Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [288,2,Mod(49,288)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(288, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("288.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 288 = 2^{5} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 288.r (of order \(6\), 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: | \(2.29969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 288.49 |
Dual form | 288.2.r.a.241.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.866025 | + | 1.50000i | 0.500000 | + | 0.866025i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.73205 | − | 1.00000i | −0.774597 | − | 0.447214i | 0.0599153 | − | 0.998203i | \(-0.480917\pi\) |
−0.834512 | + | 0.550990i | \(0.814250\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | + | 3.46410i | 0.755929 | + | 1.30931i | 0.944911 | + | 0.327327i | \(0.106148\pi\) |
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.50000 | + | 2.59808i | −0.500000 | + | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.59808 | + | 1.50000i | −0.783349 | + | 0.452267i | −0.837616 | − | 0.546259i | \(-0.816051\pi\) |
0.0542666 | + | 0.998526i | \(0.482718\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.73205 | + | 1.00000i | 0.480384 | + | 0.277350i | 0.720577 | − | 0.693375i | \(-0.243877\pi\) |
−0.240192 | + | 0.970725i | \(0.577210\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 3.46410i | − | 0.894427i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.00000 | 1.21268 | 0.606339 | − | 0.795206i | \(-0.292637\pi\) | ||||
0.606339 | + | 0.795206i | \(0.292637\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000i | 0.229416i | 0.993399 | + | 0.114708i | \(0.0365932\pi\) | ||||
−0.993399 | + | 0.114708i | \(0.963407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.46410 | + | 6.00000i | −0.755929 | + | 1.30931i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | − | 1.73205i | 0.208514 | − | 0.361158i | −0.742732 | − | 0.669588i | \(-0.766471\pi\) |
0.951247 | + | 0.308431i | \(0.0998038\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | + | 3.46410i | −0.359211 | + | 0.622171i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) |
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.50000 | − | 2.59808i | −0.783349 | − | 0.452267i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 8.00000i | − | 1.35225i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.00000i | − | 0.328798i | −0.986394 | − | 0.164399i | \(-0.947432\pi\) | ||
0.986394 | − | 0.164399i | \(-0.0525685\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.46410i | 0.554700i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.50000 | − | 4.33013i | 0.390434 | − | 0.676252i | −0.602072 | − | 0.798441i | \(-0.705658\pi\) |
0.992507 | + | 0.122189i | \(0.0389915\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.52628 | − | 5.50000i | 1.45274 | − | 0.838742i | 0.454108 | − | 0.890947i | \(-0.349958\pi\) |
0.998636 | + | 0.0522047i | \(0.0166248\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.19615 | − | 3.00000i | 0.774597 | − | 0.447214i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00000 | − | 5.19615i | −0.437595 | − | 0.757937i | 0.559908 | − | 0.828554i | \(-0.310836\pi\) |
−0.997503 | + | 0.0706177i | \(0.977503\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.50000 | + | 7.79423i | −0.642857 | + | 1.11346i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.33013 | + | 7.50000i | 0.606339 | + | 1.05021i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.00000 | 0.809040 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.50000 | + | 0.866025i | −0.198680 | + | 0.114708i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.866025 | + | 0.500000i | 0.112747 | + | 0.0650945i | 0.555313 | − | 0.831641i | \(-0.312598\pi\) |
−0.442566 | + | 0.896736i | \(0.645932\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.3923 | − | 6.00000i | 1.33060 | − | 0.768221i | 0.345207 | − | 0.938527i | \(-0.387809\pi\) |
0.985391 | + | 0.170305i | \(0.0544754\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −12.0000 | −1.51186 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.00000 | − | 3.46410i | −0.248069 | − | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.59808 | − | 1.50000i | −0.317406 | − | 0.183254i | 0.332830 | − | 0.942987i | \(-0.391996\pi\) |
−0.650236 | + | 0.759733i | \(0.725330\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.46410 | 0.417029 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.00000 | 1.05337 | 0.526685 | − | 0.850060i | \(-0.323435\pi\) | ||||
0.526685 | + | 0.850060i | \(0.323435\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.866025 | − | 1.50000i | 0.100000 | − | 0.173205i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.3923 | − | 6.00000i | −1.18431 | − | 0.683763i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.00000 | − | 12.1244i | −0.787562 | − | 1.36410i | −0.927457 | − | 0.373930i | \(-0.878010\pi\) |
0.139895 | − | 0.990166i | \(-0.455323\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.46410 | + | 2.00000i | −0.380235 | + | 0.219529i | −0.677920 | − | 0.735135i | \(-0.737119\pi\) |
0.297686 | + | 0.954664i | \(0.403785\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.66025 | − | 5.00000i | −0.939336 | − | 0.542326i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.0000 | −1.48400 | −0.741999 | − | 0.670402i | \(-0.766122\pi\) | ||||
−0.741999 | + | 0.670402i | \(0.766122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.00000i | 0.838628i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.92820 | −0.718421 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00000 | − | 1.73205i | 0.102598 | − | 0.177705i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.500000 | − | 0.866025i | −0.0507673 | − | 0.0879316i | 0.839525 | − | 0.543321i | \(-0.182833\pi\) |
−0.890292 | + | 0.455389i | \(0.849500\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 9.00000i | − | 0.904534i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.1244 | − | 7.00000i | 1.20642 | − | 0.696526i | 0.244443 | − | 0.969664i | \(-0.421395\pi\) |
0.961975 | + | 0.273138i | \(0.0880614\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.00000 | + | 5.19615i | −0.295599 | + | 0.511992i | −0.975124 | − | 0.221660i | \(-0.928852\pi\) |
0.679525 | + | 0.733652i | \(0.262186\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 12.0000 | − | 6.92820i | 1.17108 | − | 0.676123i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.00000i | 0.290021i | 0.989430 | + | 0.145010i | \(0.0463216\pi\) | ||||
−0.989430 | + | 0.145010i | \(0.953678\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 20.0000i | 1.91565i | 0.287348 | + | 0.957826i | \(0.407226\pi\) | ||||
−0.287348 | + | 0.957826i | \(0.592774\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.00000 | − | 1.73205i | 0.284747 | − | 0.164399i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.00000 | + | 5.19615i | −0.282216 | + | 0.488813i | −0.971930 | − | 0.235269i | \(-0.924403\pi\) |
0.689714 | + | 0.724082i | \(0.257736\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.46410 | + | 2.00000i | −0.323029 | + | 0.186501i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.19615 | + | 3.00000i | −0.480384 | + | 0.277350i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.0000 | + | 17.3205i | 0.916698 | + | 1.58777i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | + | 1.73205i | −0.0909091 | + | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.66025 | 0.780869 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0000i | 1.07331i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.00000 | 0.177471 | 0.0887357 | − | 0.996055i | \(-0.471717\pi\) | ||||
0.0887357 | + | 0.996055i | \(0.471717\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 16.5000 | + | 9.52628i | 1.45274 | + | 0.838742i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.46410 | + | 2.00000i | 0.302660 | + | 0.174741i | 0.643637 | − | 0.765331i | \(-0.277425\pi\) |
−0.340977 | + | 0.940072i | \(0.610758\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.46410 | + | 2.00000i | −0.300376 | + | 0.173422i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.00000 | + | 5.19615i | 0.774597 | + | 0.447214i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.50000 | + | 7.79423i | 0.384461 | + | 0.665906i | 0.991694 | − | 0.128618i | \(-0.0410540\pi\) |
−0.607233 | + | 0.794524i | \(0.707721\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.2583 | − | 6.50000i | −0.954919 | − | 0.551323i | −0.0603135 | − | 0.998179i | \(-0.519210\pi\) |
−0.894606 | + | 0.446857i | \(0.852543\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.19615 | − | 9.00000i | 0.437595 | − | 0.757937i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.00000 | −0.501745 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −15.5885 | −1.28571 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.5885 | + | 9.00000i | 1.27706 | + | 0.737309i | 0.976306 | − | 0.216394i | \(-0.0694297\pi\) |
0.300750 | + | 0.953703i | \(0.402763\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.00000 | − | 5.19615i | −0.244137 | − | 0.422857i | 0.717752 | − | 0.696299i | \(-0.245171\pi\) |
−0.961888 | + | 0.273442i | \(0.911838\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.50000 | + | 12.9904i | −0.606339 | + | 1.05021i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.92820 | − | 4.00000i | 0.556487 | − | 0.321288i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.46410 | − | 2.00000i | −0.276465 | − | 0.159617i | 0.355357 | − | 0.934731i | \(-0.384359\pi\) |
−0.631822 | + | 0.775113i | \(0.717693\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.00000 | 0.630488 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 4.00000i | − | 0.313304i | −0.987654 | − | 0.156652i | \(-0.949930\pi\) | ||
0.987654 | − | 0.156652i | \(-0.0500701\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.19615 | + | 9.00000i | 0.404520 | + | 0.700649i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | + | 1.73205i | −0.0773823 | + | 0.134030i | −0.902120 | − | 0.431486i | \(-0.857990\pi\) |
0.824737 | + | 0.565516i | \(0.191323\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.50000 | − | 7.79423i | −0.346154 | − | 0.599556i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.59808 | − | 1.50000i | −0.198680 | − | 0.114708i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −20.7846 | + | 12.0000i | −1.58022 | + | 0.912343i | −0.585399 | + | 0.810745i | \(0.699062\pi\) |
−0.994826 | + | 0.101598i | \(0.967605\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00000 | − | 3.46410i | 0.151186 | − | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.73205i | 0.130189i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.0000i | 1.49487i | 0.664335 | + | 0.747435i | \(0.268715\pi\) | ||||
−0.664335 | + | 0.747435i | \(0.731285\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 10.0000i | − | 0.743294i | −0.928374 | − | 0.371647i | \(-0.878793\pi\) | ||
0.928374 | − | 0.371647i | \(-0.121207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.0000 | + | 10.3923i | 1.33060 | + | 0.768221i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.00000 | + | 3.46410i | −0.147043 | + | 0.254686i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.9904 | + | 7.50000i | −0.949951 | + | 0.548454i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −10.3923 | − | 18.0000i | −0.755929 | − | 1.30931i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.00000 | − | 13.8564i | −0.578860 | − | 1.00261i | −0.995610 | − | 0.0935936i | \(-0.970165\pi\) |
0.416751 | − | 0.909021i | \(-0.363169\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.50000 | − | 12.9904i | 0.539862 | − | 0.935068i | −0.459049 | − | 0.888411i | \(-0.651810\pi\) |
0.998911 | − | 0.0466572i | \(-0.0148568\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.46410 | − | 6.00000i | 0.248069 | − | 0.429669i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 8.00000i | − | 0.569976i | −0.958531 | − | 0.284988i | \(-0.908010\pi\) | ||
0.958531 | − | 0.284988i | \(-0.0919897\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 5.19615i | − | 0.366508i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.66025 | + | 5.00000i | −0.604858 | + | 0.349215i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.00000 | + | 5.19615i | 0.208514 | + | 0.361158i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.50000 | − | 2.59808i | −0.103757 | − | 0.179713i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.8564 | + | 8.00000i | 0.953914 | + | 0.550743i | 0.894295 | − | 0.447478i | \(-0.147678\pi\) |
0.0596196 | + | 0.998221i | \(0.481011\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.19615 | + | 9.00000i | 0.356034 | + | 0.616670i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −22.0000 | −1.50039 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.0000 | −1.08615 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.79423 | + | 13.5000i | 0.526685 | + | 0.912245i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.66025 | + | 5.00000i | 0.582552 | + | 0.336336i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.00000 | + | 1.73205i | 0.0669650 | + | 0.115987i | 0.897564 | − | 0.440884i | \(-0.145335\pi\) |
−0.830599 | + | 0.556871i | \(0.812002\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | 0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.06218 | − | 3.50000i | 0.402361 | − | 0.232303i | −0.285141 | − | 0.958485i | \(-0.592041\pi\) |
0.687502 | + | 0.726182i | \(0.258707\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.3205 | − | 10.0000i | −1.14457 | − | 0.660819i | −0.197013 | − | 0.980401i | \(-0.563124\pi\) |
−0.947559 | + | 0.319582i | \(0.896457\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 20.7846i | − | 1.36753i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.0000 | 0.851658 | 0.425829 | − | 0.904804i | \(-0.359982\pi\) | ||||
0.425829 | + | 0.904804i | \(0.359982\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.0000i | 0.782794i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.1244 | − | 21.0000i | 0.787562 | − | 1.36410i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.0000 | + | 25.9808i | −0.970269 | + | 1.68056i | −0.275533 | + | 0.961292i | \(0.588854\pi\) |
−0.694737 | + | 0.719264i | \(0.744479\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.50000 | − | 14.7224i | −0.547533 | − | 0.948355i | −0.998443 | − | 0.0557856i | \(-0.982234\pi\) |
0.450910 | − | 0.892570i | \(-0.351100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.79423 | − | 13.5000i | 0.500000 | − | 0.866025i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.5885 | − | 9.00000i | 0.995910 | − | 0.574989i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.00000 | + | 1.73205i | −0.0636285 | + | 0.110208i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.00000 | − | 3.46410i | −0.380235 | − | 0.219529i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 15.0000i | − | 0.946792i | −0.880850 | − | 0.473396i | \(-0.843028\pi\) | ||
0.880850 | − | 0.473396i | \(-0.156972\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00000i | 0.377217i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 17.3205i | − | 1.08465i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.50000 | + | 12.9904i | −0.467837 | + | 0.810318i | −0.999325 | − | 0.0367485i | \(-0.988300\pi\) |
0.531487 | + | 0.847066i | \(0.321633\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.92820 | − | 4.00000i | 0.430498 | − | 0.248548i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.00000 | − | 6.92820i | −0.246651 | − | 0.427211i | 0.715944 | − | 0.698158i | \(-0.245997\pi\) |
−0.962594 | + | 0.270947i | \(0.912663\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.1244 | − | 21.0000i | −0.741999 | − | 1.28518i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 12.0000i | − | 0.731653i | −0.930683 | − | 0.365826i | \(-0.880786\pi\) | ||
0.930683 | − | 0.365826i | \(-0.119214\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.0000 | −0.728948 | −0.364474 | − | 0.931214i | \(-0.618751\pi\) | ||||
−0.364474 | + | 0.931214i | \(0.618751\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −12.0000 | + | 6.92820i | −0.726273 | + | 0.419314i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.59808 | + | 1.50000i | 0.156670 | + | 0.0904534i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.73205 | − | 1.00000i | 0.104069 | − | 0.0600842i | −0.447062 | − | 0.894503i | \(-0.647530\pi\) |
0.551131 | + | 0.834419i | \(0.314196\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.00000 | − | 10.3923i | −0.359211 | − | 0.622171i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.00000 | + | 5.19615i | 0.178965 | + | 0.309976i | 0.941526 | − | 0.336939i | \(-0.109392\pi\) |
−0.762561 | + | 0.646916i | \(0.776058\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.3205 | − | 10.0000i | −1.02960 | − | 0.594438i | −0.112728 | − | 0.993626i | \(-0.535959\pi\) |
−0.916869 | + | 0.399188i | \(0.869292\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.46410 | 0.205196 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.0000 | 1.18056 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.00000 | 0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.866025 | − | 1.50000i | 0.0507673 | − | 0.0879316i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.3923 | + | 6.00000i | 0.607125 | + | 0.350524i | 0.771839 | − | 0.635818i | \(-0.219337\pi\) |
−0.164714 | + | 0.986341i | \(0.552670\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.00000 | − | 1.73205i | −0.0582223 | − | 0.100844i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.5000 | − | 7.79423i | 0.783349 | − | 0.452267i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.46410 | − | 2.00000i | 0.200334 | − | 0.115663i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 38.1051 | + | 22.0000i | 2.19634 | + | 1.26806i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 21.0000 | + | 12.1244i | 1.20642 | + | 0.696526i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −24.0000 | −1.37424 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 9.00000i | − | 0.513657i | −0.966457 | − | 0.256829i | \(-0.917322\pi\) | ||
0.966457 | − | 0.256829i | \(-0.0826776\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.3923 | −0.591198 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.0000 | − | 17.3205i | 0.567048 | − | 0.982156i | −0.429808 | − | 0.902920i | \(-0.641419\pi\) |
0.996856 | − | 0.0792356i | \(-0.0252479\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.500000 | + | 0.866025i | 0.0282617 | + | 0.0489506i | 0.879810 | − | 0.475325i | \(-0.157669\pi\) |
−0.851549 | + | 0.524276i | \(0.824336\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 20.7846 | + | 12.0000i | 1.17108 | + | 0.676123i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.0526 | + | 11.0000i | −1.07010 | + | 0.617822i | −0.928208 | − | 0.372061i | \(-0.878651\pi\) |
−0.141890 | + | 0.989882i | \(0.545318\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.50000 | + | 2.59808i | −0.251166 | + | 0.145010i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.00000i | 0.278207i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 2.00000i | − | 0.110940i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −30.0000 | + | 17.3205i | −1.65900 | + | 0.957826i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.0000 | − | 20.7846i | 0.661581 | − | 1.14589i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.3205 | − | 10.0000i | 0.952021 | − | 0.549650i | 0.0583130 | − | 0.998298i | \(-0.481428\pi\) |
0.893708 | + | 0.448649i | \(0.148095\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.19615 | + | 3.00000i | 0.284747 | + | 0.164399i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.00000 | + | 5.19615i | 0.163908 | + | 0.283896i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.50000 | + | 6.06218i | −0.190657 | + | 0.330228i | −0.945468 | − | 0.325714i | \(-0.894395\pi\) |
0.754811 | + | 0.655942i | \(0.227729\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.3923 | −0.564433 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 12.0000i | − | 0.649836i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.00000 | −0.431959 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.00000 | − | 3.46410i | −0.323029 | − | 0.186501i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.2583 | − | 6.50000i | −0.604379 | − | 0.348938i | 0.166383 | − | 0.986061i | \(-0.446791\pi\) |
−0.770762 | + | 0.637123i | \(0.780124\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.8564 | − | 8.00000i | 0.741716 | − | 0.428230i | −0.0809766 | − | 0.996716i | \(-0.525804\pi\) |
0.822693 | + | 0.568486i | \(0.192471\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.00000 | − | 5.19615i | −0.480384 | − | 0.277350i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.50000 | − | 12.9904i | −0.399185 | − | 0.691408i | 0.594441 | − | 0.804139i | \(-0.297373\pi\) |
−0.993626 | + | 0.112731i | \(0.964040\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.3923 | − | 6.00000i | −0.551566 | − | 0.318447i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −17.3205 | + | 30.0000i | −0.916698 | + | 1.58777i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.00000 | 0.211112 | 0.105556 | − | 0.994413i | \(-0.466338\pi\) | ||||
0.105556 | + | 0.994413i | \(0.466338\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.0000 | 0.947368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.46410 | −0.181818 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.5885 | − | 9.00000i | −0.815937 | − | 0.471082i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.00000 | + | 15.5885i | 0.469796 | + | 0.813711i | 0.999404 | − | 0.0345320i | \(-0.0109941\pi\) |
−0.529607 | + | 0.848243i | \(0.677661\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.50000 | + | 12.9904i | 0.390434 | + | 0.676252i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.5167 | − | 13.0000i | −1.16587 | − | 0.673114i | −0.213165 | − | 0.977016i | \(-0.568377\pi\) |
−0.952703 | + | 0.303902i | \(0.901711\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −18.0000 | + | 10.3923i | −0.929516 | + | 0.536656i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 5.00000i | − | 0.256833i | −0.991720 | − | 0.128416i | \(-0.959011\pi\) | ||
0.991720 | − | 0.128416i | \(-0.0409894\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.73205 | + | 3.00000i | 0.0887357 | + | 0.153695i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.00000 | − | 15.5885i | 0.459879 | − | 0.796533i | −0.539076 | − | 0.842257i | \(-0.681226\pi\) |
0.998954 | + | 0.0457244i | \(0.0145596\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.0000 | + | 20.7846i | 0.611577 | + | 1.05928i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 33.0000i | 1.67748i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.92820 | + | 4.00000i | −0.351274 | + | 0.202808i | −0.665246 | − | 0.746624i | \(-0.731673\pi\) |
0.313972 | + | 0.949432i | \(0.398340\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.00000 | − | 8.66025i | 0.252861 | − | 0.437968i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.92820i | 0.349482i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 28.0000i | 1.40883i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 22.0000i | − | 1.10415i | −0.833795 | − | 0.552074i | \(-0.813837\pi\) | ||
0.833795 | − | 0.552074i | \(-0.186163\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.00000 | − | 3.46410i | −0.300376 | − | 0.173422i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.50000 | − | 12.9904i | 0.374532 | − | 0.648709i | −0.615725 | − | 0.787961i | \(-0.711137\pi\) |
0.990257 | + | 0.139253i | \(0.0444700\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.92820 | + | 4.00000i | −0.345118 | + | 0.199254i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.0000i | 0.894427i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.00000 | + | 5.19615i | 0.148704 | + | 0.257564i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.5000 | + | 26.8468i | −0.766426 | + | 1.32749i | 0.173064 | + | 0.984911i | \(0.444633\pi\) |
−0.939490 | + | 0.342578i | \(0.888700\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.79423 | + | 13.5000i | −0.384461 | + | 0.665906i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.00000i | 0.196827i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.00000 | 0.392705 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 22.5167i | − | 1.10265i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −31.1769 | − | 18.0000i | −1.52309 | − | 0.879358i | −0.999627 | − | 0.0273103i | \(-0.991306\pi\) |
−0.523465 | − | 0.852047i | \(-0.675361\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.0526 | + | 11.0000i | −0.928565 | + | 0.536107i | −0.886357 | − | 0.463002i | \(-0.846772\pi\) |
−0.0422075 | + | 0.999109i | \(0.513439\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18.0000 | 0.875190 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.50000 | − | 4.33013i | −0.121268 | − | 0.210042i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 41.5692 | + | 24.0000i | 2.01168 | + | 1.16144i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.19615 | − | 9.00000i | −0.250873 | − | 0.434524i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 36.0000 | 1.73406 | 0.867029 | − | 0.498257i | \(-0.166026\pi\) | ||||
0.867029 | + | 0.498257i | \(0.166026\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.00000 | 0.240285 | 0.120142 | − | 0.992757i | \(-0.461665\pi\) | ||||
0.120142 | + | 0.992757i | \(0.461665\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.73205 | + | 1.00000i | 0.0828552 | + | 0.0478365i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.5000 | − | 23.3827i | −0.642857 | − | 1.11346i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.79423 | + | 4.50000i | −0.370315 | + | 0.213801i | −0.673596 | − | 0.739100i | \(-0.735251\pi\) |
0.303281 | + | 0.952901i | \(0.401918\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24.2487 | + | 14.0000i | 1.14950 | + | 0.663664i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 31.1769i | 1.47462i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.0000 | 0.991051 | 0.495526 | − | 0.868593i | \(-0.334975\pi\) | ||||
0.495526 | + | 0.868593i | \(0.334975\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.0000i | 0.706322i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.19615 | − | 9.00000i | 0.244137 | − | 0.422857i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.00000 | − | 13.8564i | 0.375046 | − | 0.649598i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.5000 | + | 32.0429i | 0.865393 | + | 1.49891i | 0.866656 | + | 0.498906i | \(0.166265\pi\) |
−0.00126243 | + | 0.999999i | \(0.500402\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −25.9808 | −1.21268 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.19615 | − | 3.00000i | 0.242009 | − | 0.139724i | −0.374091 | − | 0.927392i | \(-0.622045\pi\) |
0.616100 | + | 0.787668i | \(0.288712\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.00000 | − | 8.66025i | 0.232370 | − | 0.402476i | −0.726135 | − | 0.687552i | \(-0.758685\pi\) |
0.958505 | + | 0.285076i | \(0.0920187\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 12.0000 | + | 6.92820i | 0.556487 | + | 0.321288i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 29.0000i | − | 1.34196i | −0.741475 | − | 0.670980i | \(-0.765874\pi\) | ||
0.741475 | − | 0.670980i | \(-0.234126\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 12.0000i | − | 0.554109i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 6.92820i | − | 0.319235i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16.5000 | + | 28.5788i | −0.758671 | + | 1.31406i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.866025 | − | 0.500000i | 0.0397360 | − | 0.0229416i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.00000 | + | 13.8564i | 0.365529 | + | 0.633115i | 0.988861 | − | 0.148842i | \(-0.0475547\pi\) |
−0.623332 | + | 0.781958i | \(0.714221\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.00000 | − | 3.46410i | 0.0911922 | − | 0.157949i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.92820 | + | 12.0000i | 0.315244 | + | 0.546019i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.00000i | 0.0908153i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.0000 | −0.906287 | −0.453143 | − | 0.891438i | \(-0.649697\pi\) | ||||
−0.453143 | + | 0.891438i | \(0.649697\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.00000 | − | 3.46410i | 0.271329 | − | 0.156652i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.4545 | + | 9.50000i | 0.742580 | + | 0.428729i | 0.823007 | − | 0.568032i | \(-0.192295\pi\) |
−0.0804264 | + | 0.996761i | \(0.525628\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.00000 | + | 15.5885i | −0.404520 | + | 0.700649i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.0000 | + | 20.7846i | 0.538274 | + | 0.932317i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.9904 | + | 7.50000i | 0.581529 | + | 0.335746i | 0.761741 | − | 0.647882i | \(-0.224345\pi\) |
−0.180212 | + | 0.983628i | \(0.557678\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.46410 | −0.154765 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −36.0000 | −1.60516 | −0.802580 | − | 0.596544i | \(-0.796540\pi\) | ||||
−0.802580 | + | 0.596544i | \(0.796540\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −28.0000 | −1.24598 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.79423 | − | 13.5000i | 0.346154 | − | 0.599556i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.1769 | − | 18.0000i | −1.38189 | − | 0.797836i | −0.389509 | − | 0.921023i | \(-0.627355\pi\) |
−0.992384 | + | 0.123187i | \(0.960689\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.0000 | + | 31.1769i | 0.796273 | + | 1.37919i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 5.19615i | − | 0.229416i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.3923 | − | 6.00000i | 0.457940 | − | 0.264392i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.5885 | + | 9.00000i | 0.685580 | + | 0.395820i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −36.0000 | − | 20.7846i | −1.58022 | − | 0.912343i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.0000 | 0.657162 | 0.328581 | − | 0.944476i | \(-0.393430\pi\) | ||||
0.328581 | + | 0.944476i | \(0.393430\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 36.0000i | − | 1.57417i | −0.616844 | − | 0.787085i | \(-0.711589\pi\) | ||
0.616844 | − | 0.787085i | \(-0.288411\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.92820 | 0.302372 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.0000 | + | 17.3205i | −0.435607 | + | 0.754493i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.50000 | + | 16.4545i | 0.413043 | + | 0.715412i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.59808 | + | 1.50000i | −0.112747 | + | 0.0650945i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.66025 | − | 5.00000i | 0.375117 | − | 0.216574i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.00000 | − | 5.19615i | 0.129701 | − | 0.224649i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −30.0000 | + | 17.3205i | −1.29460 | + | 0.747435i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 27.0000i | − | 1.16297i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.0000i | 0.945854i | 0.881102 | + | 0.472927i | \(0.156803\pi\) | ||||
−0.881102 | + | 0.472927i | \(0.843197\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.0000 | − | 8.66025i | 0.643712 | − | 0.371647i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20.0000 | − | 34.6410i | 0.856706 | − | 1.48386i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.3109 | + | 17.5000i | −1.29600 | + | 0.748246i | −0.979711 | − | 0.200417i | \(-0.935770\pi\) |
−0.316289 | + | 0.948663i | \(0.602437\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 36.0000i | 1.53644i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.0000 | − | 48.4974i | 1.19068 | − | 2.06232i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.92820 | −0.294086 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.0000i | 1.01691i | 0.861088 | + | 0.508456i | \(0.169784\pi\) | ||||
−0.861088 | + | 0.508456i | \(0.830216\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.0000 | 0.930501 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22.5000 | − | 12.9904i | −0.949951 | − | 0.548454i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.79423 | + | 4.50000i | 0.328488 | + | 0.189652i | 0.655169 | − | 0.755482i | \(-0.272597\pi\) |
−0.326682 | + | 0.945134i | \(0.605931\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.3923 | − | 6.00000i | 0.437208 | − | 0.252422i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18.0000 | − | 31.1769i | 0.755929 | − | 1.30931i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.5000 | − | 33.7750i | −0.817483 | − | 1.41592i | −0.907532 | − | 0.419984i | \(-0.862036\pi\) |
0.0900490 | − | 0.995937i | \(-0.471298\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.33013 | + | 2.50000i | 0.181210 | + | 0.104622i | 0.587861 | − | 0.808962i | \(-0.299970\pi\) |
−0.406651 | + | 0.913584i | \(0.633303\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.8564 | − | 24.0000i | 0.578860 | − | 1.00261i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.00000 | −0.0834058 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.0000 | −1.37381 | −0.686904 | − | 0.726748i | \(-0.741031\pi\) | ||||
−0.686904 | + | 0.726748i | \(0.741031\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 25.9808 | 1.07972 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.8564 | − | 8.00000i | −0.574861 | − | 0.331896i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.0000 | 0.496139 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −32.0429 | + | 18.5000i | −1.32255 | + | 0.763577i | −0.984135 | − | 0.177419i | \(-0.943225\pi\) |
−0.338418 | + | 0.940996i | \(0.609892\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.46410 | − | 2.00000i | −0.142736 | − | 0.0824086i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.0000 | − | 6.92820i | 0.493614 | − | 0.284988i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −30.0000 | −1.23195 | −0.615976 | − | 0.787765i | \(-0.711238\pi\) | ||||
−0.615976 | + | 0.787765i | \(0.711238\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 40.0000i | − | 1.63984i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.92820 | + | 12.0000i | 0.283552 | + | 0.491127i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.0000 | − | 32.9090i | 0.776319 | − | 1.34462i | −0.157731 | − | 0.987482i | \(-0.550418\pi\) |
0.934050 | − | 0.357142i | \(-0.116249\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.50000 | − | 4.33013i | −0.101977 | − | 0.176630i | 0.810522 | − | 0.585708i | \(-0.199184\pi\) |
−0.912499 | + | 0.409079i | \(0.865850\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.79423 | − | 4.50000i | 0.317406 | − | 0.183254i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.46410 | − | 2.00000i | 0.140836 | − | 0.0813116i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.0000 | + | 17.3205i | −0.405887 | + | 0.703018i | −0.994424 | − | 0.105453i | \(-0.966371\pi\) |
0.588537 | + | 0.808470i | \(0.299704\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 12.0000i | − | 0.485468i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 34.0000i | − | 1.37325i | −0.727013 | − | 0.686624i | \(-0.759092\pi\) | ||
0.727013 | − | 0.686624i | \(-0.240908\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −15.0000 | − | 8.66025i | −0.604858 | − | 0.349215i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.50000 | + | 4.33013i | −0.100646 | + | 0.174324i | −0.911951 | − | 0.410299i | \(-0.865424\pi\) |
0.811305 | + | 0.584623i | \(0.198758\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.59808 | − | 1.50000i | 0.104425 | − | 0.0602901i | −0.446878 | − | 0.894595i | \(-0.647464\pi\) |
0.551303 | + | 0.834305i | \(0.314131\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.19615 | + | 9.00000i | −0.208514 | + | 0.361158i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −28.0000 | − | 48.4974i | −1.12180 | − | 1.94301i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | − | 16.4545i | 0.380000 | − | 0.658179i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.59808 | − | 4.50000i | 0.103757 | − | 0.179713i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 10.0000i | − | 0.398726i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.0000 | −1.35352 | −0.676759 | − | 0.736204i | \(-0.736616\pi\) | ||||
−0.676759 | + | 0.736204i | \(0.736616\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 27.7128i | 1.10149i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.46410 | − | 2.00000i | −0.137469 | − | 0.0793676i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.5885 | + | 9.00000i | −0.617637 | + | 0.356593i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.00000 | + | 15.5885i | −0.356034 | + | 0.616670i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.5000 | + | 26.8468i | 0.612213 | + | 1.06038i | 0.990867 | + | 0.134846i | \(0.0430539\pi\) |
−0.378653 | + | 0.925539i | \(0.623613\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.33013 | − | 2.50000i | −0.170764 | − | 0.0985904i | 0.412182 | − | 0.911101i | \(-0.364767\pi\) |
−0.582946 | + | 0.812511i | \(0.698100\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −19.0526 | − | 33.0000i | −0.750194 | − | 1.29937i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.0000 | −0.943537 | −0.471769 | − | 0.881722i | \(-0.656384\pi\) | ||||
−0.471769 | + | 0.881722i | \(0.656384\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.00000 | −0.117760 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.8564 | − | 24.0000i | −0.543075 | − | 0.940634i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 31.1769 | + | 18.0000i | 1.22005 | + | 0.704394i | 0.964928 | − | 0.262515i | \(-0.0845520\pi\) |
0.255119 | + | 0.966910i | \(0.417885\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.00000 | − | 6.92820i | −0.156293 | − | 0.270707i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −13.5000 | + | 23.3827i | −0.526685 | + | 0.912245i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.3923 | + | 6.00000i | −0.404827 | + | 0.233727i | −0.688565 | − | 0.725175i | \(-0.741759\pi\) |
0.283738 | + | 0.958902i | \(0.408425\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.1244 | + | 7.00000i | 0.471583 | + | 0.272268i | 0.716902 | − | 0.697174i | \(-0.245559\pi\) |
−0.245319 | + | 0.969442i | \(0.578893\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 17.3205i | 0.672673i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.00000 | 0.310227 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.73205 | + | 3.00000i | −0.0669650 | + | 0.115987i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.0000 | + | 31.1769i | −0.694882 | + | 1.20357i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.0000 | − | 22.5167i | −0.501113 | − | 0.867953i | −0.999999 | − | 0.00128586i | \(-0.999591\pi\) |
0.498886 | − | 0.866668i | \(-0.333743\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.59808 | + | 4.50000i | 0.100000 | + | 0.173205i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 41.5692 | − | 24.0000i | 1.59763 | − | 0.922395i | 0.605693 | − | 0.795698i | \(-0.292896\pi\) |
0.991941 | − | 0.126697i | \(-0.0404375\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.00000 | − | 3.46410i | 0.0767530 | − | 0.132940i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.5000 | + | 6.06218i | 0.402361 | + | 0.232303i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.0000i | 1.33924i | 0.742705 | + | 0.669619i | \(0.233543\pi\) | ||||
−0.742705 | + | 0.669619i | \(0.766457\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 18.0000i | − | 0.687745i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 34.6410i | − | 1.32164i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.2487 | − | 14.0000i | 0.922464 | − | 0.532585i | 0.0380440 | − | 0.999276i | \(-0.487887\pi\) |
0.884420 | + | 0.466691i | \(0.154554\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 31.1769 | − | 18.0000i | 1.18431 | − | 0.683763i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.0000 | + | 22.5167i | 0.493118 | + | 0.854106i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.5000 | − | 21.6506i | 0.473471 | − | 0.820076i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.2583 | + | 19.5000i | 0.425829 | + | 0.737558i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 10.0000i | − | 0.377695i | −0.982006 | − | 0.188847i | \(-0.939525\pi\) | ||
0.982006 | − | 0.188847i | \(-0.0604752\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.00000 | 0.0754314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −18.0000 | + | 10.3923i | −0.677919 | + | 0.391397i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 48.4974 | + | 28.0000i | 1.82393 | + | 1.05305i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.92820 | − | 4.00000i | 0.260194 | − | 0.150223i | −0.364229 | − | 0.931309i | \(-0.618667\pi\) |
0.624423 | + | 0.781086i | \(0.285334\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 42.0000 | 1.57512 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.00000 | + | 6.92820i | 0.149801 | + | 0.259463i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.3923 | + | 6.00000i | 0.388650 | + | 0.224387i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −51.9615 | −1.94054 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34.0000 | 1.26799 | 0.633993 | − | 0.773339i | \(-0.281415\pi\) | ||||
0.633993 | + | 0.773339i | \(0.281415\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.0000 | −0.893807 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.7224 | − | 25.5000i | 0.547533 | − | 0.948355i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.00000 | + | 5.19615i | 0.111264 | + | 0.192715i | 0.916280 | − | 0.400538i | \(-0.131177\pi\) |
−0.805016 | + | 0.593253i | \(0.797843\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 47.6314 | − | 27.5000i | 1.76171 | − | 1.01712i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.2487 | − | 14.0000i | −0.895647 | − | 0.517102i | −0.0198613 | − | 0.999803i | \(-0.506322\pi\) |
−0.875785 | + | 0.482701i | \(0.839656\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 27.0000 | + | 15.5885i | 0.995910 | + | 0.574989i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.00000 | 0.331519 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 41.0000i | 1.50821i | 0.656754 | + | 0.754105i | \(0.271929\pi\) | ||||
−0.656754 | + | 0.754105i | \(0.728071\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.46410 | −0.127257 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.0000 | + | 38.1051i | −0.807102 | + | 1.39794i | 0.107761 | + | 0.994177i | \(0.465632\pi\) |
−0.914863 | + | 0.403764i | \(0.867702\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.0000 | − | 31.1769i | −0.659469 | − | 1.14223i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 12.0000i | − | 0.439057i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.3923 | + | 6.00000i | −0.379727 | + | 0.219235i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.00000 | − | 1.73205i | 0.0364905 | − | 0.0632034i | −0.847203 | − | 0.531269i | \(-0.821715\pi\) |
0.883694 | + | 0.468065i | \(0.155049\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22.5000 | − | 12.9904i | 0.819946 | − | 0.473396i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.0000i | 0.436725i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.0000i | 1.30844i | 0.756303 | + | 0.654221i | \(0.227003\pi\) | ||||
−0.756303 | + | 0.654221i | \(0.772997\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.00000 | + | 5.19615i | −0.326679 | + | 0.188608i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.00000 | + | 12.1244i | −0.253750 | + | 0.439508i | −0.964555 | − | 0.263881i | \(-0.914997\pi\) |
0.710805 | + | 0.703389i | \(0.248331\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −69.2820 | + | 40.0000i | −2.50818 | + | 1.44810i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 25.9808 | − | 15.0000i | 0.939336 | − | 0.542326i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.00000 | + | 1.73205i | 0.0361079 | + | 0.0625407i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.0000 | + | 29.4449i | −0.613036 | + | 1.06181i | 0.377690 | + | 0.925932i | \(0.376718\pi\) |
−0.990726 | + | 0.135877i | \(0.956615\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.9808 | −0.935674 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38.0000i | 1.36677i | 0.730061 | + | 0.683383i | \(0.239492\pi\) | ||||
−0.730061 | + | 0.683383i | \(0.760508\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.00000 | 0.143684 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.0000 | + | 6.92820i | 0.430498 | + | 0.248548i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.33013 | + | 2.50000i | 0.155143 | + | 0.0895718i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.5885 | + | 9.00000i | −0.557799 | + | 0.322045i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.00000 | + | 6.92820i | 0.142766 | + | 0.247278i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.3923 | − | 6.00000i | −0.370446 | − | 0.213877i | 0.303207 | − | 0.952925i | \(-0.401942\pi\) |
−0.673653 | + | 0.739048i | \(0.735276\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.92820 | − | 12.0000i | 0.246651 | − | 0.427211i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −24.0000 | −0.853342 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.0000 | 0.852265 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.0526 | − | 11.0000i | −0.674876 | − | 0.389640i | 0.123045 | − | 0.992401i | \(-0.460734\pi\) |
−0.797922 | + | 0.602761i | \(0.794067\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.0000 | − | 25.9808i | −0.530662 | − | 0.919133i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21.0000 | − | 36.3731i | 0.741999 | − | 1.28518i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −23.3827 | + | 13.5000i | −0.825157 | + | 0.476405i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.8564 | − | 8.00000i | −0.488374 | − | 0.281963i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.0000 | − | 10.3923i | 0.633630 | − | 0.365826i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.00000 | −0.316423 | −0.158212 | − | 0.987405i | \(-0.550573\pi\) | ||||
−0.158212 | + | 0.987405i | \(0.550573\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 7.00000i | − | 0.245803i | −0.992419 | − | 0.122902i | \(-0.960780\pi\) | ||
0.992419 | − | 0.122902i | \(-0.0392200\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.3923 | − | 18.0000i | −0.364474 | − | 0.631288i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.00000 | + | 6.92820i | −0.140114 | + | 0.242684i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.50000 | + | 9.52628i | 0.192421 | + | 0.333282i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −20.7846 | − | 12.0000i | −0.726273 | − | 0.419314i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.2487 | + | 14.0000i | −0.846286 | + | 0.488603i | −0.859396 | − | 0.511311i | \(-0.829160\pi\) |
0.0131101 | + | 0.999914i | \(0.495827\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.0000 | − | 22.5167i | 0.453152 | − | 0.784881i | −0.545428 | − | 0.838157i | \(-0.683633\pi\) |
0.998580 | + | 0.0532760i | \(0.0169663\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.19615i | 0.180907i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 48.0000i | − | 1.66912i | −0.550914 | − | 0.834562i | \(-0.685721\pi\) | ||
0.550914 | − | 0.834562i | \(-0.314279\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.0000i | 1.11141i | 0.831381 | + | 0.555703i | \(0.187551\pi\) | ||||
−0.831381 | + | 0.555703i | \(0.812449\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.00000 | + | 1.73205i | 0.104069 | + | 0.0600842i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −22.5000 | + | 38.9711i | −0.779579 | + | 1.35027i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.46410 | − | 2.00000i | 0.119880 | − | 0.0692129i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.3923 | − | 18.0000i | 0.359211 | − | 0.622171i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.00000 | + | 3.46410i | 0.0690477 | + | 0.119594i | 0.898482 | − | 0.439010i | \(-0.144671\pi\) |
−0.829435 | + | 0.558604i | \(0.811337\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.5000 | + | 25.1147i | −0.500000 | + | 0.866025i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.19615 | + | 9.00000i | −0.178965 | + | 0.309976i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18.0000i | 0.619219i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.00000 | −0.274883 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 34.6410i | − | 1.18888i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.46410 | − | 2.00000i | −0.118748 | − | 0.0685591i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −36.3731 | + | 21.0000i | −1.24539 | + | 0.719026i | −0.970186 | − | 0.242360i | \(-0.922079\pi\) |
−0.275204 | + | 0.961386i | \(0.588745\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.00000 | + | 5.19615i | 0.102598 | + | 0.177705i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.00000 | − | 5.19615i | −0.102478 | − | 0.177497i | 0.810227 | − | 0.586116i | \(-0.199344\pi\) |
−0.912705 | + | 0.408619i | \(0.866010\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.3109 | − | 17.5000i | −1.03419 | − | 0.597092i | −0.116011 | − | 0.993248i | \(-0.537011\pi\) |
−0.918183 | + | 0.396156i | \(0.870344\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.3205 | + | 30.0000i | 0.590281 | + | 1.02240i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.00000 | −0.204242 | −0.102121 | − | 0.994772i | \(-0.532563\pi\) | ||||
−0.102121 | + | 0.994772i | \(0.532563\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 48.0000 | 1.63205 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.92820 | + | 12.0000i | 0.235294 | + | 0.407541i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 36.3731 | + | 21.0000i | 1.23387 | + | 0.712376i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.00000 | − | 5.19615i | −0.101651 | − | 0.176065i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.00000 | 0.101535 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −41.5692 | + | 24.0000i | −1.40530 | + | 0.811348i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.92820 | − | 4.00000i | −0.233949 | − | 0.135070i | 0.378444 | − | 0.925624i | \(-0.376459\pi\) |
−0.612392 | + | 0.790554i | \(0.709793\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20.7846i | 0.701047i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.00000 | −0.0673817 | −0.0336909 | − | 0.999432i | \(-0.510726\pi\) | ||||
−0.0336909 | + | 0.999432i | \(0.510726\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.0000i | 0.774012i | 0.922077 | + | 0.387006i | \(0.126491\pi\) | ||||
−0.922077 | + | 0.387006i | \(0.873509\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.73205 | − | 3.00000i | 0.0582223 | − | 0.100844i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.0000 | − | 25.9808i | 0.503651 | − | 0.872349i | −0.496340 | − | 0.868128i | \(-0.665323\pi\) |
0.999991 | − | 0.00422062i | \(-0.00134347\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.00000 | + | 6.92820i | 0.134156 | + | 0.232364i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23.3827 | + | 13.5000i | 0.783349 | + | 0.452267i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.19615 | − | 3.00000i | 0.173883 | − | 0.100391i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.0000 | − | 34.6410i | 0.668526 | − | 1.15792i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.00000 | + | 3.46410i | 0.200334 | + | 0.115663i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 76.2102i | 2.53612i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.0000 | + | 17.3205i | −0.332411 | + | 0.575753i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.6506 | − | 12.5000i | 0.718898 | − | 0.415056i | −0.0954492 | − | 0.995434i | \(-0.530429\pi\) |
0.814347 | + | 0.580379i | \(0.197095\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 42.0000i | 1.39305i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.00000 | + | 10.3923i | 0.198789 | + | 0.344312i | 0.948136 | − | 0.317865i | \(-0.102966\pi\) |
−0.749347 | + | 0.662177i | \(0.769633\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.00000 | − | 10.3923i | 0.198571 | − | 0.343935i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −20.7846 | − | 36.0000i | −0.687118 | − | 1.19012i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.0000i | 0.528367i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.0000 | 1.38545 | 0.692726 | − | 0.721201i | \(-0.256409\pi\) | ||||
0.692726 | + | 0.721201i | \(0.256409\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.5000 | − | 7.79423i | 0.444840 | − | 0.256829i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.3923 | + | 6.00000i | 0.342067 | + | 0.197492i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.73205 | + | 1.00000i | −0.0569495 | + | 0.0328798i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.00000 | − | 15.5885i | −0.295599 | − | 0.511992i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.00000 | − | 12.1244i | −0.229663 | − | 0.397787i | 0.728046 | − | 0.685529i | \(-0.240429\pi\) |
−0.957708 | + | 0.287742i | \(0.907096\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.79423 | − | 4.50000i | −0.255446 | − | 0.147482i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 34.6410 | 1.13410 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 30.0000 | 0.981105 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.00000 | 0.0653372 | 0.0326686 | − | 0.999466i | \(-0.489599\pi\) | ||||
0.0326686 | + | 0.999466i | \(0.489599\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.866025 | + | 1.50000i | −0.0282617 | + | 0.0489506i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.7846 | + | 12.0000i | 0.677559 | + | 0.391189i | 0.798935 | − | 0.601418i | \(-0.205397\pi\) |
−0.121376 | + | 0.992607i | \(0.538731\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.00000 | − | 8.66025i | −0.162822 | − | 0.282017i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 41.5692i | 1.35225i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.59808 | + | 1.50000i | −0.0844261 | + | 0.0487435i | −0.541619 | − | 0.840624i | \(-0.682188\pi\) |
0.457193 | + | 0.889368i | \(0.348855\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.5885 | + | 9.00000i | 0.506023 | + | 0.292152i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −33.0000 | − | 19.0526i | −1.07010 | − | 0.617822i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.0000 | −0.680257 | −0.340128 | − | 0.940379i | \(-0.610471\pi\) | ||||
−0.340128 | + | 0.940379i | \(0.610471\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 32.0000i | 1.03550i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.0000 | + | 31.1769i | −0.581250 | + | 1.00676i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.79423 | − | 4.50000i | −0.251166 | − | 0.145010i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −25.9808 | + | 15.0000i | −0.836350 | + | 0.482867i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.00000 | + | 3.46410i | −0.0643157 | + | 0.111398i | −0.896390 | − | 0.443266i | \(-0.853820\pi\) |
0.832075 | + | 0.554664i | \(0.187153\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.50000 | + | 4.33013i | −0.240935 | + | 0.139104i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.0000i | 0.385098i | 0.981287 | + | 0.192549i | \(0.0616755\pi\) | ||||
−0.981287 | + | 0.192549i | \(0.938325\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 52.0000i | − | 1.66704i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.00000 | − | 1.73205i | 0.0960769 | − | 0.0554700i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.5000 | − | 26.8468i | 0.495889 | − | 0.858905i | −0.504100 | − | 0.863645i | \(-0.668176\pi\) |
0.999989 | + | 0.00474056i | \(0.00150897\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.3731 | − | 21.0000i | 1.16249 | − | 0.671163i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −51.9615 | − | 30.0000i | −1.65900 | − | 0.957826i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.0000 | + | 39.8372i | 0.733586 | + | 1.27061i | 0.955341 | + | 0.295506i | \(0.0954882\pi\) |
−0.221755 | + | 0.975102i | \(0.571178\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.00000 | + | 13.8564i | −0.254901 | + | 0.441502i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 41.5692 | 1.32316 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 22.0000i | − | 0.699559i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −56.0000 | −1.77890 | −0.889449 | − | 0.457034i | \(-0.848912\pi\) | ||||
−0.889449 | + | 0.457034i | \(0.848912\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 30.0000 | + | 17.3205i | 0.952021 | + | 0.549650i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.8564 | − | 8.00000i | −0.439278 | − | 0.253617i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.3923 | − | 6.00000i | 0.329128 | − | 0.190022i | −0.326326 | − | 0.945257i | \(-0.605811\pi\) |
0.655454 | + | 0.755235i | \(0.272477\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.3923i | 0.328798i |
(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 | 288.2.r.a.49.2 | 4 | ||
3.2 | odd | 2 | 864.2.r.a.145.2 | 4 | |||
4.3 | odd | 2 | 72.2.n.a.13.1 | ✓ | 4 | ||
8.3 | odd | 2 | 72.2.n.a.13.2 | yes | 4 | ||
8.5 | even | 2 | inner | 288.2.r.a.49.1 | 4 | ||
9.2 | odd | 6 | 864.2.r.a.721.1 | 4 | |||
9.4 | even | 3 | 2592.2.d.b.1297.2 | 2 | |||
9.5 | odd | 6 | 2592.2.d.a.1297.1 | 2 | |||
9.7 | even | 3 | inner | 288.2.r.a.241.1 | 4 | ||
12.11 | even | 2 | 216.2.n.a.37.2 | 4 | |||
24.5 | odd | 2 | 864.2.r.a.145.1 | 4 | |||
24.11 | even | 2 | 216.2.n.a.37.1 | 4 | |||
36.7 | odd | 6 | 72.2.n.a.61.2 | yes | 4 | ||
36.11 | even | 6 | 216.2.n.a.181.1 | 4 | |||
36.23 | even | 6 | 648.2.d.a.325.2 | 2 | |||
36.31 | odd | 6 | 648.2.d.d.325.1 | 2 | |||
72.5 | odd | 6 | 2592.2.d.a.1297.2 | 2 | |||
72.11 | even | 6 | 216.2.n.a.181.2 | 4 | |||
72.13 | even | 6 | 2592.2.d.b.1297.1 | 2 | |||
72.29 | odd | 6 | 864.2.r.a.721.2 | 4 | |||
72.43 | odd | 6 | 72.2.n.a.61.1 | yes | 4 | ||
72.59 | even | 6 | 648.2.d.a.325.1 | 2 | |||
72.61 | even | 6 | inner | 288.2.r.a.241.2 | 4 | ||
72.67 | odd | 6 | 648.2.d.d.325.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.2.n.a.13.1 | ✓ | 4 | 4.3 | odd | 2 | ||
72.2.n.a.13.2 | yes | 4 | 8.3 | odd | 2 | ||
72.2.n.a.61.1 | yes | 4 | 72.43 | odd | 6 | ||
72.2.n.a.61.2 | yes | 4 | 36.7 | odd | 6 | ||
216.2.n.a.37.1 | 4 | 24.11 | even | 2 | |||
216.2.n.a.37.2 | 4 | 12.11 | even | 2 | |||
216.2.n.a.181.1 | 4 | 36.11 | even | 6 | |||
216.2.n.a.181.2 | 4 | 72.11 | even | 6 | |||
288.2.r.a.49.1 | 4 | 8.5 | even | 2 | inner | ||
288.2.r.a.49.2 | 4 | 1.1 | even | 1 | trivial | ||
288.2.r.a.241.1 | 4 | 9.7 | even | 3 | inner | ||
288.2.r.a.241.2 | 4 | 72.61 | even | 6 | inner | ||
648.2.d.a.325.1 | 2 | 72.59 | even | 6 | |||
648.2.d.a.325.2 | 2 | 36.23 | even | 6 | |||
648.2.d.d.325.1 | 2 | 36.31 | odd | 6 | |||
648.2.d.d.325.2 | 2 | 72.67 | odd | 6 | |||
864.2.r.a.145.1 | 4 | 24.5 | odd | 2 | |||
864.2.r.a.145.2 | 4 | 3.2 | odd | 2 | |||
864.2.r.a.721.1 | 4 | 9.2 | odd | 6 | |||
864.2.r.a.721.2 | 4 | 72.29 | odd | 6 | |||
2592.2.d.a.1297.1 | 2 | 9.5 | odd | 6 | |||
2592.2.d.a.1297.2 | 2 | 72.5 | odd | 6 | |||
2592.2.d.b.1297.1 | 2 | 72.13 | even | 6 | |||
2592.2.d.b.1297.2 | 2 | 9.4 | even | 3 |