Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [32,20,Mod(17,32)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(32, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 20, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("32.17");
S:= CuspForms(chi, 20);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 32 = 2^{5} \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 32.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: | \(73.2213428980\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 9 x^{17} + 847482358 x^{16} - 6779858660 x^{15} + \cdots + 11\!\cdots\!76 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | multiple of \( 2^{306}\cdot 3^{16}\cdot 5^{4}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 8) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 17.10 | ||
Root | \(0.500000 - 222.384i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 32.17 |
Dual form | 32.20.b.a.17.9 |
$q$-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 \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(31\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 889.536i | 0.0260923i | 0.999915 | + | 0.0130461i | \(0.00415283\pi\) | ||||
−0.999915 | + | 0.0130461i | \(0.995847\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.56401e6i | 1.27401i | 0.770860 | + | 0.637005i | \(0.219827\pi\) | ||||
−0.770860 | + | 0.637005i | \(0.780173\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.51327e6 | 0.0422727 | 0.0211363 | − | 0.999777i | \(-0.493272\pi\) | ||||
0.0211363 | + | 0.999777i | \(0.493272\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.16147e9 | 0.999319 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 1.78940e9i | − 0.228811i | −0.993434 | − | 0.114405i | \(-0.963504\pi\) | ||||
0.993434 | − | 0.114405i | \(-0.0364962\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 3.40689e10i | − 0.891037i | −0.895273 | − | 0.445519i | \(-0.853019\pi\) | ||||
0.895273 | − | 0.445519i | \(-0.146981\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.94939e9 | −0.0332418 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.37021e11 | −0.893794 | −0.446897 | − | 0.894586i | \(-0.647471\pi\) | ||||
−0.446897 | + | 0.894586i | \(0.647471\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 2.55409e12i | − 1.81584i | −0.419144 | − | 0.907920i | \(-0.637670\pi\) | ||||
0.419144 | − | 0.907920i | \(-0.362330\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.01471e9i | 0.00110299i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.58979e12 | 0.647114 | 0.323557 | − | 0.946209i | \(-0.395121\pi\) | ||||
0.323557 | + | 0.946209i | \(0.395121\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.18847e13 | −0.623102 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.06704e12i | 0.0521667i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.17732e13i | 1.17472i | 0.809325 | + | 0.587361i | \(0.199833\pi\) | ||||
−0.809325 | + | 0.587361i | \(0.800167\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.96656e13 | 0.473241 | 0.236620 | − | 0.971602i | \(-0.423960\pi\) | ||||
0.236620 | + | 0.971602i | \(0.423960\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.59173e12 | 0.00597018 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.51119e13i | 0.0538558i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 7.21521e14i | − 0.912710i | −0.889798 | − | 0.456355i | \(-0.849155\pi\) | ||||
0.889798 | − | 0.456355i | \(-0.150845\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.03055e13 | 0.0232492 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.74108e15 | −0.830561 | −0.415281 | − | 0.909693i | \(-0.636317\pi\) | ||||
−0.415281 | + | 0.909693i | \(0.636317\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 3.57351e15i | − 1.08429i | −0.840285 | − | 0.542145i | \(-0.817612\pi\) | ||||
0.840285 | − | 0.542145i | \(-0.182388\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.46243e15i | 1.27314i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.43582e16 | 1.87142 | 0.935709 | − | 0.352774i | \(-0.114761\pi\) | ||||
0.935709 | + | 0.352774i | \(0.114761\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.13785e16 | −0.998213 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 3.88746e14i | − 0.0233211i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.88104e16i | 0.783029i | 0.920172 | + | 0.391515i | \(0.128049\pi\) | ||||
−0.920172 | + | 0.391515i | \(0.871951\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.95622e15 | 0.291507 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.27196e15 | 0.0473794 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 4.76955e16i | − 0.716775i | −0.933573 | − | 0.358388i | \(-0.883327\pi\) | ||||
0.933573 | − | 0.358388i | \(-0.116673\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 1.16266e17i | − 1.27297i | −0.771290 | − | 0.636484i | \(-0.780388\pi\) | ||||
0.771290 | − | 0.636484i | \(-0.219612\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.24203e15 | 0.0422439 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.89560e17 | 1.13519 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.76329e17i | 0.791793i | 0.918295 | + | 0.395897i | \(0.129566\pi\) | ||||
−0.918295 | + | 0.395897i | \(0.870434\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.97232e15i | 0.0168847i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.82001e16 | −0.176535 | −0.0882675 | − | 0.996097i | \(-0.528133\pi\) | ||||
−0.0882675 | + | 0.996097i | \(0.528133\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.94941e17 | 1.18279 | 0.591394 | − | 0.806383i | \(-0.298578\pi\) | ||||
0.591394 | + | 0.806383i | \(0.298578\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 1.05719e16i | − 0.0162581i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 8.07603e15i | − 0.00967244i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.48803e18 | 1.39687 | 0.698433 | − | 0.715676i | \(-0.253881\pi\) | ||||
0.698433 | + | 0.715676i | \(0.253881\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.34809e18 | 0.997958 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 1.21993e18i | − 0.716296i | −0.933665 | − | 0.358148i | \(-0.883408\pi\) | ||||
0.933665 | − | 0.358148i | \(-0.116592\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 2.43159e18i | − 1.13870i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.16356e16 | −0.0306511 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.29788e18 | 0.997768 | 0.498884 | − | 0.866669i | \(-0.333743\pi\) | ||||
0.498884 | + | 0.866669i | \(0.333743\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 1.53762e17i | − 0.0376665i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.19700e16i | 0.0123479i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.42110e19 | 2.31340 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.52106e18 | 0.603822 | 0.301911 | − | 0.953336i | \(-0.402375\pi\) | ||||
0.301911 | + | 0.953336i | \(0.402375\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 2.07833e18i | − 0.228655i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.01147e19i | 0.920238i | 0.887857 | + | 0.460119i | \(0.152193\pi\) | ||||
−0.887857 | + | 0.460119i | \(0.847807\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.82500e19 | 1.37819 | 0.689096 | − | 0.724670i | \(-0.258008\pi\) | ||||
0.689096 | + | 0.724670i | \(0.258008\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.23379e16 | −0.00140522 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 2.72881e19i | − 1.43492i | −0.696600 | − | 0.717459i | \(-0.745305\pi\) | ||||
0.696600 | − | 0.717459i | \(-0.254695\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 1.32939e19i | − 0.586272i | −0.956071 | − | 0.293136i | \(-0.905301\pi\) | ||||
0.956071 | − | 0.293136i | \(-0.0946989\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.41819e17 | 0.0238146 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.83425e19 | 0.574399 | 0.287199 | − | 0.957871i | \(-0.407276\pi\) | ||||
0.287199 | + | 0.957871i | \(0.407276\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.11016e19i | 0.824430i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 3.95700e19i | − 0.890431i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.97239e18 | −0.0377831 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.79571e19 | 0.947646 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 1.54875e18i | − 0.0216712i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.99983e19i | 0.480171i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.55505e20 | −1.60550 | −0.802748 | − | 0.596319i | \(-0.796630\pi\) | ||||
−0.802748 | + | 0.596319i | \(0.796630\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.17877e18 | 0.0282916 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.39001e20i | 1.83790i | 0.394376 | + | 0.918949i | \(0.370961\pi\) | ||||
−0.394376 | + | 0.918949i | \(0.629039\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 1.15273e19i | − 0.0767604i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.15010e19 | −0.0664610 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.33463e20 | −1.17320 | −0.586602 | − | 0.809875i | \(-0.699535\pi\) | ||||
−0.586602 | + | 0.809875i | \(0.699535\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 4.01632e20i | − 1.75868i | −0.476190 | − | 0.879342i | \(-0.657983\pi\) | ||||
0.476190 | − | 0.879342i | \(-0.342017\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.27721e19i | 0.0488295i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.09627e19 | −0.203879 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.10627e20 | −1.49661 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 1.01216e19i | − 0.0260456i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.08909e20i | 1.15178i | 0.817526 | + | 0.575892i | \(0.195345\pi\) | ||||
−0.817526 | + | 0.575892i | \(0.804655\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.58863e20 | −0.715563 | −0.357782 | − | 0.933805i | \(-0.616467\pi\) | ||||
−0.357782 | + | 0.933805i | \(0.616467\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.07586e20 | −0.893185 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.87620e20i | 0.602913i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 1.45807e20i | − 0.200786i | −0.994948 | − | 0.100393i | \(-0.967990\pi\) | ||||
0.994948 | − | 0.100393i | \(-0.0320099\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.67326e19 | −0.0204310 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.52282e19 | 0.0273553 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.25859e21i | 1.21367i | 0.794828 | + | 0.606835i | \(0.207561\pi\) | ||||
−0.794828 | + | 0.606835i | \(0.792439\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.85642e18i | 0.00760608i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.81697e20 | −0.292356 | −0.146178 | − | 0.989258i | \(-0.546697\pi\) | ||||
−0.146178 | + | 0.989258i | \(0.546697\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.01232e20 | 0.206053 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 2.96650e21i | − 1.81460i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.20483e20i | 0.394626i | 0.980341 | + | 0.197313i | \(0.0632216\pi\) | ||||
−0.980341 | + | 0.197313i | \(0.936778\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.36390e19 | −0.0263402 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.24268e19 | 0.0187023 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.54740e21i | 0.613055i | 0.951862 | + | 0.306528i | \(0.0991672\pi\) | ||||
−0.951862 | + | 0.306528i | \(0.900833\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 3.95197e21i | − 1.40886i | −0.709774 | − | 0.704429i | \(-0.751203\pi\) | ||||
0.709774 | − | 0.704429i | \(-0.248797\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.03422e20 | 0.0332146 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.01455e21 | 1.16280 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.82003e20i | 0.204509i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.32912e18i | 0.00220523i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.73400e21 | 1.01254 | 0.506269 | − | 0.862375i | \(-0.331024\pi\) | ||||
0.506269 | + | 0.862375i | \(0.331024\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.86311e21 | 1.52335 | 0.761676 | − | 0.647959i | \(-0.224377\pi\) | ||||
0.761676 | + | 0.647959i | \(0.224377\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.68620e20i | 0.0296197i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.32685e21i | 0.849261i | 0.905367 | + | 0.424630i | \(0.139596\pi\) | ||||
−0.905367 | + | 0.424630i | \(0.860404\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.72615e21 | 0.250019 | 0.125010 | − | 0.992156i | \(-0.460104\pi\) | ||||
0.125010 | + | 0.992156i | \(0.460104\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.56851e20 | −0.0206597 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.14197e20i | 0.0496586i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 9.68738e21i | − 1.05814i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.49237e21 | 0.646674 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.57029e21 | −0.415483 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 1.43551e22i | − 1.19213i | −0.802936 | − | 0.596065i | \(-0.796730\pi\) | ||||
0.802936 | − | 0.596065i | \(-0.203270\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 6.06664e19i | − 0.00460619i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.98831e22 | 1.38140 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.14419e20 | 0.0200052 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.29221e20i | 0.0308616i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.48888e22i | 0.796403i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.36844e22 | −0.671938 | −0.335969 | − | 0.941873i | \(-0.609064\pi\) | ||||
−0.335969 | + | 0.941873i | \(0.609064\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.38038e22 | −0.622678 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 2.28444e22i | − 0.947400i | −0.880686 | − | 0.473700i | \(-0.842918\pi\) | ||||
0.880686 | − | 0.473700i | \(-0.157082\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.15938e22i | 0.442371i | 0.975232 | + | 0.221186i | \(0.0709927\pi\) | ||||
−0.975232 | + | 0.221186i | \(0.929007\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.18392e18 | 0.000252376 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.44196e22 | −0.466736 | −0.233368 | − | 0.972388i | \(-0.574975\pi\) | ||||
−0.233368 | + | 0.972388i | \(0.574975\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.98892e22i | 2.38421i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.32366e21i | 0.0364474i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.79540e22 | −1.47334 | −0.736671 | − | 0.676252i | \(-0.763603\pi\) | ||||
−0.736671 | + | 0.676252i | \(0.763603\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.53834e22 | 0.596195 | 0.298097 | − | 0.954535i | \(-0.403648\pi\) | ||||
0.298097 | + | 0.954535i | \(0.403648\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.60162e21i | 0.0782057i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 6.33102e22i | − 1.27173i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.70151e22 | −1.61798 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.08517e21 | 0.0186898 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 2.45272e22i | − 0.391514i | −0.980652 | − | 0.195757i | \(-0.937284\pi\) | ||||
0.980652 | − | 0.195757i | \(-0.0627164\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 1.00023e22i | − 0.148067i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.16298e21 | 0.0297113 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.84682e22 | −1.00076 | −0.500379 | − | 0.865807i | \(-0.666806\pi\) | ||||
−0.500379 | + | 0.865807i | \(0.666806\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 3.25642e21i | − 0.0385827i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.06592e23i | 1.17392i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.14964e22 | −0.629898 | −0.314949 | − | 0.949109i | \(-0.601987\pi\) | ||||
−0.314949 | + | 0.949109i | \(0.601987\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.04661e23 | −0.997588 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.93358e21i | 0.0260340i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.37452e21i | 0.0278975i | 0.999903 | + | 0.0139487i | \(0.00444016\pi\) | ||||
−0.999903 | + | 0.0139487i | \(0.995560\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.70540e23 | 1.31407 | 0.657035 | − | 0.753860i | \(-0.271811\pi\) | ||||
0.657035 | + | 0.753860i | \(0.271811\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.36777e20 | 0.000982805 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.12665e22i | 0.142572i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.88428e22i | 0.618568i | 0.950970 | + | 0.309284i | \(0.100089\pi\) | ||||
−0.950970 | + | 0.309284i | \(0.899911\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.09145e22 | 0.472918 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.54967e23 | 0.846309 | 0.423154 | − | 0.906058i | \(-0.360923\pi\) | ||||
0.423154 | + | 0.906058i | \(0.360923\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 9.10357e22i | − 0.464773i | −0.972624 | − | 0.232386i | \(-0.925347\pi\) | ||||
0.972624 | − | 0.232386i | \(-0.0746534\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.26412e22i | 0.0603618i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.85796e21 | −0.0351101 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.80854e22 | −0.201133 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.02165e21i | 0.0157551i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 3.76601e23i | − 1.38242i | −0.722655 | − | 0.691209i | \(-0.757078\pi\) | ||||
0.722655 | − | 0.691209i | \(-0.242922\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.65378e23 | 0.913179 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.69876e21 | 0.0119363 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 1.90438e23i | − 0.576603i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 1.61282e22i | − 0.0458358i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.99739e21 | −0.0240111 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.46903e23 | 1.62178 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 4.06724e22i | − 0.0958265i | −0.998852 | − | 0.0479132i | \(-0.984743\pi\) | ||||
0.998852 | − | 0.0479132i | \(-0.0152571\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.62340e22i | 0.0359601i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.11001e23 | 0.439604 | 0.219802 | − | 0.975544i | \(-0.429459\pi\) | ||||
0.219802 | + | 0.975544i | \(0.429459\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.32064e23 | 0.846988 | 0.423494 | − | 0.905899i | \(-0.360803\pi\) | ||||
0.423494 | + | 0.905899i | \(0.360803\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.91667e22i | 0.0538192i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.37604e22i | 0.0412849i | 0.999787 | + | 0.0206424i | \(0.00657116\pi\) | ||||
−0.999787 | + | 0.0206424i | \(0.993429\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.64219e23 | 0.268789 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.42737e22 | 0.0374403 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.11619e24i | 1.62299i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.04900e23i | 0.555208i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.18254e22 | 0.0152972 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.48025e22 | 0.0791098 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 1.23591e24i | − 1.42437i | −0.701994 | − | 0.712183i | \(-0.747707\pi\) | ||||
0.701994 | − | 0.712183i | \(-0.252293\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 8.38025e23i | − 0.912088i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.81094e23 | −1.00875 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.39486e23 | −0.621366 | −0.310683 | − | 0.950514i | \(-0.600558\pi\) | ||||
−0.310683 | + | 0.950514i | \(0.600558\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.63163e22i | 0.0149874i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 1.24659e23i | − 0.108282i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.02801e23 | −0.0844698 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.76660e22 | −0.0215112 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.84162e23i | 0.503534i | 0.967788 | + | 0.251767i | \(0.0810117\pi\) | ||||
−0.967788 | + | 0.251767i | \(0.918988\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.64379e23i | 0.253928i | 0.991907 | + | 0.126964i | \(0.0405233\pi\) | ||||
−0.991907 | + | 0.126964i | \(0.959477\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.04218e22 | 0.0464825 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.48650e23 | −0.343112 | −0.171556 | − | 0.985174i | \(-0.554879\pi\) | ||||
−0.171556 | + | 0.985174i | \(0.554879\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 3.79466e23i | − 0.224907i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 1.75451e21i | 0 0.000985845i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.28269e24 | −0.683479 | −0.341739 | − | 0.939795i | \(-0.611016\pi\) | ||||
−0.341739 | + | 0.939795i | \(0.611016\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.54497e24 | −2.29727 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.15550e22i | 0.0247262i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.31026e24i | 1.50688i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.23278e24 | 0.532793 | 0.266396 | − | 0.963864i | \(-0.414167\pi\) | ||||
0.266396 | + | 0.963864i | \(0.414167\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.02221e24 | −0.829996 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.48965e22i | 0.0331008i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.86125e24i | 0.689559i | 0.938684 | + | 0.344780i | \(0.112046\pi\) | ||||
−0.938684 | + | 0.344780i | \(0.887954\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.55799e22 | −0.0125288 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.12661e24 | 1.04672 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.18195e24i | 0.376292i | 0.982141 | + | 0.188146i | \(0.0602479\pi\) | ||||
−0.982141 | + | 0.188146i | \(0.939752\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 1.38327e23i | − 0.0418910i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.42588e24 | −0.987150 | −0.493575 | − | 0.869703i | \(-0.664310\pi\) | ||||
−0.493575 | + | 0.869703i | \(0.664310\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.49351e22 | 0.0123228 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 4.15053e24i | − 1.08355i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 6.91661e24i | − 1.71938i | −0.510815 | − | 0.859691i | \(-0.670656\pi\) | ||||
0.510815 | − | 0.859691i | \(-0.329344\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.44285e24 | −0.578387 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.12600e23 | −0.0479549 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.27942e24i | 1.77962i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 6.65245e24i | − 1.36293i | −0.731853 | − | 0.681463i | \(-0.761344\pi\) | ||||
0.731853 | − | 0.681463i | \(-0.238656\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.02540e22 | 0.00200285 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.41010e24 | 1.19397 | 0.596984 | − | 0.802253i | \(-0.296365\pi\) | ||||
0.596984 | + | 0.802253i | \(0.296365\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 2.37343e24i | − 0.421675i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.50081e24i | 1.27141i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.29109e24 | −0.208838 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.52154e24 | 0.852490 | 0.426245 | − | 0.904608i | \(-0.359836\pi\) | ||||
0.426245 | + | 0.904608i | \(0.359836\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 2.07674e23i | − 0.0306115i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 2.15263e23i | − 0.0303000i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.78770e24 | 0.912569 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.57266e23 | 0.0458880 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 3.31446e24i | − 0.406799i | −0.979096 | − | 0.203400i | \(-0.934801\pi\) | ||||
0.979096 | − | 0.203400i | \(-0.0651990\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.93632e24i | 0.461754i | 0.972983 | + | 0.230877i | \(0.0741595\pi\) | ||||
−0.972983 | + | 0.230877i | \(0.925841\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.66766e25 | 1.87014 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.19388e24 | 0.556925 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 5.24738e23i | − 0.0538118i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 5.42285e22i | − 0.00531966i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.03414e24 | −0.0970610 | −0.0485305 | − | 0.998822i | \(-0.515454\pi\) | ||||
−0.0485305 | + | 0.998822i | \(0.515454\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.24817e24 | −0.201927 | −0.100963 | − | 0.994890i | \(-0.532193\pi\) | ||||
−0.100963 | + | 0.994890i | \(0.532193\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 4.54221e23i | − 0.0390499i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 1.42768e25i | − 1.17506i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.13798e25 | 0.896856 | 0.448428 | − | 0.893819i | \(-0.351984\pi\) | ||||
0.448428 | + | 0.893819i | \(0.351984\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.32158e25 | −0.997533 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 2.12719e25i | − 1.53805i | −0.639216 | − | 0.769027i | \(-0.720741\pi\) | ||||
0.639216 | − | 0.769027i | \(-0.279259\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.83494e25i | 1.27117i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.52693e23 | −0.0300526 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.43638e24 | 0.345915 | 0.172958 | − | 0.984929i | \(-0.444668\pi\) | ||||
0.172958 | + | 0.984929i | \(0.444668\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.11548e24i | 0.190041i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 3.19222e23i | − 0.0186707i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.55533e23 | 0.0479876 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.03816e25 | 0.558549 | 0.279274 | − | 0.960211i | \(-0.409906\pi\) | ||||
0.279274 | + | 0.960211i | \(0.409906\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 9.03340e23i | − 0.0466263i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 2.01328e25i | − 0.997117i | −0.866856 | − | 0.498559i | \(-0.833863\pi\) | ||||
0.866856 | − | 0.498559i | \(-0.166137\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.68246e25 | −0.799699 | −0.399849 | − | 0.916581i | \(-0.630938\pi\) | ||||
−0.399849 | + | 0.916581i | \(0.630938\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.44802e23 | −0.0157314 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.96900e25i | 1.30047i | 0.759734 | + | 0.650234i | \(0.225329\pi\) | ||||
−0.759734 | + | 0.650234i | \(0.774671\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.95818e23i | 0.0334712i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.29701e23 | 0.00523895 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.39444e24 | −0.248097 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.03547e25i | 1.13145i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.18478e25i | 0.782496i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.48219e25 | −1.19857 | −0.599287 | − | 0.800534i | \(-0.704549\pi\) | ||||
−0.599287 | + | 0.800534i | \(0.704549\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.45814e25 | −0.813258 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.24414e22i | 0 0.000713760i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.51552e25i | 0.769276i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.81856e25 | −1.12299 | −0.561494 | − | 0.827481i | \(-0.689773\pi\) | ||||
−0.561494 | + | 0.827481i | \(0.689773\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.11956e24 | −0.0316674 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 4.66960e25i | − 1.27059i | −0.772270 | − | 0.635294i | \(-0.780879\pi\) | ||||
0.772270 | − | 0.635294i | \(-0.219121\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 4.01068e25i | − 1.04996i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.15639e25 | 0.291309 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.07805e23 | −0.00746261 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 1.20220e25i | − 0.280558i | −0.990112 | − | 0.140279i | \(-0.955200\pi\) | ||||
0.990112 | − | 0.140279i | \(-0.0447999\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 3.39533e23i | − 0.00762823i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.04737e25 | −0.659218 | −0.329609 | − | 0.944118i | \(-0.606917\pi\) | ||||
−0.329609 | + | 0.944118i | \(0.606917\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.62783e25 | −1.17239 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.67957e23i | 0.00537637i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.44729e25i | 0.279728i | 0.990171 | + | 0.139864i | \(0.0446665\pi\) | ||||
−0.990171 | + | 0.139864i | \(0.955333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.68513e24 | 0.0499996 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.27942e24 | 0.0947264 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.01543e26i | 1.75583i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 2.56925e25i | − 0.428200i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.40896e23 | −0.0102967 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.00543e25 | 0.620426 | 0.310213 | − | 0.950667i | \(-0.399600\pi\) | ||||
0.310213 | + | 0.950667i | \(0.399600\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 2.12968e25i | − 0.318088i | −0.987271 | − | 0.159044i | \(-0.949159\pi\) | ||||
0.987271 | − | 0.159044i | \(-0.0508412\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 4.77138e22i | 0 0.000687276i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.04453e25 | −0.422979 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.33697e25 | −0.581243 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 5.53969e25i | − 0.716287i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.93166e25i | 0.740061i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.51831e26 | 1.82810 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.37647e24 | −0.0159960 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.03607e25i | 0.228402i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.51095e26i | 1.63635i | 0.574971 | + | 0.818174i | \(0.305013\pi\) | ||||
−0.574971 | + | 0.818174i | \(0.694987\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.51542e24 | 0.0367603 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.39672e25 | 0.746917 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 1.21086e26i | − 1.18090i | −0.807075 | − | 0.590449i | \(-0.798951\pi\) | ||||
0.807075 | − | 0.590449i | \(-0.201049\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 1.35039e26i | − 1.27210i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.34397e26 | 2.13311 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.71589e24 | 0.0590493 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.57109e24i | 0.0303401i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 2.13063e26i | − 1.74938i | −0.484683 | − | 0.874690i | \(-0.661065\pi\) | ||||
0.484683 | − | 0.874690i | \(-0.338935\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.21746e26 | −0.966142 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.95620e23 | −0.00533611 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 2.61624e25i | − 0.194020i | −0.995283 | − | 0.0970102i | \(-0.969072\pi\) | ||||
0.995283 | − | 0.0970102i | \(-0.0309279\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.02058e26i | 0.731790i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.08431e24 | 0.0421864 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.22661e26 | 0.822508 | 0.411254 | − | 0.911521i | \(-0.365091\pi\) | ||||
0.411254 | + | 0.911521i | \(0.365091\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 2.63692e25i | − 0.171023i | −0.996337 | − | 0.0855113i | \(-0.972748\pi\) | ||||
0.996337 | − | 0.0855113i | \(-0.0272524\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.21107e24i | 0.0264194i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.64332e25 | −0.403218 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.48000e26 | 0.869141 | 0.434571 | − | 0.900638i | \(-0.356900\pi\) | ||||
0.434571 | + | 0.900638i | \(0.356900\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.99452e24i | 0.0397477i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 5.50587e24i | − 0.0302798i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.36593e25 | 0.179165 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.20168e26 | 1.13442 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.16221e26i | 1.57735i | 0.614809 | + | 0.788676i | \(0.289233\pi\) | ||||
−0.614809 | + | 0.788676i | \(0.710767\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 1.77932e26i | − 0.859329i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.73842e24 | −0.0221591 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.11232e25 | 0.186238 | 0.0931188 | − | 0.995655i | \(-0.470316\pi\) | ||||
0.0931188 | + | 0.995655i | \(0.470316\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 1.09744e25i | − 0.0481360i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.53547e24i | 0.00652357i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.03552e26 | 0.426191 | 0.213096 | − | 0.977031i | \(-0.431645\pi\) | ||||
0.213096 | + | 0.977031i | \(0.431645\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.98522e26 | −0.791592 | −0.395796 | − | 0.918338i | \(-0.629531\pi\) | ||||
−0.395796 | + | 0.918338i | \(0.629531\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.04800e26i | 0.791254i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.22474e26i | 1.20731i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.20554e26 | −1.52591 | −0.762956 | − | 0.646450i | \(-0.776253\pi\) | ||||
−0.762956 | + | 0.646450i | \(0.776253\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.68443e23 | −0.00129571 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 4.89168e26i | − 1.66750i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 2.47119e26i | − 0.816641i | −0.912839 | − | 0.408320i | \(-0.866115\pi\) | ||||
0.912839 | − | 0.408320i | \(-0.133885\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.61727e24 | 0.0276094 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.47234e26 | −1.38939 | −0.694697 | − | 0.719303i | \(-0.744462\pi\) | ||||
−0.694697 | + | 0.719303i | \(0.744462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.70369e25i | 0.292331i | 0.989260 | + | 0.146166i | \(0.0466933\pi\) | ||||
−0.989260 | + | 0.146166i | \(0.953307\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.15543e25i | 0.0337578i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.48842e25 | 0.0421783 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.49234e26 | −1.23485 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 4.06543e24i | − 0.0108409i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.15320e26i | 0.815774i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.42435e26 | 0.357551 | 0.178776 | − | 0.983890i | \(-0.442786\pi\) | ||||
0.178776 | + | 0.983890i | \(0.442786\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.27694e25 | 0.0311054 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 8.65232e26i | − 2.04542i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.87654e26i | 0.889445i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.92124e25 | −0.176415 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.22851e26 | −1.56278 | −0.781389 | − | 0.624044i | \(-0.785488\pi\) | ||||
−0.781389 | + | 0.624044i | \(0.785488\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.33528e26i | 1.95940i | 0.200470 | + | 0.979700i | \(0.435753\pi\) | ||||
−0.200470 | + | 0.979700i | \(0.564247\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.76867e25i | 0.0360437i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.11281e26 | 1.01174 | 0.505870 | − | 0.862610i | \(-0.331172\pi\) | ||||
0.505870 | + | 0.862610i | \(0.331172\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.53461e25 | −0.164006 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.79687e23i | 0 0.000521980i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 3.98338e26i | − 0.722065i | −0.932553 | − | 0.361033i | \(-0.882424\pi\) | ||||
0.932553 | − | 0.361033i | \(-0.117576\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.32980e27 | −2.34150 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.91006e26 | 1.18198 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.20018e26i | 0.698001i | 0.937123 | + | 0.349000i | \(0.113479\pi\) | ||||
−0.937123 | + | 0.349000i | \(0.886521\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.64134e26i | 0.749427i | 0.927141 | + | 0.374713i | \(0.122259\pi\) | ||||
−0.927141 | + | 0.374713i | \(0.877741\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.32441e25 | −0.0207800 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.41381e25 | 0.0977936 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.12993e26i | 0.760179i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 1.21728e25i | − 0.0175324i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.08045e26 | −0.291269 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.53795e26 | 0.345414 | 0.172707 | − | 0.984973i | \(-0.444749\pi\) | ||||
0.172707 | + | 0.984973i | \(0.444749\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 2.45663e25i | − 0.0325052i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 6.54796e26i | − 0.842391i | −0.906970 | − | 0.421195i | \(-0.861611\pi\) | ||||
0.906970 | − | 0.421195i | \(-0.138389\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.04048e25 | 0.0255252 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.03209e25 | 0.0247198 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1.26437e27i | − 1.49582i | −0.663802 | − | 0.747909i | \(-0.731058\pi\) | ||||
0.663802 | − | 0.747909i | \(-0.268942\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 1.29899e27i | − 1.49467i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.03131e25 | −0.0115425 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.40850e26 | 0.697708 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.15641e25i | 0.0863889i | 0.999067 | + | 0.0431944i | \(0.0137535\pi\) | ||||
−0.999067 | + | 0.0431944i | \(0.986247\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 9.38007e24i | − 0.00966585i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.23469e27 | 2.24058 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.60887e26 | 0.742350 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 1.28267e25i | − 0.0121782i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.50490e27i | 1.39055i | 0.718744 | + | 0.695275i | \(0.244717\pi\) | ||||
−0.718744 | + | 0.695275i | \(0.755283\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.84283e27 | −1.65733 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.10643e25 | −0.0622093 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.56504e25i | 0.0389009i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.48850e25i | 0.0123484i | 0.999981 | + | 0.00617420i | \(0.00196532\pi\) | ||||
−0.999981 | + | 0.00617420i | \(0.998035\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.72830e27 | 1.39591 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.89416e26 | 0.306241 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 3.39197e26i | − 0.259744i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 5.15522e25i | − 0.0384428i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.98917e25 | −0.0434953 | −0.0217476 | − | 0.999763i | \(-0.506923\pi\) | ||||
−0.0217476 | + | 0.999763i | \(0.506923\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.23672e25 | 0.0582599 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.25795e25i | 0.0155561i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 1.09070e27i | − 0.731972i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.58883e27 | 1.03872 | 0.519362 | − | 0.854554i | \(-0.326169\pi\) | ||||
0.519362 | + | 0.854554i | \(0.326169\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.56363e27 | 0.995917 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.56170e27i | 0.969131i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.88881e26i | 0.477006i | 0.971142 | + | 0.238503i | \(0.0766566\pi\) | ||||
−0.971142 | + | 0.238503i | \(0.923343\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.63167e25 | 0.0331824 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.15522e26 | 0.181171 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 7.06002e26i | − 0.395079i | −0.980295 | − | 0.197539i | \(-0.936705\pi\) | ||||
0.980295 | − | 0.197539i | \(-0.0632950\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 7.74030e25i | − 0.0422168i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.24185e27 | 1.72345 | 0.861726 | − | 0.507373i | \(-0.169384\pi\) | ||||
0.861726 | + | 0.507373i | \(0.169384\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.83158e27 | −1.46738 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 1.41691e27i | − 0.715808i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 1.23158e26i | − 0.0606579i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.47111e27 | −1.66682 | −0.833411 | − | 0.552654i | \(-0.813615\pi\) | ||||
−0.833411 | + | 0.552654i | \(0.813615\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.18178e25 | 0.0102155 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 1.99672e27i | − 0.911635i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.85845e26i | 0.394409i | 0.980362 | + | 0.197205i | \(0.0631863\pi\) | ||||
−0.980362 | + | 0.197205i | \(0.936814\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.89745e24 | 0.00386339 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.97430e26 | 0.168309 | 0.0841543 | − | 0.996453i | \(-0.473181\pi\) | ||||
0.0841543 | + | 0.996453i | \(0.473181\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 5.99988e25i | − 0.0247833i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 2.82422e27i | − 1.13793i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.62493e27 | −0.638674 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.90265e27 | −1.11300 | −0.556499 | − | 0.830848i | \(-0.687856\pi\) | ||||
−0.556499 | + | 0.830848i | \(0.687856\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 6.98003e25i | − 0.0261120i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.03505e27i | 1.10780i | 0.832584 | + | 0.553899i | \(0.186861\pi\) | ||||
−0.832584 | + | 0.553899i | \(0.813139\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.27957e26 | −0.294877 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.89670e24 | 0.00100671 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.44688e27i | 1.50817i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.22037e26i | 0.0403931i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.89699e26 | −0.0612814 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.11273e26 | 0.255803 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.60790e27i | 0.494879i | 0.968903 | + | 0.247440i | \(0.0795892\pi\) | ||||
−0.968903 | + | 0.247440i | \(0.920411\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 5.47033e25i | − 0.0164355i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.27847e25 | 0.0242814 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.96104e27 | −1.13426 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 9.31001e25i | − 0.0260293i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.46654e27i | 0.673341i | 0.941623 | + | 0.336670i | \(0.109301\pi\) | ||||
−0.941623 | + | 0.336670i | \(0.890699\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.27483e27 | −1.67266 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.83039e27 | 0.997089 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 1.06459e27i | − 0.270634i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.40370e26i | 0.0348509i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.00175e24 | −0.000727908 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.85670e27 | 0.913492 | 0.456746 | − | 0.889597i | \(-0.349015\pi\) | ||||
0.456746 | + | 0.889597i | \(0.349015\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.23598e27i | 0.748700i | 0.927288 | + | 0.374350i | \(0.122134\pi\) | ||||
−0.927288 | + | 0.374350i | \(0.877866\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.51702e26i | 0.0342870i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.00279e27 | −1.54623 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.12709e27 | −1.96890 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 1.78590e26i | − 0.0376409i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 8.58529e27i | − 1.76805i | −0.467439 | − | 0.884026i | \(-0.654823\pi\) | ||||
0.467439 | − | 0.884026i | \(-0.345177\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.42172e25 | −0.00688566 | −0.00344283 | − | 0.999994i | \(-0.501096\pi\) | ||||
−0.00344283 | + | 0.999994i | \(0.501096\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.89173e25 | −0.00372004 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 7.32223e25i | − 0.0140715i | −0.999975 | − | 0.00703576i | \(-0.997760\pi\) | ||||
0.999975 | − | 0.00703576i | \(-0.00223957\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 3.74412e26i | − 0.0703205i | −0.999382 | − | 0.0351602i | \(-0.988806\pi\) | ||||
0.999382 | − | 0.0351602i | \(-0.0111942\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.79242e25 | −0.0161398 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.97265e27 | 0.892196 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 2.12377e27i | − 0.372465i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.44002e26i | 0.0246874i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.83835e27 | 1.48126 | 0.740632 | − | 0.671911i | \(-0.234526\pi\) | ||||
0.740632 | + | 0.671911i | \(0.234526\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.31906e27 | −0.379971 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.37849e26i | 0.0220821i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.67606e27i | 0.262513i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.61576e26 | 0.0400595 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.09795e25 | 0.0121270 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 4.03315e27i | − 0.590627i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.18640e28i | 1.69908i | 0.527525 | + | 0.849540i | \(0.323120\pi\) | ||||
−0.527525 | + | 0.849540i | \(0.676880\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.65057e28 | 2.31182 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.48012e27 | −0.339746 | −0.169873 | − | 0.985466i | \(-0.554336\pi\) | ||||
−0.169873 | + | 0.985466i | \(0.554336\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 8.04241e27i | − 1.07758i | −0.842439 | − | 0.538792i | \(-0.818881\pi\) | ||||
0.842439 | − | 0.538792i | \(-0.181119\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 6.98993e24i | 0 0.000916101i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.84578e27 | −0.621242 | −0.310621 | − | 0.950534i | \(-0.600537\pi\) | ||||
−0.310621 | + | 0.950534i | \(0.600537\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.00878e27 | −0.502758 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 4.27737e25i | − 0.00524802i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 2.66268e27i | − 0.319618i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.00731e27 | 0.705517 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.25108e27 | 0.603411 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.80523e26i | 0.0202981i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.11292e28i | 1.22452i | 0.790655 | + | 0.612261i | \(0.209740\pi\) | ||||
−0.790655 | + | 0.612261i | \(0.790260\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.35000e26 | 0.0360704 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.49766e28 | 1.57813 | 0.789065 | − | 0.614310i | \(-0.210565\pi\) | ||||
0.789065 | + | 0.614310i | \(0.210565\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.18632e28i | 1.22342i | 0.791082 | + | 0.611711i | \(0.209518\pi\) | ||||
−0.791082 | + | 0.611711i | \(0.790482\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.36063e26i | 0.0238269i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.21862e28 | 1.20391 | 0.601953 | − | 0.798532i | \(-0.294389\pi\) | ||||
0.601953 | + | 0.798532i | \(0.294389\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.01836e26 | −0.0678686 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 2.41227e27i | − 0.228343i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 3.66722e28i | − 3.39819i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.60976e27 | −0.781039 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.69401e26 | 0.0150449 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.39343e27i | 0.555926i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 8.22055e27i | − 0.699867i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.43466e25 | 0.00119596 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.19888e28 | 1.79490 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 2.10303e28i | − 1.68103i | −0.541789 | − | 0.840515i | \(-0.682253\pi\) | ||||
0.541789 | − | 0.840515i | \(-0.317747\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.17479e28i | 0.919612i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.47120e27 | −0.726074 | −0.363037 | − | 0.931775i | \(-0.618260\pi\) | ||||
−0.363037 | + | 0.931775i | \(0.618260\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.18294e27 | −0.163896 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.75443e26i | 0.0423158i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.07867e27i | 0.0776929i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.97843e28 | −1.39580 | −0.697901 | − | 0.716194i | \(-0.745883\pi\) | ||||
−0.697901 | + | 0.716194i | \(0.745883\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.61796e25 | 0.00250033 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.32350e27i | 0.157299i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.57509e27i | 0.568712i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.11969e28 | 1.37725 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.35154e27 | 0.149693 | 0.0748467 | − | 0.997195i | \(-0.476153\pi\) | ||||
0.0748467 | + | 0.997195i | \(0.476153\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.90618e28i | 1.81259i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.87693e26i | 0.0114703i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.35108e27 | −0.260547 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.37072e28 | −1.39109 | −0.695544 | − | 0.718483i | \(-0.744837\pi\) | ||||
−0.695544 | + | 0.718483i | \(0.744837\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.84337e26i | 0.0220998i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.63014e28i | 0.918592i | 0.888283 | + | 0.459296i | \(0.151898\pi\) | ||||
−0.888283 | + | 0.459296i | \(0.848102\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.73226e27 | −0.537468 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.19073e25 | −0.00280948 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1.67186e28i | − 0.886899i | −0.896299 | − | 0.443449i | \(-0.853755\pi\) | ||||
0.896299 | − | 0.443449i | \(-0.146245\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 2.02690e28i | − 1.05391i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.11357e25 | −0.00107722 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.74178e27 | −0.236896 | −0.118448 | − | 0.992960i | \(-0.537792\pi\) | ||||
−0.118448 | + | 0.992960i | \(0.537792\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.63400e28i | 1.28998i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.46078e26i | 0.00701330i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.05368e27 | −0.0495945 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.68174e28 | −0.776043 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 3.16943e28i | − 1.43394i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.37504e28i | 1.94077i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.60277e27 | −0.156706 | −0.0783529 | − | 0.996926i | \(-0.524966\pi\) | ||||
−0.0783529 | + | 0.996926i | \(0.524966\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.92892e26 | −0.0423474 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 4.48458e27i | − 0.187559i | −0.995593 | − | 0.0937797i | \(-0.970105\pi\) | ||||
0.995593 | − | 0.0937797i | \(-0.0298949\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 1.81267e27i | − 0.0743443i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.60173e26 | −0.0144866 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.13619e28 | −1.23710 | −0.618550 | − | 0.785746i | \(-0.712279\pi\) | ||||
−0.618550 | + | 0.785746i | \(0.712279\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 5.90121e27i | − 0.228300i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 1.54404e28i | − 0.585873i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.43983e27 | −0.202454 | −0.101227 | − | 0.994863i | \(-0.532277\pi\) | ||||
−0.101227 | + | 0.994863i | \(0.532277\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.96386e28 | −1.08197 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.76441e25i | 0.00206415i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 1.99752e28i | − 0.701659i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.64392e28 | −1.60024 | −0.800120 | − | 0.599841i | \(-0.795231\pi\) | ||||
−0.800120 | + | 0.599841i | \(0.795231\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.09939e27 | 0.0371649 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.60430e27i | 0.318527i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.60787e27i | 0.280086i | 0.990145 | + | 0.140043i | \(0.0447241\pi\) | ||||
−0.990145 | + | 0.140043i | \(0.955276\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.49141e27 | 0.0476131 |
(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 | 32.20.b.a.17.10 | 18 | ||
4.3 | odd | 2 | 8.20.b.a.5.1 | ✓ | 18 | ||
8.3 | odd | 2 | 8.20.b.a.5.2 | yes | 18 | ||
8.5 | even | 2 | inner | 32.20.b.a.17.9 | 18 | ||
12.11 | even | 2 | 72.20.d.b.37.18 | 18 | |||
24.11 | even | 2 | 72.20.d.b.37.17 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.20.b.a.5.1 | ✓ | 18 | 4.3 | odd | 2 | ||
8.20.b.a.5.2 | yes | 18 | 8.3 | odd | 2 | ||
32.20.b.a.17.9 | 18 | 8.5 | even | 2 | inner | ||
32.20.b.a.17.10 | 18 | 1.1 | even | 1 | trivial | ||
72.20.d.b.37.17 | 18 | 24.11 | even | 2 | |||
72.20.d.b.37.18 | 18 | 12.11 | even | 2 |