Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3744,2,Mod(1873,3744)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3744, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3744.1873");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3744.g (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(29.8959905168\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 104) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1873.4 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3744.1873 |
Dual form | 3744.2.g.b.1873.2 |
$q$-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 \(\left(\mathbb{Z}/3744\mathbb{Z}\right)^\times\).
\(n\) | \(703\) | \(2017\) | \(2081\) | \(2341\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.46410i | 1.54919i | 0.632456 | + | 0.774597i | \(0.282047\pi\) | ||||
−0.632456 | + | 0.774597i | \(0.717953\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.73205 | 1.78855 | 0.894274 | − | 0.447521i | \(-0.147693\pi\) | ||||
0.894274 | + | 0.447521i | \(0.147693\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 1.26795i | − 0.382301i | −0.981561 | − | 0.191151i | \(-0.938778\pi\) | ||||
0.981561 | − | 0.191151i | \(-0.0612219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000i | 0.277350i | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.46410 | 0.355097 | 0.177548 | − | 0.984112i | \(-0.443183\pi\) | ||||
0.177548 | + | 0.984112i | \(0.443183\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.73205i | 0.626775i | 0.949625 | + | 0.313388i | \(0.101464\pi\) | ||||
−0.949625 | + | 0.313388i | \(0.898536\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.00000 | −1.40000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 2.00000i | − 0.371391i | −0.982607 | − | 0.185695i | \(-0.940546\pi\) | ||||
0.982607 | − | 0.185695i | \(-0.0594537\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.26795 | 0.586941 | 0.293471 | − | 0.955968i | \(-0.405190\pi\) | ||||
0.293471 | + | 0.955968i | \(0.405190\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 16.3923i | 2.77081i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.92820i | 0.810192i | 0.914274 | + | 0.405096i | \(0.132762\pi\) | ||||
−0.914274 | + | 0.405096i | \(0.867238\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.92820 | 0.769656 | 0.384828 | − | 0.922988i | \(-0.374261\pi\) | ||||
0.384828 | + | 0.922988i | \(0.374261\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.46410i | 1.13826i | 0.822246 | + | 0.569132i | \(0.192721\pi\) | ||||
−0.822246 | + | 0.569132i | \(0.807279\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.26795 | 0.476679 | 0.238340 | − | 0.971182i | \(-0.423397\pi\) | ||||
0.238340 | + | 0.971182i | \(0.423397\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.3923 | 2.19890 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 10.9282i | − 1.50110i | −0.660811 | − | 0.750552i | \(-0.729788\pi\) | ||||
0.660811 | − | 0.750552i | \(-0.270212\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.39230 | 0.592258 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.196152i | 0.0255369i | 0.999918 | + | 0.0127684i | \(0.00406443\pi\) | ||||
−0.999918 | + | 0.0127684i | \(0.995936\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 10.9282i | − 1.39921i | −0.714528 | − | 0.699607i | \(-0.753359\pi\) | ||||
0.714528 | − | 0.699607i | \(-0.246641\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.46410 | −0.429669 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.73205i | 0.333773i | 0.985976 | + | 0.166887i | \(0.0533714\pi\) | ||||
−0.985976 | + | 0.166887i | \(0.946629\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.19615 | 0.260635 | 0.130318 | − | 0.991472i | \(-0.458400\pi\) | ||||
0.130318 | + | 0.991472i | \(0.458400\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.535898 | −0.0627222 | −0.0313611 | − | 0.999508i | \(-0.509984\pi\) | ||||
−0.0313611 | + | 0.999508i | \(0.509984\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 6.00000i | − 0.683763i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.46410 | 0.164724 | 0.0823622 | − | 0.996602i | \(-0.473754\pi\) | ||||
0.0823622 | + | 0.996602i | \(0.473754\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.73205i | 0.738939i | 0.929243 | + | 0.369469i | \(0.120461\pi\) | ||||
−0.929243 | + | 0.369469i | \(0.879539\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.07180i | 0.550114i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.3205 | −1.83597 | −0.917985 | − | 0.396615i | \(-0.870185\pi\) | ||||
−0.917985 | + | 0.396615i | \(0.870185\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.73205i | 0.496054i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.46410 | −0.970996 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.3923 | −1.46132 | −0.730659 | − | 0.682743i | \(-0.760787\pi\) | ||||
−0.730659 | + | 0.682743i | \(0.760787\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.0000i | 1.19404i | 0.802225 | + | 0.597022i | \(0.203650\pi\) | ||||
−0.802225 | + | 0.597022i | \(0.796350\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.92820 | 0.682656 | 0.341328 | − | 0.939944i | \(-0.389123\pi\) | ||||
0.341328 | + | 0.939944i | \(0.389123\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 8.92820i | − 0.863122i | −0.902084 | − | 0.431561i | \(-0.857963\pi\) | ||||
0.902084 | − | 0.431561i | \(-0.142037\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 2.00000i | − 0.191565i | −0.995402 | − | 0.0957826i | \(-0.969465\pi\) | ||||
0.995402 | − | 0.0957826i | \(-0.0305354\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.46410 | −0.890308 | −0.445154 | − | 0.895454i | \(-0.646851\pi\) | ||||
−0.445154 | + | 0.895454i | \(0.646851\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.8564i | 1.29212i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.92820 | 0.635107 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.39230 | 0.853846 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 6.92820i | − 0.619677i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.00000 | 0.354943 | 0.177471 | − | 0.984126i | \(-0.443208\pi\) | ||||
0.177471 | + | 0.984126i | \(0.443208\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 7.85641i | − 0.686417i | −0.939259 | − | 0.343209i | \(-0.888486\pi\) | ||||
0.939259 | − | 0.343209i | \(-0.111514\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.9282i | 1.12102i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.928203 | 0.0793018 | 0.0396509 | − | 0.999214i | \(-0.487375\pi\) | ||||
0.0396509 | + | 0.999214i | \(0.487375\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0000i | 0.848189i | 0.905618 | + | 0.424094i | \(0.139408\pi\) | ||||
−0.905618 | + | 0.424094i | \(0.860592\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.26795 | 0.106031 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.92820 | 0.575356 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 0.928203i | − 0.0760414i | −0.999277 | − | 0.0380207i | \(-0.987895\pi\) | ||||
0.999277 | − | 0.0380207i | \(-0.0121053\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.1244 | −1.39356 | −0.696780 | − | 0.717285i | \(-0.745385\pi\) | ||||
−0.696780 | + | 0.717285i | \(0.745385\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.3205i | 0.909285i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 3.07180i | − 0.245156i | −0.992459 | − | 0.122578i | \(-0.960884\pi\) | ||||
0.992459 | − | 0.122578i | \(-0.0391162\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.9282 | 1.49175 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 13.2679i | − 1.03923i | −0.854402 | − | 0.519613i | \(-0.826076\pi\) | ||||
0.854402 | − | 0.519613i | \(-0.173924\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.6603 | 0.902298 | 0.451149 | − | 0.892449i | \(-0.351014\pi\) | ||||
0.451149 | + | 0.892449i | \(0.351014\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.92820i | 0.526742i | 0.964695 | + | 0.263371i | \(0.0848343\pi\) | ||||
−0.964695 | + | 0.263371i | \(0.915166\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −33.1244 | −2.50397 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.3923i | 0.776757i | 0.921500 | + | 0.388379i | \(0.126965\pi\) | ||||
−0.921500 | + | 0.388379i | \(0.873035\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.92820i | 0.366310i | 0.983084 | + | 0.183155i | \(0.0586311\pi\) | ||||
−0.983084 | + | 0.183155i | \(0.941369\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −17.0718 | −1.25514 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 1.85641i | − 0.135754i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.4641 | −1.55309 | −0.776544 | − | 0.630063i | \(-0.783029\pi\) | ||||
−0.776544 | + | 0.630063i | \(0.783029\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.3923 | −1.61183 | −0.805917 | − | 0.592029i | \(-0.798327\pi\) | ||||
−0.805917 | + | 0.592029i | \(0.798327\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.9282i | 1.20608i | 0.797709 | + | 0.603042i | \(0.206045\pi\) | ||||
−0.797709 | + | 0.603042i | \(0.793955\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.7846 | 1.75693 | 0.878467 | − | 0.477803i | \(-0.158567\pi\) | ||||
0.878467 | + | 0.477803i | \(0.158567\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 9.46410i | − 0.664250i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.0718i | 1.19235i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.46410 | 0.239617 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 19.8564i | − 1.36697i | −0.729964 | − | 0.683486i | \(-0.760463\pi\) | ||||
0.729964 | − | 0.683486i | \(-0.239537\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −25.8564 | −1.76339 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.4641 | 1.04977 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.46410i | 0.0984861i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.1962 | −0.682785 | −0.341392 | − | 0.939921i | \(-0.610899\pi\) | ||||
−0.341392 | + | 0.939921i | \(0.610899\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 27.1244i | 1.80031i | 0.435573 | + | 0.900153i | \(0.356546\pi\) | ||||
−0.435573 | + | 0.900153i | \(0.643454\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 29.3205i | 1.93755i | 0.247934 | + | 0.968777i | \(0.420248\pi\) | ||||
−0.247934 | + | 0.968777i | \(0.579752\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.07180 | −0.201240 | −0.100620 | − | 0.994925i | \(-0.532083\pi\) | ||||
−0.100620 | + | 0.994925i | \(0.532083\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.3205i | 0.738469i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.2679 | 0.987602 | 0.493801 | − | 0.869575i | \(-0.335607\pi\) | ||||
0.493801 | + | 0.869575i | \(0.335607\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.60770 | −0.618886 | −0.309443 | − | 0.950918i | \(-0.600143\pi\) | ||||
−0.309443 | + | 0.950918i | \(0.600143\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 53.3205i | 3.40652i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.73205 | −0.173836 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 14.3923i | − 0.908434i | −0.890891 | − | 0.454217i | \(-0.849919\pi\) | ||||
0.890891 | − | 0.454217i | \(-0.150081\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 5.07180i | − 0.318861i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.85641 | −0.240556 | −0.120278 | − | 0.992740i | \(-0.538379\pi\) | ||||
−0.120278 | + | 0.992740i | \(0.538379\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 23.3205i | 1.44907i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.32051 | 0.451402 | 0.225701 | − | 0.974197i | \(-0.427533\pi\) | ||||
0.225701 | + | 0.974197i | \(0.427533\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 37.8564 | 2.32550 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 19.8564i | − 1.21067i | −0.795972 | − | 0.605333i | \(-0.793040\pi\) | ||||
0.795972 | − | 0.605333i | \(-0.206960\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.80385 | 0.595541 | 0.297771 | − | 0.954637i | \(-0.403757\pi\) | ||||
0.297771 | + | 0.954637i | \(0.403757\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.87564i | 0.535221i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 25.8564i | − 1.55356i | −0.629771 | − | 0.776780i | \(-0.716851\pi\) | ||||
0.629771 | − | 0.776780i | \(-0.283149\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.3205 | 1.51049 | 0.755247 | − | 0.655440i | \(-0.227517\pi\) | ||||
0.755247 | + | 0.655440i | \(0.227517\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 12.5359i | − 0.745182i | −0.927996 | − | 0.372591i | \(-0.878469\pi\) | ||||
0.927996 | − | 0.372591i | \(-0.121531\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 23.3205 | 1.37657 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.8564 | −0.873906 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 19.0718i | − 1.11419i | −0.830450 | − | 0.557093i | \(-0.811917\pi\) | ||||
0.830450 | − | 0.557093i | \(-0.188083\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.679492 | −0.0395615 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.00000i | 0.231326i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 35.3205i | 2.03584i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 37.8564 | 2.16765 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.73205i | 0.155926i | 0.996956 | + | 0.0779632i | \(0.0248417\pi\) | ||||
−0.996956 | + | 0.0779632i | \(0.975158\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.9282 | 0.846501 | 0.423250 | − | 0.906013i | \(-0.360889\pi\) | ||||
0.423250 | + | 0.906013i | \(0.360889\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.3923 | −1.15264 | −0.576321 | − | 0.817224i | \(-0.695512\pi\) | ||||
−0.576321 | + | 0.817224i | \(0.695512\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.46410i | 0.194563i | 0.995257 | + | 0.0972817i | \(0.0310148\pi\) | ||||
−0.995257 | + | 0.0972817i | \(0.968985\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.53590 | −0.141983 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.00000i | 0.222566i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 7.00000i | − 0.388290i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.4641 | 0.852564 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.5167i | 1.51245i | 0.654310 | + | 0.756226i | \(0.272959\pi\) | ||||
−0.654310 | + | 0.756226i | \(0.727041\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.46410 | −0.517079 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.46410 | −0.297649 | −0.148824 | − | 0.988864i | \(-0.547549\pi\) | ||||
−0.148824 | + | 0.988864i | \(0.547549\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 4.14359i | − 0.224388i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 39.7128 | 2.14429 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 20.9282i | − 1.12348i | −0.827312 | − | 0.561742i | \(-0.810131\pi\) | ||||
0.827312 | − | 0.561742i | \(-0.189869\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.3923i | 1.62686i | 0.581661 | + | 0.813431i | \(0.302403\pi\) | ||||
−0.581661 | + | 0.813431i | \(0.697597\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.9282 | 1.32679 | 0.663397 | − | 0.748267i | \(-0.269114\pi\) | ||||
0.663397 | + | 0.748267i | \(0.269114\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.60770i | 0.403775i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.5167 | −0.713382 | −0.356691 | − | 0.934222i | \(-0.616095\pi\) | ||||
−0.356691 | + | 0.934222i | \(0.616095\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.5359 | 0.607153 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 1.85641i | − 0.0971688i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.2487 | −1.37017 | −0.685086 | − | 0.728462i | \(-0.740235\pi\) | ||||
−0.685086 | + | 0.728462i | \(0.740235\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 51.7128i | − 2.68480i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.7846i | 1.38685i | 0.720527 | + | 0.693427i | \(0.243900\pi\) | ||||
−0.720527 | + | 0.693427i | \(0.756100\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.00000 | 0.103005 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.5885i | 0.852092i | 0.904702 | + | 0.426046i | \(0.140094\pi\) | ||||
−0.904702 | + | 0.426046i | \(0.859906\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −27.6603 | −1.41337 | −0.706686 | − | 0.707527i | \(-0.749811\pi\) | ||||
−0.706686 | + | 0.707527i | \(0.749811\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20.7846 | 1.05928 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 2.00000i | − 0.101404i | −0.998714 | − | 0.0507020i | \(-0.983854\pi\) | ||||
0.998714 | − | 0.0507020i | \(-0.0161459\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.85641 | 0.296171 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.07180i | 0.255190i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 11.4641i | − 0.575367i | −0.957726 | − | 0.287683i | \(-0.907115\pi\) | ||||
0.957726 | − | 0.287683i | \(-0.0928851\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.4641 | −0.572490 | −0.286245 | − | 0.958156i | \(-0.592407\pi\) | ||||
−0.286245 | + | 0.958156i | \(0.592407\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.26795i | 0.162788i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.24871 | 0.309737 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.928203 | −0.0458967 | −0.0229483 | − | 0.999737i | \(-0.507305\pi\) | ||||
−0.0229483 | + | 0.999737i | \(0.507305\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.928203i | 0.0456739i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −23.3205 | −1.14476 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.7846i | 0.526863i | 0.964678 | + | 0.263431i | \(0.0848542\pi\) | ||||
−0.964678 | + | 0.263431i | \(0.915146\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 24.2487i | − 1.18181i | −0.806741 | − | 0.590905i | \(-0.798771\pi\) | ||||
0.806741 | − | 0.590905i | \(-0.201229\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.2487 | −0.497136 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 51.7128i | − 2.50256i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.8756 | 0.716535 | 0.358267 | − | 0.933619i | \(-0.383368\pi\) | ||||
0.358267 | + | 0.933619i | \(0.383368\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.7846 | 1.67164 | 0.835821 | − | 0.549002i | \(-0.184992\pi\) | ||||
0.835821 | + | 0.549002i | \(0.184992\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.9282i | 0.522767i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.9282 | 0.521575 | 0.260787 | − | 0.965396i | \(-0.416018\pi\) | ||||
0.260787 | + | 0.965396i | \(0.416018\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 30.0000i | − 1.42534i | −0.701498 | − | 0.712672i | \(-0.747485\pi\) | ||||
0.701498 | − | 0.712672i | \(-0.252515\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 60.0000i | − 2.84427i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −38.3923 | −1.81184 | −0.905922 | − | 0.423444i | \(-0.860821\pi\) | ||||
−0.905922 | + | 0.423444i | \(0.860821\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 6.24871i | − 0.294240i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −16.3923 | −0.768483 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.0000 | −0.654892 | −0.327446 | − | 0.944870i | \(-0.606188\pi\) | ||||
−0.327446 | + | 0.944870i | \(0.606188\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 7.07180i | − 0.329366i | −0.986347 | − | 0.164683i | \(-0.947340\pi\) | ||||
0.986347 | − | 0.164683i | \(-0.0526602\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.6603 | 0.727794 | 0.363897 | − | 0.931439i | \(-0.381446\pi\) | ||||
0.363897 | + | 0.931439i | \(0.381446\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 12.2487i | − 0.566803i | −0.959001 | − | 0.283401i | \(-0.908537\pi\) | ||||
0.959001 | − | 0.283401i | \(-0.0914629\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.9282i | 0.596969i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.46410 | 0.435160 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 19.1244i | − 0.877486i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.7321 | 1.13004 | 0.565018 | − | 0.825078i | \(-0.308869\pi\) | ||||
0.565018 | + | 0.825078i | \(0.308869\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.92820 | −0.224707 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 49.8564i | − 2.26386i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.4449 | −0.745188 | −0.372594 | − | 0.927994i | \(-0.621532\pi\) | ||||
−0.372594 | + | 0.927994i | \(0.621532\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.2487i | 1.09433i | 0.837025 | + | 0.547165i | \(0.184293\pi\) | ||||
−0.837025 | + | 0.547165i | \(0.815707\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 2.92820i | − 0.131880i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.3923 | 0.466159 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.7321i | 0.480433i | 0.970719 | + | 0.240216i | \(0.0772184\pi\) | ||||
−0.970719 | + | 0.240216i | \(0.922782\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 37.4641 | 1.67044 | 0.835221 | − | 0.549915i | \(-0.185340\pi\) | ||||
0.835221 | + | 0.549915i | \(0.185340\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −41.5692 | −1.84981 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.39230i | 0.283334i | 0.989914 | + | 0.141667i | \(0.0452462\pi\) | ||||
−0.989914 | + | 0.141667i | \(0.954754\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.53590 | −0.112182 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.0000i | 1.05757i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 4.14359i | − 0.182235i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.1769 | −1.62875 | −0.814375 | − | 0.580339i | \(-0.802920\pi\) | ||||
−0.814375 | + | 0.580339i | \(0.802920\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 14.0000i | − 0.612177i | −0.952003 | − | 0.306089i | \(-0.900980\pi\) | ||||
0.952003 | − | 0.306089i | \(-0.0990204\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.78461 | 0.208421 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.92820i | 0.213464i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 30.9282 | 1.33714 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 19.5167i | − 0.840642i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 16.9282i | − 0.727800i | −0.931438 | − | 0.363900i | \(-0.881445\pi\) | ||||
0.931438 | − | 0.363900i | \(-0.118555\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.92820 | 0.296772 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 15.8564i | − 0.677971i | −0.940792 | − | 0.338985i | \(-0.889916\pi\) | ||||
0.940792 | − | 0.338985i | \(-0.110084\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.46410 | 0.232779 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.92820 | 0.294617 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.78461i | 0.287473i | 0.989616 | + | 0.143737i | \(0.0459118\pi\) | ||||
−0.989616 | + | 0.143737i | \(0.954088\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.46410 | −0.315698 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 0.535898i | − 0.0225854i | −0.999936 | − | 0.0112927i | \(-0.996405\pi\) | ||||
0.999936 | − | 0.0112927i | \(-0.00359466\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 32.7846i | − 1.37926i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.0000 | 0.586911 | 0.293455 | − | 0.955973i | \(-0.405195\pi\) | ||||
0.293455 | + | 0.955973i | \(0.405195\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 37.3205i | − 1.56181i | −0.624647 | − | 0.780907i | \(-0.714757\pi\) | ||||
0.624647 | − | 0.780907i | \(-0.285243\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −28.0000 | −1.16768 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.9282 | −0.871253 | −0.435626 | − | 0.900128i | \(-0.643473\pi\) | ||||
−0.435626 | + | 0.900128i | \(0.643473\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 31.8564i | 1.32163i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.8564 | −0.573874 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 21.6603i | − 0.894014i | −0.894530 | − | 0.447007i | \(-0.852490\pi\) | ||||
0.894530 | − | 0.447007i | \(-0.147510\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.92820i | 0.367880i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.8564 | −0.815405 | −0.407702 | − | 0.913115i | \(-0.633670\pi\) | ||||
−0.407702 | + | 0.913115i | \(0.633670\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 24.0000i | 0.983904i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.1769 | 0.701830 | 0.350915 | − | 0.936407i | \(-0.385871\pi\) | ||||
0.350915 | + | 0.936407i | \(0.385871\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.3923 | 0.668656 | 0.334328 | − | 0.942457i | \(-0.391491\pi\) | ||||
0.334328 | + | 0.942457i | \(0.391491\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 32.5359i | 1.32277i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.3205 | 1.10891 | 0.554453 | − | 0.832215i | \(-0.312928\pi\) | ||||
0.554453 | + | 0.832215i | \(0.312928\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.26795i | 0.132207i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 44.6410i | − 1.80303i | −0.432744 | − | 0.901517i | \(-0.642455\pi\) | ||||
0.432744 | − | 0.901517i | \(-0.357545\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.67949 | −0.268906 | −0.134453 | − | 0.990920i | \(-0.542928\pi\) | ||||
−0.134453 | + | 0.990920i | \(0.542928\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 12.5885i | − 0.505973i | −0.967470 | − | 0.252986i | \(-0.918587\pi\) | ||||
0.967470 | − | 0.252986i | \(-0.0814128\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −81.9615 | −3.28372 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.21539i | 0.287696i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.94744 | 0.157145 | 0.0785726 | − | 0.996908i | \(-0.474964\pi\) | ||||
0.0785726 | + | 0.996908i | \(0.474964\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.8564i | 0.549875i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.3923i | 0.609865i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.2487 | −1.03676 | −0.518381 | − | 0.855150i | \(-0.673465\pi\) | ||||
−0.518381 | + | 0.855150i | \(0.673465\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.26795i | 0.365492i | 0.983160 | + | 0.182746i | \(0.0584986\pi\) | ||||
−0.983160 | + | 0.182746i | \(0.941501\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.1436 | 0.398786 | 0.199393 | − | 0.979920i | \(-0.436103\pi\) | ||||
0.199393 | + | 0.979920i | \(0.436103\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.248711 | 0.00976277 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.9282i | 0.662452i | 0.943551 | + | 0.331226i | \(0.107462\pi\) | ||||
−0.943551 | + | 0.331226i | \(0.892538\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.2154 | 1.06339 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.0000i | 0.545363i | 0.962104 | + | 0.272681i | \(0.0879105\pi\) | ||||
−0.962104 | + | 0.272681i | \(0.912090\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 17.3205i | − 0.673690i | −0.941560 | − | 0.336845i | \(-0.890640\pi\) | ||||
0.941560 | − | 0.336845i | \(-0.109360\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −44.7846 | −1.73667 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 8.00000i | − 0.309761i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.8564 | −0.534921 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.1769 | −1.12469 | −0.562344 | − | 0.826904i | \(-0.690100\pi\) | ||||
−0.562344 | + | 0.826904i | \(0.690100\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 34.9282i | − 1.34240i | −0.741276 | − | 0.671200i | \(-0.765779\pi\) | ||||
0.741276 | − | 0.671200i | \(-0.234221\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −68.1051 | −2.61363 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 28.1962i | − 1.07890i | −0.842019 | − | 0.539448i | \(-0.818633\pi\) | ||||
0.842019 | − | 0.539448i | \(-0.181367\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.21539i | 0.122854i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.9282 | 0.416331 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 46.8372i | − 1.78177i | −0.454229 | − | 0.890885i | \(-0.650085\pi\) | ||||
0.454229 | − | 0.890885i | \(-0.349915\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −34.6410 | −1.31401 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.21539 | 0.273302 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 28.6410i | − 1.08176i | −0.841101 | − | 0.540878i | \(-0.818092\pi\) | ||||
0.841101 | − | 0.540878i | \(-0.181908\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.4641 | −0.507808 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 56.7846i | 2.13561i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 5.32051i | − 0.199816i | −0.994997 | − | 0.0999079i | \(-0.968145\pi\) | ||||
0.994997 | − | 0.0999079i | \(-0.0318548\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.0718 | 0.489543 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.39230i | 0.164263i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.0718 | 0.636671 | 0.318335 | − | 0.947978i | \(-0.396876\pi\) | ||||
0.318335 | + | 0.947978i | \(0.396876\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 32.7846 | 1.22096 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14.0000i | 0.519947i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.07180 | 0.336454 | 0.168227 | − | 0.985748i | \(-0.446196\pi\) | ||||
0.168227 | + | 0.985748i | \(0.446196\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.9282i | 0.404194i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.67949i | 0.0989693i | 0.998775 | + | 0.0494846i | \(0.0157579\pi\) | ||||
−0.998775 | + | 0.0494846i | \(0.984242\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.46410 | 0.127602 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 53.7654i | 1.97779i | 0.148612 | + | 0.988896i | \(0.452519\pi\) | ||||
−0.148612 | + | 0.988896i | \(0.547481\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.8038 | −0.799906 | −0.399953 | − | 0.916536i | \(-0.630973\pi\) | ||||
−0.399953 | + | 0.916536i | \(0.630973\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.21539 | 0.117803 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 42.2487i | − 1.54373i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.9282 | −0.544738 | −0.272369 | − | 0.962193i | \(-0.587807\pi\) | ||||
−0.272369 | + | 0.962193i | \(0.587807\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 59.3205i | − 2.15889i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 0.784610i | − 0.0285171i | −0.999898 | − | 0.0142586i | \(-0.995461\pi\) | ||||
0.999898 | − | 0.0142586i | \(-0.00453880\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.7846 | 0.825941 | 0.412971 | − | 0.910744i | \(-0.364491\pi\) | ||||
0.412971 | + | 0.910744i | \(0.364491\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 9.46410i | − 0.342623i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.196152 | −0.00708265 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.5359 | 0.884787 | 0.442394 | − | 0.896821i | \(-0.354129\pi\) | ||||
0.442394 | + | 0.896821i | \(0.354129\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 20.5359i | − 0.738625i | −0.929305 | − | 0.369312i | \(-0.879593\pi\) | ||||
0.929305 | − | 0.369312i | \(-0.120407\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22.8756 | −0.821717 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.4641i | 0.482402i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 2.78461i | − 0.0996412i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.6410 | 0.379794 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.87564i | 0.173798i | 0.996217 | + | 0.0868990i | \(0.0276957\pi\) | ||||
−0.996217 | + | 0.0868990i | \(0.972304\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −44.7846 | −1.59236 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.9282 | 0.388072 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30.0000i | 1.06265i | 0.847167 | + | 0.531327i | \(0.178307\pi\) | ||||
−0.847167 | + | 0.531327i | \(0.821693\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.78461 | 0.169267 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.679492i | 0.0239787i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 65.5692i | 2.31101i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.46410 | −0.0514751 | −0.0257375 | − | 0.999669i | \(-0.508193\pi\) | ||||
−0.0257375 | + | 0.999669i | \(0.508193\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 52.5885i | − 1.84663i | −0.384043 | − | 0.923315i | \(-0.625469\pi\) | ||||
0.384043 | − | 0.923315i | \(-0.374531\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 45.9615 | 1.60996 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.3923 | −0.713436 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 0.248711i | − 0.00868008i | −0.999991 | − | 0.00434004i | \(-0.998619\pi\) | ||||
0.999991 | − | 0.00434004i | \(-0.00138148\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.0000 | −0.697156 | −0.348578 | − | 0.937280i | \(-0.613335\pi\) | ||||
−0.348578 | + | 0.937280i | \(0.613335\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.26795i | 0.183185i | 0.995797 | + | 0.0915923i | \(0.0291956\pi\) | ||||
−0.995797 | + | 0.0915923i | \(0.970804\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.7846i | 0.444028i | 0.975043 | + | 0.222014i | \(0.0712630\pi\) | ||||
−0.975043 | + | 0.222014i | \(0.928737\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 22.5359 | 0.780823 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 40.3923i | 1.39783i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.9808 | 1.06957 | 0.534787 | − | 0.844987i | \(-0.320392\pi\) | ||||
0.534787 | + | 0.844987i | \(0.320392\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.0000 | 0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 3.46410i | − 0.119169i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 44.4449 | 1.52714 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.7128i | 0.675747i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.17691i | 0.245733i | 0.992423 | + | 0.122866i | \(0.0392087\pi\) | ||||
−0.992423 | + | 0.122866i | \(0.960791\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.8564 | −0.678282 | −0.339141 | − | 0.940736i | \(-0.610136\pi\) | ||||
−0.339141 | + | 0.940736i | \(0.610136\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 18.0000i | − 0.614152i | −0.951685 | − | 0.307076i | \(-0.900649\pi\) | ||||
0.951685 | − | 0.307076i | \(-0.0993506\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.73205 | 0.161081 | 0.0805404 | − | 0.996751i | \(-0.474335\pi\) | ||||
0.0805404 | + | 0.996751i | \(0.474335\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.0000 | −0.816024 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 1.85641i | − 0.0629743i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.73205 | −0.0925720 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 32.7846i | − 1.10832i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 16.5359i | − 0.558378i | −0.960236 | − | 0.279189i | \(-0.909934\pi\) | ||||
0.960236 | − | 0.279189i | \(-0.0900655\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.7128 | −0.731523 | −0.365762 | − | 0.930709i | \(-0.619191\pi\) | ||||
−0.365762 | + | 0.930709i | \(0.619191\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 24.5359i | − 0.825699i | −0.910799 | − | 0.412849i | \(-0.864534\pi\) | ||||
0.910799 | − | 0.412849i | \(-0.135466\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.2487 | −0.612732 | −0.306366 | − | 0.951914i | \(-0.599113\pi\) | ||||
−0.306366 | + | 0.951914i | \(0.599113\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.9282 | 0.634832 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.92820i | 0.298771i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −36.0000 | −1.20335 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 6.53590i | − 0.217984i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 16.0000i | − 0.533037i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17.0718 | −0.567486 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 54.1051i | 1.79653i | 0.439453 | + | 0.898265i | \(0.355172\pi\) | ||||
−0.439453 | + | 0.898265i | \(0.644828\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.3205 | −1.03769 | −0.518847 | − | 0.854867i | \(-0.673639\pi\) | ||||
−0.518847 | + | 0.854867i | \(0.673639\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.53590 | 0.282497 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 37.1769i | − 1.22769i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.679492 | 0.0224144 | 0.0112072 | − | 0.999937i | \(-0.496433\pi\) | ||||
0.0112072 | + | 0.999937i | \(0.496433\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.19615i | 0.0722872i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 34.4974i | − 1.13427i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.4641 | −0.901068 | −0.450534 | − | 0.892759i | \(-0.648766\pi\) | ||||
−0.450534 | + | 0.892759i | \(0.648766\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 42.0526i | 1.37822i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.43078 | 0.210309 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.7128 | 1.36270 | 0.681349 | − | 0.731959i | \(-0.261394\pi\) | ||||
0.681349 | + | 0.731959i | \(0.261394\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.2487i | 0.529693i | 0.964291 | + | 0.264846i | \(0.0853213\pi\) | ||||
−0.964291 | + | 0.264846i | \(0.914679\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.7128 | 0.641938 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.4449i | 0.339412i | 0.985495 | + | 0.169706i | \(0.0542819\pi\) | ||||
−0.985495 | + | 0.169706i | \(0.945718\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 0.535898i | − 0.0173960i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.14359 | 0.134224 | 0.0671121 | − | 0.997745i | \(-0.478621\pi\) | ||||
0.0671121 | + | 0.997745i | \(0.478621\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 74.3538i | − 2.40603i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.39230 | 0.141835 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.3205 | −0.655500 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 77.5692i | − 2.49704i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42.9808 | −1.38217 | −0.691084 | − | 0.722774i | \(-0.742867\pi\) | ||||
−0.691084 | + | 0.722774i | \(0.742867\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 43.8564i | − 1.40742i | −0.710488 | − | 0.703710i | \(-0.751526\pi\) | ||||
0.710488 | − | 0.703710i | \(-0.248474\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 47.3205i | 1.51703i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37.6077 | 1.20318 | 0.601588 | − | 0.798806i | \(-0.294535\pi\) | ||||
0.601588 | + | 0.798806i | \(0.294535\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.9615i | 0.701893i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.80385 | 0.185114 | 0.0925570 | − | 0.995707i | \(-0.470496\pi\) | ||||
0.0925570 | + | 0.995707i | \(0.470496\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −58.6410 | −1.86846 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 29.8564i | 0.949378i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.3205 | 1.37612 | 0.688061 | − | 0.725653i | \(-0.258462\pi\) | ||||
0.688061 | + | 0.725653i | \(0.258462\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 85.8564i | 2.72183i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 49.5692i | − 1.56987i | −0.619576 | − | 0.784936i | \(-0.712696\pi\) | ||||
0.619576 | − | 0.784936i | \(-0.287304\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3744.2.g.b.1873.4 | 4 | ||
3.2 | odd | 2 | 416.2.b.b.209.1 | 4 | |||
4.3 | odd | 2 | 936.2.g.b.469.1 | 4 | |||
8.3 | odd | 2 | 936.2.g.b.469.2 | 4 | |||
8.5 | even | 2 | inner | 3744.2.g.b.1873.2 | 4 | ||
12.11 | even | 2 | 104.2.b.b.53.4 | yes | 4 | ||
24.5 | odd | 2 | 416.2.b.b.209.4 | 4 | |||
24.11 | even | 2 | 104.2.b.b.53.3 | ✓ | 4 | ||
48.5 | odd | 4 | 3328.2.a.m.1.2 | 2 | |||
48.11 | even | 4 | 3328.2.a.bd.1.2 | 2 | |||
48.29 | odd | 4 | 3328.2.a.bc.1.1 | 2 | |||
48.35 | even | 4 | 3328.2.a.n.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
104.2.b.b.53.3 | ✓ | 4 | 24.11 | even | 2 | ||
104.2.b.b.53.4 | yes | 4 | 12.11 | even | 2 | ||
416.2.b.b.209.1 | 4 | 3.2 | odd | 2 | |||
416.2.b.b.209.4 | 4 | 24.5 | odd | 2 | |||
936.2.g.b.469.1 | 4 | 4.3 | odd | 2 | |||
936.2.g.b.469.2 | 4 | 8.3 | odd | 2 | |||
3328.2.a.m.1.2 | 2 | 48.5 | odd | 4 | |||
3328.2.a.n.1.1 | 2 | 48.35 | even | 4 | |||
3328.2.a.bc.1.1 | 2 | 48.29 | odd | 4 | |||
3328.2.a.bd.1.2 | 2 | 48.11 | even | 4 | |||
3744.2.g.b.1873.2 | 4 | 8.5 | even | 2 | inner | ||
3744.2.g.b.1873.4 | 4 | 1.1 | even | 1 | trivial |