Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,10,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, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.199");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
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: | \(115.883063137\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 1305x^{4} + 433104x^{2} + 16000000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2}\cdot 5^{8} \) |
Twist minimal: | no (minimal twist has level 25) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.3 | ||
Root | \(-6.48955i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.199 |
Dual form | 225.10.b.m.199.4 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 20.2014i | − 0.892785i | −0.894837 | − | 0.446393i | \(-0.852709\pi\) | ||||
0.894837 | − | 0.446393i | \(-0.147291\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 103.903 | 0.202935 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4010.25i | 0.631292i | 0.948877 | + | 0.315646i | \(0.102221\pi\) | ||||
−0.948877 | + | 0.315646i | \(0.897779\pi\) | |||||||
\(8\) | − 12442.1i | − 1.07396i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 42110.0 | 0.867198 | 0.433599 | − | 0.901106i | \(-0.357243\pi\) | ||||
0.433599 | + | 0.901106i | \(0.357243\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 123743.i | 1.20165i | 0.799382 | + | 0.600824i | \(0.205161\pi\) | ||||
−0.799382 | + | 0.600824i | \(0.794839\pi\) | |||||||
\(14\) | 81012.8 | 0.563608 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −198150. | −0.755883 | ||||||||
\(17\) | 319945.i | 0.929085i | 0.885551 | + | 0.464543i | \(0.153781\pi\) | ||||
−0.885551 | + | 0.464543i | \(0.846219\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.08733e6 | −1.91412 | −0.957059 | − | 0.289893i | \(-0.906380\pi\) | ||||
−0.957059 | + | 0.289893i | \(0.906380\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 850682.i | − 0.774221i | ||||||||
\(23\) | − 1.50672e6i | − 1.12268i | −0.827585 | − | 0.561341i | \(-0.810286\pi\) | ||||
0.827585 | − | 0.561341i | \(-0.189714\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.49979e6 | 1.07281 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 416676.i | 0.128111i | ||||||||
\(29\) | −2.62160e6 | −0.688295 | −0.344148 | − | 0.938916i | \(-0.611832\pi\) | ||||
−0.344148 | + | 0.938916i | \(0.611832\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.27023e6 | 0.635991 | 0.317996 | − | 0.948092i | \(-0.396990\pi\) | ||||
0.317996 | + | 0.948092i | \(0.396990\pi\) | |||||||
\(32\) | − 2.36745e6i | − 0.399122i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.46335e6 | 0.829473 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.51034e6i | 0.220204i | 0.993920 | + | 0.110102i | \(0.0351177\pi\) | ||||
−0.993920 | + | 0.110102i | \(0.964882\pi\) | |||||||
\(38\) | 2.19655e7i | 1.70890i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.95349e7 | −1.63233 | −0.816165 | − | 0.577819i | \(-0.803904\pi\) | ||||
−0.816165 | + | 0.577819i | \(0.803904\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 1.42413e7i | − 0.635244i | −0.948217 | − | 0.317622i | \(-0.897116\pi\) | ||||
0.948217 | − | 0.317622i | \(-0.102884\pi\) | |||||||
\(44\) | 4.37534e6 | 0.175985 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.04378e7 | −1.00231 | ||||||||
\(47\) | 1.35318e6i | 0.0404496i | 0.999795 | + | 0.0202248i | \(0.00643820\pi\) | ||||
−0.999795 | + | 0.0202248i | \(0.993562\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.42715e7 | 0.601470 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.28573e7i | 0.243856i | ||||||||
\(53\) | − 9.73342e7i | − 1.69443i | −0.531249 | − | 0.847216i | \(-0.678277\pi\) | ||||
0.531249 | − | 0.847216i | \(-0.321723\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.98960e7 | 0.677984 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.29599e7i | 0.614500i | ||||||||
\(59\) | −7.48924e6 | −0.0804644 | −0.0402322 | − | 0.999190i | \(-0.512810\pi\) | ||||
−0.0402322 | + | 0.999190i | \(0.512810\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.11752e7 | −0.843126 | −0.421563 | − | 0.906799i | \(-0.638518\pi\) | ||||
−0.421563 | + | 0.906799i | \(0.638518\pi\) | |||||||
\(62\) | − 6.60633e7i | − 0.567803i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.49279e8 | −1.11221 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 2.94376e8i | − 1.78470i | −0.451344 | − | 0.892350i | \(-0.649055\pi\) | ||||
0.451344 | − | 0.892350i | \(-0.350945\pi\) | |||||||
\(68\) | 3.32432e7i | 0.188544i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.56193e8 | −0.729455 | −0.364728 | − | 0.931114i | \(-0.618838\pi\) | ||||
−0.364728 | + | 0.931114i | \(0.618838\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 2.82539e8i | − 1.16446i | −0.813023 | − | 0.582232i | \(-0.802180\pi\) | ||||
0.813023 | − | 0.582232i | \(-0.197820\pi\) | |||||||
\(74\) | 5.07124e7 | 0.196594 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.12976e8 | −0.388441 | ||||||||
\(77\) | 1.68872e8i | 0.547455i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.55294e8 | 1.60399 | 0.801994 | − | 0.597332i | \(-0.203772\pi\) | ||||
0.801994 | + | 0.597332i | \(0.203772\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.96647e8i | 1.45732i | ||||||||
\(83\) | − 6.48378e6i | − 0.0149960i | −0.999972 | − | 0.00749802i | \(-0.997613\pi\) | ||||
0.999972 | − | 0.00749802i | \(-0.00238672\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.87694e8 | −0.567137 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 5.23937e8i | − 0.931338i | ||||||||
\(89\) | −5.99001e8 | −1.01198 | −0.505990 | − | 0.862539i | \(-0.668873\pi\) | ||||
−0.505990 | + | 0.862539i | \(0.668873\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.96242e8 | −0.758591 | ||||||||
\(92\) | − 1.56552e8i | − 0.227831i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.73361e7 | 0.0361128 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 9.25317e8i | − 1.06125i | −0.847606 | − | 0.530625i | \(-0.821957\pi\) | ||||
0.847606 | − | 0.530625i | \(-0.178043\pi\) | |||||||
\(98\) | − 4.90319e8i | − 0.536984i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.58959e8 | −0.916967 | −0.458483 | − | 0.888703i | \(-0.651607\pi\) | ||||
−0.458483 | + | 0.888703i | \(0.651607\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.60441e8i | 0.140458i | 0.997531 | + | 0.0702292i | \(0.0223731\pi\) | ||||
−0.997531 | + | 0.0702292i | \(0.977627\pi\) | |||||||
\(104\) | 1.53963e9 | 1.29052 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.96629e9 | −1.51276 | ||||||||
\(107\) | 9.60457e8i | 0.708355i | 0.935178 | + | 0.354178i | \(0.115239\pi\) | ||||
−0.935178 | + | 0.354178i | \(0.884761\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.98912e8 | −0.677810 | −0.338905 | − | 0.940821i | \(-0.610057\pi\) | ||||
−0.338905 | + | 0.940821i | \(0.610057\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 7.94632e8i | − 0.477183i | ||||||||
\(113\) | − 2.50705e9i | − 1.44647i | −0.690601 | − | 0.723236i | \(-0.742654\pi\) | ||||
0.690601 | − | 0.723236i | \(-0.257346\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.72391e8 | −0.139679 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.51293e8i | 0.0718374i | ||||||||
\(119\) | −1.28306e9 | −0.586524 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.84695e8 | −0.247968 | ||||||||
\(122\) | 1.84187e9i | 0.752730i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.39786e8 | 0.129065 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.47541e9i | 0.844364i | 0.906511 | + | 0.422182i | \(0.138736\pi\) | ||||
−0.906511 | + | 0.422182i | \(0.861264\pi\) | |||||||
\(128\) | 1.80351e9i | 0.593845i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.92402e9 | −0.570808 | −0.285404 | − | 0.958407i | \(-0.592128\pi\) | ||||
−0.285404 | + | 0.958407i | \(0.592128\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 4.36045e9i | − 1.20837i | ||||||||
\(134\) | −5.94680e9 | −1.59335 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.98079e9 | 0.997802 | ||||||||
\(137\) | 4.48594e8i | 0.108796i | 0.998519 | + | 0.0543978i | \(0.0173239\pi\) | ||||
−0.998519 | + | 0.0543978i | \(0.982676\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.48415e9 | −1.01886 | −0.509429 | − | 0.860513i | \(-0.670143\pi\) | ||||
−0.509429 | + | 0.860513i | \(0.670143\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.15532e9i | 0.651247i | ||||||||
\(143\) | 5.21084e9i | 1.04207i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.70769e9 | −1.03962 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.60831e8i | 0.0446870i | ||||||||
\(149\) | −2.20480e9 | −0.366463 | −0.183232 | − | 0.983070i | \(-0.558656\pi\) | ||||
−0.183232 | + | 0.983070i | \(0.558656\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.21248e9 | −0.502857 | −0.251428 | − | 0.967876i | \(-0.580900\pi\) | ||||
−0.251428 | + | 0.967876i | \(0.580900\pi\) | |||||||
\(152\) | 1.35286e10i | 2.05569i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.41145e9 | 0.488760 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.08870e10i | 1.43007i | 0.699088 | + | 0.715036i | \(0.253590\pi\) | ||||
−0.699088 | + | 0.715036i | \(0.746410\pi\) | |||||||
\(158\) | − 1.12177e10i | − 1.43202i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.04232e9 | 0.708740 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.19994e10i | 1.33142i | 0.746212 | + | 0.665708i | \(0.231870\pi\) | ||||
−0.746212 | + | 0.665708i | \(0.768130\pi\) | |||||||
\(164\) | −3.06875e9 | −0.331257 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.30982e8 | −0.0133882 | ||||||||
\(167\) | 9.68608e9i | 0.963660i | 0.876265 | + | 0.481830i | \(0.160028\pi\) | ||||
−0.876265 | + | 0.481830i | \(0.839972\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.70793e9 | −0.443956 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 1.47971e9i | − 0.128913i | ||||||||
\(173\) | − 7.35665e9i | − 0.624414i | −0.950014 | − | 0.312207i | \(-0.898932\pi\) | ||||
0.950014 | − | 0.312207i | \(-0.101068\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −8.34410e9 | −0.655500 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.21007e10i | 0.903481i | ||||||||
\(179\) | −2.00351e9 | −0.145866 | −0.0729329 | − | 0.997337i | \(-0.523236\pi\) | ||||
−0.0729329 | + | 0.997337i | \(0.523236\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.63414e9 | 0.390188 | 0.195094 | − | 0.980785i | \(-0.437499\pi\) | ||||
0.195094 | + | 0.980785i | \(0.437499\pi\) | |||||||
\(182\) | 1.00248e10i | 0.677258i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.87467e10 | −1.20572 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.34729e10i | 0.805701i | ||||||||
\(188\) | 1.40599e8i | 0.00820864i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.16925e9 | −0.498521 | −0.249261 | − | 0.968436i | \(-0.580188\pi\) | ||||
−0.249261 | + | 0.968436i | \(0.580188\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 3.16327e10i | − 1.64107i | −0.571594 | − | 0.820536i | \(-0.693675\pi\) | ||||
0.571594 | − | 0.820536i | \(-0.306325\pi\) | |||||||
\(194\) | −1.86927e10 | −0.947469 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.52187e9 | 0.122059 | ||||||||
\(197\) | 2.59858e10i | 1.22924i | 0.788822 | + | 0.614621i | \(0.210691\pi\) | ||||
−0.788822 | + | 0.614621i | \(0.789309\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.05766e10 | −0.478088 | −0.239044 | − | 0.971009i | \(-0.576834\pi\) | ||||
−0.239044 | + | 0.971009i | \(0.576834\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.93723e10i | 0.818654i | ||||||||
\(203\) | − 1.05133e10i | − 0.434515i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.24113e9 | 0.125399 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 2.45198e10i | − 0.908304i | ||||||||
\(209\) | −4.57873e10 | −1.65992 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.80228e10 | 0.625965 | 0.312983 | − | 0.949759i | \(-0.398672\pi\) | ||||
0.312983 | + | 0.949759i | \(0.398672\pi\) | |||||||
\(212\) | − 1.01133e10i | − 0.343859i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.94026e10 | 0.632409 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.31145e10i | 0.401496i | ||||||||
\(218\) | 2.01794e10i | 0.605139i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.95911e10 | −1.11643 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.44522e10i | 1.20371i | 0.798606 | + | 0.601855i | \(0.205571\pi\) | ||||
−0.798606 | + | 0.601855i | \(0.794429\pi\) | |||||||
\(224\) | 9.49405e9 | 0.251962 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.06460e10 | −1.29139 | ||||||||
\(227\) | 5.59677e10i | 1.39901i | 0.714627 | + | 0.699505i | \(0.246596\pi\) | ||||
−0.714627 | + | 0.699505i | \(0.753404\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.47705e9 | 0.0354923 | 0.0177462 | − | 0.999843i | \(-0.494351\pi\) | ||||
0.0177462 | + | 0.999843i | \(0.494351\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.26182e10i | 0.739203i | ||||||||
\(233\) | 7.83279e9i | 0.174106i | 0.996204 | + | 0.0870532i | \(0.0277450\pi\) | ||||
−0.996204 | + | 0.0870532i | \(0.972255\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7.78152e8 | −0.0163290 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.59197e10i | 0.523640i | ||||||||
\(239\) | 5.56371e10 | 1.10300 | 0.551498 | − | 0.834176i | \(-0.314057\pi\) | ||||
0.551498 | + | 0.834176i | \(0.314057\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.16053e10 | −0.221606 | −0.110803 | − | 0.993842i | \(-0.535342\pi\) | ||||
−0.110803 | + | 0.993842i | \(0.535342\pi\) | |||||||
\(242\) | 1.18117e10i | 0.221382i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9.47334e9 | −0.171100 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 1.34549e11i | − 2.30009i | ||||||||
\(248\) | − 4.06886e10i | − 0.683030i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.45974e10 | 0.550189 | 0.275094 | − | 0.961417i | \(-0.411291\pi\) | ||||
0.275094 | + | 0.961417i | \(0.411291\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 6.34479e10i | − 0.973587i | ||||||||
\(254\) | 5.00067e10 | 0.753836 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.99972e10 | −0.582036 | ||||||||
\(257\) | − 3.67735e10i | − 0.525818i | −0.964821 | − | 0.262909i | \(-0.915318\pi\) | ||||
0.964821 | − | 0.262909i | \(-0.0846820\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.00671e10 | −0.139013 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.88680e10i | 0.509609i | ||||||||
\(263\) | − 1.33758e11i | − 1.72392i | −0.506974 | − | 0.861962i | \(-0.669236\pi\) | ||||
0.506974 | − | 0.861962i | \(-0.330764\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8.80873e10 | −1.07881 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 3.05864e10i | − 0.362178i | ||||||||
\(269\) | −1.42461e11 | −1.65886 | −0.829429 | − | 0.558612i | \(-0.811334\pi\) | ||||
−0.829429 | + | 0.558612i | \(0.811334\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.11046e11 | −1.25067 | −0.625333 | − | 0.780358i | \(-0.715037\pi\) | ||||
−0.625333 | + | 0.780358i | \(0.715037\pi\) | |||||||
\(272\) | − 6.33972e10i | − 0.702279i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.06224e9 | 0.0971310 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 2.80726e10i | − 0.286500i | −0.989687 | − | 0.143250i | \(-0.954245\pi\) | ||||
0.989687 | − | 0.143250i | \(-0.0457552\pi\) | |||||||
\(278\) | 9.05861e10i | 0.909620i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.47143e10 | −0.523507 | −0.261753 | − | 0.965135i | \(-0.584301\pi\) | ||||
−0.261753 | + | 0.965135i | \(0.584301\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 1.09950e11i | − 1.01895i | −0.860484 | − | 0.509477i | \(-0.829839\pi\) | ||||
0.860484 | − | 0.509477i | \(-0.170161\pi\) | |||||||
\(284\) | −1.62288e10 | −0.148032 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.05266e11 | 0.930341 | ||||||||
\(287\) | − 1.18442e11i | − 1.03048i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.62229e10 | 0.136801 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 2.93566e10i | − 0.236310i | ||||||||
\(293\) | 2.30453e11i | 1.82675i | 0.407124 | + | 0.913373i | \(0.366532\pi\) | ||||
−0.407124 | + | 0.913373i | \(0.633468\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.12339e10 | 0.236490 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.45400e10i | 0.327173i | ||||||||
\(299\) | 1.86446e11 | 1.34907 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.71111e10 | 0.401025 | ||||||||
\(302\) | 6.48966e10i | 0.448943i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.15454e11 | 1.44685 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 6.85036e10i | − 0.440140i | −0.975484 | − | 0.220070i | \(-0.929371\pi\) | ||||
0.975484 | − | 0.220070i | \(-0.0706286\pi\) | |||||||
\(308\) | 1.75462e10i | 0.111098i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.98797e11 | 1.20500 | 0.602502 | − | 0.798118i | \(-0.294171\pi\) | ||||
0.602502 | + | 0.798118i | \(0.294171\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 6.15202e10i | − 0.362300i | −0.983455 | − | 0.181150i | \(-0.942018\pi\) | ||||
0.983455 | − | 0.181150i | \(-0.0579820\pi\) | |||||||
\(314\) | 2.19932e11 | 1.27675 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.76965e10 | 0.325505 | ||||||||
\(317\) | − 2.25932e11i | − 1.25664i | −0.777955 | − | 0.628320i | \(-0.783743\pi\) | ||||
0.777955 | − | 0.628320i | \(-0.216257\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.10395e11 | −0.596888 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − 1.22063e11i | − 0.632753i | ||||||||
\(323\) | − 3.47885e11i | − 1.77838i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.42404e11 | 1.18867 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.67476e11i | 1.75306i | ||||||||
\(329\) | −5.42658e9 | −0.0255355 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.38825e10 | −0.384101 | −0.192050 | − | 0.981385i | \(-0.561514\pi\) | ||||
−0.192050 | + | 0.981385i | \(0.561514\pi\) | |||||||
\(332\) | − 6.73682e8i | − 0.00304322i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.95673e11 | 0.860341 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.19457e11i | 0.926862i | 0.886133 | + | 0.463431i | \(0.153382\pi\) | ||||
−0.886133 | + | 0.463431i | \(0.846618\pi\) | |||||||
\(338\) | 9.51069e10i | 0.396357i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.37710e11 | 0.551530 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.59163e11i | 1.01100i | ||||||||
\(344\) | −1.77191e11 | −0.682228 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.48615e11 | −0.557467 | ||||||||
\(347\) | − 1.85960e11i | − 0.688551i | −0.938869 | − | 0.344276i | \(-0.888125\pi\) | ||||
0.938869 | − | 0.344276i | \(-0.111875\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.73237e11 | −0.985881 | −0.492940 | − | 0.870063i | \(-0.664078\pi\) | ||||
−0.492940 | + | 0.870063i | \(0.664078\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 9.96932e10i | − 0.346117i | ||||||||
\(353\) | 3.02861e11i | 1.03814i | 0.854731 | + | 0.519072i | \(0.173722\pi\) | ||||
−0.854731 | + | 0.519072i | \(0.826278\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.22378e10 | −0.205366 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.04738e10i | 0.130227i | ||||||||
\(359\) | 2.47660e11 | 0.786919 | 0.393460 | − | 0.919342i | \(-0.371278\pi\) | ||||
0.393460 | + | 0.919342i | \(0.371278\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.59591e11 | 2.66385 | ||||||||
\(362\) | − 1.13818e11i | − 0.348354i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.15609e10 | −0.153944 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 2.66354e11i | − 0.766412i | −0.923663 | − | 0.383206i | \(-0.874820\pi\) | ||||
0.923663 | − | 0.383206i | \(-0.125180\pi\) | |||||||
\(368\) | 2.98556e11i | 0.848616i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.90335e11 | 1.06968 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 5.20850e11i | − 1.39323i | −0.717445 | − | 0.696616i | \(-0.754688\pi\) | ||||
0.717445 | − | 0.696616i | \(-0.245312\pi\) | |||||||
\(374\) | 2.72172e11 | 0.719318 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.68364e10 | 0.0434414 | ||||||||
\(377\) | − 3.24405e11i | − 0.827088i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.28308e10 | −0.0817344 | −0.0408672 | − | 0.999165i | \(-0.513012\pi\) | ||||
−0.0408672 | + | 0.999165i | \(0.513012\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.85232e11i | 0.445072i | ||||||||
\(383\) | 7.15293e10i | 0.169859i | 0.996387 | + | 0.0849297i | \(0.0270666\pi\) | ||||
−0.996387 | + | 0.0849297i | \(0.972933\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.39025e11 | −1.46513 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 9.61429e10i | − 0.215365i | ||||||||
\(389\) | −2.02681e11 | −0.448787 | −0.224394 | − | 0.974499i | \(-0.572040\pi\) | ||||
−0.224394 | + | 0.974499i | \(0.572040\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.82067e11 | 1.04307 | ||||||||
\(392\) | − 3.01989e11i | − 0.645956i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.24949e11 | 1.09745 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 1.63266e10i | − 0.0329867i | −0.999864 | − | 0.0164934i | \(-0.994750\pi\) | ||||
0.999864 | − | 0.0164934i | \(-0.00525024\pi\) | |||||||
\(398\) | 2.13663e11i | 0.426830i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.20766e11 | 1.58515 | 0.792574 | − | 0.609776i | \(-0.208741\pi\) | ||||
0.792574 | + | 0.609776i | \(0.208741\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.04670e11i | 0.764237i | ||||||||
\(404\) | −9.96383e10 | −0.186085 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.12383e11 | −0.387929 | ||||||||
\(407\) | 1.05710e11i | 0.190960i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.24628e11 | 0.750332 | 0.375166 | − | 0.926958i | \(-0.377586\pi\) | ||||
0.375166 | + | 0.926958i | \(0.377586\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.66702e10i | 0.0285039i | ||||||||
\(413\) | − 3.00337e10i | − 0.0507966i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.92956e11 | 0.479603 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 9.24969e11i | 1.48195i | ||||||||
\(419\) | −1.26375e10 | −0.0200308 | −0.0100154 | − | 0.999950i | \(-0.503188\pi\) | ||||
−0.0100154 | + | 0.999950i | \(0.503188\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.04545e10 | −0.0472479 | −0.0236240 | − | 0.999721i | \(-0.507520\pi\) | ||||
−0.0236240 | + | 0.999721i | \(0.507520\pi\) | |||||||
\(422\) | − 3.64085e11i | − 0.558853i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.21104e12 | −1.81976 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 3.65635e11i | − 0.532259i | ||||||||
\(428\) | 9.97940e10i | 0.143750i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.05830e11 | −0.566495 | −0.283248 | − | 0.959047i | \(-0.591412\pi\) | ||||
−0.283248 | + | 0.959047i | \(0.591412\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.36978e11i | 0.187265i | 0.995607 | + | 0.0936324i | \(0.0298478\pi\) | ||||
−0.995607 | + | 0.0936324i | \(0.970152\pi\) | |||||||
\(434\) | 2.64931e11 | 0.358450 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.03790e11 | −0.137551 | ||||||||
\(437\) | 1.63829e12i | 2.14895i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.84981e11 | −1.00872 | −0.504358 | − | 0.863495i | \(-0.668271\pi\) | ||||
−0.504358 | + | 0.863495i | \(0.668271\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.99797e11i | 0.996734i | ||||||||
\(443\) | − 8.87799e11i | − 1.09521i | −0.836737 | − | 0.547605i | \(-0.815540\pi\) | ||||
0.836737 | − | 0.547605i | \(-0.184460\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8.97998e11 | 1.07465 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 5.98645e11i | − 0.702131i | ||||||||
\(449\) | 8.35477e11 | 0.970122 | 0.485061 | − | 0.874480i | \(-0.338797\pi\) | ||||
0.485061 | + | 0.874480i | \(0.338797\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.24371e12 | −1.41555 | ||||||||
\(452\) | − 2.60489e11i | − 0.293540i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.13063e12 | 1.24902 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 6.01172e11i | − 0.644727i | −0.946616 | − | 0.322364i | \(-0.895523\pi\) | ||||
0.946616 | − | 0.322364i | \(-0.104477\pi\) | |||||||
\(458\) | − 2.98384e10i | − 0.0316870i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.52807e12 | −1.57576 | −0.787879 | − | 0.615829i | \(-0.788821\pi\) | ||||
−0.787879 | + | 0.615829i | \(0.788821\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 7.80402e11i | − 0.789231i | −0.918846 | − | 0.394615i | \(-0.870878\pi\) | ||||
0.918846 | − | 0.394615i | \(-0.129122\pi\) | |||||||
\(464\) | 5.19469e11 | 0.520270 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.58234e11 | 0.155440 | ||||||||
\(467\) | − 4.04751e11i | − 0.393788i | −0.980425 | − | 0.196894i | \(-0.936915\pi\) | ||||
0.980425 | − | 0.196894i | \(-0.0630855\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.18052e12 | 1.12667 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9.31820e10i | 0.0864158i | ||||||||
\(473\) | − 5.99700e11i | − 0.550883i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.33313e11 | −0.119026 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − 1.12395e12i | − 0.984738i | ||||||||
\(479\) | −2.06972e12 | −1.79640 | −0.898199 | − | 0.439588i | \(-0.855124\pi\) | ||||
−0.898199 | + | 0.439588i | \(0.855124\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.10638e11 | −0.264607 | ||||||||
\(482\) | 2.34444e11i | 0.197846i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.07514e10 | −0.0503213 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.41184e11i | 0.194298i | 0.995270 | + | 0.0971490i | \(0.0309723\pi\) | ||||
−0.995270 | + | 0.0971490i | \(0.969028\pi\) | |||||||
\(488\) | 1.13441e12i | 0.905485i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.27883e12 | −1.76948 | −0.884739 | − | 0.466088i | \(-0.845663\pi\) | ||||
−0.884739 | + | 0.466088i | \(0.845663\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 8.38767e11i | − 0.639485i | ||||||||
\(494\) | −2.71809e12 | −2.05349 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.47997e11 | −0.480735 | ||||||||
\(497\) | − 6.26373e11i | − 0.460499i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.88752e11 | −0.713896 | −0.356948 | − | 0.934124i | \(-0.616183\pi\) | ||||
−0.356948 | + | 0.934124i | \(0.616183\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 6.98916e11i | − 0.491200i | ||||||||
\(503\) | − 1.22385e12i | − 0.852455i | −0.904616 | − | 0.426228i | \(-0.859842\pi\) | ||||
0.904616 | − | 0.426228i | \(-0.140158\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.28174e12 | −0.869204 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.57201e11i | 0.171351i | ||||||||
\(509\) | 1.58447e12 | 1.04629 | 0.523146 | − | 0.852243i | \(-0.324758\pi\) | ||||
0.523146 | + | 0.852243i | \(0.324758\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.13305e12 | 0.735117 | ||||||||
\(512\) | 1.73140e12i | 1.11348i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.42877e11 | −0.469443 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.69823e10i | 0.0350778i | ||||||||
\(518\) | 2.03369e11i | 0.124109i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.71561e12 | 1.61472 | 0.807362 | − | 0.590057i | \(-0.200895\pi\) | ||||
0.807362 | + | 0.590057i | \(0.200895\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 2.16171e12i | − 1.26340i | −0.775214 | − | 0.631698i | \(-0.782358\pi\) | ||||
0.775214 | − | 0.631698i | \(-0.217642\pi\) | |||||||
\(524\) | −1.99911e11 | −0.115837 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.70210e12 | −1.53909 | ||||||||
\(527\) | 1.04630e12i | 0.590890i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.69046e11 | −0.260415 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − 4.53062e11i | − 0.245220i | ||||||||
\(533\) | − 3.65475e12i | − 1.96149i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.66265e12 | −1.91670 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.87791e12i | 1.48100i | ||||||||
\(539\) | 1.02207e12 | 0.521594 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.29090e12 | −1.14979 | −0.574895 | − | 0.818227i | \(-0.694957\pi\) | ||||
−0.574895 | + | 0.818227i | \(0.694957\pi\) | |||||||
\(542\) | 2.24329e12i | 1.11658i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.57453e11 | 0.370818 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.39447e12i | 1.62117i | 0.585620 | + | 0.810586i | \(0.300851\pi\) | ||||
−0.585620 | + | 0.810586i | \(0.699149\pi\) | |||||||
\(548\) | 4.66101e10i | 0.0220784i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.85053e12 | 1.31748 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.22687e12i | 1.01259i | ||||||||
\(554\) | −5.67107e11 | −0.255783 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.65915e11 | −0.206762 | ||||||||
\(557\) | 1.74706e12i | 0.769060i | 0.923113 | + | 0.384530i | \(0.125636\pi\) | ||||
−0.923113 | + | 0.384530i | \(0.874364\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.76226e12 | 0.763340 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.10531e12i | 0.467379i | ||||||||
\(563\) | 2.58864e12i | 1.08588i | 0.839770 | + | 0.542942i | \(0.182690\pi\) | ||||
−0.839770 | + | 0.542942i | \(0.817310\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.22114e12 | −0.909707 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.94337e12i | 0.783407i | ||||||||
\(569\) | −1.99294e12 | −0.797055 | −0.398527 | − | 0.917156i | \(-0.630479\pi\) | ||||
−0.398527 | + | 0.917156i | \(0.630479\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.50761e10 | 0.0138086 | 0.00690428 | − | 0.999976i | \(-0.497802\pi\) | ||||
0.00690428 | + | 0.999976i | \(0.497802\pi\) | |||||||
\(572\) | 5.41420e11i | 0.211471i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.39270e12 | −0.919995 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.75900e11i | 0.291417i | 0.989328 | + | 0.145708i | \(0.0465461\pi\) | ||||
−0.989328 | + | 0.145708i | \(0.953454\pi\) | |||||||
\(578\) | − 3.27726e11i | − 0.122134i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.60016e10 | 0.00946689 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 4.09874e12i | − 1.46941i | ||||||||
\(584\) | −3.51538e12 | −1.25059 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.65548e12 | 1.63089 | ||||||||
\(587\) | 1.24477e12i | 0.432730i | 0.976313 | + | 0.216365i | \(0.0694201\pi\) | ||||
−0.976313 | + | 0.216365i | \(0.930580\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.55581e12 | −1.21736 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 4.97424e11i | − 0.166448i | ||||||||
\(593\) | 2.57794e11i | 0.0856103i | 0.999083 | + | 0.0428052i | \(0.0136295\pi\) | ||||
−0.999083 | + | 0.0428052i | \(0.986371\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.29084e11 | −0.0743681 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 3.76648e12i | − 1.20443i | ||||||||
\(599\) | 2.32089e12 | 0.736604 | 0.368302 | − | 0.929706i | \(-0.379939\pi\) | ||||
0.368302 | + | 0.929706i | \(0.379939\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.78665e12 | 0.558605 | 0.279302 | − | 0.960203i | \(-0.409897\pi\) | ||||
0.279302 | + | 0.960203i | \(0.409897\pi\) | |||||||
\(602\) | − 1.15373e12i | − 0.358029i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.33785e11 | −0.102047 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.45787e12i | 0.435883i | 0.975962 | + | 0.217941i | \(0.0699342\pi\) | ||||
−0.975962 | + | 0.217941i | \(0.930066\pi\) | |||||||
\(608\) | 2.57419e12i | 0.763966i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.67447e11 | −0.0486062 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.42075e12i | 0.406394i | 0.979138 | + | 0.203197i | \(0.0651331\pi\) | ||||
−0.979138 | + | 0.203197i | \(0.934867\pi\) | |||||||
\(614\) | −1.38387e12 | −0.392950 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.10112e12 | 0.587946 | ||||||||
\(617\) | 1.20441e12i | 0.334573i | 0.985908 | + | 0.167286i | \(0.0535004\pi\) | ||||
−0.985908 | + | 0.167286i | \(0.946500\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.91349e12 | 1.34519 | 0.672593 | − | 0.740013i | \(-0.265181\pi\) | ||||
0.672593 | + | 0.740013i | \(0.265181\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 4.01598e12i | − 1.07581i | ||||||||
\(623\) | − 2.40214e12i | − 0.638856i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.24280e12 | −0.323456 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.13118e12i | 0.290211i | ||||||||
\(629\) | −8.03171e11 | −0.204588 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.58663e12 | 1.15176 | 0.575879 | − | 0.817535i | \(-0.304660\pi\) | ||||
0.575879 | + | 0.817535i | \(0.304660\pi\) | |||||||
\(632\) | − 6.90903e12i | − 1.72262i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.56414e12 | −1.12191 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.00344e12i | 0.722755i | ||||||||
\(638\) | 2.23014e12i | 0.532893i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.30636e12 | 0.539593 | 0.269796 | − | 0.962917i | \(-0.413044\pi\) | ||||
0.269796 | + | 0.962917i | \(0.413044\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.59493e12i | 0.598654i | 0.954151 | + | 0.299327i | \(0.0967622\pi\) | ||||
−0.954151 | + | 0.299327i | \(0.903238\pi\) | |||||||
\(644\) | 6.27813e11 | 0.143828 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.02777e12 | −1.58771 | ||||||||
\(647\) | 5.14811e12i | 1.15499i | 0.816394 | + | 0.577495i | \(0.195970\pi\) | ||||
−0.816394 | + | 0.577495i | \(0.804030\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.15372e11 | −0.0697786 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.24676e12i | 0.270191i | ||||||||
\(653\) | − 4.42559e12i | − 0.952492i | −0.879312 | − | 0.476246i | \(-0.841997\pi\) | ||||
0.879312 | − | 0.476246i | \(-0.158003\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.85234e12 | 1.23385 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.09625e11i | 0.0227977i | ||||||||
\(659\) | 1.09827e12 | 0.226842 | 0.113421 | − | 0.993547i | \(-0.463819\pi\) | ||||
0.113421 | + | 0.993547i | \(0.463819\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.99232e11 | 0.162842 | 0.0814209 | − | 0.996680i | \(-0.474054\pi\) | ||||
0.0814209 | + | 0.996680i | \(0.474054\pi\) | |||||||
\(662\) | 1.69455e12i | 0.342919i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.06719e10 | −0.0161052 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.95000e12i | 0.772736i | ||||||||
\(668\) | 1.00641e12i | 0.195560i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.83939e12 | −0.731157 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.68445e12i | 1.44393i | 0.691931 | + | 0.721963i | \(0.256760\pi\) | ||||
−0.691931 | + | 0.721963i | \(0.743240\pi\) | |||||||
\(674\) | 4.43334e12 | 0.827488 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.89167e11 | −0.0900942 | ||||||||
\(677\) | 1.28854e12i | 0.235749i | 0.993029 | + | 0.117874i | \(0.0376080\pi\) | ||||
−0.993029 | + | 0.117874i | \(0.962392\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.71076e12 | 0.669959 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 2.78193e12i | − 0.492398i | ||||||||
\(683\) | 8.11444e11i | 0.142681i | 0.997452 | + | 0.0713404i | \(0.0227277\pi\) | ||||
−0.997452 | + | 0.0713404i | \(0.977272\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 5.23546e12 | 0.902602 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.82191e12i | 0.480170i | ||||||||
\(689\) | 1.20445e13 | 2.03611 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.26741e12 | 0.378338 | 0.189169 | − | 0.981945i | \(-0.439421\pi\) | ||||
0.189169 | + | 0.981945i | \(0.439421\pi\) | |||||||
\(692\) | − 7.64375e11i | − 0.126715i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.75665e12 | −0.614728 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 9.44955e12i | − 1.51657i | ||||||||
\(698\) | 5.51977e12i | 0.880180i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.92113e12 | 0.769721 | 0.384861 | − | 0.922975i | \(-0.374249\pi\) | ||||
0.384861 | + | 0.922975i | \(0.374249\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 2.72956e12i | − 0.421496i | ||||||||
\(704\) | −6.28612e12 | −0.964508 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.11822e12 | 0.926839 | ||||||||
\(707\) | − 3.84566e12i | − 0.578874i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.12354e12 | 0.910112 | 0.455056 | − | 0.890463i | \(-0.349619\pi\) | ||||
0.455056 | + | 0.890463i | \(0.349619\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.45283e12i | 1.08683i | ||||||||
\(713\) | − 4.92732e12i | − 0.714016i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.08170e11 | −0.0296012 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − 5.00307e12i | − 0.702550i | ||||||||
\(719\) | −2.30376e11 | −0.0321483 | −0.0160741 | − | 0.999871i | \(-0.505117\pi\) | ||||
−0.0160741 | + | 0.999871i | \(0.505117\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.43408e11 | −0.0886702 | ||||||||
\(722\) | − 1.73650e13i | − 2.37824i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.85402e11 | 0.0791827 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 9.25894e12i | − 1.22930i | −0.788801 | − | 0.614648i | \(-0.789298\pi\) | ||||
0.788801 | − | 0.614648i | \(-0.210702\pi\) | |||||||
\(728\) | 6.17430e12i | 0.814698i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.55643e12 | 0.590196 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 7.22531e12i | − 0.924461i | −0.886760 | − | 0.462231i | \(-0.847049\pi\) | ||||
0.886760 | − | 0.462231i | \(-0.152951\pi\) | |||||||
\(734\) | −5.38074e12 | −0.684241 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.56707e12 | −0.448086 | ||||||||
\(737\) | − 1.23962e13i | − 1.54769i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.24725e13 | 1.53834 | 0.769170 | − | 0.639044i | \(-0.220670\pi\) | ||||
0.769170 | + | 0.639044i | \(0.220670\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − 7.88531e12i | − 0.954996i | ||||||||
\(743\) | 1.15645e13i | 1.39212i | 0.717986 | + | 0.696058i | \(0.245064\pi\) | ||||
−0.717986 | + | 0.696058i | \(0.754936\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.05219e13 | −1.24386 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.39987e12i | 0.163505i | ||||||||
\(749\) | −3.85167e12 | −0.447179 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.70732e12 | −0.425285 | −0.212642 | − | 0.977130i | \(-0.568207\pi\) | ||||
−0.212642 | + | 0.977130i | \(0.568207\pi\) | |||||||
\(752\) | − 2.68132e11i | − 0.0305752i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.55344e12 | −0.738412 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.86635e11i | 0.0538607i | 0.999637 | + | 0.0269303i | \(0.00857323\pi\) | ||||
−0.999637 | + | 0.0269303i | \(0.991427\pi\) | |||||||
\(758\) | 6.63228e11i | 0.0729712i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.28395e12 | 0.463035 | 0.231518 | − | 0.972831i | \(-0.425631\pi\) | ||||
0.231518 | + | 0.972831i | \(0.425631\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 4.00589e12i | − 0.427896i | ||||||||
\(764\) | −9.52709e11 | −0.101167 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.44499e12 | 0.151648 | ||||||||
\(767\) | − 9.26745e11i | − 0.0966899i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.03625e12 | 0.416207 | 0.208103 | − | 0.978107i | \(-0.433271\pi\) | ||||
0.208103 | + | 0.978107i | \(0.433271\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 3.28672e12i | − 0.333031i | ||||||||
\(773\) | − 1.21916e13i | − 1.22815i | −0.789247 | − | 0.614076i | \(-0.789529\pi\) | ||||
0.789247 | − | 0.614076i | \(-0.210471\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.15129e13 | −1.13974 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.09445e12i | 0.400671i | ||||||||
\(779\) | 3.21141e13 | 3.12447 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.57728e12 | −0.632582 | ||||||||
\(782\) | − 9.73844e12i | − 0.931235i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.80940e12 | −0.454641 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.20299e12i | 0.111783i | 0.998437 | + | 0.0558913i | \(0.0178000\pi\) | ||||
−0.998437 | + | 0.0558913i | \(0.982200\pi\) | |||||||
\(788\) | 2.69999e12i | 0.249456i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.00539e13 | 0.913147 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 1.12823e13i | − 1.01314i | ||||||||
\(794\) | −3.29821e11 | −0.0294501 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.09894e12 | −0.0970208 | ||||||||
\(797\) | 1.72611e13i | 1.51533i | 0.652646 | + | 0.757663i | \(0.273659\pi\) | ||||
−0.652646 | + | 0.757663i | \(0.726341\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.32943e11 | −0.0375811 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − 1.65806e13i | − 1.41520i | ||||||||
\(803\) | − 1.18977e13i | − 1.00982i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.17490e12 | 0.682299 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.19315e13i | 0.984788i | ||||||||
\(809\) | 7.44408e12 | 0.611002 | 0.305501 | − | 0.952192i | \(-0.401176\pi\) | ||||
0.305501 | + | 0.952192i | \(0.401176\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.59955e12 | −0.779214 | −0.389607 | − | 0.920981i | \(-0.627389\pi\) | ||||
−0.389607 | + | 0.920981i | \(0.627389\pi\) | |||||||
\(812\) | − 1.09235e12i | − 0.0881783i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.13550e12 | 0.170486 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.54849e13i | 1.21593i | ||||||||
\(818\) | − 8.57808e12i | − 0.669885i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.04043e12 | 0.387189 | 0.193595 | − | 0.981082i | \(-0.437985\pi\) | ||||
0.193595 | + | 0.981082i | \(0.437985\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.62323e13i | 1.23333i | 0.787225 | + | 0.616666i | \(0.211517\pi\) | ||||
−0.787225 | + | 0.616666i | \(0.788483\pi\) | |||||||
\(824\) | 1.99622e12 | 0.150847 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.06724e11 | −0.0453504 | ||||||||
\(827\) | − 1.74898e13i | − 1.30020i | −0.759850 | − | 0.650099i | \(-0.774727\pi\) | ||||
0.759850 | − | 0.650099i | \(-0.225273\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.04102e13 | 0.765535 | 0.382768 | − | 0.923845i | \(-0.374971\pi\) | ||||
0.382768 | + | 0.923845i | \(0.374971\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 1.84722e13i | − 1.33649i | ||||||||
\(833\) | 7.76555e12i | 0.558817i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.75742e12 | −0.336855 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.55296e11i | 0.0178832i | ||||||||
\(839\) | −2.66219e13 | −1.85485 | −0.927426 | − | 0.374006i | \(-0.877984\pi\) | ||||
−0.927426 | + | 0.374006i | \(0.877984\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.63439e12 | −0.526250 | ||||||||
\(842\) | 6.15225e11i | 0.0421822i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.87261e12 | 0.127030 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 2.34477e12i | − 0.156540i | ||||||||
\(848\) | 1.92868e13i | 1.28079i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.78237e12 | 0.247219 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 7.30064e12i | − 0.472161i | −0.971734 | − | 0.236080i | \(-0.924137\pi\) | ||||
0.971734 | − | 0.236080i | \(-0.0758629\pi\) | |||||||
\(854\) | −7.38635e12 | −0.475192 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.19501e13 | 0.760747 | ||||||||
\(857\) | − 1.18598e13i | − 0.751041i | −0.926814 | − | 0.375520i | \(-0.877464\pi\) | ||||
0.926814 | − | 0.375520i | \(-0.122536\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.67692e13 | −1.05085 | −0.525427 | − | 0.850839i | \(-0.676094\pi\) | ||||
−0.525427 | + | 0.850839i | \(0.676094\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.19834e12i | 0.505759i | ||||||||
\(863\) | − 6.71596e12i | − 0.412154i | −0.978536 | − | 0.206077i | \(-0.933930\pi\) | ||||
0.978536 | − | 0.206077i | \(-0.0660698\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.76716e12 | 0.167187 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.36263e12i | 0.0814776i | ||||||||
\(869\) | 2.33834e13 | 1.39098 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.64270e13 | 2.14458 | ||||||||
\(872\) | 1.24286e13i | 0.727943i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.30959e13 | 1.91855 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.79757e13i | 1.59692i | 0.602051 | + | 0.798458i | \(0.294351\pi\) | ||||
−0.602051 | + | 0.798458i | \(0.705649\pi\) | |||||||
\(878\) | 1.58577e13i | 0.900566i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.06225e13 | −1.15332 | −0.576660 | − | 0.816984i | \(-0.695644\pi\) | ||||
−0.576660 | + | 0.816984i | \(0.695644\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 2.02048e13i | − 1.11849i | −0.829003 | − | 0.559244i | \(-0.811091\pi\) | ||||
0.829003 | − | 0.559244i | \(-0.188909\pi\) | |||||||
\(884\) | −4.11362e12 | −0.226563 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.79348e13 | −0.977788 | ||||||||
\(887\) | 3.19954e13i | 1.73553i | 0.496978 | + | 0.867763i | \(0.334443\pi\) | ||||
−0.496978 | + | 0.867763i | \(0.665557\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.92701e12 | −0.533041 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.61870e12i | 0.244275i | ||||||||
\(893\) | − 1.47135e12i | − 0.0774254i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −7.23252e12 | −0.374890 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − 1.68778e13i | − 0.866110i | ||||||||
\(899\) | −8.57323e12 | −0.437750 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.11416e13 | 1.57427 | ||||||||
\(902\) | 2.51248e13i | 1.26378i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.11930e13 | −1.55346 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 2.40537e12i | − 0.118018i | −0.998257 | − | 0.0590091i | \(-0.981206\pi\) | ||||
0.998257 | − | 0.0590091i | \(-0.0187941\pi\) | |||||||
\(908\) | 5.81519e12i | 0.283908i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.11773e13 | 1.49970 | 0.749852 | − | 0.661606i | \(-0.230125\pi\) | ||||
0.749852 | + | 0.661606i | \(0.230125\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 2.73032e11i | − 0.0130045i | ||||||||
\(914\) | −1.21445e13 | −0.575603 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.53469e11 | 0.00720263 | ||||||||
\(917\) | − 7.71582e12i | − 0.360346i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.42677e13 | −1.58477 | −0.792383 | − | 0.610024i | \(-0.791160\pi\) | ||||
−0.792383 | + | 0.610024i | \(0.791160\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.08692e13i | 1.40681i | ||||||||
\(923\) | − 1.93278e13i | − 0.876548i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.57652e13 | −0.704614 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.20648e12i | 0.274713i | ||||||||
\(929\) | −2.52782e13 | −1.11346 | −0.556730 | − | 0.830693i | \(-0.687944\pi\) | ||||
−0.556730 | + | 0.830693i | \(0.687944\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.63910e13 | −1.15129 | ||||||||
\(932\) | 8.13848e11i | 0.0353323i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −8.17655e12 | −0.351568 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 2.72636e13i | − 1.15546i | −0.816227 | − | 0.577731i | \(-0.803938\pi\) | ||||
0.816227 | − | 0.577731i | \(-0.196062\pi\) | |||||||
\(938\) | − 2.38482e13i | − 1.00587i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.57383e13 | −0.654340 | −0.327170 | − | 0.944966i | \(-0.606095\pi\) | ||||
−0.327170 | + | 0.944966i | \(0.606095\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.45008e13i | 1.83259i | ||||||||
\(944\) | 1.48399e12 | 0.0608217 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.21148e13 | −0.491820 | ||||||||
\(947\) | − 9.71128e12i | − 0.392375i | −0.980566 | − | 0.196188i | \(-0.937144\pi\) | ||||
0.980566 | − | 0.196188i | \(-0.0628562\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.49624e13 | 1.39927 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.59640e13i | 0.629905i | ||||||||
\(953\) | − 4.15385e12i | − 0.163130i | −0.996668 | − | 0.0815648i | \(-0.974008\pi\) | ||||
0.996668 | − | 0.0815648i | \(-0.0259917\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.78084e12 | 0.223836 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.18114e13i | 1.60380i | ||||||||
\(959\) | −1.79897e12 | −0.0686818 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.57452e13 | −0.595515 | ||||||||
\(962\) | 6.27532e12i | 0.236237i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.20582e12 | −0.0449715 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1.84544e13i | − 0.678706i | −0.940659 | − | 0.339353i | \(-0.889792\pi\) | ||||
0.940659 | − | 0.339353i | \(-0.110208\pi\) | |||||||
\(968\) | 7.27484e12i | 0.266308i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.95973e12 | 0.106848 | 0.0534238 | − | 0.998572i | \(-0.482987\pi\) | ||||
0.0534238 | + | 0.998572i | \(0.482987\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 1.79826e13i | − 0.643197i | ||||||||
\(974\) | 4.87226e12 | 0.173466 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.80664e13 | 0.637304 | ||||||||
\(977\) | 4.44178e13i | 1.55967i | 0.625988 | + | 0.779833i | \(0.284696\pi\) | ||||
−0.625988 | + | 0.779833i | \(0.715304\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.52239e13 | −0.877588 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.60356e13i | 1.57976i | ||||||||
\(983\) | − 4.57558e13i | − 1.56299i | −0.623914 | − | 0.781493i | \(-0.714459\pi\) | ||||
0.623914 | − | 0.781493i | \(-0.285541\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.69443e13 | −0.570922 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 1.39800e13i | − 0.466769i | ||||||||
\(989\) | −2.14576e13 | −0.713177 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.30469e13 | 0.429710 | 0.214855 | − | 0.976646i | \(-0.431072\pi\) | ||||
0.214855 | + | 0.976646i | \(0.431072\pi\) | |||||||
\(992\) | − 7.74210e12i | − 0.253838i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.26536e13 | −0.411127 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.07578e12i | 0.162695i | 0.996686 | + | 0.0813476i | \(0.0259224\pi\) | ||||
−0.996686 | + | 0.0813476i | \(0.974078\pi\) | |||||||
\(998\) | 1.99742e13i | 0.637356i | ||||||||
\(999\) | 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 | 225.10.b.m.199.3 | 6 | ||
3.2 | odd | 2 | 25.10.b.c.24.4 | 6 | |||
5.2 | odd | 4 | 225.10.a.m.1.3 | 3 | |||
5.3 | odd | 4 | 225.10.a.p.1.1 | 3 | |||
5.4 | even | 2 | inner | 225.10.b.m.199.4 | 6 | ||
12.11 | even | 2 | 400.10.c.q.49.3 | 6 | |||
15.2 | even | 4 | 25.10.a.d.1.1 | yes | 3 | ||
15.8 | even | 4 | 25.10.a.c.1.3 | ✓ | 3 | ||
15.14 | odd | 2 | 25.10.b.c.24.3 | 6 | |||
60.23 | odd | 4 | 400.10.a.y.1.2 | 3 | |||
60.47 | odd | 4 | 400.10.a.u.1.2 | 3 | |||
60.59 | even | 2 | 400.10.c.q.49.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.10.a.c.1.3 | ✓ | 3 | 15.8 | even | 4 | ||
25.10.a.d.1.1 | yes | 3 | 15.2 | even | 4 | ||
25.10.b.c.24.3 | 6 | 15.14 | odd | 2 | |||
25.10.b.c.24.4 | 6 | 3.2 | odd | 2 | |||
225.10.a.m.1.3 | 3 | 5.2 | odd | 4 | |||
225.10.a.p.1.1 | 3 | 5.3 | odd | 4 | |||
225.10.b.m.199.3 | 6 | 1.1 | even | 1 | trivial | ||
225.10.b.m.199.4 | 6 | 5.4 | even | 2 | inner | ||
400.10.a.u.1.2 | 3 | 60.47 | odd | 4 | |||
400.10.a.y.1.2 | 3 | 60.23 | odd | 4 | |||
400.10.c.q.49.3 | 6 | 12.11 | even | 2 | |||
400.10.c.q.49.4 | 6 | 60.59 | even | 2 |