Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,16,Mod(47,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 16, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.47");
S:= CuspForms(chi, 16);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 16 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(68.4928824480\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 10 x^{19} + 8885809 x^{18} - 79971996 x^{17} + 21106062365235 x^{16} - 168846686224596 x^{15} + \cdots + 85\!\cdots\!61 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{194}\cdot 3^{63}\cdot 5^{6}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 47.12 | ||
Root | \(0.500000 + 361.292i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 48.47 |
Dual form | 48.16.c.d.47.11 |
$q$-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 \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(31\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 660.169 | + | 3730.02i | 0.174279 | + | 0.984696i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 233484.i | − | 1.33654i | −0.743920 | − | 0.668269i | \(-0.767036\pi\) | ||
0.743920 | − | 0.668269i | \(-0.232964\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 674260.i | 0.309451i | 0.987958 | + | 0.154725i | \(0.0494493\pi\) | ||||
−0.987958 | + | 0.154725i | \(0.950551\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.34773e7 | + | 4.92490e6i | −0.939253 | + | 0.343224i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.99491e7 | −0.308659 | −0.154329 | − | 0.988019i | \(-0.549322\pi\) | ||||
−0.154329 | + | 0.988019i | \(0.549322\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.08051e7 | −0.268760 | −0.134380 | − | 0.990930i | \(-0.542904\pi\) | ||||
−0.134380 | + | 0.990930i | \(0.542904\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.70900e8 | − | 1.54139e8i | 1.31608 | − | 0.232931i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.15809e9i | 1.86663i | 0.359058 | + | 0.933315i | \(0.383098\pi\) | ||||
−0.359058 | + | 0.933315i | \(0.616902\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.41564e9i | − | 0.363328i | −0.983361 | − | 0.181664i | \(-0.941852\pi\) | ||
0.983361 | − | 0.181664i | \(-0.0581484\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.51500e9 | + | 4.45126e8i | −0.304715 | + | 0.0539309i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.57568e10 | 0.964961 | 0.482481 | − | 0.875907i | \(-0.339736\pi\) | ||||
0.482481 | + | 0.875907i | \(0.339736\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.39970e10 | −0.786334 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.72673e10 | − | 4.70192e10i | −0.501664 | − | 0.865062i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.11059e11i | − | 1.19555i | −0.801664 | − | 0.597775i | \(-0.796051\pi\) | ||
0.801664 | − | 0.597775i | \(-0.203949\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.32822e11i | − | 1.51989i | −0.649988 | − | 0.759944i | \(-0.725226\pi\) | ||
0.649988 | − | 0.759944i | \(-0.274774\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.31698e10 | − | 7.44108e10i | −0.0537929 | − | 0.303935i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.57429e11 | 0.413593 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.75428e11 | −0.650151 | −0.325075 | − | 0.945688i | \(-0.605390\pi\) | ||||
−0.325075 | + | 0.945688i | \(0.605390\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.01417e10 | − | 2.26804e11i | −0.0468393 | − | 0.264647i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.06884e11i | 0.246091i | 0.992401 | + | 0.123045i | \(0.0392661\pi\) | ||||
−0.992401 | + | 0.123045i | \(0.960734\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.01153e12i | 0.567498i | 0.958899 | + | 0.283749i | \(0.0915783\pi\) | ||||
−0.958899 | + | 0.283749i | \(0.908422\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.14988e12 | + | 3.14672e12i | 0.458733 | + | 1.25535i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.21635e12 | 1.21396 | 0.606978 | − | 0.794719i | \(-0.292382\pi\) | ||||
0.606978 | + | 0.794719i | \(0.292382\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.29294e12 | 0.904240 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.17798e13 | + | 2.08488e12i | −1.83806 | + | 0.325315i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 9.07188e12i | − | 1.06079i | −0.847751 | − | 0.530394i | \(-0.822044\pi\) | ||
0.847751 | − | 0.530394i | \(-0.177956\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.65779e12i | 0.412534i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.28035e12 | − | 9.34559e11i | 0.357768 | − | 0.0633206i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.24088e12 | 0.274166 | 0.137083 | − | 0.990560i | \(-0.456227\pi\) | ||||
0.137083 | + | 0.990560i | \(0.456227\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.39988e13 | 0.977723 | 0.488862 | − | 0.872361i | \(-0.337412\pi\) | ||||
0.488862 | + | 0.872361i | \(0.337412\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.32066e12 | − | 9.08717e12i | −0.106211 | − | 0.290653i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.41970e13i | 0.359208i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 8.59195e13i | − | 1.73193i | −0.500102 | − | 0.865966i | \(-0.666704\pi\) | ||
0.500102 | − | 0.865966i | \(-0.333296\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.04022e13 | + | 5.87733e13i | 0.168173 | + | 0.950194i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.22093e14 | 1.59314 | 0.796572 | − | 0.604544i | \(-0.206645\pi\) | ||||
0.796572 | + | 0.604544i | \(0.206645\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.98083e13 | 0.527692 | 0.263846 | − | 0.964565i | \(-0.415009\pi\) | ||||
0.263846 | + | 0.964565i | \(0.415009\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.58421e13 | − | 8.95094e13i | −0.137042 | − | 0.774300i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 1.34509e13i | − | 0.0955148i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1.48059e14i | − | 0.867422i | −0.901052 | − | 0.433711i | \(-0.857204\pi\) | ||
0.901052 | − | 0.433711i | \(-0.142796\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.57382e14 | − | 1.32748e14i | 0.764394 | − | 0.644749i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.90447e14 | −1.57934 | −0.789672 | − | 0.613530i | \(-0.789749\pi\) | ||||
−0.789672 | + | 0.613530i | \(0.789749\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.37363e14 | 2.49482 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.14252e14 | − | 7.33176e13i | 1.17725 | − | 0.208360i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.10097e14i | 0.743143i | 0.928404 | + | 0.371571i | \(0.121181\pi\) | ||||
−0.928404 | + | 0.371571i | \(0.878819\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 4.09984e13i | − | 0.0831681i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.68433e14 | − | 1.53702e14i | 1.49663 | − | 0.264885i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.30528e14 | −0.485602 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.87836e14 | 0.864365 | 0.432182 | − | 0.901786i | \(-0.357744\pi\) | ||||
0.432182 | + | 0.901786i | \(0.357744\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.68860e14 | − | 9.82474e13i | 0.289909 | − | 0.105939i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.57452e15i | 1.46130i | 0.682753 | + | 0.730649i | \(0.260782\pi\) | ||||
−0.682753 | + | 0.730649i | \(0.739218\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.78318e14i | − | 0.783792i | −0.920010 | − | 0.391896i | \(-0.871819\pi\) | ||
0.920010 | − | 0.391896i | \(-0.128181\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.03930e14 | + | 5.87212e14i | 0.0720807 | + | 0.407263i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.57547e15 | 0.948487 | 0.474244 | − | 0.880394i | \(-0.342722\pi\) | ||||
0.474244 | + | 0.880394i | \(0.342722\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.81784e15 | 1.47644 | 0.738222 | − | 0.674558i | \(-0.235666\pi\) | ||||
0.738222 | + | 0.674558i | \(0.235666\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.47846e14 | − | 1.40036e15i | −0.113308 | − | 0.640201i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 3.29733e15i | − | 1.31848i | −0.751931 | − | 0.659241i | \(-0.770878\pi\) | ||
0.751931 | − | 0.659241i | \(-0.229122\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 3.67896e15i | − | 1.28971i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.19486e14 | − | 2.99459e14i | 0.252434 | − | 0.0922450i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.12938e15 | −0.577630 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.77928e15 | −0.904730 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.14468e15 | + | 2.02595e14i | −0.242325 | + | 0.0428885i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.52245e15i | − | 0.285573i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.51152e15i | 0.251701i | 0.992049 | + | 0.125851i | \(0.0401660\pi\) | ||||
−0.992049 | + | 0.125851i | \(0.959834\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.77303e15 | + | 6.67780e14i | −0.558814 | + | 0.0989033i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.11587e16 | 1.47258 | 0.736292 | − | 0.676664i | \(-0.236575\pi\) | ||||
0.736292 | + | 0.676664i | \(0.236575\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.54506e14 | 0.112432 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.09782e16 | + | 6.36646e15i | −1.15619 | + | 0.670493i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.37722e15i | 0.601488i | 0.953705 | + | 0.300744i | \(0.0972349\pi\) | ||||
−0.953705 | + | 0.300744i | \(0.902765\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.45074e16i | 1.22738i | 0.789547 | + | 0.613690i | \(0.210316\pi\) | ||||
−0.789547 | + | 0.613690i | \(0.789684\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.78351e15 | + | 1.57271e16i | 0.211567 | + | 1.19538i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.21301e15 | 0.0829552 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.59304e16 | −1.59790 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.83406e15 | + | 1.60128e16i | 0.157590 | + | 0.890402i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 1.83936e16i | − | 0.924208i | −0.886826 | − | 0.462104i | \(-0.847095\pi\) | ||
0.886826 | − | 0.462104i | \(-0.152905\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.85994e16i | 0.845612i | 0.906220 | + | 0.422806i | \(0.138955\pi\) | ||||
−0.906220 | + | 0.422806i | \(0.861045\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.55533e16 | − | 4.25625e16i | −0.640673 | − | 1.75324i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.43602e16 | −2.03139 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.69034e16 | −1.25262 | −0.626310 | − | 0.779574i | \(-0.715436\pi\) | ||||
−0.626310 | + | 0.779574i | \(0.715436\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.38383e16 | − | 5.98898e15i | 1.04455 | − | 0.184873i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.06242e16i | 0.298608i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 3.09611e16i | − | 0.793249i | −0.917981 | − | 0.396624i | \(-0.870182\pi\) | ||
0.917981 | − | 0.396624i | \(-0.129818\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.73737e16 | + | 3.07493e15i | −0.406221 | + | 0.0718962i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.54317e16 | 0.543253 | 0.271626 | − | 0.962403i | \(-0.412439\pi\) | ||||
0.271626 | + | 0.962403i | \(0.412439\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.74886e16 | −0.927768 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.97186e15 | + | 1.90789e16i | 0.124703 | + | 0.341257i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.45522e13i | 0.00105819i | 1.00000 | 0.000529097i | \(0.000168417\pi\) | |||||
−1.00000 | 0.000529097i | \(0.999832\pi\) | ||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1.61802e16i | − | 0.243332i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.45987e15 | + | 1.95486e16i | 0.0477815 | + | 0.269970i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.13379e16 | 0.143925 | 0.0719623 | − | 0.997407i | \(-0.477074\pi\) | ||||
0.0719623 | + | 0.997407i | \(0.477074\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.68399e16 | −0.547050 | −0.273525 | − | 0.961865i | \(-0.588190\pi\) | ||||
−0.273525 | + | 0.961865i | \(0.588190\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.58433e16 | + | 8.95162e16i | 0.170397 | + | 0.962760i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.76563e16i | 0.868951i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 6.30013e16i | − | 0.576152i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.17032e16 | − | 1.83852e16i | 0.267694 | − | 0.155241i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.78711e16 | −0.451556 | −0.225778 | − | 0.974179i | \(-0.572492\pi\) | ||||
−0.225778 | + | 0.974179i | \(0.572492\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.27639e17 | 1.64274 | 0.821368 | − | 0.570399i | \(-0.193211\pi\) | ||||
0.821368 | + | 0.570399i | \(0.193211\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.29551e16 | + | 9.37242e15i | −0.353711 | + | 0.0626025i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.44969e17i | − | 0.896972i | −0.893790 | − | 0.448486i | \(-0.851963\pi\) | ||
0.893790 | − | 0.448486i | \(-0.148037\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3.50807e16i | − | 0.201220i | −0.994926 | − | 0.100610i | \(-0.967921\pi\) | ||
0.994926 | − | 0.100610i | \(-0.0320794\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.20482e17 | − | 5.67214e16i | 1.70543 | − | 0.301840i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.48825e16 | 0.369964 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.16524e16 | 0.328910 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.12359e17 | + | 7.76007e16i | −0.906343 | + | 0.331198i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.82407e16i | 0.112145i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 3.61413e17i | − | 1.33624i | −0.744053 | − | 0.668121i | \(-0.767099\pi\) | ||
0.744053 | − | 0.668121i | \(-0.232901\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.06024e16 | + | 4.55412e17i | 0.277652 | + | 1.56876i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.36175e17 | 0.758483 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.56983e17 | 0.470331 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.28819e16 | + | 1.85786e17i | 0.0919657 | + | 0.519616i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.92028e17i | − | 0.501676i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 6.88674e17i | − | 1.68162i | −0.541333 | − | 0.840808i | \(-0.682080\pi\) | ||
0.541333 | − | 0.840808i | \(-0.317920\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.23414e17 | − | 1.18183e17i | 0.738567 | − | 0.269889i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.73830e17 | 1.43998 | 0.719990 | − | 0.693985i | \(-0.244147\pi\) | ||||
0.719990 | + | 0.693985i | \(0.244147\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.84722e17 | −0.569710 | −0.284855 | − | 0.958571i | \(-0.591946\pi\) | ||||
−0.284855 | + | 0.958571i | \(0.591946\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.01722e16 | − | 8.87987e15i | 0.0940531 | − | 0.0166463i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.22753e17i | 1.62150i | 0.585395 | + | 0.810748i | \(0.300939\pi\) | ||||
−0.585395 | + | 0.810748i | \(0.699061\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 9.84449e17i | − | 1.62250i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.52262e17 | − | 9.77437e16i | 0.854147 | − | 0.151174i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.07511e18 | −1.56124 | −0.780620 | − | 0.625006i | \(-0.785097\pi\) | ||||
−0.780620 | + | 0.625006i | \(0.785097\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.39636e17 | −0.326907 | −0.163453 | − | 0.986551i | \(-0.552263\pi\) | ||||
−0.163453 | + | 0.986551i | \(0.552263\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.99053e17 | + | 4.99402e17i | 0.768100 | + | 0.640329i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 1.00233e18i | − | 1.20855i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.60778e16i | 0.0976482i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.57761e17 | − | 1.45638e18i | −0.275247 | − | 1.55517i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.33508e18 | −1.34263 | −0.671314 | − | 0.741173i | \(-0.734270\pi\) | ||||
−0.671314 | + | 0.741173i | \(0.734270\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.14335e17 | −0.297844 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.86785e17 | + | 2.75038e18i | 0.434796 | + | 2.45664i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.84718e17i | 0.239837i | 0.992784 | + | 0.119918i | \(0.0382633\pi\) | ||||
−0.992784 | + | 0.119918i | \(0.961737\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 2.53136e17i | − | 0.201190i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.46953e17 | + | 1.49677e18i | 0.410342 | + | 1.12293i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.91491e17 | 0.489912 | 0.244956 | − | 0.969534i | \(-0.421226\pi\) | ||||
0.244956 | + | 0.969534i | \(0.421226\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.11814e18 | −1.41778 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.15667e18 | + | 2.04716e17i | −0.731770 | + | 0.129514i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.32968e18i | 0.795437i | 0.917508 | + | 0.397718i | \(0.130198\pi\) | ||||
−0.917508 | + | 0.397718i | \(0.869802\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.14254e18i | 0.646549i | 0.946305 | + | 0.323274i | \(0.104784\pi\) | ||||
−0.946305 | + | 0.323274i | \(0.895216\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.52925e17 | − | 2.70659e16i | 0.0818953 | − | 0.0144945i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.78720e17 | 0.242709 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.39679e18 | −1.15089 | −0.575443 | − | 0.817842i | \(-0.695170\pi\) | ||||
−0.575443 | + | 0.817842i | \(0.695170\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.14663e18 | + | 3.13781e18i | 0.521663 | + | 1.42756i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 5.48051e17i | − | 0.236332i | −0.992994 | − | 0.118166i | \(-0.962298\pi\) | ||
0.992994 | − | 0.118166i | \(-0.0377016\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 3.91086e18i | − | 1.59909i | −0.600604 | − | 0.799547i | \(-0.705073\pi\) | ||
0.600604 | − | 0.799547i | \(-0.294927\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.18204e17 | − | 1.23288e18i | −0.0846304 | − | 0.478171i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.06919e17 | −0.0761530 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.11114e18 | −2.48431 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.54088e17 | + | 2.56565e18i | 0.150641 | + | 0.851137i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 2.82414e18i | − | 0.889978i | −0.895536 | − | 0.444989i | \(-0.853208\pi\) | ||
0.895536 | − | 0.444989i | \(-0.146792\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1.22366e18i | − | 0.366434i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.43958e17 | + | 9.37993e17i | 0.154843 | + | 0.267009i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.58095e17 | −0.259343 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.82033e17 | −0.175613 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.87301e18 | + | 1.03945e18i | −1.43894 | + | 0.254674i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 5.60333e18i | − | 1.30676i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 6.34266e18i | − | 1.40843i | −0.709989 | − | 0.704213i | \(-0.751300\pi\) | ||
0.709989 | − | 0.704213i | \(-0.248700\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.64915e18 | − | 6.45855e17i | 0.771797 | − | 0.136599i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.91698e18 | 1.59535 | 0.797676 | − | 0.603086i | \(-0.206062\pi\) | ||||
0.797676 | + | 0.603086i | \(0.206062\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.58201e18 | 0.303827 | 0.151913 | − | 0.988394i | \(-0.451457\pi\) | ||||
0.151913 | + | 0.988394i | \(0.451457\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.12171e18 | + | 7.75319e17i | −0.388469 | + | 0.141955i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.87775e18i | 1.20089i | 0.799668 | + | 0.600443i | \(0.205009\pi\) | ||||
−0.799668 | + | 0.600443i | \(0.794991\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.21553e18i | 0.369017i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.04008e18 | + | 5.87654e18i | 0.165302 | + | 0.933972i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.47071e18 | 0.678200 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.45914e18 | 0.211335 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.86025e18 | + | 1.05106e19i | 0.257314 | + | 1.45385i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.84292e18i | 0.375660i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 1.06554e19i | − | 1.34543i | −0.739901 | − | 0.672716i | \(-0.765128\pi\) | ||
0.739901 | − | 0.672716i | \(-0.234872\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.05974e18 | − | 1.84895e18i | 0.610656 | − | 0.223148i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.00608e19 | −2.31479 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.07898e18 | 1.00187 | 0.500937 | − | 0.865484i | \(-0.332989\pi\) | ||||
0.500937 | + | 0.865484i | \(0.332989\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.22991e19 | − | 2.17680e18i | 1.29831 | − | 0.229784i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.64460e18i | 0.469127i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.09564e18i | 0.589269i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.37226e19 | − | 2.42874e18i | 1.26997 | − | 0.224769i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.54972e18 | 0.669052 | 0.334526 | − | 0.942386i | \(-0.391424\pi\) | ||||
0.334526 | + | 0.942386i | \(0.391424\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.08687e19 | 0.922544 | 0.461272 | − | 0.887259i | \(-0.347393\pi\) | ||||
0.461272 | + | 0.887259i | \(0.347393\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.65799e18 | + | 2.85901e18i | 0.134827 | + | 0.232494i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.68337e18i | 0.209108i | 0.994519 | + | 0.104554i | \(0.0333415\pi\) | ||||
−0.994519 | + | 0.104554i | \(0.966658\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 2.85068e19i | − | 2.12930i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.40575e18 | − | 7.94262e18i | −0.100669 | − | 0.568791i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.47485e19 | −1.01284 | −0.506420 | − | 0.862287i | \(-0.669031\pi\) | ||||
−0.506420 | + | 0.862287i | \(0.669031\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.31771e19 | 0.867992 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.49497e18 | − | 1.40968e19i | −0.157676 | − | 0.890884i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 1.16294e19i | − | 0.705280i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.50154e18i | 0.0874058i | 0.999045 | + | 0.0437029i | \(0.0139155\pi\) | ||||
−0.999045 | + | 0.0437029i | \(0.986085\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.51137e18 | − | 4.13595e18i | −0.0844643 | − | 0.231142i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.11680e18 | 0.328262 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.12055e19 | −1.09303 | −0.546515 | − | 0.837449i | \(-0.684046\pi\) | ||||
−0.546515 | + | 0.837449i | \(0.684046\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.67876e18 | − | 1.00507e18i | 0.281202 | − | 0.0497694i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.75294e18i | 0.321316i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.63029e19i | − | 0.745538i | −0.927924 | − | 0.372769i | \(-0.878408\pi\) | ||
0.927924 | − | 0.372769i | \(-0.121592\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.63799e18 | + | 9.97857e17i | −0.247849 | + | 0.0438663i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.83078e19 | 1.61918 | 0.809591 | − | 0.586994i | \(-0.199689\pi\) | ||||
0.809591 | + | 0.586994i | \(0.199689\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.14056e18 | −0.127659 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.98167e18 | − | 1.36326e19i | −0.194779 | − | 0.533025i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.75023e19i | 1.03454i | 0.855823 | + | 0.517269i | \(0.173051\pi\) | ||||
−0.855823 | + | 0.517269i | \(0.826949\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.97615e19i | 1.80123i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.36665e18 | + | 4.16223e19i | 0.256641 | + | 1.45005i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.45692e19 | −1.15934 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.07740e18 | −0.260821 | −0.130411 | − | 0.991460i | \(-0.541630\pi\) | ||||
−0.130411 | + | 0.991460i | \(0.541630\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.30135e17 | + | 3.56033e18i | 0.0195946 | + | 0.110712i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 3.96351e19i | − | 1.18713i | −0.804787 | − | 0.593564i | \(-0.797720\pi\) | ||
0.804787 | − | 0.593564i | \(-0.202280\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.41568e19i | 0.408485i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.09945e19 | − | 3.67461e19i | −0.861732 | − | 1.02164i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.48947e18 | 0.200675 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.14027e19 | 0.552768 | 0.276384 | − | 0.961047i | \(-0.410864\pi\) | ||||
0.276384 | + | 0.961047i | \(0.410864\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.37872e19 | + | 4.21004e18i | −0.592283 | + | 0.104827i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.53371e18i | 0.0848410i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.11630e19i | 2.11085i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.41130e19 | + | 9.57735e18i | −1.20860 | + | 0.213907i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.09808e19 | 0.452081 | 0.226041 | − | 0.974118i | \(-0.427422\pi\) | ||||
0.226041 | + | 0.974118i | \(0.427422\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.10248e19 | −0.437136 | −0.218568 | − | 0.975822i | \(-0.570138\pi\) | ||||
−0.218568 | + | 0.975822i | \(0.570138\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.68249e19 | + | 2.07651e19i | −1.14021 | + | 0.416659i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 7.57848e19i | − | 1.46779i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.61814e19i | 0.302557i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.00791e17 | + | 4.52455e18i | 0.0144574 | + | 0.0816857i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.00534e19 | −0.523979 | −0.261989 | − | 0.965071i | \(-0.584379\pi\) | ||||
−0.261989 | + | 0.965071i | \(0.584379\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.42776e19 | −1.41923 | −0.709615 | − | 0.704590i | \(-0.751131\pi\) | ||||
−0.709615 | + | 0.704590i | \(0.751131\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.71185e19 | − | 9.67211e19i | −0.278481 | − | 1.57345i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 2.23059e19i | − | 0.350598i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.62509e19i | 1.00625i | 0.864212 | + | 0.503127i | \(0.167817\pi\) | ||||
−0.864212 | + | 0.503127i | \(0.832183\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.78570e19 | + | 2.11423e19i | −0.849311 | + | 0.310357i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.17664e19 | 0.876444 | 0.438222 | − | 0.898867i | \(-0.355608\pi\) | ||||
0.438222 | + | 0.898867i | \(0.355608\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.24025e19 | 0.993239 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.86086e19 | − | 1.21429e19i | 0.910064 | − | 0.161070i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.35538e20i | 1.73865i | 0.494241 | + | 0.869325i | \(0.335446\pi\) | ||||
−0.494241 | + | 0.869325i | \(0.664554\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 6.12207e18i | − | 0.0759581i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.93761e19 | + | 1.22787e19i | −0.832671 | + | 0.147373i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.57246e18 | −0.111157 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.22417e19 | −0.137553 | −0.0687765 | − | 0.997632i | \(-0.521910\pi\) | ||||
−0.0687765 | + | 0.997632i | \(0.521910\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.48491e20 | − | 8.61126e19i | 1.61475 | − | 0.936422i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.28302e19i | 0.661319i | 0.943750 | + | 0.330660i | \(0.107271\pi\) | ||||
−0.943750 | + | 0.330660i | \(0.892729\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.58526e19i | 0.569097i | 0.958662 | + | 0.284548i | \(0.0918436\pi\) | ||||
−0.958662 | + | 0.284548i | \(0.908156\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.58869e19 | − | 2.02765e20i | −0.354029 | − | 2.00030i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.26782e20 | −1.21111 | −0.605553 | − | 0.795805i | \(-0.707048\pi\) | ||||
−0.605553 | + | 0.795805i | \(0.707048\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.79321e19 | 0.535948 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.43625e19 | − | 1.37651e20i | −0.218306 | − | 1.23345i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 2.01791e19i | − | 0.175163i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.39710e19i | 0.285697i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.46781e19 | + | 1.22264e20i | 0.364088 | + | 0.996348i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.41200e20 | −1.11511 | −0.557556 | − | 0.830139i | \(-0.688261\pi\) | ||||
−0.557556 | + | 0.830139i | \(0.688261\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.28279e19 | 0.174735 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.96285e19 | + | 7.01376e18i | −0.294038 | + | 0.0520412i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 1.60598e20i | − | 1.15526i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 3.60932e19i | − | 0.251744i | −0.992047 | − | 0.125872i | \(-0.959827\pi\) | ||
0.992047 | − | 0.125872i | \(-0.0401728\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.15486e20 | − | 2.04396e19i | 0.781109 | − | 0.138247i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.60429e20 | 1.70836 | 0.854179 | − | 0.519979i | \(-0.174060\pi\) | ||||
0.854179 | + | 0.519979i | \(0.174060\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.50734e20 | 2.23165 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.29392e19 | − | 6.27743e19i | −0.141592 | − | 0.387474i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.23227e19i | 0.493000i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.54438e20i | 0.897431i | 0.893675 | + | 0.448715i | \(0.148118\pi\) | ||||
−0.893675 | + | 0.448715i | \(0.851882\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.67892e19 | + | 9.48608e19i | 0.0946777 | + | 0.534939i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.90819e19 | −0.487562 | −0.243781 | − | 0.969830i | \(-0.578388\pi\) | ||||
−0.243781 | + | 0.969830i | \(0.578388\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.67625e20 | 1.95308 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.13505e19 | − | 1.77134e20i | −0.161691 | − | 0.913570i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 3.52183e19i | − | 0.176354i | −0.996105 | − | 0.0881769i | \(-0.971896\pi\) | ||
0.996105 | − | 0.0881769i | \(-0.0281041\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.35837e19i | 0.163295i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.65621e19 | + | 3.86005e19i | −0.314302 | + | 0.182269i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.28421e20 | −1.04757 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.41126e19 | −0.374698 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.40781e17 | + | 4.26154e16i | −0.00104200 | + | 0.000184421i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.03731e20i | 1.69750i | 0.528796 | + | 0.848749i | \(0.322644\pi\) | ||||
−0.528796 | + | 0.848749i | \(0.677356\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.24552e19i | 0.336865i | 0.985713 | + | 0.168432i | \(0.0538705\pi\) | ||||
−0.985713 | + | 0.168432i | \(0.946130\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.03526e19 | − | 1.06817e19i | 0.239608 | − | 0.0424077i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.35275e20 | 2.83707 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.83577e19 | −0.0688495 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.06327e19 | + | 2.58108e19i | −0.257512 | + | 0.0941005i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 1.86601e19i | − | 0.0661393i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 3.67846e20i | − | 1.26769i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.48493e18 | + | 4.22906e19i | 0.0250831 | + | 0.141722i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.56403e19 | −0.279102 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.46914e18 | −0.00465675 | −0.00232838 | − | 0.999997i | \(-0.500741\pi\) | ||||
−0.00232838 | + | 0.999997i | \(0.500741\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.09223e19 | − | 1.74714e20i | −0.0953395 | − | 0.538678i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 6.57918e20i | − | 1.97332i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 2.66460e20i | − | 0.777547i | −0.921333 | − | 0.388773i | \(-0.872899\pi\) | ||
0.921333 | − | 0.388773i | \(-0.127101\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.23438e20 | + | 1.18192e20i | −0.918330 | + | 0.335579i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.57219e20 | −0.434378 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.98299e19 | 0.268425 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.26960e20 | + | 5.78680e19i | −0.855653 | + | 0.151440i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 1.49699e20i | − | 0.381333i | −0.981655 | − | 0.190666i | \(-0.938935\pi\) | ||
0.981655 | − | 0.190666i | \(-0.0610648\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6.15061e19i | − | 0.152521i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.34996e20 | − | 4.15915e19i | 0.567335 | − | 0.100411i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.49912e20 | 0.587456 | 0.293728 | − | 0.955889i | \(-0.405104\pi\) | ||||
0.293728 | + | 0.955889i | \(0.405104\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.69873e20 | −1.76220 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.95067e19 | + | 1.06116e20i | 0.199518 | + | 0.236542i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.43611e20i | 0.311777i | 0.987775 | + | 0.155889i | \(0.0498241\pi\) | ||||
−0.987775 | + | 0.155889i | \(0.950176\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.22654e20i | 1.10521i | 0.833444 | + | 0.552603i | \(0.186365\pi\) | ||||
−0.833444 | + | 0.552603i | \(0.813635\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.82047e19 | − | 2.15861e20i | −0.0786969 | − | 0.444645i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.78117e20 | −0.758782 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.91872e20 | −1.15720 | −0.578601 | − | 0.815611i | \(-0.696401\pi\) | ||||
−0.578601 | + | 0.815611i | \(0.696401\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.50281e20 | + | 8.49101e20i | 0.286295 | + | 1.61760i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 2.63263e20i | − | 0.488729i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.80976e20i | 0.327422i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.99187e19 | − | 1.91337e20i | −0.123289 | − | 0.337387i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.64727e20 | −0.970627 | −0.485314 | − | 0.874340i | \(-0.661295\pi\) | ||||
−0.485314 | + | 0.874340i | \(0.661295\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.29591e20 | −0.552219 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.40739e20 | − | 9.57042e19i | 0.883245 | − | 0.156324i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.01714e21i | 1.61984i | 0.586541 | + | 0.809919i | \(0.300489\pi\) | ||||
−0.586541 | + | 0.809919i | \(0.699511\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.97174e20i | 0.772025i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.30852e20 | − | 2.31592e19i | 0.198140 | − | 0.0350684i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.30711e20 | −0.193024 | −0.0965122 | − | 0.995332i | \(-0.530769\pi\) | ||||
−0.0965122 | + | 0.995332i | \(0.530769\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.46190e20 | −0.498604 | −0.249302 | − | 0.968426i | \(-0.580201\pi\) | ||||
−0.249302 | + | 0.968426i | \(0.580201\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.23145e20 | + | 1.15796e21i | 0.594442 | + | 1.62672i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.82400e20i | 1.20921i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.03144e21i | − | 1.37888i | −0.724342 | − | 0.689440i | \(-0.757857\pi\) | ||
0.724342 | − | 0.689440i | \(-0.242143\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.94351e19 | + | 2.79313e20i | 0.0644772 | + | 0.364303i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.56376e20 | −0.326263 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.60952e19 | −0.0944939 | −0.0472469 | − | 0.998883i | \(-0.515045\pi\) | ||||
−0.0472469 | + | 0.998883i | \(0.515045\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.73027e19 | + | 2.67265e20i | 0.0573221 | + | 0.323876i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 6.93023e20i | − | 0.819613i | −0.912173 | − | 0.409806i | \(-0.865596\pi\) | ||
0.912173 | − | 0.409806i | \(-0.134404\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.36199e20i | 0.965228i | 0.875833 | + | 0.482614i | \(0.160313\pi\) | ||||
−0.875833 | + | 0.482614i | \(0.839687\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.29645e20 | − | 7.40874e20i | −0.484087 | − | 0.834752i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.09086e20 | −0.229966 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.08780e21 | −1.16801 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.05338e20 | + | 1.86436e19i | −0.110428 | + | 0.0195445i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.18564e21i | − | 1.21359i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.82218e21i | − | 1.82125i | −0.413231 | − | 0.910626i | \(-0.635600\pi\) | ||
0.413231 | − | 0.910626i | \(-0.364400\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.34808e21 | − | 2.38594e20i | 1.31579 | − | 0.232879i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.52914e20 | 0.336408 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.61032e20 | −0.243024 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.64549e21 | + | 6.01298e20i | −1.49637 | + | 0.546806i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 1.29181e21i | − | 1.14753i | −0.819020 | − | 0.573765i | \(-0.805482\pi\) | ||
0.819020 | − | 0.573765i | \(-0.194518\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 7.29523e20i | − | 0.633077i | −0.948580 | − | 0.316538i | \(-0.897479\pi\) | ||
0.948580 | − | 0.316538i | \(-0.102521\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.55916e20 | + | 8.80940e20i | 0.132188 | + | 0.746876i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.41481e20 | 0.614211 | 0.307106 | − | 0.951675i | \(-0.400639\pi\) | ||||
0.307106 | + | 0.951675i | \(0.400639\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.04551e20 | −0.0846238 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.03635e20 | + | 5.85549e20i | 0.0819690 | + | 0.463133i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.77635e21i | 1.37303i | 0.727116 | + | 0.686515i | \(0.240860\pi\) | ||||
−0.727116 | + | 0.686515i | \(0.759140\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 2.60538e21i | − | 1.96816i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.71279e20 | + | 2.45301e20i | −0.495636 | + | 0.181117i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.76695e21 | 1.27522 | 0.637608 | − | 0.770361i | \(-0.279924\pi\) | ||||
0.637608 | + | 0.770361i | \(0.279924\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.56633e21 | 1.10503 | 0.552514 | − | 0.833504i | \(-0.313669\pi\) | ||||
0.552514 | + | 0.833504i | \(0.313669\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.16270e20 | − | 1.26771e20i | 0.493998 | − | 0.0874317i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 2.22861e20i | − | 0.150270i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1.74993e21i | − | 1.15366i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.56877e21 | − | 4.54641e20i | 1.65588 | − | 0.293071i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.78755e20 | −0.301783 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.66276e20 | 0.225785 | 0.112892 | − | 0.993607i | \(-0.463988\pi\) | ||||
0.112892 | + | 0.993607i | \(0.463988\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.54333e20 | + | 1.12832e21i | 0.394476 | + | 0.680228i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.07554e20i | 0.417200i | 0.978001 | + | 0.208600i | \(0.0668907\pi\) | ||||
−0.978001 | + | 0.208600i | \(0.933109\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.63780e20i | 0.267478i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.44842e20 | + | 2.51340e21i | 0.250959 | + | 1.41794i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.58706e21 | −0.875869 | −0.437934 | − | 0.899007i | \(-0.644290\pi\) | ||||
−0.437934 | + | 0.899007i | \(0.644290\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.48898e21 | 0.803911 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.87964e20 | − | 1.06202e21i | −0.0992888 | − | 0.560992i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.51617e20i | 0.285097i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.17696e20i | 0.261812i | 0.991395 | + | 0.130906i | \(0.0417886\pi\) | ||||
−0.991395 | + | 0.130906i | \(0.958211\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.62442e19 | + | 1.81281e20i | 0.0327830 | + | 0.0897126i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.38724e21 | 1.64044 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.69168e20 | −0.459360 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.44189e21 | + | 6.09173e20i | −1.59668 | + | 0.282593i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.19828e20i | 0.0544095i | 0.999630 | + | 0.0272048i | \(0.00866061\pi\) | ||||
−0.999630 | + | 0.0272048i | \(0.991339\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.31469e20i | 0.236218i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.67202e21 | − | 6.49903e20i | 1.59767 | − | 0.282768i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.06164e21 | −0.452200 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.33867e21 | 1.39228 | 0.696141 | − | 0.717905i | \(-0.254899\pi\) | ||||
0.696141 | + | 0.717905i | \(0.254899\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.29173e20 | + | 1.99542e21i | 0.297720 | + | 0.814729i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 3.66854e21i | − | 1.46663i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 2.83218e20i | − | 0.110873i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.09757e20 | − | 4.01020e21i | −0.272092 | − | 1.53735i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.60481e20 | −0.247967 | −0.123983 | − | 0.992284i | \(-0.539567\pi\) | ||||
−0.123983 | + | 0.992284i | \(0.539567\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.59640e20 | 0.242545 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.58200e20 | − | 8.93848e20i | −0.0569731 | − | 0.321904i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.66508e21i | 0.940102i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 3.40066e21i | − | 1.17505i | −0.809207 | − | 0.587524i | \(-0.800103\pi\) | ||
0.809207 | − | 0.587524i | \(-0.199897\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.46731e21 | + | 2.56417e21i | −0.496666 | + | 0.867942i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.19450e21 | −1.05931 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.06235e21 | −0.345135 | −0.172568 | − | 0.984998i | \(-0.555206\pi\) | ||||
−0.172568 | + | 0.984998i | \(0.555206\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.73872e21 | − | 6.61708e20i | 1.19006 | − | 0.210626i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.71402e21i | 0.534576i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.26887e21i | 0.387779i | 0.981023 | + | 0.193890i | \(0.0621104\pi\) | ||||
−0.981023 | + | 0.193890i | \(0.937890\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.21072e20 | + | 5.68259e19i | −0.0961538 | + | 0.0170181i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.98374e21 | −1.16916 | −0.584581 | − | 0.811336i | \(-0.698741\pi\) | ||||
−0.584581 | + | 0.811336i | \(0.698741\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.29460e21 | −1.23524 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.26216e21 | − | 1.92291e21i | 1.48340 | − | 0.542069i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.06228e21i | 0.293510i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.62217e21i | 0.439336i | 0.975575 | + | 0.219668i | \(0.0704973\pi\) | ||||
−0.975575 | + | 0.219668i | \(0.929503\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.81381e20 | − | 4.97990e21i | −0.233992 | − | 1.32208i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.34265e21 | 1.13019 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.96207e21 | −1.26603 | −0.633015 | − | 0.774140i | \(-0.718183\pi\) | ||||
−0.633015 | + | 0.774140i | \(0.718183\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.07514e20 | − | 1.17248e21i | −0.0519081 | − | 0.293286i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.21368e20i | 0.201443i | 0.994915 | + | 0.100722i | \(0.0321152\pi\) | ||||
−0.994915 | + | 0.100722i | \(0.967885\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.89995e21i | 0.456887i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.93764e21 | + | 3.63144e21i | −2.34327 | + | 0.856284i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.18672e20 | −0.0736849 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.71911e21 | 0.616566 | 0.308283 | − | 0.951295i | \(-0.400246\pi\) | ||||
0.308283 | + | 0.951295i | \(0.400246\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.06200e21 | + | 1.87962e20i | −0.236167 | + | 0.0417986i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 5.76469e21i | − | 1.25727i | −0.777699 | − | 0.628636i | \(-0.783613\pi\) | ||
0.777699 | − | 0.628636i | \(-0.216387\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.58704e21i | 1.19514i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.44204e20 | − | 1.67113e20i | 0.198111 | − | 0.0350632i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.34436e20 | 0.0894117 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.43566e21 | −0.491738 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.22190e21 | + | 3.02827e21i | −1.03423 | + | 0.599765i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.61634e21i | 1.67417i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1.95348e21i | − | 0.372391i | −0.982513 | − | 0.186196i | \(-0.940384\pi\) | ||
0.982513 | − | 0.186196i | \(-0.0596158\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.56501e20 | + | 2.57928e21i | 0.0853816 | + | 0.482415i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.22326e21 | 0.408006 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.45925e21 | −0.262773 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.39833e21 | − | 7.90070e21i | −0.247090 | − | 1.39609i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 9.60790e21i | − | 1.66606i | −0.553227 | − | 0.833031i | \(-0.686604\pi\) | ||
0.553227 | − | 0.833031i | \(-0.313396\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.33156e22i | 2.26601i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.52719e21 | − | 4.17926e21i | −0.255065 | − | 0.697999i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.93632e20 | −0.162877 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.48057e21 | 0.399101 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.95975e21 | + | 8.77815e20i | −0.783264 | + | 0.138628i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 6.95217e21i | − | 1.07772i | −0.842395 | − | 0.538861i | \(-0.818855\pi\) | ||
0.842395 | − | 0.538861i | \(-0.181145\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.95049e21i | 0.753341i | 0.926347 | + | 0.376671i | \(0.122931\pi\) | ||||
−0.926347 | + | 0.376671i | \(0.877069\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.26170e21 | + | 7.54269e20i | −0.636654 | + | 0.112680i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.22891e21 | −1.06021 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.43196e21 | 0.206188 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.01913e20 | + | 5.52546e20i | 0.0285453 | + | 0.0781159i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 4.90883e21i | − | 0.681404i | −0.940171 | − | 0.340702i | \(-0.889335\pi\) | ||
0.940171 | − | 0.340702i | \(-0.110665\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.19170e22i | 1.62430i | 0.583448 | + | 0.812151i | \(0.301703\pi\) | ||||
−0.583448 | + | 0.812151i | \(0.698297\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.16036e20 | + | 1.78564e21i | 0.0422992 | + | 0.238995i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.34832e22 | 1.77215 | 0.886075 | − | 0.463541i | \(-0.153421\pi\) | ||||
0.886075 | + | 0.463541i | \(0.153421\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.23135e21 | 0.417086 | 0.208543 | − | 0.978013i | \(-0.433128\pi\) | ||||
0.208543 | + | 0.978013i | \(0.433128\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.58229e21 | − | 8.94009e21i | −0.200576 | − | 1.13327i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.35575e22i | 1.68788i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 5.93788e21i | − | 0.726078i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.09471e22 | + | 6.34842e21i | −1.31480 | + | 0.762474i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.00134e21 | −0.236105 | −0.118053 | − | 0.993007i | \(-0.537665\pi\) | ||||
−0.118053 | + | 0.993007i | \(0.537665\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.70487e21 | −0.429342 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.04424e21 | − | 3.61806e20i | 0.232716 | − | 0.0411879i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.10878e22i | 1.24000i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 2.54822e21i | − | 0.279969i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.45876e22 | − | 2.58183e21i | 1.57462 | − | 0.278689i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.91556e21 | −0.627370 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.80434e22 | 1.88019 | 0.940093 | − | 0.340918i | \(-0.110738\pi\) | ||||
0.940093 | + | 0.340918i | \(0.110738\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.45461e21 | − | 1.62781e21i | 0.456104 | − | 0.166671i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 9.02494e21i | − | 0.908005i | −0.891001 | − | 0.454002i | \(-0.849996\pi\) | ||
0.891001 | − | 0.454002i | \(-0.150004\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 2.00161e21i | − | 0.197894i | −0.995093 | − | 0.0989468i | \(-0.968453\pi\) | ||
0.995093 | − | 0.0989468i | \(-0.0315474\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.36602e20 | − | 7.71815e20i | −0.0132719 | − | 0.0749876i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.87787e22 | 1.79301 | 0.896506 | − | 0.443031i | \(-0.146097\pi\) | ||||
0.896506 | + | 0.443031i | \(0.146097\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.50719e19 | 0.00141432 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.69456e21 | − | 2.65247e22i | −0.432964 | − | 2.44629i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.95364e21i | 0.267737i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.22434e21i | 0.465474i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.27015e21 | + | 3.38752e21i | −0.811858 | + | 0.296671i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.02652e21 | 0.0883707 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.78746e21 | 0.828272 | 0.414136 | − | 0.910215i | \(-0.364084\pi\) | ||||
0.414136 | + | 0.910215i | \(0.364084\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.05341e22 | − | 1.86441e21i | 0.876358 | − | 0.155105i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 9.05471e21i | − | 0.740551i | −0.928922 | − | 0.370276i | \(-0.879263\pi\) | ||
0.928922 | − | 0.370276i | \(-0.120737\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1.31593e22i | − | 1.05810i | −0.848589 | − | 0.529052i | \(-0.822548\pi\) | ||
0.848589 | − | 0.529052i | \(-0.177452\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.56428e21 | − | 8.07822e20i | 0.360826 | − | 0.0638618i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.51131e22 | −1.17470 | −0.587349 | − | 0.809333i | \(-0.699829\pi\) | ||||
−0.587349 | + | 0.809333i | \(0.699829\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.01915e21 | −0.0778891 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.13963e21 | + | 2.64821e21i | −0.235937 | + | 0.199008i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 5.96882e21i | − | 0.441065i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 2.64721e21i | − | 0.192361i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.32505e20 | − | 3.57372e21i | −0.0451981 | − | 0.255374i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.58570e22 | −1.81710 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.86499e22 | 1.98010 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.50257e20 | − | 2.54400e21i | −0.0306057 | − | 0.172925i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.09364e22i | 0.731153i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1.17651e22i | − | 0.773642i | −0.922155 | − | 0.386821i | \(-0.873573\pi\) | ||
0.922155 | − | 0.386821i | \(-0.126427\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.75437e21 | − | 2.12203e22i | −0.501553 | − | 1.37253i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.36959e22 | 0.871372 | 0.435686 | − | 0.900099i | \(-0.356506\pi\) | ||||
0.435686 | + | 0.900099i | \(0.356506\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.78908e21 | 0.487478 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.09006e22 | − | 3.69915e21i | 1.28677 | − | 0.227742i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.52388e21i | 0.455693i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.78557e22i | 1.65977i | 0.557937 | + | 0.829883i | \(0.311593\pi\) | ||||
−0.557937 | + | 0.829883i | \(0.688407\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.36583e22 | − | 4.18723e21i | 1.38687 | − | 0.245460i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.42390e21 | −0.428173 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.00916e21 | 0.511236 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.81811e21 | + | 1.31850e22i | 0.269017 | + | 0.736179i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.05970e22i | 1.13158i | 0.824549 | + | 0.565791i | \(0.191429\pi\) | ||||
−0.824549 | + | 0.565791i | \(0.808571\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 6.07723e21i | − | 0.328536i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.22655e21 | + | 2.95305e22i | 0.278037 | + | 1.57094i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.47098e22 | −0.770049 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.97549e22 | −1.01772 | −0.508860 | − | 0.860849i | \(-0.669933\pi\) | ||||
−0.508860 | + | 0.860849i | \(0.669933\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.04439e21 | + | 5.90092e21i | 0.0529507 | + | 0.299177i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.70307e22i | 1.34876i | 0.738385 | + | 0.674380i | \(0.235589\pi\) | ||||
−0.738385 | + | 0.674380i | \(0.764411\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.83552e21i | 0.237468i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.29264e21 | − | 7.40217e21i | −0.207485 | − | 0.357784i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.69694e22 | 1.75881 | 0.879403 | − | 0.476078i | \(-0.157942\pi\) | ||||
0.879403 | + | 0.476078i | \(0.157942\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.02860e21 | −0.141822 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.56542e22 | + | 4.54048e21i | −1.18251 | + | 0.209290i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 2.08028e22i | − | 0.943896i | −0.881626 | − | 0.471948i | \(-0.843551\pi\) | ||
0.881626 | − | 0.471948i | \(-0.156449\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.35120e22i | 0.603522i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.26397e21 | + | 1.46262e21i | −0.363370 | + | 0.0643121i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.29990e21 | −0.186131 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.07410e22 | −1.31006 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.12330e22 | + | 7.75902e21i | −0.890870 | + | 0.325544i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 5.31501e22i | − | 2.19558i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 7.67088e21i | − | 0.311994i | −0.987758 | − | 0.155997i | \(-0.950141\pi\) | ||
0.987758 | − | 0.155997i | \(-0.0498590\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.95143e21 | + | 1.66759e22i | 0.118196 | + | 0.667821i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.34132e22 | 0.923244 | 0.461622 | − | 0.887077i | \(-0.347268\pi\) | ||||
0.461622 | + | 0.887077i | \(0.347268\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.78177e21 | −0.379814 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.63280e20 | + | 5.44263e21i | 0.0368314 | + | 0.208101i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 2.67718e22i | − | 1.00802i | −0.863698 | − | 0.504010i | \(-0.831858\pi\) | ||
0.863698 | − | 0.504010i | \(-0.168142\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 6.18616e21i | − | 0.229378i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.79767e22 | + | 1.38775e22i | −1.38675 | + | 0.506752i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.75557e21 | −0.0631345 | −0.0315673 | − | 0.999502i | \(-0.510050\pi\) | ||||
−0.0315673 | + | 0.999502i | \(0.510050\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.38479e22 | −1.19884 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.06041e22 | + | 1.87681e21i | −0.369911 | + | 0.0654698i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.59385e22i | 0.547614i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 5.14963e22i | − | 1.74270i | −0.490659 | − | 0.871352i | \(-0.663244\pi\) | ||
0.490659 | − | 0.871352i | \(-0.336756\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.97451e22 | − | 7.03440e21i | 1.32484 | − | 0.234481i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.19078e21 | −0.268938 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.52853e22 | −0.817812 | −0.408906 | − | 0.912576i | \(-0.634090\pi\) | ||||
−0.408906 | + | 0.912576i | \(0.634090\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.02369e22 | + | 1.76524e22i | 0.326157 | + | 0.562421i |
(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 | 48.16.c.d.47.12 | yes | 20 | |
3.2 | odd | 2 | inner | 48.16.c.d.47.10 | yes | 20 | |
4.3 | odd | 2 | inner | 48.16.c.d.47.9 | ✓ | 20 | |
12.11 | even | 2 | inner | 48.16.c.d.47.11 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.16.c.d.47.9 | ✓ | 20 | 4.3 | odd | 2 | inner | |
48.16.c.d.47.10 | yes | 20 | 3.2 | odd | 2 | inner | |
48.16.c.d.47.11 | yes | 20 | 12.11 | even | 2 | inner | |
48.16.c.d.47.12 | yes | 20 | 1.1 | even | 1 | trivial |