | \(0.495297\pi\) | |||||||
\(212\) | − 1.53062e13i | − 2.45482i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.75965e13 | −2.68009 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.41402e12i | 0.199493i | ||||||||
\(218\) | − 5.41719e12i | − 0.745184i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.36328e12 | −0.301548 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 2.22568e12i | − 0.270263i | −0.990828 | − | 0.135132i | \(-0.956854\pi\) | ||||
0.990828 | − | 0.135132i | \(-0.0431457\pi\) | |||||||
\(224\) | 5.24344e11 | 0.0621230 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.80538e13 | −3.16516 | ||||||||
\(227\) | 4.15848e11i | 0.0457923i | 0.999738 | + | 0.0228961i | \(0.00728870\pi\) | ||||
−0.999738 | + | 0.0228961i | \(0.992711\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.81248e13 | −1.90186 | −0.950928 | − | 0.309414i | \(-0.899867\pi\) | ||||
−0.950928 | + | 0.309414i | \(0.899867\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.66713e12i | 0.162850i | ||||||||
\(233\) | − 1.87641e10i | − 0.00179007i | −1.00000 | 0.000895033i | \(-0.999715\pi\) | |||||
1.00000 | 0.000895033i | \(-0.000284898\pi\) | ||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.24122e12 | −0.199282 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.67849e12i | 0.566898i | ||||||||
\(239\) | −1.76252e13 | −1.46200 | −0.730999 | − | 0.682379i | \(-0.760946\pi\) | ||||
−0.730999 | + | 0.682379i | \(0.760946\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.90117e11 | −0.0705267 | −0.0352633 | − | 0.999378i | \(-0.511227\pi\) | ||||
−0.0352633 | + | 0.999378i | \(0.511227\pi\) | |||||||
\(242\) | − 9.47880e12i | − 0.734123i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.99799e13 | −1.47894 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 1.49499e13i | − 1.03468i | ||||||||
\(248\) | − 7.89856e12i | − 0.534643i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.42280e13 | 1.53502 | 0.767508 | − | 0.641040i | \(-0.221497\pi\) | ||||
0.767508 | + | 0.641040i | \(0.221497\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 9.76677e12i | − 0.592364i | ||||||||
\(254\) | 1.95213e13 | 1.15857 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.45806e13 | −1.96568 | ||||||||
\(257\) | − 7.80492e12i | − 0.434246i | −0.976144 | − | 0.217123i | \(-0.930333\pi\) | ||||
0.976144 | − | 0.217123i | \(-0.0696673\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.84532e13 | 0.983837 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 7.63556e12i | − 0.382106i | ||||||||
\(263\) | 1.65956e13i | 0.813272i | 0.913590 | + | 0.406636i | \(0.133298\pi\) | ||||
−0.913590 | + | 0.406636i | \(0.866702\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.22477e13 | −1.94515 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 2.13601e13i | − 0.943762i | ||||||||
\(269\) | 2.85236e13 | 1.23471 | 0.617357 | − | 0.786683i | \(-0.288203\pi\) | ||||
0.617357 | + | 0.786683i | \(0.288203\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.33800e13 | 0.971658 | 0.485829 | − | 0.874054i | \(-0.338518\pi\) | ||||
0.485829 | + | 0.874054i | \(0.338518\pi\) | |||||||
\(272\) | − 1.18108e13i | − 0.481006i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.20911e13 | 0.472976 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 3.03641e13i | − 1.11872i | −0.828924 | − | 0.559361i | \(-0.811047\pi\) | ||||
0.828924 | − | 0.559361i | \(-0.188953\pi\) | |||||||
\(278\) | − 8.78487e13i | − 3.17314i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.59749e13 | −0.543942 | −0.271971 | − | 0.962306i | \(-0.587675\pi\) | ||||
−0.271971 | + | 0.962306i | \(0.587675\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 2.87045e13i | − 0.939993i | −0.882668 | − | 0.469997i | \(-0.844255\pi\) | ||||
0.882668 | − | 0.469997i | \(-0.155745\pi\) | |||||||
\(284\) | −5.98583e13 | −1.92253 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.81201e13 | 1.17799 | ||||||||
\(287\) | 2.49516e13i | 0.756394i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.47587e13 | 0.722419 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.63870e13i | 1.55444i | ||||||||
\(293\) | 4.81754e13i | 1.30333i | 0.758508 | + | 0.651663i | \(0.225929\pi\) | ||||
−0.758508 | + | 0.651663i | \(0.774071\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.03077e14 | −2.63669 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.07997e14i | 2.66209i | ||||||||
\(299\) | 1.17325e13 | 0.283923 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.65926e13 | 0.620362 | ||||||||
\(302\) | 5.44909e13i | 1.24820i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.47143e13 | 1.65044 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.57350e13i | 0.538597i | 0.963057 | + | 0.269298i | \(0.0867918\pi\) | ||||
−0.963057 | + | 0.269298i | \(0.913208\pi\) | |||||||
\(308\) | − 7.14627e13i | − 1.46910i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.46043e13 | −0.674446 | −0.337223 | − | 0.941425i | \(-0.609488\pi\) | ||||
−0.337223 | + | 0.941425i | \(0.609488\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 1.26066e13i | − 0.237194i | −0.992942 | − | 0.118597i | \(-0.962160\pi\) | ||||
0.992942 | − | 0.118597i | \(-0.0378397\pi\) | |||||||
\(314\) | 1.66239e14 | 3.07341 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.50161e13 | 0.268089 | ||||||||
\(317\) | 8.18243e13i | 1.43568i | 0.696210 | + | 0.717838i | \(0.254868\pi\) | ||||
−0.696210 | + | 0.717838i | \(0.745132\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.85754e12 | −0.116230 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − 3.31555e13i | − 0.533764i | ||||||||
\(323\) | − 6.01801e13i | − 0.952443i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.27580e13 | 0.191905 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 1.39377e14i | − 2.02714i | ||||||||
\(329\) | 4.31874e13 | 0.617703 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.40115e13 | −0.470513 | −0.235256 | − | 0.971933i | \(-0.575593\pi\) | ||||
−0.235256 | + | 0.971933i | \(0.575593\pi\) | |||||||
\(332\) | − 3.53895e13i | − 0.481520i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.87135e11 | 0.00904558 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 5.99439e13i | − 0.751244i | −0.926773 | − | 0.375622i | \(-0.877429\pi\) | ||||
0.926773 | − | 0.375622i | \(-0.122571\pi\) | |||||||
\(338\) | − 9.39960e13i | − 1.15896i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.24897e13 | 0.381590 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 8.83888e13i | − 1.00526i | ||||||||
\(344\) | −1.48543e14 | −1.66257 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.70064e13 | −0.618024 | ||||||||
\(347\) | − 9.78685e13i | − 1.04431i | −0.852850 | − | 0.522157i | \(-0.825128\pi\) | ||||
0.852850 | − | 0.522157i | \(-0.174872\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.42790e14 | 1.47624 | 0.738120 | − | 0.674670i | \(-0.235714\pi\) | ||||
0.738120 | + | 0.674670i | \(0.235714\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 1.20478e13i | − 0.118829i | ||||||||
\(353\) | 1.44246e14i | 1.40069i | 0.713804 | + | 0.700346i | \(0.246971\pi\) | ||||
−0.713804 | + | 0.700346i | \(0.753029\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.02808e14 | 0.952911 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 3.06050e14i | − 2.75065i | ||||||||
\(359\) | −1.24349e14 | −1.10059 | −0.550293 | − | 0.834972i | \(-0.685484\pi\) | ||||
−0.550293 | + | 0.834972i | \(0.685484\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.64205e14 | 2.26804 | ||||||||
\(362\) | − 1.77786e14i | − 1.50314i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.58461e13 | 0.704147 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 1.60110e14i | − 1.25532i | −0.778488 | − | 0.627659i | \(-0.784013\pi\) | ||||
0.778488 | − | 0.627659i | \(-0.215987\pi\) | |||||||
\(368\) | 5.86351e13i | 0.452892i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.05277e14 | 0.777641 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.47258e13i | 0.249031i | 0.992218 | + | 0.124516i | \(0.0397377\pi\) | ||||
−0.992218 | + | 0.124516i | \(0.960262\pi\) | |||||||
\(374\) | 1.53450e14 | 1.08436 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.41239e14 | −1.65545 | ||||||||
\(377\) | − 8.23777e12i | − 0.0557099i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.46500e14 | 0.962327 | 0.481163 | − | 0.876631i | \(-0.340214\pi\) | ||||
0.481163 | + | 0.876631i | \(0.340214\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.64193e14i | 1.66178i | ||||||||
\(383\) | 6.43419e13i | 0.398933i | 0.979905 | + | 0.199467i | \(0.0639210\pi\) | ||||
−0.979905 | + | 0.199467i | \(0.936079\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.84478e14 | 2.28371 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.57777e14i | 0.910899i | ||||||||
\(389\) | −3.98900e13 | −0.227061 | −0.113530 | − | 0.993535i | \(-0.536216\pi\) | ||||
−0.113530 | + | 0.993535i | \(0.536216\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.72287e13 | 0.261357 | ||||||||
\(392\) | 1.87117e14i | 1.02103i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.95912e14 | −2.63133 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.06552e14i | 0.542268i | 0.962542 | + | 0.271134i | \(0.0873986\pi\) | ||||
−0.962542 | + | 0.271134i | \(0.912601\pi\) | |||||||
\(398\) | − 2.95272e14i | − 1.48206i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.41445e13 | −0.164447 | −0.0822236 | − | 0.996614i | \(-0.526202\pi\) | ||||
−0.0822236 | + | 0.996614i | \(0.526202\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.90289e13i | 0.182898i | ||||||||
\(404\) | 3.75783e13 | 0.173716 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.32795e13 | −0.104732 | ||||||||
\(407\) | − 4.23996e14i | − 1.88188i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.33349e13 | −0.230427 | −0.115213 | − | 0.993341i | \(-0.536755\pi\) | ||||
−0.115213 | + | 0.993341i | \(0.536755\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.96049e14i | 0.813635i | ||||||||
\(413\) | − 1.54153e13i | − 0.0631288i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.44726e13 | 0.0569553 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 9.70716e14i | 3.72068i | ||||||||
\(419\) | −1.01288e14 | −0.383159 | −0.191580 | − | 0.981477i | \(-0.561361\pi\) | ||||
−0.191580 | + | 0.981477i | \(0.561361\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.57928e14 | −0.581981 | −0.290991 | − | 0.956726i | \(-0.593985\pi\) | ||||
−0.290991 | + | 0.956726i | \(0.593985\pi\) | |||||||
\(422\) | − 1.40005e13i | − 0.0509244i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.88067e14 | −2.08408 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 1.37424e14i | − 0.468499i | ||||||||
\(428\) | 9.10504e14i | 3.06437i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.13171e14 | −1.66202 | −0.831012 | − | 0.556254i | \(-0.812238\pi\) | ||||
−0.831012 | + | 0.556254i | \(0.812238\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.49248e13i | 0.236560i | 0.992980 | + | 0.118280i | \(0.0377381\pi\) | ||||
−0.992980 | + | 0.118280i | \(0.962262\pi\) | |||||||
\(434\) | 1.10294e14 | 0.343841 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.80305e14 | −0.852030 | ||||||||
\(437\) | 2.98766e14i | 0.896773i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.68335e14 | 1.07817 | 0.539086 | − | 0.842250i | \(-0.318770\pi\) | ||||
0.539086 | + | 0.842250i | \(0.318770\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.84335e14i | 0.519740i | ||||||||
\(443\) | − 1.11248e14i | − 0.309793i | −0.987931 | − | 0.154896i | \(-0.950496\pi\) | ||||
0.987931 | − | 0.154896i | \(-0.0495043\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.73603e14 | −0.465818 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 2.58602e14i | − 0.677022i | ||||||||
\(449\) | −8.83314e13 | −0.228434 | −0.114217 | − | 0.993456i | \(-0.536436\pi\) | ||||
−0.114217 | + | 0.993456i | \(0.536436\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.73308e14 | 1.44683 | ||||||||
\(452\) | 1.45161e15i | 3.61899i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.24361e13 | 0.0789263 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 9.42094e12i | − 0.0221083i | −0.999939 | − | 0.0110541i | \(-0.996481\pi\) | ||||
0.999939 | − | 0.0110541i | \(-0.00351871\pi\) | |||||||
\(458\) | 1.41373e15i | 3.27799i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.97134e14 | 1.55941 | 0.779706 | − | 0.626146i | \(-0.215369\pi\) | ||||
0.779706 | + | 0.626146i | \(0.215369\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.87941e14i | 0.410513i | 0.978708 | + | 0.205256i | \(0.0658028\pi\) | ||||
−0.978708 | + | 0.205256i | \(0.934197\pi\) | |||||||
\(464\) | 4.11694e13 | 0.0888640 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.46360e12 | −0.00308531 | ||||||||
\(467\) | − 3.20007e14i | − 0.666678i | −0.942807 | − | 0.333339i | \(-0.891825\pi\) | ||||
0.942807 | − | 0.333339i | \(-0.108175\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.46917e14 | 0.298966 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.61081e13i | 0.169185i | ||||||||
\(473\) | − 6.11013e14i | − 1.18663i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.45569e14 | 0.648181 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.37477e15i | 2.51986i | ||||||||
\(479\) | −1.50382e14 | −0.272491 | −0.136245 | − | 0.990675i | \(-0.543504\pi\) | ||||
−0.136245 | + | 0.990675i | \(0.543504\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.09334e14 | 0.901996 | ||||||||
\(482\) | 6.94291e13i | 0.121558i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.90467e14 | −0.839384 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.76546e14i | 0.292045i | 0.989281 | + | 0.146022i | \(0.0466471\pi\) | ||||
−0.989281 | + | 0.146022i | \(0.953353\pi\) | |||||||
\(488\) | 7.67632e14i | 1.25558i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.60958e14 | 1.36155 | 0.680775 | − | 0.732492i | \(-0.261643\pi\) | ||||
0.680775 | + | 0.732492i | \(0.261643\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 3.31607e13i | − 0.0512821i | ||||||||
\(494\) | −1.16609e15 | −1.78334 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.95053e14 | −0.291745 | ||||||||
\(497\) | − 4.11711e14i | − 0.609021i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.01209e14 | −0.869907 | −0.434953 | − | 0.900453i | \(-0.643235\pi\) | ||||
−0.434953 | + | 0.900453i | \(0.643235\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 1.88979e15i | − 2.64571i | ||||||||
\(503\) | 1.09203e15i | 1.51221i | 0.654453 | + | 0.756103i | \(0.272899\pi\) | ||||
−0.654453 | + | 0.756103i | \(0.727101\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −7.61808e14 | −1.02098 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 1.01010e15i | − 1.32469i | ||||||||
\(509\) | 8.76371e14 | 1.13695 | 0.568474 | − | 0.822702i | \(-0.307534\pi\) | ||||
0.568474 | + | 0.822702i | \(0.307534\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.87835e14 | −0.492416 | ||||||||
\(512\) | 1.28839e15i | 1.61832i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.08784e14 | −0.748455 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 9.92308e14i | − 1.18154i | ||||||||
\(518\) | − 1.43935e15i | − 1.69571i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.71989e14 | 0.424544 | 0.212272 | − | 0.977211i | \(-0.431914\pi\) | ||||
0.212272 | + | 0.977211i | \(0.431914\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.73507e14i | 1.08788i | 0.839125 | + | 0.543939i | \(0.183068\pi\) | ||||
−0.839125 | + | 0.543939i | \(0.816932\pi\) | |||||||
\(524\) | −3.95091e14 | −0.436893 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.29445e15 | 1.40173 | ||||||||
\(527\) | 1.57109e14i | 0.168361i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.18341e14 | 0.753919 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.18605e15i | 2.22405i | ||||||||
\(533\) | 6.88699e14i | 0.693473i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8.20661e14 | −0.801230 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 2.22484e15i | − 2.12812i | ||||||||
\(539\) | −7.69683e14 | −0.728741 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.74606e15 | 1.61985 | 0.809925 | − | 0.586533i | \(-0.199508\pi\) | ||||
0.809925 | + | 0.586533i | \(0.199508\pi\) | |||||||
\(542\) | − 1.82364e15i | − 1.67472i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.82588e13 | 0.0524285 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.74624e14i | 0.152467i | 0.997090 | + | 0.0762333i | \(0.0242894\pi\) | ||||
−0.997090 | + | 0.0762333i | \(0.975711\pi\) | |||||||
\(548\) | − 6.25639e14i | − 0.540793i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.09772e14 | 0.175960 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.03282e14i | 0.0849254i | ||||||||
\(554\) | −2.36840e15 | −1.92820 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.54561e15 | −3.62811 | ||||||||
\(557\) | − 1.58365e15i | − 1.25157i | −0.779995 | − | 0.625785i | \(-0.784779\pi\) | ||||
0.779995 | − | 0.625785i | \(-0.215221\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.33993e14 | 0.568757 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.24604e15i | 0.937523i | ||||||||
\(563\) | − 9.75798e14i | − 0.727049i | −0.931585 | − | 0.363525i | \(-0.881573\pi\) | ||||
0.931585 | − | 0.363525i | \(-0.118427\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.23895e15 | −1.62015 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.29977e15i | 1.63218i | ||||||||
\(569\) | 1.92427e15 | 1.35254 | 0.676269 | − | 0.736655i | \(-0.263596\pi\) | ||||
0.676269 | + | 0.736655i | \(0.263596\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.61132e15 | 1.11092 | 0.555461 | − | 0.831543i | \(-0.312542\pi\) | ||||
0.555461 | + | 0.831543i | \(0.312542\pi\) | |||||||
\(572\) | − 1.97247e15i | − 1.34689i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.94623e15 | 1.30370 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 2.53250e15i | − 1.64848i | −0.566242 | − | 0.824239i | \(-0.691603\pi\) | ||||
0.566242 | − | 0.824239i | \(-0.308397\pi\) | |||||||
\(578\) | − 1.93118e15i | − 1.24514i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.43412e14 | 0.152536 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 2.41894e15i | − 1.48747i | ||||||||
\(584\) | 2.16640e15 | 1.31968 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.75768e15 | 2.24638 | ||||||||
\(587\) | 3.11508e15i | 1.84484i | 0.386186 | + | 0.922421i | \(0.373792\pi\) | ||||
−0.386186 | + | 0.922421i | \(0.626208\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.93860e14 | −0.577685 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.54547e15i | 1.43879i | ||||||||
\(593\) | − 2.20723e15i | − 1.23608i | −0.786146 | − | 0.618040i | \(-0.787927\pi\) | ||||
0.786146 | − | 0.618040i | \(-0.212073\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.58817e15 | 3.04379 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 9.15138e14i | − 0.489362i | ||||||||
\(599\) | 3.41159e15 | 1.80763 | 0.903813 | − | 0.427927i | \(-0.140756\pi\) | ||||
0.903813 | + | 0.427927i | \(0.140756\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.57545e15 | −0.819588 | −0.409794 | − | 0.912178i | \(-0.634399\pi\) | ||||
−0.409794 | + | 0.912178i | \(0.634399\pi\) | |||||||
\(602\) | − 2.07422e15i | − 1.06924i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.81956e15 | 1.42718 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 5.05592e14i | − 0.249036i | −0.992217 | − | 0.124518i | \(-0.960262\pi\) | ||||
0.992217 | − | 0.124518i | \(-0.0397385\pi\) | |||||||
\(608\) | 3.68541e14i | 0.179894i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.19203e15 | 0.566319 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.98375e15i | 0.925665i | 0.886446 | + | 0.462832i | \(0.153167\pi\) | ||||
−0.886446 | + | 0.462832i | \(0.846833\pi\) | |||||||
\(614\) | 2.00733e15 | 0.928310 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.74561e15 | −1.24723 | ||||||||
\(617\) | 1.93099e15i | 0.869382i | 0.900580 | + | 0.434691i | \(0.143142\pi\) | ||||
−0.900580 | + | 0.434691i | \(0.856858\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.47689e14 | −0.419148 | −0.209574 | − | 0.977793i | \(-0.567208\pi\) | ||||
−0.209574 | + | 0.977793i | \(0.567208\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.69913e15i | 1.16246i | ||||||||
\(623\) | 7.07124e14i | 0.301864i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −9.83314e14 | −0.408821 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 8.60181e15i | − 3.51408i | ||||||||
\(629\) | 2.05030e15 | 0.830306 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.00593e15 | 0.400318 | 0.200159 | − | 0.979763i | \(-0.435854\pi\) | ||||
0.200159 | + | 0.979763i | \(0.435854\pi\) | |||||||
\(632\) | − 5.76922e14i | − 0.227601i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.38230e15 | 2.47449 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 9.24597e14i | − 0.349290i | ||||||||
\(638\) | 5.34888e14i | 0.200332i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.13144e15 | −0.412966 | −0.206483 | − | 0.978450i | \(-0.566202\pi\) | ||||
−0.206483 | + | 0.978450i | \(0.566202\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.68306e14i | 0.311539i | 0.987793 | + | 0.155769i | \(0.0497857\pi\) | ||||
−0.987793 | + | 0.155769i | \(0.950214\pi\) | |||||||
\(644\) | −1.71559e15 | −0.610296 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.69405e15 | −1.64160 | ||||||||
\(647\) | 1.37636e15i | 0.477265i | 0.971110 | + | 0.238633i | \(0.0766992\pi\) | ||||
−0.971110 | + | 0.238633i | \(0.923301\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.54195e14 | −0.120753 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 6.60146e14i | − 0.219421i | ||||||||
\(653\) | 2.55276e15i | 0.841370i | 0.907207 | + | 0.420685i | \(0.138210\pi\) | ||||
−0.907207 | + | 0.420685i | \(0.861790\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.44187e15 | −1.10617 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − 3.36862e15i | − 1.06466i | ||||||||
\(659\) | 9.26792e14 | 0.290478 | 0.145239 | − | 0.989397i | \(-0.453605\pi\) | ||||
0.145239 | + | 0.989397i | \(0.453605\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.90332e15 | −0.586683 | −0.293342 | − | 0.956008i | \(-0.594767\pi\) | ||||
−0.293342 | + | 0.956008i | \(0.594767\pi\) | |||||||
\(662\) | 2.65289e15i | 0.810963i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.35967e15 | −0.408799 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.64627e14i | 0.0482847i | ||||||||
\(668\) | − 3.55548e13i | − 0.0103426i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.15756e15 | −0.896143 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 4.92990e15i | − 1.37643i | −0.725505 | − | 0.688217i | \(-0.758394\pi\) | ||||
0.725505 | − | 0.688217i | \(-0.241606\pi\) | |||||||
\(674\) | −4.67563e15 | −1.29482 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.86369e15 | −1.32513 | ||||||||
\(677\) | − 4.30293e14i | − 0.116286i | −0.998308 | − | 0.0581429i | \(-0.981482\pi\) | ||||
0.998308 | − | 0.0581429i | \(-0.0185179\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.08521e15 | −0.288555 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 2.53420e15i | − 0.657698i | ||||||||
\(683\) | − 3.81244e15i | − 0.981498i | −0.871301 | − | 0.490749i | \(-0.836723\pi\) | ||||
0.871301 | − | 0.490749i | \(-0.163277\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.89433e15 | −1.73264 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.66823e15i | 0.907236i | ||||||||
\(689\) | 2.90580e15 | 0.712952 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.03729e15 | 0.974901 | 0.487450 | − | 0.873151i | \(-0.337927\pi\) | ||||
0.487450 | + | 0.873151i | \(0.337927\pi\) | |||||||
\(692\) | 2.94972e15i | 0.706638i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.63374e15 | −1.79995 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.77232e15i | 0.638356i | ||||||||
\(698\) | − 1.11376e16i | − 2.54441i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.71267e15 | 1.05152 | 0.525761 | − | 0.850632i | \(-0.323781\pi\) | ||||
0.525761 | + | 0.850632i | \(0.323781\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.29700e16i | 2.84896i | ||||||||
\(704\) | −5.94185e15 | −1.29501 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.12512e16 | 2.41419 | ||||||||
\(707\) | 2.58467e14i | 0.0550299i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.66706e14 | −0.181684 | −0.0908422 | − | 0.995865i | \(-0.528956\pi\) | ||||
−0.0908422 | + | 0.995865i | \(0.528956\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 3.94991e15i | − 0.808997i | ||||||||
\(713\) | − 7.79972e14i | − 0.158521i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.58361e16 | −3.14505 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.69924e15i | 1.89694i | ||||||||
\(719\) | 2.62666e13 | 0.00509795 | 0.00254897 | − | 0.999997i | \(-0.499189\pi\) | ||||
0.00254897 | + | 0.999997i | \(0.499189\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.34844e15 | −0.257744 | ||||||||
\(722\) | − 2.06080e16i | − 3.90913i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9.19929e15 | −1.71867 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 5.68018e15i | − 1.03734i | −0.854973 | − | 0.518672i | \(-0.826427\pi\) | ||||
0.854973 | − | 0.518672i | \(-0.173573\pi\) | |||||||
\(728\) | − 3.29823e15i | − 0.597803i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.95465e15 | 0.523552 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.62312e15i | 0.283320i | 0.989915 | + | 0.141660i | \(0.0452440\pi\) | ||||
−0.989915 | + | 0.141660i | \(0.954756\pi\) | |||||||
\(734\) | −1.24885e16 | −2.16363 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.89227e14 | −0.0493641 | ||||||||
\(737\) | − 3.37568e15i | − 0.571861i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.64794e15 | −0.608840 | −0.304420 | − | 0.952538i | \(-0.598463\pi\) | ||||
−0.304420 | + | 0.952538i | \(0.598463\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − 8.21164e15i | − 1.34032i | ||||||||
\(743\) | 6.76045e15i | 1.09531i | 0.836704 | + | 0.547655i | \(0.184479\pi\) | ||||
−0.836704 | + | 0.547655i | \(0.815521\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.70861e15 | 0.429224 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 7.94007e15i | − 1.23984i | ||||||||
\(749\) | −6.26254e15 | −0.970734 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.64833e13 | 0.00404532 | 0.00202266 | − | 0.999998i | \(-0.499356\pi\) | ||||
0.00202266 | + | 0.999998i | \(0.499356\pi\) | |||||||
\(752\) | 5.95734e15i | 0.903347i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.42546e14 | −0.0960200 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.37364e15i | 1.07809i | 0.842277 | + | 0.539045i | \(0.181215\pi\) | ||||
−0.842277 | + | 0.539045i | \(0.818785\pi\) | |||||||
\(758\) | − 1.14270e16i | − 1.65864i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.20983e15 | −0.881991 | −0.440996 | − | 0.897509i | \(-0.645375\pi\) | ||||
−0.440996 | + | 0.897509i | \(0.645375\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 1.92796e15i | − 0.269907i | ||||||||
\(764\) | 1.36703e16 | 1.90005 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.01866e15 | 0.687591 | ||||||||
\(767\) | − 4.25484e14i | − 0.0578774i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.86195e15 | 1.18832 | 0.594162 | − | 0.804346i | \(-0.297484\pi\) | ||||
0.594162 | + | 0.804346i | \(0.297484\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 1.98943e16i | − 2.61116i | ||||||||
\(773\) | − 2.95047e15i | − 0.384507i | −0.981345 | − | 0.192254i | \(-0.938420\pi\) | ||||
0.981345 | − | 0.192254i | \(-0.0615796\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.06184e15 | 0.773330 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.11142e15i | 0.391355i | ||||||||
\(779\) | −1.75375e16 | −2.19034 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.45980e15 | −1.16493 | ||||||||
\(782\) | − 3.68384e15i | − 0.450468i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.62081e15 | 0.557160 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.35545e16i | 1.60038i | 0.599746 | + | 0.800190i | \(0.295268\pi\) | ||||
−0.599746 | + | 0.800190i | \(0.704732\pi\) | |||||||
\(788\) | 2.56603e16i | 3.00862i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.98429e15 | −1.14643 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 3.79308e15i | − 0.429526i | ||||||||
\(794\) | 8.31105e15 | 0.934638 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.52784e16 | −1.69456 | ||||||||
\(797\) | 1.59922e16i | 1.76152i | 0.473558 | + | 0.880762i | \(0.342969\pi\) | ||||
−0.473558 | + | 0.880762i | \(0.657031\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.79846e15 | 0.521308 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.66327e15i | 0.283437i | ||||||||
\(803\) | 8.91121e15i | 0.941892i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.04426e15 | 0.315238 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 1.44377e15i | − 0.147481i | ||||||||
\(809\) | 9.45859e15 | 0.959643 | 0.479821 | − | 0.877366i | \(-0.340701\pi\) | ||||
0.479821 | + | 0.877366i | \(0.340701\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.07996e16 | −1.08092 | −0.540461 | − | 0.841369i | \(-0.681750\pi\) | ||||
−0.540461 | + | 0.841369i | \(0.681750\pi\) | |||||||
\(812\) | 1.20456e15i | 0.119749i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.30717e16 | −3.24356 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.86909e16i | 1.79642i | ||||||||
\(818\) | 4.16012e15i | 0.397158i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.10411e16 | 1.03306 | 0.516529 | − | 0.856270i | \(-0.327224\pi\) | ||||
0.516529 | + | 0.856270i | \(0.327224\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 1.26104e16i | − 1.16420i | −0.813117 | − | 0.582101i | \(-0.802231\pi\) | ||||
0.813117 | − | 0.582101i | \(-0.197769\pi\) | |||||||
\(824\) | 7.53224e15 | 0.690756 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.20239e15 | −0.108807 | ||||||||
\(827\) | 7.86172e14i | 0.0706704i | 0.999376 | + | 0.0353352i | \(0.0112499\pi\) | ||||
−0.999376 | + | 0.0353352i | \(0.988750\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.92589e15 | 0.525659 | 0.262829 | − | 0.964842i | \(-0.415344\pi\) | ||||
0.262829 | + | 0.964842i | \(0.415344\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 7.13777e15i | − 0.620704i | ||||||||
\(833\) | − 3.72192e15i | − 0.321528i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5.02283e16 | 4.25416 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.90044e15i | 0.660403i | ||||||||
\(839\) | 2.10209e16 | 1.74566 | 0.872831 | − | 0.488022i | \(-0.162282\pi\) | ||||
0.872831 | + | 0.488022i | \(0.162282\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.20849e16 | −0.990526 | ||||||||
\(842\) | 1.23184e16i | 1.00309i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.24437e14 | −0.0582260 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 3.37348e15i | − 0.265901i | ||||||||
\(848\) | 1.45222e16i | 1.13725i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.01788e16 | −0.781775 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.98378e16i | 1.50409i | 0.659110 | + | 0.752046i | \(0.270933\pi\) | ||||
−0.659110 | + | 0.752046i | \(0.729067\pi\) | |||||||
\(854\) | −1.07190e16 | −0.807491 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.49818e16 | 2.60157 | ||||||||
\(857\) | − 7.96639e15i | − 0.588663i | −0.955703 | − | 0.294332i | \(-0.904903\pi\) | ||||
0.955703 | − | 0.294332i | \(-0.0950970\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.59749e16 | 1.16540 | 0.582701 | − | 0.812687i | \(-0.301996\pi\) | ||||
0.582701 | + | 0.812687i | \(0.301996\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.00274e16i | 2.86462i | ||||||||
\(863\) | − 4.02926e15i | − 0.286527i | −0.989685 | − | 0.143264i | \(-0.954240\pi\) | ||||
0.989685 | − | 0.143264i | \(-0.0457596\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5.84413e15 | 0.407729 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 5.70699e15i | − 0.393142i | ||||||||
\(869\) | 2.37310e15 | 0.162445 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.05511e15 | 0.274096 | ||||||||
\(872\) | 1.07694e16i | 0.723352i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.33037e16 | 1.54565 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.76958e15i | 0.635884i | 0.948110 | + | 0.317942i | \(0.102992\pi\) | ||||
−0.948110 | + | 0.317942i | \(0.897008\pi\) | |||||||
\(878\) | − 2.87301e16i | − 1.85831i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.62583e16 | −1.03207 | −0.516033 | − | 0.856569i | \(-0.672592\pi\) | ||||
−0.516033 | + | 0.856569i | \(0.672592\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1.66061e16i | − 1.04108i | −0.853837 | − | 0.520540i | \(-0.825731\pi\) | ||||
0.853837 | − | 0.520540i | \(-0.174269\pi\) | |||||||
\(884\) | 9.53818e15 | 0.594262 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.67733e15 | −0.533950 | ||||||||
\(887\) | 1.91314e16i | 1.16995i | 0.811051 | + | 0.584975i | \(0.198896\pi\) | ||||
−0.811051 | + | 0.584975i | \(0.801104\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.94758e15 | 0.419637 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.98286e15i | 0.532608i | ||||||||
\(893\) | 3.03547e16i | 1.78872i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.90971e16 | −1.10477 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.88985e15i | 0.393722i | ||||||||
\(899\) | −5.47641e14 | −0.0311041 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.16972e16 | 0.656287 | ||||||||
\(902\) | − 4.47180e16i | − 2.49372i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.57710e16 | 3.07243 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1.07252e16i | − 0.580182i | −0.956999 | − | 0.290091i | \(-0.906314\pi\) | ||||
0.956999 | − | 0.290091i | \(-0.0936855\pi\) | |||||||
\(908\) | − 1.67836e15i | − 0.0902430i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.82249e16 | 1.49032 | 0.745162 | − | 0.666883i | \(-0.232372\pi\) | ||||
0.745162 | + | 0.666883i | \(0.232372\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 5.59284e15i | − 0.291771i | ||||||||
\(914\) | −7.34833e14 | −0.0381052 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.31516e16 | 3.74799 | ||||||||
\(917\) | − 2.71748e15i | − 0.138399i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.83551e16 | −0.923679 | −0.461839 | − | 0.886964i | \(-0.652810\pi\) | ||||
−0.461839 | + | 0.886964i | \(0.652810\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 5.43764e16i | − 2.68776i | ||||||||
\(923\) | − 1.13638e16i | − 0.558359i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.46594e16 | 0.707549 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.03075e14i | 0.00968596i | ||||||||
\(929\) | −1.10125e16 | −0.522155 | −0.261078 | − | 0.965318i | \(-0.584078\pi\) | ||||
−0.261078 | + | 0.965318i | \(0.584078\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.35446e16 | 1.10323 | ||||||||
\(932\) | 7.57317e13i | 0.00352769i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.49605e16 | −1.14907 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.36357e15i | 0.378289i | 0.981949 | + | 0.189145i | \(0.0605715\pi\) | ||||
−0.981949 | + | 0.189145i | \(0.939429\pi\) | |||||||
\(938\) | − 1.14595e16i | − 0.515289i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.22942e16 | −0.985028 | −0.492514 | − | 0.870305i | \(-0.663922\pi\) | ||||
−0.492514 | + | 0.870305i | \(0.663922\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1.37633e16i | − 0.601045i | ||||||||
\(944\) | 2.12642e15 | 0.0923214 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.76590e16 | −2.04524 | ||||||||
\(947\) | 3.78038e16i | 1.61291i | 0.591293 | + | 0.806457i | \(0.298618\pi\) | ||||
−0.591293 | + | 0.806457i | \(0.701382\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.07048e16 | −0.451454 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 1.32768e16i | − 0.550290i | ||||||||
\(953\) | 4.79568e15i | 0.197624i | 0.995106 | + | 0.0988119i | \(0.0315042\pi\) | ||||
−0.995106 | + | 0.0988119i | \(0.968496\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 7.11355e16 | 2.88116 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.17298e16i | 0.469657i | ||||||||
\(959\) | 4.30321e15 | 0.171313 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.28139e16 | −0.897884 | ||||||||
\(962\) | − 3.97280e16i | − 1.55466i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.59251e15 | 0.138987 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.37420e16i | 1.28329i | 0.767002 | + | 0.641645i | \(0.221748\pi\) | ||||
−0.767002 | + | 0.641645i | \(0.778252\pi\) | |||||||
\(968\) | 1.88439e16i | 0.712616i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.58587e16 | −1.33318 | −0.666590 | − | 0.745425i | \(-0.732247\pi\) | ||||
−0.666590 | + | 0.745425i | \(0.732247\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 3.12651e16i | − 1.14932i | ||||||||
\(974\) | 1.37706e16 | 0.503360 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.89565e16 | 0.685147 | ||||||||
\(977\) | 1.20023e16i | 0.431366i | 0.976463 | + | 0.215683i | \(0.0691977\pi\) | ||||
−0.976463 | + | 0.215683i | \(0.930802\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.62474e16 | 0.577405 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 6.71547e16i | − 2.34673i | ||||||||
\(983\) | − 4.42687e15i | − 0.153834i | −0.997038 | − | 0.0769170i | \(-0.975492\pi\) | ||||
0.997038 | − | 0.0769170i | \(-0.0245076\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.58653e15 | −0.0883884 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.03378e16i | 2.03904i | ||||||||
\(989\) | −1.46684e16 | −0.492951 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.79167e16 | −1.26016 | −0.630080 | − | 0.776530i | \(-0.716978\pi\) | ||||
−0.630080 | + | 0.776530i | \(0.716978\pi\) | |||||||
\(992\) | − 9.62130e14i | − 0.0317994i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.21135e16 | −1.04969 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.76003e13i | 0.00185183i | 1.00000 | 0.000925915i | \(0.000294728\pi\) | |||||
−1.00000 | 0.000925915i | \(0.999705\pi\) | ||||||||
\(998\) | 4.68943e16i | 1.49935i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 225.12.b.a.199.1 | 2 | ||
3.2 | odd | 2 | 75.12.b.a.49.2 | 2 | |||
5.2 | odd | 4 | 225.12.a.f.1.1 | 1 | |||
5.3 | odd | 4 | 9.12.a.a.1.1 | 1 | |||
5.4 | even | 2 | inner | 225.12.b.a.199.2 | 2 | ||
15.2 | even | 4 | 75.12.a.a.1.1 | 1 | |||
15.8 | even | 4 | 3.12.a.a.1.1 | ✓ | 1 | ||
15.14 | odd | 2 | 75.12.b.a.49.1 | 2 | |||
20.3 | even | 4 | 144.12.a.l.1.1 | 1 | |||
45.13 | odd | 12 | 81.12.c.e.55.1 | 2 | |||
45.23 | even | 12 | 81.12.c.a.55.1 | 2 | |||
45.38 | even | 12 | 81.12.c.a.28.1 | 2 | |||
45.43 | odd | 12 | 81.12.c.e.28.1 | 2 | |||
60.23 | odd | 4 | 48.12.a.f.1.1 | 1 | |||
105.83 | odd | 4 | 147.12.a.c.1.1 | 1 | |||
120.53 | even | 4 | 192.12.a.q.1.1 | 1 | |||
120.83 | odd | 4 | 192.12.a.g.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.12.a.a.1.1 | ✓ | 1 | 15.8 | even | 4 | ||
9.12.a.a.1.1 | 1 | 5.3 | odd | 4 | |||
48.12.a.f.1.1 | 1 | 60.23 | odd | 4 | |||
75.12.a.a.1.1 | 1 | 15.2 | even | 4 | |||
75.12.b.a.49.1 | 2 | 15.14 | odd | 2 | |||
75.12.b.a.49.2 | 2 | 3.2 | odd | 2 | |||
81.12.c.a.28.1 | 2 | 45.38 | even | 12 | |||
81.12.c.a.55.1 | 2 | 45.23 | even | 12 | |||
81.12.c.e.28.1 | 2 | 45.43 | odd | 12 | |||
81.12.c.e.55.1 | 2 | 45.13 | odd | 12 | |||
144.12.a.l.1.1 | 1 | 20.3 | even | 4 | |||
147.12.a.c.1.1 | 1 | 105.83 | odd | 4 | |||
192.12.a.g.1.1 | 1 | 120.83 | odd | 4 | |||
192.12.a.q.1.1 | 1 | 120.53 | even | 4 | |||
225.12.a.f.1.1 | 1 | 5.2 | odd | 4 | |||
225.12.b.a.199.1 | 2 | 1.1 | even | 1 | trivial | ||
225.12.b.a.199.2 | 2 | 5.4 | even | 2 | inner |