Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,2,Mod(767,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1280.767");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.n (of order \(4\), degree \(2\), 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: | \(10.2208514587\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.49787136.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 320) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 767.4 | ||
Root | \(-1.09445 - 0.895644i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1280.767 |
Dual form | 1280.2.n.n.1023.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 2.18890 | + | 2.18890i | 1.26376 | + | 1.26376i | 0.949255 | + | 0.314508i | \(0.101839\pi\) |
0.314508 | + | 0.949255i | \(0.398161\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.18890 | − | 0.456850i | −0.978906 | − | 0.204310i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.79129 | − | 1.79129i | 0.677043 | − | 0.677043i | −0.282287 | − | 0.959330i | \(-0.591093\pi\) |
0.959330 | + | 0.282287i | \(0.0910930\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.58258i | 2.19419i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.913701i | 0.275491i | 0.990468 | + | 0.137746i | \(0.0439856\pi\) | ||||
−0.990468 | + | 0.137746i | \(0.956014\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.73205 | + | 1.73205i | −0.480384 | + | 0.480384i | −0.905254 | − | 0.424870i | \(-0.860320\pi\) |
0.424870 | + | 0.905254i | \(0.360320\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.79129 | − | 5.79129i | −0.978906 | − | 1.49530i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.00000 | + | 3.00000i | 0.727607 | + | 0.727607i | 0.970143 | − | 0.242536i | \(-0.0779791\pi\) |
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.46410 | −0.794719 | −0.397360 | − | 0.917663i | \(-0.630073\pi\) | ||||
−0.397360 | + | 0.917663i | \(0.630073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.84190 | 1.71124 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.79129 | + | 3.79129i | 0.790538 | + | 0.790538i | 0.981582 | − | 0.191043i | \(-0.0611871\pi\) |
−0.191043 | + | 0.981582i | \(0.561187\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.58258 | + | 2.00000i | 0.916515 | + | 0.400000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7.84190 | + | 7.84190i | −1.50918 | + | 1.50918i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.29150i | 0.982607i | 0.870988 | + | 0.491304i | \(0.163479\pi\) | ||||
−0.870988 | + | 0.491304i | \(0.836521\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.58258i | 1.36187i | 0.732343 | + | 0.680935i | \(0.238427\pi\) | ||||
−0.732343 | + | 0.680935i | \(0.761573\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.00000 | + | 2.00000i | −0.348155 | + | 0.348155i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.73930 | + | 3.10260i | −0.801088 | + | 0.524435i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.19615 | − | 5.19615i | −0.854242 | − | 0.854242i | 0.136410 | − | 0.990652i | \(-0.456443\pi\) |
−0.990652 | + | 0.136410i | \(0.956443\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.58258 | −1.21418 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.58258 | −0.247157 | −0.123578 | − | 0.992335i | \(-0.539437\pi\) | ||||
−0.123578 | + | 0.992335i | \(0.539437\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.361500 | − | 0.361500i | −0.0551282 | − | 0.0551282i | 0.679005 | − | 0.734133i | \(-0.262411\pi\) |
−0.734133 | + | 0.679005i | \(0.762411\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.00725 | − | 14.4086i | 0.448295 | − | 2.14791i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.79129 | − | 3.79129i | 0.553016 | − | 0.553016i | −0.374294 | − | 0.927310i | \(-0.622115\pi\) |
0.927310 | + | 0.374294i | \(0.122115\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.582576i | 0.0832251i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 13.1334i | 1.83904i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.64575 | + | 2.64575i | −0.363422 | + | 0.363422i | −0.865071 | − | 0.501649i | \(-0.832727\pi\) |
0.501649 | + | 0.865071i | \(0.332727\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.417424 | − | 2.00000i | 0.0562855 | − | 0.269680i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.58258 | − | 7.58258i | −1.00434 | − | 1.00434i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.29150 | 0.688895 | 0.344447 | − | 0.938806i | \(-0.388066\pi\) | ||||
0.344447 | + | 0.938806i | \(0.388066\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.20520 | 0.794495 | 0.397247 | − | 0.917712i | \(-0.369965\pi\) | ||||
0.397247 | + | 0.917712i | \(0.369965\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11.7913 | + | 11.7913i | 1.48556 | + | 1.48556i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.58258 | − | 3.00000i | 0.568399 | − | 0.372104i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.361500 | − | 0.361500i | 0.0441643 | − | 0.0441643i | −0.684680 | − | 0.728844i | \(-0.740058\pi\) |
0.728844 | + | 0.684680i | \(0.240058\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 16.5975i | 1.99811i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 4.41742i | − | 0.524252i | −0.965034 | − | 0.262126i | \(-0.915576\pi\) | ||
0.965034 | − | 0.262126i | \(-0.0844236\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.58258 | − | 8.58258i | 1.00451 | − | 1.00451i | 0.00452474 | − | 0.999990i | \(-0.498560\pi\) |
0.999990 | − | 0.00452474i | \(-0.00144028\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.65300 | + | 14.4086i | 0.652753 | + | 1.66376i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.63670 | + | 1.63670i | 0.186519 | + | 0.186519i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.0000 | −1.35011 | −0.675053 | − | 0.737769i | \(-0.735879\pi\) | ||||
−0.675053 | + | 0.737769i | \(0.735879\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −14.5826 | −1.62029 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.10260 | + | 3.10260i | 0.340555 | + | 0.340555i | 0.856576 | − | 0.516021i | \(-0.172587\pi\) |
−0.516021 | + | 0.856576i | \(0.672587\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.19615 | − | 7.93725i | −0.563602 | − | 0.860916i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.5826 | + | 11.5826i | −1.24178 | + | 1.24178i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 15.1652i | − | 1.60750i | −0.594965 | − | 0.803751i | \(-0.702834\pi\) | ||
0.594965 | − | 0.803751i | \(-0.297166\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.20520i | 0.650482i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −16.5975 | + | 16.5975i | −1.72108 | + | 1.72108i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.58258 | + | 1.58258i | 0.777956 | + | 0.162369i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.58258 | − | 8.58258i | −0.871429 | − | 0.871429i | 0.121200 | − | 0.992628i | \(-0.461326\pi\) |
−0.992628 | + | 0.121200i | \(0.961326\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.01450 | −0.604480 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.5112 | 1.74243 | 0.871215 | − | 0.490901i | \(-0.163332\pi\) | ||||
0.871215 | + | 0.490901i | \(0.163332\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.37386 | − | 3.37386i | −0.332437 | − | 0.332437i | 0.521075 | − | 0.853511i | \(-0.325531\pi\) |
−0.853511 | + | 0.521075i | \(0.825531\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −17.1652 | − | 3.58258i | −1.67515 | − | 0.349624i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.361500 | + | 0.361500i | −0.0349475 | + | 0.0349475i | −0.724365 | − | 0.689417i | \(-0.757867\pi\) |
0.689417 | + | 0.724365i | \(0.257867\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 9.66930i | − | 0.926151i | −0.886319 | − | 0.463076i | \(-0.846746\pi\) | ||
0.886319 | − | 0.463076i | \(-0.153254\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 22.7477i | − | 2.15912i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.58258 | − | 4.58258i | 0.431092 | − | 0.431092i | −0.457907 | − | 0.889000i | \(-0.651401\pi\) |
0.889000 | + | 0.457907i | \(0.151401\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.56670 | − | 10.0308i | −0.612348 | − | 0.935377i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −11.4014 | − | 11.4014i | −1.05406 | − | 1.05406i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.7477 | 0.985243 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.1652 | 0.924105 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.46410 | − | 3.46410i | −0.312348 | − | 0.312348i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.11710 | − | 6.47135i | −0.815459 | − | 0.578815i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.79129 | + | 5.79129i | −0.513894 | + | 0.513894i | −0.915717 | − | 0.401823i | \(-0.868377\pi\) |
0.401823 | + | 0.915717i | \(0.368377\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 1.58258i | − | 0.139338i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.01450i | 0.525490i | 0.964865 | + | 0.262745i | \(0.0846277\pi\) | ||||
−0.964865 | + | 0.262745i | \(0.915372\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.20520 | + | 6.20520i | −0.538059 | + | 0.538059i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 20.7477 | − | 13.5826i | 1.78568 | − | 1.16900i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.16515 | + | 6.16515i | 0.526724 | + | 0.526724i | 0.919594 | − | 0.392870i | \(-0.128518\pi\) |
−0.392870 | + | 0.919594i | \(0.628518\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.8027 | −1.93410 | −0.967050 | − | 0.254585i | \(-0.918061\pi\) | ||||
−0.967050 | + | 0.254585i | \(0.918061\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.5975 | 1.39776 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.58258 | − | 1.58258i | −0.132342 | − | 0.132342i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.41742 | − | 11.5826i | 0.200756 | − | 0.961881i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.27520 | + | 1.27520i | −0.105177 | + | 0.105177i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 0.913701i | − | 0.0748533i | −0.999299 | − | 0.0374266i | \(-0.988084\pi\) | ||
0.999299 | − | 0.0374266i | \(-0.0119160\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 14.7477i | − | 1.20015i | −0.799943 | − | 0.600077i | \(-0.795137\pi\) | ||
0.799943 | − | 0.600077i | \(-0.204863\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −19.7477 | + | 19.7477i | −1.59651 | + | 1.59651i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.46410 | − | 16.5975i | 0.278243 | − | 1.33314i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.47315 | + | 4.47315i | 0.356996 | + | 0.356996i | 0.862705 | − | 0.505708i | \(-0.168769\pi\) |
−0.505708 | + | 0.862705i | \(0.668769\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.5826 | −0.918558 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.5826 | 1.07046 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.361500 | + | 0.361500i | 0.0283149 | + | 0.0283149i | 0.721122 | − | 0.692808i | \(-0.243626\pi\) |
−0.692808 | + | 0.721122i | \(0.743626\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.29150 | − | 3.46410i | 0.411943 | − | 0.269680i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.7913 | + | 15.7913i | −1.22197 | + | 1.22197i | −0.255035 | + | 0.966932i | \(0.582087\pi\) |
−0.966932 | + | 0.255035i | \(0.917913\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000i | 0.538462i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 22.8027i | − | 1.74377i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.66025 | − | 8.66025i | 0.658427 | − | 0.658427i | −0.296581 | − | 0.955008i | \(-0.595846\pi\) |
0.955008 | + | 0.296581i | \(0.0958464\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.7913 | − | 4.62614i | 0.891338 | − | 0.349703i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.5826 | + | 11.5826i | 0.870600 | + | 0.870600i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.1479 | 1.43118 | 0.715591 | − | 0.698520i | \(-0.246157\pi\) | ||||
0.715591 | + | 0.698520i | \(0.246157\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.92820 | 0.514969 | 0.257485 | − | 0.966282i | \(-0.417106\pi\) | ||||
0.257485 | + | 0.966282i | \(0.417106\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.5826 | + | 13.5826i | 1.00405 | + | 1.00405i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.00000 | + | 13.7477i | 0.661693 | + | 1.01075i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.74110 | + | 2.74110i | −0.200449 | + | 0.200449i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 28.0942i | 2.04355i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 4.41742i | − | 0.319634i | −0.987147 | − | 0.159817i | \(-0.948910\pi\) | ||
0.987147 | − | 0.159817i | \(-0.0510903\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.16515 | + | 4.16515i | −0.299814 | + | 0.299814i | −0.840941 | − | 0.541127i | \(-0.817998\pi\) |
0.541127 | + | 0.840941i | \(0.317998\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 16.5975 | + | 3.46410i | 1.18857 | + | 0.248069i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.64575 | + | 2.64575i | 0.188502 | + | 0.188502i | 0.795048 | − | 0.606546i | \(-0.207446\pi\) |
−0.606546 | + | 0.795048i | \(0.707446\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.00000 | −0.283552 | −0.141776 | − | 0.989899i | \(-0.545281\pi\) | ||||
−0.141776 | + | 0.989899i | \(0.545281\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.58258 | 0.111626 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.47860 | + | 9.47860i | 0.665268 | + | 0.665268i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.46410 | + | 0.723000i | 0.241943 | + | 0.0504965i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −24.9564 | + | 24.9564i | −1.73459 | + | 1.73459i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 3.16515i | − | 0.218938i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 23.5257i | − | 1.61958i | −0.586722 | − | 0.809788i | \(-0.699582\pi\) | ||
0.586722 | − | 0.809788i | \(-0.300418\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.66930 | − | 9.66930i | 0.662530 | − | 0.662530i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.626136 | + | 0.956439i | 0.0427022 | + | 0.0652286i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.5826 | + | 13.5826i | 0.922045 | + | 0.922045i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 37.5728 | 2.53894 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.3923 | −0.699062 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.37386 | − | 1.37386i | −0.0920007 | − | 0.0920007i | 0.659609 | − | 0.751609i | \(-0.270722\pi\) |
−0.751609 | + | 0.659609i | \(0.770722\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.1652 | + | 30.1652i | −0.877677 | + | 2.01101i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.8582 | − | 11.8582i | 0.787057 | − | 0.787057i | −0.193954 | − | 0.981011i | \(-0.562131\pi\) |
0.981011 | + | 0.193954i | \(0.0621312\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 3.46410i | − | 0.228914i | −0.993428 | − | 0.114457i | \(-0.963487\pi\) | ||
0.993428 | − | 0.114457i | \(-0.0365129\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.16515i | 0.471432i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.1652 | − | 12.1652i | 0.796966 | − | 0.796966i | −0.185650 | − | 0.982616i | \(-0.559439\pi\) |
0.982616 | + | 0.185650i | \(0.0594392\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.0308 | + | 6.56670i | −0.654338 | + | 0.428364i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −26.2668 | − | 26.2668i | −1.70621 | − | 1.70621i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.1652 | 0.980952 | 0.490476 | − | 0.871455i | \(-0.336823\pi\) | ||||
0.490476 | + | 0.871455i | \(0.336823\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.7477 | 1.07882 | 0.539408 | − | 0.842045i | \(-0.318648\pi\) | ||||
0.539408 | + | 0.842045i | \(0.318648\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.39410 | − | 8.39410i | −0.538482 | − | 0.538482i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.266150 | − | 1.27520i | 0.0170037 | − | 0.0814696i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.00000 | − | 6.00000i | 0.381771 | − | 0.381771i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.5826i | 0.860761i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.9427i | 0.816936i | 0.912773 | + | 0.408468i | \(0.133937\pi\) | ||||
−0.912773 | + | 0.408468i | \(0.866063\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.46410 | + | 3.46410i | −0.217786 | + | 0.217786i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.00000 | − | 28.7477i | 0.375735 | − | 1.80025i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.74773 | + | 7.74773i | 0.483290 | + | 0.483290i | 0.906181 | − | 0.422891i | \(-0.138985\pi\) |
−0.422891 | + | 0.906181i | \(0.638985\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.6156 | −1.15672 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −34.8317 | −2.15603 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.2087 | + | 14.2087i | 0.876147 | + | 0.876147i | 0.993133 | − | 0.116987i | \(-0.0373235\pi\) |
−0.116987 | + | 0.993133i | \(0.537324\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.00000 | − | 4.58258i | 0.430007 | − | 0.281505i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 33.1950 | − | 33.1950i | 2.03150 | − | 2.03150i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 13.3241i | − | 0.812385i | −0.913788 | − | 0.406193i | \(-0.866856\pi\) | ||
0.913788 | − | 0.406193i | \(-0.133144\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.7477i | 1.13884i | 0.822046 | + | 0.569422i | \(0.192833\pi\) | ||||
−0.822046 | + | 0.569422i | \(0.807167\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13.5826 | + | 13.5826i | −0.822055 | + | 0.822055i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.82740 | + | 4.18710i | −0.110196 | + | 0.252492i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.7937 | + | 21.7937i | 1.30945 | + | 1.30945i | 0.921808 | + | 0.387646i | \(0.126712\pi\) |
0.387646 | + | 0.921808i | \(0.373288\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −49.9129 | −2.98821 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.7477 | −0.999086 | −0.499543 | − | 0.866289i | \(-0.666499\pi\) | ||||
−0.499543 | + | 0.866289i | \(0.666499\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.4412 | − | 22.4412i | −1.33399 | − | 1.33399i | −0.901765 | − | 0.432226i | \(-0.857728\pi\) |
−0.432226 | − | 0.901765i | \(-0.642272\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 13.1334 | + | 20.0616i | 0.777956 | + | 1.18835i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.83485 | + | 2.83485i | −0.167336 | + | 0.167336i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000i | 0.0588235i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 37.5728i | − | 2.20256i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.1389 | + | 18.1389i | −1.05968 | + | 1.05968i | −0.0615814 | + | 0.998102i | \(0.519614\pi\) |
−0.998102 | + | 0.0615814i | \(0.980386\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.5826 | − | 2.41742i | −0.674364 | − | 0.140748i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.16515 | − | 7.16515i | −0.415764 | − | 0.415764i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.1334 | −0.759525 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.29510 | −0.0746484 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 38.3303 | + | 38.3303i | 2.20202 | + | 2.20202i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.5826 | − | 2.83485i | −0.777736 | − | 0.162323i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.56670 | + | 6.56670i | −0.374782 | + | 0.374782i | −0.869215 | − | 0.494434i | \(-0.835375\pi\) |
0.494434 | + | 0.869215i | \(0.335375\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 14.7701i | − | 0.840242i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 19.5826i | − | 1.11043i | −0.831708 | − | 0.555213i | \(-0.812637\pi\) | ||
0.831708 | − | 0.555213i | \(-0.187363\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.58258 | − | 6.58258i | 0.372069 | − | 0.372069i | −0.496161 | − | 0.868230i | \(-0.665258\pi\) |
0.868230 | + | 0.496161i | \(0.165258\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −20.4231 | − | 31.1968i | −1.15071 | − | 1.75774i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.1425 | + | 14.1425i | 0.794320 | + | 0.794320i | 0.982193 | − | 0.187874i | \(-0.0601596\pi\) |
−0.187874 | + | 0.982193i | \(0.560160\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.83485 | −0.270700 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.58258 | −0.0883308 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.3923 | − | 10.3923i | −0.578243 | − | 0.578243i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.4014 | + | 4.47315i | −0.632433 | + | 0.248126i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 21.1652 | − | 21.1652i | 1.17044 | − | 1.17044i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 13.5826i | − | 0.748832i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 9.66930i | − | 0.531473i | −0.964046 | − | 0.265737i | \(-0.914385\pi\) | ||
0.964046 | − | 0.265737i | \(-0.0856151\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 34.2041 | − | 34.2041i | 1.87437 | − | 1.87437i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.956439 | + | 0.626136i | −0.0522559 | + | 0.0342095i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.00000 | + | 1.00000i | 0.0544735 | + | 0.0544735i | 0.733819 | − | 0.679345i | \(-0.237736\pi\) |
−0.679345 | + | 0.733819i | \(0.737736\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 20.0616 | 1.08960 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.92820 | −0.375183 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.5826 | + | 13.5826i | 0.733390 | + | 0.733390i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.58258 | − | 36.3303i | 0.408232 | − | 1.95596i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.27520 | + | 1.27520i | −0.0684564 | + | 0.0684564i | −0.740506 | − | 0.672050i | \(-0.765414\pi\) |
0.672050 | + | 0.740506i | \(0.265414\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 10.3923i | − | 0.556287i | −0.960539 | − | 0.278144i | \(-0.910281\pi\) | ||
0.960539 | − | 0.278144i | \(-0.0897191\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 27.1652i | − | 1.44997i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.1652 | − | 24.1652i | 1.28618 | − | 1.28618i | 0.349093 | − | 0.937088i | \(-0.386490\pi\) |
0.937088 | − | 0.349093i | \(-0.113510\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.01810 | + | 9.66930i | −0.107110 | + | 0.513193i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 23.5257 | + | 23.5257i | 1.24511 | + | 1.24511i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −27.1652 | −1.43372 | −0.716861 | − | 0.697216i | \(-0.754422\pi\) | ||||
−0.716861 | + | 0.697216i | \(0.754422\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.00000 | −0.368421 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 22.2505 | + | 22.2505i | 1.16785 | + | 1.16785i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −22.7074 | + | 14.8655i | −1.18856 | + | 0.778094i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.5390 | − | 16.5390i | 0.863330 | − | 0.863330i | −0.128394 | − | 0.991723i | \(-0.540982\pi\) |
0.991723 | + | 0.128394i | \(0.0409821\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 10.4174i | − | 0.542309i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.47860i | 0.492105i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.19615 | − | 5.19615i | 0.269047 | − | 0.269047i | −0.559669 | − | 0.828716i | \(-0.689072\pi\) |
0.828716 | + | 0.559669i | \(0.189072\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.79129 | − | 34.1216i | −0.299061 | − | 1.76203i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.16515 | − | 9.16515i | −0.472029 | − | 0.472029i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.3923 | 0.533817 | 0.266908 | − | 0.963722i | \(-0.413998\pi\) | ||||
0.266908 | + | 0.963722i | \(0.413998\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −25.3531 | −1.29888 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.3739 | − | 17.3739i | −0.887763 | − | 0.887763i | 0.106545 | − | 0.994308i | \(-0.466021\pi\) |
−0.994308 | + | 0.106545i | \(0.966021\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.83485 | − | 4.33030i | −0.144477 | − | 0.220693i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.37960 | − | 2.37960i | 0.120962 | − | 0.120962i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 35.5547i | − | 1.80270i | −0.433096 | − | 0.901348i | \(-0.642579\pi\) | ||
0.433096 | − | 0.901348i | \(-0.357421\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.7477i | 1.15040i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.1652 | + | 13.1652i | −0.664094 | + | 0.664094i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 26.2668 | + | 5.48220i | 1.32163 | + | 0.275840i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.93725 | + | 7.93725i | 0.398359 | + | 0.398359i | 0.877654 | − | 0.479295i | \(-0.159107\pi\) |
−0.479295 | + | 0.877654i | \(0.659107\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −27.1652 | −1.35996 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.3303 | −1.21500 | −0.607499 | − | 0.794321i | \(-0.707827\pi\) | ||||
−0.607499 | + | 0.794321i | \(0.707827\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.1334 | − | 13.1334i | −0.654222 | − | 0.654222i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 31.9198 | + | 6.66205i | 1.58611 | + | 0.331040i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.74773 | − | 4.74773i | 0.235336 | − | 0.235336i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 16.4174i | − | 0.811789i | −0.913920 | − | 0.405895i | \(-0.866960\pi\) | ||
0.913920 | − | 0.405895i | \(-0.133040\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 26.9898i | 1.33131i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.47860 | − | 9.47860i | 0.466412 | − | 0.466412i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.37386 | − | 8.20871i | −0.263793 | − | 0.402950i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −49.9129 | − | 49.9129i | −2.44424 | − | 2.44424i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.9753 | 1.02471 | 0.512355 | − | 0.858773i | \(-0.328773\pi\) | ||||
0.512355 | + | 0.858773i | \(0.328773\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.1334 | −0.640083 | −0.320042 | − | 0.947404i | \(-0.603697\pi\) | ||||
−0.320042 | + | 0.947404i | \(0.603697\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 24.9564 | + | 24.9564i | 1.21342 | + | 1.21342i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.74773 | + | 19.7477i | 0.375820 | + | 0.957905i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.1153 | − | 11.1153i | 0.537907 | − | 0.537907i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 6.92820i | − | 0.334497i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.7477i | 0.517700i | 0.965918 | + | 0.258850i | \(0.0833435\pi\) | ||||
−0.965918 | + | 0.258850i | \(0.916656\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.41742 | + | 5.41742i | −0.260345 | + | 0.260345i | −0.825194 | − | 0.564849i | \(-0.808934\pi\) |
0.564849 | + | 0.825194i | \(0.308934\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 30.6446 | − | 20.0616i | 1.46930 | − | 0.961881i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.1334 | − | 13.1334i | −0.628256 | − | 0.628256i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.4955 | 1.21683 | 0.608416 | − | 0.793618i | \(-0.291805\pi\) | ||||
0.608416 | + | 0.793618i | \(0.291805\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.83485 | −0.182612 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.4086 | + | 14.4086i | 0.684574 | + | 0.684574i | 0.961027 | − | 0.276454i | \(-0.0891592\pi\) |
−0.276454 | + | 0.961027i | \(0.589159\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.92820 | + | 33.1950i | −0.328428 | + | 1.57359i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.00000 | − | 2.00000i | 0.0945968 | − | 0.0945968i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.5826i | 0.924159i | 0.886839 | + | 0.462079i | \(0.152897\pi\) | ||||
−0.886839 | + | 0.462079i | \(0.847103\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1.44600i | − | 0.0680895i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 32.2813 | − | 32.2813i | 1.51671 | − | 1.51671i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.83485 | − | 13.5826i | 0.132900 | − | 0.636761i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.5826 | − | 12.5826i | −0.588588 | − | 0.588588i | 0.348661 | − | 0.937249i | \(-0.386636\pi\) |
−0.937249 | + | 0.348661i | \(0.886636\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −47.0514 | −2.19617 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.65480 | 0.170221 | 0.0851106 | − | 0.996372i | \(-0.472876\pi\) | ||||
0.0851106 | + | 0.996372i | \(0.472876\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.2087 | + | 12.2087i | 0.567387 | + | 0.567387i | 0.931396 | − | 0.364009i | \(-0.118592\pi\) |
−0.364009 | + | 0.931396i | \(0.618592\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 43.9129 | − | 28.7477i | 2.03641 | − | 1.33314i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.2360 | + | 16.2360i | −0.751313 | + | 0.751313i | −0.974724 | − | 0.223411i | \(-0.928281\pi\) |
0.223411 | + | 0.974724i | \(0.428281\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 1.29510i | − | 0.0598022i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.5826i | 0.902317i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.330303 | − | 0.330303i | 0.0151873 | − | 0.0151873i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15.8745 | − | 6.92820i | −0.728372 | − | 0.317888i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −17.4159 | − | 17.4159i | −0.797417 | − | 0.797417i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.4955 | −1.53045 | −0.765223 | − | 0.643765i | \(-0.777371\pi\) | ||||
−0.765223 | + | 0.643765i | \(0.777371\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.0000 | 0.820729 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 29.7309 | + | 29.7309i | 1.35280 | + | 1.35280i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.8655 | + | 22.7074i | 0.675006 | + | 1.03109i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.3739 | + | 13.3739i | −0.606028 | + | 0.606028i | −0.941906 | − | 0.335878i | \(-0.890967\pi\) |
0.335878 | + | 0.941906i | \(0.390967\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.58258i | 0.0715665i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 27.1805i | − | 1.22664i | −0.789835 | − | 0.613320i | \(-0.789834\pi\) | ||
0.789835 | − | 0.613320i | \(-0.210166\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.8745 | + | 15.8745i | −0.714952 | + | 0.714952i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.1652 | + | 2.74773i | 0.591730 | + | 0.123501i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.91288 | − | 7.91288i | −0.354941 | − | 0.354941i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.2487 | −1.08552 | −0.542761 | − | 0.839887i | \(-0.682621\pi\) | ||||
−0.542761 | + | 0.839887i | \(0.682621\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −69.1311 | −3.08855 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.5390 | − | 14.5390i | −0.648263 | − | 0.648263i | 0.304310 | − | 0.952573i | \(-0.401574\pi\) |
−0.952573 | + | 0.304310i | \(0.901574\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −38.3303 | − | 8.00000i | −1.70568 | − | 0.355995i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −15.3223 | + | 15.3223i | −0.680488 | + | 0.680488i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 3.84550i | − | 0.170449i | −0.996362 | − | 0.0852244i | \(-0.972839\pi\) | ||
0.996362 | − | 0.0852244i | \(-0.0271607\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 30.7477i | − | 1.36020i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 27.1652 | − | 27.1652i | 1.19937 | − | 1.19937i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.84370 | + | 8.92640i | 0.257504 | + | 0.393344i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.46410 | + | 3.46410i | 0.152351 | + | 0.152351i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 37.9129 | 1.66419 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.8348 | 0.649927 | 0.324963 | − | 0.945727i | \(-0.394648\pi\) | ||||
0.324963 | + | 0.945727i | \(0.394648\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.8872 | − | 23.8872i | −1.04451 | − | 1.04451i | −0.998962 | − | 0.0455529i | \(-0.985495\pi\) |
−0.0455529 | − | 0.998962i | \(-0.514505\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 35.9361 | + | 15.6838i | 1.56838 | + | 0.684497i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −22.7477 | + | 22.7477i | −0.990907 | + | 0.990907i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.74773i | 0.249901i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 34.8317i | 1.51157i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.74110 | − | 2.74110i | 0.118730 | − | 0.118730i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.956439 | − | 0.626136i | 0.0413505 | − | 0.0270702i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 41.9129 | + | 41.9129i | 1.80867 | + | 1.80867i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.532300 | −0.0229278 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.1652 | + | 15.1652i | 0.650799 | + | 0.650799i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.41742 | + | 21.1652i | −0.189222 | + | 0.906615i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.1642 | + | 23.1642i | −0.990430 | + | 0.990430i | −0.999955 | − | 0.00952449i | \(-0.996968\pi\) |
0.00952449 | + | 0.999955i | \(0.496968\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 40.8462i | 1.74327i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 18.3303i | − | 0.780897i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.4955 | + | 21.4955i | −0.914080 | + | 0.914080i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.3923 | + | 49.7925i | −0.441129 | + | 2.11357i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.8800 | + | 20.8800i | 0.884712 | + | 0.884712i | 0.994009 | − | 0.109297i | \(-0.0348599\pi\) |
−0.109297 | + | 0.994009i | \(0.534860\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.25227 | 0.0529655 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.0000 | −0.506640 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.6675 | − | 11.6675i | −0.491727 | − | 0.491727i | 0.417123 | − | 0.908850i | \(-0.363038\pi\) |
−0.908850 | + | 0.417123i | \(0.863038\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.1244 | + | 7.93725i | −0.510075 | + | 0.333923i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −26.1216 | + | 26.1216i | −1.09700 | + | 1.09700i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.7477i | 0.953634i | 0.879002 | + | 0.476817i | \(0.158210\pi\) | ||||
−0.879002 | + | 0.476817i | \(0.841790\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.22330i | 0.344135i | 0.985085 | + | 0.172067i | \(0.0550447\pi\) | ||||
−0.985085 | + | 0.172067i | \(0.944955\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.66930 | − | 9.66930i | 0.403941 | − | 0.403941i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.79129 | + | 24.9564i | 0.408325 | + | 1.04076i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.7477 | + | 15.7477i | 0.655586 | + | 0.655586i | 0.954333 | − | 0.298746i | \(-0.0965684\pi\) |
−0.298746 | + | 0.954333i | \(0.596568\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.2342 | −0.757788 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.1153 | 0.461141 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.41742 | − | 2.41742i | −0.100119 | − | 0.100119i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 19.7477 | + | 30.1652i | 0.816468 | + | 1.24718i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.54860 | + | 4.54860i | −0.187741 | + | 0.187741i | −0.794719 | − | 0.606978i | \(-0.792382\pi\) |
0.606978 | + | 0.794719i | \(0.292382\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 26.2668i | − | 1.08231i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.5826i | 0.476444i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.1652 | + | 18.1652i | −0.745953 | + | 0.745953i | −0.973717 | − | 0.227763i | \(-0.926859\pi\) |
0.227763 | + | 0.973717i | \(0.426859\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −23.5257 | − | 4.91010i | −0.964460 | − | 0.201295i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.75560 | − | 8.75560i | −0.358343 | − | 0.358343i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.66970 | 0.231658 | 0.115829 | − | 0.993269i | \(-0.463048\pi\) | ||||
0.115829 | + | 0.993269i | \(0.463048\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.7477 | −1.00948 | −0.504740 | − | 0.863271i | \(-0.668412\pi\) | ||||
−0.504740 | + | 0.863271i | \(0.668412\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.37960 | + | 2.37960i | 0.0969049 | + | 0.0969049i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22.2505 | − | 4.64395i | −0.904612 | − | 0.188803i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.37386 | + | 7.37386i | −0.299296 | + | 0.299296i | −0.840738 | − | 0.541442i | \(-0.817879\pi\) |
0.541442 | + | 0.840738i | \(0.317879\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 41.4955i | 1.68148i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.1334i | 0.531321i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.66025 | − | 8.66025i | 0.349784 | − | 0.349784i | −0.510245 | − | 0.860029i | \(-0.670445\pi\) |
0.860029 | + | 0.510245i | \(0.170445\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.00000 | + | 9.16515i | 0.241943 | + | 0.369575i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.00000 | − | 3.00000i | −0.120775 | − | 0.120775i | 0.644136 | − | 0.764911i | \(-0.277217\pi\) |
−0.764911 | + | 0.644136i | \(0.777217\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.01810 | −0.0811143 | −0.0405572 | − | 0.999177i | \(-0.512913\pi\) | ||||
−0.0405572 | + | 0.999177i | \(0.512913\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −59.4618 | −2.38612 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −27.1652 | − | 27.1652i | −1.08835 | − | 1.08835i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.0000 | + | 18.3303i | 0.680000 | + | 0.733212i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.92820 | − | 6.92820i | 0.276686 | − | 0.276686i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 31.1769i | − | 1.24310i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.0780i | 0.679866i | 0.940450 | + | 0.339933i | \(0.110404\pi\) | ||||
−0.940450 | + | 0.339933i | \(0.889596\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 51.4955 | − | 51.4955i | 2.04676 | − | 2.04676i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.3223 | − | 10.0308i | 0.608047 | − | 0.398060i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00905 | − | 1.00905i | −0.0399800 | − | 0.0399800i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 29.0780 | 1.15031 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.9129 | −0.786511 | −0.393256 | − | 0.919429i | \(-0.628651\pi\) | ||||
−0.393256 | + | 0.919429i | \(0.628651\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.7538 | − | 10.7538i | −0.424089 | − | 0.424089i | 0.462520 | − | 0.886609i | \(-0.346945\pi\) |
−0.886609 | + | 0.462520i | \(0.846945\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.723000 | + | 3.46410i | −0.0284681 | + | 0.136399i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.5390 | + | 32.5390i | −1.27924 | + | 1.27924i | −0.338148 | + | 0.941093i | \(0.609800\pi\) |
−0.941093 | + | 0.338148i | \(0.890200\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.83485i | 0.189784i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 59.4618i | 2.33049i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.47315 | − | 4.47315i | 0.175048 | − | 0.175048i | −0.614145 | − | 0.789193i | \(-0.710499\pi\) |
0.789193 | + | 0.614145i | \(0.210499\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.74773 | − | 13.1652i | 0.107363 | − | 0.514405i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 56.4955 | + | 56.4955i | 2.20410 | + | 2.20410i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.4865 | 1.49922 | 0.749611 | − | 0.661879i | \(-0.230241\pi\) | ||||
0.749611 | + | 0.661879i | \(0.230241\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.9542 | 1.47625 | 0.738124 | − | 0.674665i | \(-0.235712\pi\) | ||||
0.738124 | + | 0.674665i | \(0.235712\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −22.7477 | − | 22.7477i | −0.883449 | − | 0.883449i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 16.4174 | − | 10.7477i | 0.636640 | − | 0.416779i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.0616 | + | 20.0616i | −0.776789 | + | 0.776789i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 6.01450i | − | 0.232534i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.66970i | 0.218876i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.41742 | + | 9.41742i | −0.363015 | + | 0.363015i | −0.864922 | − | 0.501907i | \(-0.832632\pi\) |
0.501907 | + | 0.864922i | \(0.332632\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −51.6199 | + | 20.2523i | −1.98685 | + | 0.779512i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.45505 | − | 2.45505i | −0.0943553 | − | 0.0943553i | 0.658354 | − | 0.752709i | \(-0.271253\pi\) |
−0.752709 | + | 0.658354i | \(0.771253\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −30.7477 | −1.17999 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 51.9129 | 1.98931 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.8335 | + | 32.8335i | 1.25634 | + | 1.25634i | 0.952828 | + | 0.303512i | \(0.0981592\pi\) |
0.303512 | + | 0.952828i | \(0.401841\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.6784 | − | 16.3115i | −0.407999 | − | 0.623229i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.58258 | − | 7.58258i | 0.289293 | − | 0.289293i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 9.16515i | − | 0.349164i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.1515i | 0.576391i | 0.957572 | + | 0.288195i | \(0.0930552\pi\) | ||||
−0.957572 | + | 0.288195i | \(0.906945\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.7737 | + | 10.7737i | −0.409259 | + | 0.409259i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 49.9129 | + | 10.4174i | 1.89330 | + | 0.395155i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.74773 | − | 4.74773i | −0.179833 | − | 0.179833i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 53.2566 | 2.01435 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.1624 | 0.950371 | 0.475186 | − | 0.879886i | \(-0.342381\pi\) | ||||
0.475186 | + | 0.879886i | \(0.342381\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.0000 | + | 18.0000i | 0.678883 | + | 0.678883i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −36.3303 | − | 7.58258i | −1.36828 | − | 0.285576i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 31.3676 | − | 31.3676i | 1.17970 | − | 1.17970i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 36.6591i | − | 1.37676i | −0.725349 | − | 0.688381i | \(-0.758322\pi\) | ||
0.725349 | − | 0.688381i | \(-0.241678\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 78.9909i | − | 2.96239i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −28.7477 | + | 28.7477i | −1.07661 | + | 1.07661i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.74110 | + | 4.18710i | 0.102511 | + | 0.156589i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 33.1950 | + | 33.1950i | 1.23969 | + | 1.23969i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 51.8258 | 1.93277 | 0.966387 | − | 0.257091i | \(-0.0827639\pi\) | ||||
0.966387 | + | 0.257091i | \(0.0827639\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.0871 | −0.450148 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 36.6591 | + | 36.6591i | 1.36337 | + | 1.36337i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.5830 | + | 24.2487i | −0.393043 | + | 0.900575i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.9564 | − | 16.9564i | 0.628880 | − | 0.628880i | −0.318907 | − | 0.947786i | \(-0.603316\pi\) |
0.947786 | + | 0.318907i | \(0.103316\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.00000i | 0.259259i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 2.16900i | − | 0.0802234i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.1425 | − | 14.1425i | 0.522364 | − | 0.522364i | −0.395921 | − | 0.918285i | \(-0.629575\pi\) |
0.918285 | + | 0.395921i | \(0.129575\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.37386 | − | 2.20871i | 0.124447 | − | 0.0814696i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.330303 | + | 0.330303i | 0.0121669 | + | 0.0121669i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.7309 | −1.09367 | −0.546835 | − | 0.837241i | \(-0.684167\pi\) | ||||
−0.546835 | + | 0.837241i | \(0.684167\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 26.2668 | 0.964935 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.7913 | − | 21.7913i | −0.799445 | − | 0.799445i | 0.183563 | − | 0.983008i | \(-0.441237\pi\) |
−0.983008 | + | 0.183563i | \(0.941237\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.417424 | + | 2.00000i | −0.0152932 | + | 0.0732743i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −20.4231 | + | 20.4231i | −0.747243 | + | 0.747243i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.29510i | 0.0473220i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 41.0780i | − | 1.49896i | −0.662028 | − | 0.749479i | \(-0.730304\pi\) | ||
0.662028 | − | 0.749479i | \(-0.269696\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −28.3303 | + | 28.3303i | −1.03241 | + | 1.03241i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.73750 | + | 32.2813i | −0.245203 | + | 1.17484i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.2759 | + | 27.2759i | 0.991358 | + | 0.991358i | 0.999963 | − | 0.00860486i | \(-0.00273905\pi\) |
−0.00860486 | + | 0.999963i | \(0.502739\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −15.1652 | −0.550460 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.00000 | −0.217500 | −0.108750 | − | 0.994069i | \(-0.534685\pi\) | ||||
−0.108750 | + | 0.994069i | \(0.534685\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.3205 | − | 17.3205i | −0.627044 | − | 0.627044i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 52.2476 | − | 34.2041i | 1.88902 | − | 1.23665i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.16515 | + | 9.16515i | −0.330934 | + | 0.330934i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 17.4955i | − | 0.630902i | −0.948942 | − | 0.315451i | \(-0.897844\pi\) | ||
0.948942 | − | 0.315451i | \(-0.102156\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 33.9180i | 1.22153i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.4630 | + | 31.4630i | −1.13164 | + | 1.13164i | −0.141740 | + | 0.989904i | \(0.545270\pi\) |
−0.989904 | + | 0.141740i | \(0.954730\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.1652 | + | 34.7477i | −0.544748 | + | 1.24818i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −40.7477 | − | 40.7477i | −1.46182 | − | 1.46182i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.48220 | 0.196420 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.03620 | 0.144427 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −41.4955 | − | 41.4955i | −1.48293 | − | 1.48293i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.74773 | − | 11.8348i | −0.276528 | − | 0.422404i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.9771 | + | 18.9771i | −0.676461 | + | 0.676461i | −0.959198 | − | 0.282737i | \(-0.908758\pi\) |
0.282737 | + | 0.959198i | \(0.408758\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 62.2029i | 2.21448i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 16.4174i | − | 0.583736i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.7477 | + | 10.7477i | −0.381663 | + | 0.381663i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 25.3531 | + | 5.29150i | 0.899182 | + | 0.187670i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.17805 | + | 3.17805i | 0.112572 | + | 0.112572i | 0.761149 | − | 0.648577i | \(-0.224635\pi\) |
−0.648577 | + | 0.761149i | \(0.724635\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.7477 | 0.804757 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 99.8258 | 3.52717 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.84190 | + | 7.84190i | 0.276735 | + | 0.276735i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −29.7309 | − | 6.20520i | −1.04788 | − | 0.218705i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 29.1652 | − | 29.1652i | 1.02666 | − | 1.02666i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 6.33030i | − | 0.222562i | −0.993789 | − | 0.111281i | \(-0.964505\pi\) | ||
0.993789 | − | 0.111281i | \(-0.0354953\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 49.7925i | − | 1.74845i | −0.485519 | − | 0.874226i | \(-0.661369\pi\) | ||
0.485519 | − | 0.874226i | \(-0.338631\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −41.0369 | + | 41.0369i | −1.43923 | + | 1.43923i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.626136 | − | 0.956439i | −0.0219326 | − | 0.0335026i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.25227 | + | 1.25227i | 0.0438115 | + | 0.0438115i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −40.8462 | −1.42728 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.8528 | 0.623067 | 0.311534 | − | 0.950235i | \(-0.399157\pi\) | ||||
0.311534 | + | 0.950235i | \(0.399157\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.79129 | + | 7.79129i | 0.271587 | + | 0.271587i | 0.829739 | − | 0.558152i | \(-0.188489\pi\) |
−0.558152 | + | 0.829739i | \(0.688489\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −13.1652 | + | 5.16515i | −0.458352 | + | 0.179827i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32.6428 | + | 32.6428i | −1.13510 | + | 1.13510i | −0.145786 | + | 0.989316i | \(0.546571\pi\) |
−0.989316 | + | 0.145786i | \(0.953429\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 23.5257i | − | 0.817082i | −0.912740 | − | 0.408541i | \(-0.866038\pi\) | ||
0.912740 | − | 0.408541i | \(-0.133962\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 95.4083i | 3.30968i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.74773 | + | 1.74773i | −0.0605552 | + | 0.0605552i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 41.7798 | − | 27.3513i | 1.44585 | − | 0.946531i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −59.4618 | − | 59.4618i | −2.05530 | − | 2.05530i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.33030 | 0.218546 | 0.109273 | − | 0.994012i | \(-0.465148\pi\) | ||||
0.109273 | + | 0.994012i | \(0.465148\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −36.6591 | − | 36.6591i | −1.26261 | − | 1.26261i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.19795 | − | 15.3223i | 0.110013 | − | 0.527103i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.2087 | − | 18.2087i | 0.625659 | − | 0.625659i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 98.2432i | − | 3.37170i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 39.4002i | − | 1.35062i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.5529 | − | 26.5529i | 0.909153 | − | 0.909153i | −0.0870511 | − | 0.996204i | \(-0.527744\pi\) |
0.996204 | + | 0.0870511i | \(0.0277443\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.4174 | + | 49.9129i | −0.356268 | + | 1.70698i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.66970 | − | 2.66970i | −0.0911951 | − | 0.0911951i | 0.660038 | − | 0.751233i | \(-0.270540\pi\) |
−0.751233 | + | 0.660038i | \(0.770540\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.7309 | −1.01441 | −0.507203 | − | 0.861827i | \(-0.669321\pi\) | ||||
−0.507203 | + | 0.861827i | \(0.669321\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.4104 | −0.422946 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.7042 | + | 17.7042i | 0.602657 | + | 0.602657i | 0.941017 | − | 0.338360i | \(-0.109872\pi\) |
−0.338360 | + | 0.941017i | \(0.609872\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.9129 | + | 15.0000i | −0.779061 | + | 0.510015i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.18890 | + | 2.18890i | −0.0743390 | + | 0.0743390i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 10.9644i | − | 0.371942i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.25227i | 0.0424316i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 56.4955 | − | 56.4955i | 1.91208 | − | 1.91208i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −27.9234 | + | 4.73930i | −0.943984 | + | 0.160218i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35.6501 | − | 35.6501i | −1.20382 | − | 1.20382i | −0.972996 | − | 0.230821i | \(-0.925859\pi\) |
−0.230821 | − | 0.972996i | \(-0.574141\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −79.4083 | −2.67838 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −46.4174 | −1.56384 | −0.781921 | − | 0.623377i | \(-0.785760\pi\) | ||||
−0.781921 | + | 0.623377i | \(0.785760\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.2179 | + | 14.2179i | 0.478471 | + | 0.478471i | 0.904642 | − | 0.426172i | \(-0.140138\pi\) |
−0.426172 | + | 0.904642i | \(0.640138\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −20.0616 | − | 30.6446i | −0.674364 | − | 1.03011i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.956439 | − | 0.956439i | 0.0321141 | − | 0.0321141i | −0.690867 | − | 0.722981i | \(-0.742771\pi\) |
0.722981 | + | 0.690867i | \(0.242771\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.7477i | 0.695856i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 13.3241i | − | 0.446374i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.1334 | + | 13.1334i | −0.439493 | + | 0.439493i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −41.9129 | − | 8.74773i | −1.40099 | − | 0.292404i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −28.7477 | − | 28.7477i | −0.959859 | − | 0.959859i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −40.1232 | −1.33818 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.8745 | −0.528857 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.83485 | − | 2.83485i | −0.0943379 | − | 0.0943379i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.1652 | − | 3.16515i | −0.504107 | − | 0.105213i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.7719 | + | 12.7719i | −0.424084 | + | 0.424084i | −0.886607 | − | 0.462523i | \(-0.846944\pi\) |
0.462523 | + | 0.886607i | \(0.346944\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 115.269i | 3.82323i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 40.4174i | − | 1.33909i | −0.742772 | − | 0.669545i | \(-0.766489\pi\) | ||
0.742772 | − | 0.669545i | \(-0.233511\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.83485 | + | 2.83485i | −0.0938198 | + | 0.0938198i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −23.5257 | − | 35.9361i | −0.777736 | − | 1.18801i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.7737 | + | 10.7737i | 0.355779 | + | 0.355779i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.66970 | 0.187026 | 0.0935130 | − | 0.995618i | \(-0.470190\pi\) | ||||
0.0935130 | + | 0.995618i | \(0.470190\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.7477 | −0.947270 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.65120 | + | 7.65120i | 0.251842 | + | 0.251842i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.4195 | − | 34.2041i | −0.441229 | − | 1.12462i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 22.2087 | − | 22.2087i | 0.729430 | − | 0.729430i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 25.9129i | − | 0.850174i | −0.905153 | − | 0.425087i | \(-0.860244\pi\) | ||
0.905153 | − | 0.425087i | \(-0.139756\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 2.01810i | − | 0.0661406i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 42.8643 | − | 42.8643i | 1.40331 | − | 1.40331i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.25227 | − | 4.74773i | 0.237175 | − | 0.155267i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.8348 | − | 15.8348i | −0.517302 | − | 0.517302i | 0.399452 | − | 0.916754i | \(-0.369200\pi\) |
−0.916754 | + | 0.399452i | \(0.869200\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28.8172 | 0.940414 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.27340 | −0.106710 | −0.0533549 | − | 0.998576i | \(-0.516991\pi\) | ||||
−0.0533549 | + | 0.998576i | \(0.516991\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.00000 | − | 6.00000i | −0.195387 | − | 0.195387i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 12.8348 | − | 61.4955i | 0.417518 | − | 2.00045i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.2831 | − | 30.2831i | 0.984069 | − | 0.984069i | −0.0158061 | − | 0.999875i | \(-0.505031\pi\) |
0.999875 | + | 0.0158061i | \(0.00503144\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29.7309i | 0.965106i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 61.9129i | 2.00766i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.9129 | + | 34.9129i | −1.13094 | + | 1.13094i | −0.140918 | + | 0.990021i | \(0.545005\pi\) |
−0.990021 | + | 0.140918i | \(0.954995\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.01810 | + | 9.66930i | −0.0653042 | + | 0.312891i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.5830 | − | 10.5830i | −0.342100 | − | 0.342100i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.0871 | 0.713230 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.4955 | −0.854692 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.37960 | − | 2.37960i | −0.0766816 | − | 0.0766816i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.0200 | − | 7.21425i | 0.354745 | − | 0.232235i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.20871 | − | 4.20871i | 0.135343 | − | 0.135343i | −0.636190 | − | 0.771533i | \(-0.719490\pi\) |
0.771533 | + | 0.636190i | \(0.219490\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 45.4955i | − | 1.46152i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 0.532300i | − | 0.0170823i | −0.999964 | − | 0.00854116i | \(-0.997281\pi\) | ||
0.999964 | − | 0.00854116i | \(-0.00271877\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −40.8462 | + | 40.8462i | −1.30947 | + | 1.30947i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −34.7477 | − | 15.1652i | −1.11282 | − | 0.485674i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.4174 | + | 19.4174i | 0.621218 | + | 0.621218i | 0.945843 | − | 0.324625i | \(-0.105238\pi\) |
−0.324625 | + | 0.945843i | \(0.605238\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.8564 | 0.442853 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 63.6489 | 2.03215 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.7042 | + | 23.7042i | 0.756045 | + | 0.756045i | 0.975600 | − | 0.219555i | \(-0.0704604\pi\) |
−0.219555 | + | 0.975600i | \(0.570460\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.58258 | − | 7.00000i | −0.146013 | − | 0.223039i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 29.7309 | − | 29.7309i | 0.946345 | − | 0.946345i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 2.74110i | − | 0.0871620i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.7477i | 0.976734i | 0.872638 | + | 0.488367i | \(0.162407\pi\) | ||||
−0.872638 | + | 0.488367i | \(0.837593\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 21.1652 | − | 21.1652i | 0.671656 | − | 0.671656i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.75560 | + | 1.82740i | 0.277571 | + | 0.0579325i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.1425 | − | 14.1425i | −0.447896 | − | 0.447896i | 0.446758 | − | 0.894655i | \(-0.352578\pi\) |
−0.894655 | + | 0.446758i | \(0.852578\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 81.4955 | 2.57840 |
(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 | 1280.2.n.n.767.4 | 8 | ||
4.3 | odd | 2 | 1280.2.n.p.767.1 | 8 | |||
5.3 | odd | 4 | 1280.2.n.p.1023.1 | 8 | |||
8.3 | odd | 2 | 1280.2.n.p.767.4 | 8 | |||
8.5 | even | 2 | inner | 1280.2.n.n.767.1 | 8 | ||
16.3 | odd | 4 | 320.2.o.e.287.4 | yes | 8 | ||
16.5 | even | 4 | 320.2.o.f.287.4 | yes | 8 | ||
16.11 | odd | 4 | 320.2.o.e.287.1 | yes | 8 | ||
16.13 | even | 4 | 320.2.o.f.287.1 | yes | 8 | ||
20.3 | even | 4 | inner | 1280.2.n.n.1023.4 | 8 | ||
40.3 | even | 4 | inner | 1280.2.n.n.1023.1 | 8 | ||
40.13 | odd | 4 | 1280.2.n.p.1023.4 | 8 | |||
80.3 | even | 4 | 320.2.o.f.223.4 | yes | 8 | ||
80.13 | odd | 4 | 320.2.o.e.223.1 | ✓ | 8 | ||
80.19 | odd | 4 | 1600.2.o.l.607.1 | 8 | |||
80.27 | even | 4 | 1600.2.o.e.543.4 | 8 | |||
80.29 | even | 4 | 1600.2.o.e.607.4 | 8 | |||
80.37 | odd | 4 | 1600.2.o.l.543.1 | 8 | |||
80.43 | even | 4 | 320.2.o.f.223.1 | yes | 8 | ||
80.53 | odd | 4 | 320.2.o.e.223.4 | yes | 8 | ||
80.59 | odd | 4 | 1600.2.o.l.607.4 | 8 | |||
80.67 | even | 4 | 1600.2.o.e.543.1 | 8 | |||
80.69 | even | 4 | 1600.2.o.e.607.1 | 8 | |||
80.77 | odd | 4 | 1600.2.o.l.543.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
320.2.o.e.223.1 | ✓ | 8 | 80.13 | odd | 4 | ||
320.2.o.e.223.4 | yes | 8 | 80.53 | odd | 4 | ||
320.2.o.e.287.1 | yes | 8 | 16.11 | odd | 4 | ||
320.2.o.e.287.4 | yes | 8 | 16.3 | odd | 4 | ||
320.2.o.f.223.1 | yes | 8 | 80.43 | even | 4 | ||
320.2.o.f.223.4 | yes | 8 | 80.3 | even | 4 | ||
320.2.o.f.287.1 | yes | 8 | 16.13 | even | 4 | ||
320.2.o.f.287.4 | yes | 8 | 16.5 | even | 4 | ||
1280.2.n.n.767.1 | 8 | 8.5 | even | 2 | inner | ||
1280.2.n.n.767.4 | 8 | 1.1 | even | 1 | trivial | ||
1280.2.n.n.1023.1 | 8 | 40.3 | even | 4 | inner | ||
1280.2.n.n.1023.4 | 8 | 20.3 | even | 4 | inner | ||
1280.2.n.p.767.1 | 8 | 4.3 | odd | 2 | |||
1280.2.n.p.767.4 | 8 | 8.3 | odd | 2 | |||
1280.2.n.p.1023.1 | 8 | 5.3 | odd | 4 | |||
1280.2.n.p.1023.4 | 8 | 40.13 | odd | 4 | |||
1600.2.o.e.543.1 | 8 | 80.67 | even | 4 | |||
1600.2.o.e.543.4 | 8 | 80.27 | even | 4 | |||
1600.2.o.e.607.1 | 8 | 80.69 | even | 4 | |||
1600.2.o.e.607.4 | 8 | 80.29 | even | 4 | |||
1600.2.o.l.543.1 | 8 | 80.37 | odd | 4 | |||
1600.2.o.l.543.4 | 8 | 80.77 | odd | 4 | |||
1600.2.o.l.607.1 | 8 | 80.19 | odd | 4 | |||
1600.2.o.l.607.4 | 8 | 80.59 | odd | 4 |