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: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 2 x^{14} - 4 x^{13} + 9 x^{12} - 10 x^{11} + 2 x^{10} - 8 x^{9} + 28 x^{8} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{20} \) |
Twist minimal: | no (minimal twist has level 312) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1873.11 | ||
Root | \(0.802079 - 1.16476i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3744.1873 |
Dual form | 3744.2.g.e.1873.6 |
$q$-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 | ||||||||
\(5\) | 1.47174i | 0.658181i | 0.944298 | + | 0.329090i | \(0.106742\pi\) | ||||
−0.944298 | + | 0.329090i | \(0.893258\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.93973 | 1.11111 | 0.555557 | − | 0.831478i | \(-0.312505\pi\) | ||||
0.555557 | + | 0.831478i | \(0.312505\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 4.32135i | − 1.30293i | −0.758677 | − | 0.651467i | \(-0.774154\pi\) | ||||
0.758677 | − | 0.651467i | \(-0.225846\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.00000i | − 0.277350i | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.88672 | −1.67027 | −0.835137 | − | 0.550041i | \(-0.814612\pi\) | ||||
−0.835137 | + | 0.550041i | \(0.814612\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.56749i | 1.50668i | 0.657629 | + | 0.753342i | \(0.271560\pi\) | ||||
−0.657629 | + | 0.753342i | \(0.728440\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.54085 | −0.738318 | −0.369159 | − | 0.929366i | \(-0.620354\pi\) | ||||
−0.369159 | + | 0.929366i | \(0.620354\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.83399 | 0.566798 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.96637i | 1.47932i | 0.672982 | + | 0.739659i | \(0.265013\pi\) | ||||
−0.672982 | + | 0.739659i | \(0.734987\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.92763 | 0.885028 | 0.442514 | − | 0.896761i | \(-0.354087\pi\) | ||||
0.442514 | + | 0.896761i | \(0.354087\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.32651i | 0.731314i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.45073i | 0.567296i | 0.958928 | + | 0.283648i | \(0.0915447\pi\) | ||||
−0.958928 | + | 0.283648i | \(0.908455\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.4381 | 1.78633 | 0.893166 | − | 0.449727i | \(-0.148479\pi\) | ||||
0.893166 | + | 0.449727i | \(0.148479\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 1.43599i | − 0.218987i | −0.993988 | − | 0.109493i | \(-0.965077\pi\) | ||||
0.993988 | − | 0.109493i | \(-0.0349229\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.41147 | 0.935209 | 0.467604 | − | 0.883938i | \(-0.345117\pi\) | ||||
0.467604 | + | 0.883938i | \(0.345117\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.64203 | 0.234575 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.46174i | 1.29967i | 0.760075 | + | 0.649835i | \(0.225162\pi\) | ||||
−0.760075 | + | 0.649835i | \(0.774838\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.35988 | 0.857566 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.602544i | 0.0784445i | 0.999231 | + | 0.0392223i | \(0.0124880\pi\) | ||||
−0.999231 | + | 0.0392223i | \(0.987512\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.75217i | 0.736490i | 0.929729 | + | 0.368245i | \(0.120041\pi\) | ||||
−0.929729 | + | 0.368245i | \(0.879959\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.47174 | 0.182546 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 8.57959i | − 1.04816i | −0.851668 | − | 0.524082i | \(-0.824409\pi\) | ||||
0.851668 | − | 0.524082i | \(-0.175591\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.26862 | −0.387914 | −0.193957 | − | 0.981010i | \(-0.562132\pi\) | ||||
−0.193957 | + | 0.981010i | \(0.562132\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.3835 | 1.80050 | 0.900249 | − | 0.435375i | \(-0.143384\pi\) | ||||
0.900249 | + | 0.435375i | \(0.143384\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 12.7036i | − 1.44771i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.85689 | −0.996478 | −0.498239 | − | 0.867040i | \(-0.666020\pi\) | ||||
−0.498239 | + | 0.867040i | \(0.666020\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.95232i | 1.09241i | 0.837652 | + | 0.546205i | \(0.183928\pi\) | ||||
−0.837652 | + | 0.546205i | \(0.816072\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 10.1354i | − 1.09934i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.10329 | 0.540947 | 0.270474 | − | 0.962727i | \(-0.412820\pi\) | ||||
0.270474 | + | 0.962727i | \(0.412820\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 2.93973i | − 0.308168i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.66561 | −0.991670 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.42874 | 0.652739 | 0.326370 | − | 0.945242i | \(-0.394175\pi\) | ||||
0.326370 | + | 0.945242i | \(0.394175\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 2.54248i | − 0.252986i | −0.991968 | − | 0.126493i | \(-0.959628\pi\) | ||||
0.991968 | − | 0.126493i | \(-0.0403721\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.5637 | 1.04088 | 0.520438 | − | 0.853899i | \(-0.325769\pi\) | ||||
0.520438 | + | 0.853899i | \(0.325769\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 2.58527i | − 0.249928i | −0.992161 | − | 0.124964i | \(-0.960118\pi\) | ||||
0.992161 | − | 0.124964i | \(-0.0398815\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.47602i | 0.237160i | 0.992945 | + | 0.118580i | \(0.0378342\pi\) | ||||
−0.992945 | + | 0.118580i | \(0.962166\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.95821 | −0.654573 | −0.327287 | − | 0.944925i | \(-0.606134\pi\) | ||||
−0.327287 | + | 0.944925i | \(0.606134\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 5.21120i | − 0.485947i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −20.2451 | −1.85587 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.67403 | −0.697639 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.5296i | 1.03124i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.3823 | 1.01002 | 0.505008 | − | 0.863115i | \(-0.331490\pi\) | ||||
0.505008 | + | 0.863115i | \(0.331490\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 1.41473i | − 0.123605i | −0.998088 | − | 0.0618026i | \(-0.980315\pi\) | ||||
0.998088 | − | 0.0618026i | \(-0.0196849\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.3067i | 1.67410i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.8444 | 1.52455 | 0.762275 | − | 0.647253i | \(-0.224082\pi\) | ||||
0.762275 | + | 0.647253i | \(0.224082\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.42851i | 0.460440i | 0.973139 | + | 0.230220i | \(0.0739446\pi\) | ||||
−0.973139 | + | 0.230220i | \(0.926055\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.32135 | −0.361369 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.7244 | −0.973658 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 8.30643i | − 0.680489i | −0.940337 | − | 0.340245i | \(-0.889490\pi\) | ||||
0.940337 | − | 0.340245i | \(-0.110510\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23.0182 | −1.87319 | −0.936596 | − | 0.350410i | \(-0.886042\pi\) | ||||
−0.936596 | + | 0.350410i | \(0.886042\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.25217i | 0.582508i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.7135i | 1.09445i | 0.836985 | + | 0.547227i | \(0.184316\pi\) | ||||
−0.836985 | + | 0.547227i | \(0.815684\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.4092 | −0.820356 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.1981i | 1.03375i | 0.856060 | + | 0.516876i | \(0.172905\pi\) | ||||
−0.856060 | + | 0.516876i | \(0.827095\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.7828 | 1.37608 | 0.688038 | − | 0.725674i | \(-0.258472\pi\) | ||||
0.688038 | + | 0.725674i | \(0.258472\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.9839i | 1.51935i | 0.650304 | + | 0.759674i | \(0.274641\pi\) | ||||
−0.650304 | + | 0.759674i | \(0.725359\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.33118 | 0.629778 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 4.32651i | − 0.323379i | −0.986842 | − | 0.161689i | \(-0.948306\pi\) | ||||
0.986842 | − | 0.161689i | \(-0.0516942\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 15.8189i | − 1.17581i | −0.808930 | − | 0.587905i | \(-0.799953\pi\) | ||||
0.808930 | − | 0.587905i | \(-0.200047\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.07856 | −0.373383 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 29.7599i | 2.17626i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.76415 | 0.489437 | 0.244718 | − | 0.969594i | \(-0.421304\pi\) | ||||
0.244718 | + | 0.969594i | \(0.421304\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.5595 | 0.832070 | 0.416035 | − | 0.909349i | \(-0.363419\pi\) | ||||
0.416035 | + | 0.909349i | \(0.363419\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 17.2065i | − 1.22591i | −0.790118 | − | 0.612955i | \(-0.789981\pi\) | ||||
0.790118 | − | 0.612955i | \(-0.210019\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.7288 | −1.61120 | −0.805599 | − | 0.592461i | \(-0.798157\pi\) | ||||
−0.805599 | + | 0.592461i | \(0.798157\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 23.4190i | 1.64369i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.8339i | 1.17573i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 28.3804 | 1.96311 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.86274i | 0.334765i | 0.985892 | + | 0.167382i | \(0.0535314\pi\) | ||||
−0.985892 | + | 0.167382i | \(0.946469\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.11340 | 0.144133 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.4859 | 0.983368 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.88672i | 0.463251i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.82908 | −0.524274 | −0.262137 | − | 0.965031i | \(-0.584427\pi\) | ||||
−0.262137 | + | 0.965031i | \(0.584427\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 5.61608i | − 0.372752i | −0.982478 | − | 0.186376i | \(-0.940326\pi\) | ||||
0.982478 | − | 0.186376i | \(-0.0596743\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.99252i | 0.462079i | 0.972944 | + | 0.231039i | \(0.0742126\pi\) | ||||
−0.972944 | + | 0.231039i | \(0.925787\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.22318 | −0.276670 | −0.138335 | − | 0.990385i | \(-0.544175\pi\) | ||||
−0.138335 | + | 0.990385i | \(0.544175\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.43599i | 0.615536i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.20923 | −0.336957 | −0.168479 | − | 0.985705i | \(-0.553885\pi\) | ||||
−0.168479 | + | 0.985705i | \(0.553885\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.1307 | 0.716995 | 0.358497 | − | 0.933531i | \(-0.383289\pi\) | ||||
0.358497 | + | 0.933531i | \(0.383289\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.41663i | 0.154393i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.56749 | 0.417879 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 2.86165i | − 0.180626i | −0.995913 | − | 0.0903130i | \(-0.971213\pi\) | ||||
0.995913 | − | 0.0903130i | \(-0.0287867\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.3012i | 0.961981i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.6744 | −0.665849 | −0.332925 | − | 0.942953i | \(-0.608035\pi\) | ||||
−0.332925 | + | 0.942953i | \(0.608035\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.1442i | 0.630331i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.22929 | −0.137464 | −0.0687321 | − | 0.997635i | \(-0.521895\pi\) | ||||
−0.0687321 | + | 0.997635i | \(0.521895\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.9252 | −0.855418 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.146614i | 0.00893920i | 0.999990 | + | 0.00446960i | \(0.00142272\pi\) | ||||
−0.999990 | + | 0.00446960i | \(0.998577\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.2326 | 0.682334 | 0.341167 | − | 0.940003i | \(-0.389178\pi\) | ||||
0.341167 | + | 0.940003i | \(0.389178\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 12.2467i | − 0.738501i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.180247i | 0.0108300i | 0.999985 | + | 0.00541498i | \(0.00172365\pi\) | ||||
−0.999985 | + | 0.00541498i | \(0.998276\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.3531 | 0.617617 | 0.308809 | − | 0.951124i | \(-0.400070\pi\) | ||||
0.308809 | + | 0.951124i | \(0.400070\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 2.86450i | − 0.170277i | −0.996369 | − | 0.0851386i | \(-0.972867\pi\) | ||||
0.996369 | − | 0.0851386i | \(-0.0271333\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 33.6250 | 1.98482 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 30.4269 | 1.78982 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.5083i | 0.847583i | 0.905760 | + | 0.423791i | \(0.139301\pi\) | ||||
−0.905760 | + | 0.423791i | \(0.860699\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.886785 | −0.0516306 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.54085i | 0.204773i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 4.22143i | − 0.243319i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.46568 | −0.484744 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 6.24005i | − 0.356138i | −0.984018 | − | 0.178069i | \(-0.943015\pi\) | ||||
0.984018 | − | 0.178069i | \(-0.0569851\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.7669 | 1.23429 | 0.617143 | − | 0.786851i | \(-0.288290\pi\) | ||||
0.617143 | + | 0.786851i | \(0.288290\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.4755 | −1.83562 | −0.917812 | − | 0.397016i | \(-0.870046\pi\) | ||||
−0.917812 | + | 0.397016i | \(0.870046\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 23.3653i | − 1.31232i | −0.754620 | − | 0.656162i | \(-0.772179\pi\) | ||||
0.754620 | − | 0.656162i | \(-0.227821\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 34.4254 | 1.92745 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 45.2284i | − 2.51658i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 2.83399i | − 0.157202i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 18.8480 | 1.03912 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 13.6094i | − 0.748039i | −0.927421 | − | 0.374020i | \(-0.877979\pi\) | ||||
0.927421 | − | 0.374020i | \(-0.122021\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.6269 | 0.689881 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.45391 | −0.351567 | −0.175783 | − | 0.984429i | \(-0.556246\pi\) | ||||
−0.175783 | + | 0.984429i | \(0.556246\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 21.2940i | − 1.15313i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.7510 | −0.850474 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.01451i | 0.322876i | 0.986883 | + | 0.161438i | \(0.0516132\pi\) | ||||
−0.986883 | + | 0.161438i | \(0.948387\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 20.5964i | − 1.10250i | −0.834340 | − | 0.551249i | \(-0.814151\pi\) | ||||
0.834340 | − | 0.551249i | \(-0.185849\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.96820 | −0.157981 | −0.0789907 | − | 0.996875i | \(-0.525170\pi\) | ||||
−0.0789907 | + | 0.996875i | \(0.525170\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 4.81054i | − 0.255317i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.05700 | 0.425232 | 0.212616 | − | 0.977136i | \(-0.431802\pi\) | ||||
0.212616 | + | 0.977136i | \(0.431802\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −24.1319 | −1.27010 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.6404i | 1.18505i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.102750 | 0.00536350 | 0.00268175 | − | 0.999996i | \(-0.499146\pi\) | ||||
0.00268175 | + | 0.999996i | \(0.499146\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 27.8150i | 1.44408i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.65302i | 0.137368i | 0.997638 | + | 0.0686842i | \(0.0218801\pi\) | ||||
−0.997638 | + | 0.0686842i | \(0.978120\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.96637 | 0.410289 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 35.9425i | 1.84624i | 0.384510 | + | 0.923121i | \(0.374371\pi\) | ||||
−0.384510 | + | 0.923121i | \(0.625629\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.8548 | 0.554653 | 0.277327 | − | 0.960776i | \(-0.410552\pi\) | ||||
0.277327 | + | 0.960776i | \(0.410552\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.6964 | 0.952854 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.412406i | 0.0209098i | 0.999945 | + | 0.0104549i | \(0.00332796\pi\) | ||||
−0.999945 | + | 0.0104549i | \(0.996672\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.3848 | 1.23319 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 13.0350i | − 0.655862i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 2.06389i | − 0.103584i | −0.998658 | − | 0.0517918i | \(-0.983507\pi\) | ||||
0.998658 | − | 0.0517918i | \(-0.0164932\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.7908 | −1.03824 | −0.519120 | − | 0.854701i | \(-0.673740\pi\) | ||||
−0.519120 | + | 0.854701i | \(0.673740\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 4.92763i | − 0.245463i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.9118 | 0.739150 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.26345 | −0.458048 | −0.229024 | − | 0.973421i | \(-0.573553\pi\) | ||||
−0.229024 | + | 0.973421i | \(0.573553\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.77132i | 0.0871608i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.6472 | −0.719002 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 35.1941i | − 1.71934i | −0.510847 | − | 0.859672i | \(-0.670668\pi\) | ||||
0.510847 | − | 0.859672i | \(-0.329332\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 38.5231i | 1.87750i | 0.344596 | + | 0.938751i | \(0.388016\pi\) | ||||
−0.344596 | + | 0.938751i | \(0.611984\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −19.5169 | −0.946709 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.9098i | 0.818325i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.89823 | −0.0914344 | −0.0457172 | − | 0.998954i | \(-0.514557\pi\) | ||||
−0.0457172 | + | 0.998954i | \(0.514557\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.4500 | −0.550251 | −0.275126 | − | 0.961408i | \(-0.588719\pi\) | ||||
−0.275126 | + | 0.961408i | \(0.588719\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 23.2545i | − 1.11241i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −38.8346 | −1.85348 | −0.926738 | − | 0.375709i | \(-0.877399\pi\) | ||||
−0.926738 | + | 0.375709i | \(0.877399\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.9374i | 1.51739i | 0.651445 | + | 0.758696i | \(0.274163\pi\) | ||||
−0.651445 | + | 0.758696i | \(0.725837\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.51069i | 0.356041i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.33864 | −0.393525 | −0.196762 | − | 0.980451i | \(-0.563043\pi\) | ||||
−0.196762 | + | 0.980451i | \(0.563043\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 49.4280i | − 2.32747i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.32651 | 0.202830 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.6899 | −1.10817 | −0.554084 | − | 0.832461i | \(-0.686931\pi\) | ||||
−0.554084 | + | 0.832461i | \(0.686931\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 20.5605i | − 0.957599i | −0.877924 | − | 0.478800i | \(-0.841072\pi\) | ||||
0.877924 | − | 0.478800i | \(-0.158928\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.3069 | −1.12964 | −0.564820 | − | 0.825214i | \(-0.691054\pi\) | ||||
−0.564820 | + | 0.825214i | \(0.691054\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 29.7179i | 1.37518i | 0.726099 | + | 0.687590i | \(0.241331\pi\) | ||||
−0.726099 | + | 0.687590i | \(0.758669\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 25.2217i | − 1.16463i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.20542 | −0.285326 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.6122i | 0.853986i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.9556 | −1.00318 | −0.501588 | − | 0.865106i | \(-0.667251\pi\) | ||||
−0.501588 | + | 0.865106i | \(0.667251\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.45073 | 0.157340 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.46141i | 0.429620i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 41.3497 | 1.87374 | 0.936868 | − | 0.349683i | \(-0.113711\pi\) | ||||
0.936868 | + | 0.349683i | \(0.113711\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.8229i | 0.939726i | 0.882739 | + | 0.469863i | \(0.155697\pi\) | ||||
−0.882739 | + | 0.469863i | \(0.844303\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 54.8621i | − 2.47087i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.60886 | −0.431016 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.0654i | 1.12208i | 0.827788 | + | 0.561042i | \(0.189599\pi\) | ||||
−0.827788 | + | 0.561042i | \(0.810401\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.4343 | 1.08947 | 0.544737 | − | 0.838607i | \(-0.316630\pi\) | ||||
0.544737 | + | 0.838607i | \(0.316630\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.74186 | 0.166510 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 34.3045i | 1.52052i | 0.649619 | + | 0.760260i | \(0.274929\pi\) | ||||
−0.649619 | + | 0.760260i | \(0.725071\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 45.2233 | 2.00056 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.5470i | 0.685085i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 27.7062i | − 1.21852i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.5126 | −1.07392 | −0.536959 | − | 0.843609i | \(-0.680427\pi\) | ||||
−0.536959 | + | 0.843609i | \(0.680427\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 21.8796i | − 0.956730i | −0.878161 | − | 0.478365i | \(-0.841230\pi\) | ||||
0.878161 | − | 0.478365i | \(-0.158770\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −33.9352 | −1.47824 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.4624 | −0.454886 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 11.4381i | − 0.495439i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.80484 | 0.164498 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 7.09577i | − 0.305636i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 25.8833i | − 1.11281i | −0.830911 | − | 0.556405i | \(-0.812180\pi\) | ||||
0.830911 | − | 0.556405i | \(-0.187820\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.64405 | −0.156094 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 42.9380i | − 1.83590i | −0.396698 | − | 0.917949i | \(-0.629844\pi\) | ||||
0.396698 | − | 0.917949i | \(-0.370156\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −52.3190 | −2.22886 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −26.0369 | −1.10720 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 15.9949i | − 0.677726i | −0.940836 | − | 0.338863i | \(-0.889958\pi\) | ||||
0.940836 | − | 0.338863i | \(-0.110042\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.43599 | −0.0607360 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.36950i | 0.0577174i | 0.999584 | + | 0.0288587i | \(0.00918729\pi\) | ||||
−0.999584 | + | 0.0288587i | \(0.990813\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 10.2406i | − 0.430827i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.23722 | 0.0518672 | 0.0259336 | − | 0.999664i | \(-0.491744\pi\) | ||||
0.0259336 | + | 0.999664i | \(0.491744\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 8.08889i | − 0.338510i | −0.985572 | − | 0.169255i | \(-0.945864\pi\) | ||||
0.985572 | − | 0.169255i | \(-0.0541361\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.0347 | −0.418478 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.86588 | −0.202569 | −0.101285 | − | 0.994857i | \(-0.532295\pi\) | ||||
−0.101285 | + | 0.994857i | \(0.532295\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 29.2572i | 1.21379i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 40.8875 | 1.69339 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 16.5324i | − 0.682364i | −0.939997 | − | 0.341182i | \(-0.889173\pi\) | ||||
0.939997 | − | 0.341182i | \(-0.110827\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 32.3621i | 1.33346i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.3723 | −0.877656 | −0.438828 | − | 0.898571i | \(-0.644606\pi\) | ||||
−0.438828 | + | 0.898571i | \(0.644606\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 29.7955i | − 1.22150i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.02621 | −0.0419299 | −0.0209649 | − | 0.999780i | \(-0.506674\pi\) | ||||
−0.0209649 | + | 0.999780i | \(0.506674\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.0228 | 1.51019 | 0.755096 | − | 0.655614i | \(-0.227590\pi\) | ||||
0.755096 | + | 0.655614i | \(0.227590\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 11.2941i | − 0.459172i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −43.5674 | −1.76835 | −0.884174 | − | 0.467158i | \(-0.845278\pi\) | ||||
−0.884174 | + | 0.467158i | \(0.845278\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 6.41147i | − 0.259380i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.5030i | 0.747327i | 0.927564 | + | 0.373664i | \(0.121899\pi\) | ||||
−0.927564 | + | 0.373664i | \(0.878101\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.9669 | 1.16617 | 0.583083 | − | 0.812413i | \(-0.301846\pi\) | ||||
0.583083 | + | 0.812413i | \(0.301846\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 34.5680i | − 1.38941i | −0.719297 | − | 0.694703i | \(-0.755536\pi\) | ||||
0.719297 | − | 0.694703i | \(-0.244464\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.0023 | 0.601055 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.79853 | −0.111941 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 23.7642i | − 0.947540i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.5139 | −0.697218 | −0.348609 | − | 0.937268i | \(-0.613346\pi\) | ||||
−0.348609 | + | 0.937268i | \(0.613346\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.7517i | 0.664773i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1.64203i | − 0.0650595i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.0016 | 0.434535 | 0.217268 | − | 0.976112i | \(-0.430286\pi\) | ||||
0.217268 | + | 0.976112i | \(0.430286\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.8557i | 0.980214i | 0.871662 | + | 0.490107i | \(0.163042\pi\) | ||||
−0.871662 | + | 0.490107i | \(0.836958\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.7660 | −1.28816 | −0.644082 | − | 0.764956i | \(-0.722761\pi\) | ||||
−0.644082 | + | 0.764956i | \(0.722761\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.60380 | 0.102208 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 37.6400i | − 1.47297i | −0.676455 | − | 0.736484i | \(-0.736485\pi\) | ||||
0.676455 | − | 0.736484i | \(-0.263515\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.08210 | 0.0813545 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 36.8040i | − 1.43368i | −0.697238 | − | 0.716840i | \(-0.745588\pi\) | ||||
0.697238 | − | 0.716840i | \(-0.254412\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 2.08080i | − 0.0809336i | −0.999181 | − | 0.0404668i | \(-0.987115\pi\) | ||||
0.999181 | − | 0.0404668i | \(-0.0128845\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −28.4143 | −1.10186 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 28.2077i | − 1.09221i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.8571 | 0.959599 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 44.3467 | 1.70944 | 0.854720 | − | 0.519089i | \(-0.173729\pi\) | ||||
0.854720 | + | 0.519089i | \(0.173729\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 36.1463i | 1.38922i | 0.719388 | + | 0.694608i | \(0.244422\pi\) | ||||
−0.719388 | + | 0.694608i | \(0.755578\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.8988 | 0.725268 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.12516i | 0.310900i | 0.987844 | + | 0.155450i | \(0.0496828\pi\) | ||||
−0.987844 | + | 0.155450i | \(0.950317\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26.2623i | 1.00343i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.46174 | 0.360464 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 8.04956i | − 0.306220i | −0.988209 | − | 0.153110i | \(-0.951071\pi\) | ||||
0.988209 | − | 0.153110i | \(-0.0489288\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.98934 | −0.303053 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −78.7710 | −2.98367 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 32.5847i | − 1.23071i | −0.788252 | − | 0.615353i | \(-0.789014\pi\) | ||||
0.788252 | − | 0.615353i | \(-0.210986\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.6626 | −0.854736 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 7.47420i | − 0.281096i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.1070i | 0.717578i | 0.933419 | + | 0.358789i | \(0.116810\pi\) | ||||
−0.933419 | + | 0.358789i | \(0.883190\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.4480 | −0.653433 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 6.35988i | − 0.237846i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.2181 | −0.604832 | −0.302416 | − | 0.953176i | \(-0.597793\pi\) | ||||
−0.302416 | + | 0.953176i | \(0.597793\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 31.0546 | 1.15653 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22.5766i | 0.838475i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.74395 | −0.287207 | −0.143604 | − | 0.989635i | \(-0.545869\pi\) | ||||
−0.143604 | + | 0.989635i | \(0.545869\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.88928i | 0.365768i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 40.9216i | − 1.51147i | −0.654875 | − | 0.755737i | \(-0.727279\pi\) | ||||
0.654875 | − | 0.755737i | \(-0.272721\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −37.0754 | −1.36569 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 22.5269i | − 0.828667i | −0.910125 | − | 0.414334i | \(-0.864015\pi\) | ||||
0.910125 | − | 0.414334i | \(-0.135985\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.15224 | 0.152331 | 0.0761655 | − | 0.997095i | \(-0.475732\pi\) | ||||
0.0761655 | + | 0.997095i | \(0.475732\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.2249 | 0.447885 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 7.60002i | − 0.277699i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.2084 | 1.46723 | 0.733613 | − | 0.679567i | \(-0.237832\pi\) | ||||
0.733613 | + | 0.679567i | \(0.237832\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 33.8767i | − 1.23290i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.6737i | 1.36928i | 0.728884 | + | 0.684638i | \(0.240040\pi\) | ||||
−0.728884 | + | 0.684638i | \(0.759960\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.75751 | 0.208710 | 0.104355 | − | 0.994540i | \(-0.466722\pi\) | ||||
0.104355 | + | 0.994540i | \(0.466722\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.27884i | 0.263512i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.602544 | 0.0217566 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.6221 | 0.635469 | 0.317734 | − | 0.948180i | \(-0.397078\pi\) | ||||
0.317734 | + | 0.948180i | \(0.397078\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 26.8263i | − 0.964873i | −0.875931 | − | 0.482437i | \(-0.839752\pi\) | ||||
0.875931 | − | 0.482437i | \(-0.160248\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.9649 | 0.501633 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 75.1196i | 2.69144i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.1248i | 0.505426i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.1826 | −0.720348 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.2119i | 0.470955i | 0.971880 | + | 0.235477i | \(0.0756654\pi\) | ||||
−0.971880 | + | 0.235477i | \(0.924335\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.4553 | −0.727306 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.75217 | 0.204266 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30.2374i | 1.07106i | 0.844516 | + | 0.535531i | \(0.179888\pi\) | ||||
−0.844516 | + | 0.535531i | \(0.820112\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −44.1540 | −1.56206 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 66.4773i | − 2.34593i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 15.3195i | − 0.539943i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.8919 | 0.734519 | 0.367259 | − | 0.930119i | \(-0.380296\pi\) | ||||
0.367259 | + | 0.930119i | \(0.380296\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 2.19807i | − 0.0771846i | −0.999255 | − | 0.0385923i | \(-0.987713\pi\) | ||||
0.999255 | − | 0.0385923i | \(-0.0122874\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.4241 | −0.680396 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.43086 | 0.329944 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.6736i | 1.00071i | 0.865819 | + | 0.500357i | \(0.166798\pi\) | ||||
−0.865819 | + | 0.500357i | \(0.833202\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.9907 | −1.14998 | −0.574992 | − | 0.818159i | \(-0.694995\pi\) | ||||
−0.574992 | + | 0.818159i | \(0.694995\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 3.70664i | − 0.128893i | −0.997921 | − | 0.0644463i | \(-0.979472\pi\) | ||||
0.997921 | − | 0.0644463i | \(-0.0205281\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 38.6208i | − 1.34136i | −0.741748 | − | 0.670678i | \(-0.766003\pi\) | ||||
0.741748 | − | 0.670678i | \(-0.233997\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.3082 | −0.391805 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26.1716i | 0.905707i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.7828 | 0.855599 | 0.427799 | − | 0.903874i | \(-0.359289\pi\) | ||||
0.427799 | + | 0.903874i | \(0.359289\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −34.4630 | −1.18838 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1.47174i | − 0.0506293i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.5596 | −0.775157 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 12.2185i | − 0.418845i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 48.8930i | − 1.67406i | −0.547154 | − | 0.837032i | \(-0.684289\pi\) | ||||
0.547154 | − | 0.837032i | \(-0.315711\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 40.4927 | 1.38320 | 0.691602 | − | 0.722279i | \(-0.256905\pi\) | ||||
0.691602 | + | 0.722279i | \(0.256905\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 36.2116i | − 1.23552i | −0.786365 | − | 0.617762i | \(-0.788039\pi\) | ||||
0.786365 | − | 0.617762i | \(-0.211961\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.0925 | −0.615877 | −0.307938 | − | 0.951406i | \(-0.599639\pi\) | ||||
−0.307938 | + | 0.951406i | \(0.599639\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −29.4110 | −1.00001 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 38.2737i | 1.29835i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.57959 | −0.290708 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 33.8939i | 1.14582i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 4.27060i | − 0.144208i | −0.997397 | − | 0.0721039i | \(-0.977029\pi\) | ||||
0.997397 | − | 0.0721039i | \(-0.0229713\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.9886 | −0.841886 | −0.420943 | − | 0.907087i | \(-0.638301\pi\) | ||||
−0.420943 | + | 0.907087i | \(0.638301\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.7898i | 1.17077i | 0.810756 | + | 0.585385i | \(0.199056\pi\) | ||||
−0.810756 | + | 0.585385i | \(0.800944\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.6922 | 0.728354 | 0.364177 | − | 0.931330i | \(-0.381350\pi\) | ||||
0.364177 | + | 0.931330i | \(0.381350\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 33.4609 | 1.12224 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 42.1072i | 1.40906i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.36748 | 0.212842 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 39.2553i | 1.30924i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 65.1604i | − 2.17081i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 23.2813 | 0.773896 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.1200i | 0.634870i | 0.948280 | + | 0.317435i | \(0.102821\pi\) | ||||
−0.948280 | + | 0.317435i | \(0.897179\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.1149 | −0.401386 | −0.200693 | − | 0.979654i | \(-0.564319\pi\) | ||||
−0.200693 | + | 0.979654i | \(0.564319\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 43.0074 | 1.42334 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 4.15891i | − 0.137339i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.22863 | −0.238451 | −0.119225 | − | 0.992867i | \(-0.538041\pi\) | ||||
−0.119225 | + | 0.992867i | \(0.538041\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.26862i | 0.107588i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.77933i | 0.321543i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 41.9587 | 1.37662 | 0.688310 | − | 0.725416i | \(-0.258353\pi\) | ||||
0.688310 | + | 0.725416i | \(0.258353\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.7840i | 0.353431i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −43.7987 | −1.43237 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.5281 | 0.637954 | 0.318977 | − | 0.947763i | \(-0.396661\pi\) | ||||
0.318977 | + | 0.947763i | \(0.396661\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 11.7669i | − 0.383591i | −0.981435 | − | 0.191795i | \(-0.938569\pi\) | ||||
0.981435 | − | 0.191795i | \(-0.0614310\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −40.5006 | −1.31888 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 34.6707i | − 1.12665i | −0.826236 | − | 0.563323i | \(-0.809523\pi\) | ||||
0.826236 | − | 0.563323i | \(-0.190477\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 15.3835i | − 0.499368i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 60.1507 | 1.94847 | 0.974236 | − | 0.225533i | \(-0.0724123\pi\) | ||||
0.974236 | + | 0.225533i | \(0.0724123\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.95505i | 0.322138i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 52.4578 | 1.69395 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.71847 | −0.216725 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.0125i | 0.547652i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39.2013 | −1.26063 | −0.630315 | − | 0.776340i | \(-0.717074\pi\) | ||||
−0.630315 | + | 0.776340i | \(0.717074\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 42.7280i | − 1.37121i | −0.727976 | − | 0.685603i | \(-0.759539\pi\) | ||||
0.727976 | − | 0.685603i | \(-0.240461\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.9584i | 0.511602i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.5858 | 0.498633 | 0.249316 | − | 0.968422i | \(-0.419794\pi\) | ||||
0.249316 | + | 0.968422i | \(0.419794\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 22.0531i | − 0.704819i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −43.4450 | −1.38568 | −0.692840 | − | 0.721091i | \(-0.743641\pi\) | ||||
−0.692840 | + | 0.721091i | \(0.743641\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.3234 | 0.806870 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.08464i | 0.161682i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.3905 | 0.330064 | 0.165032 | − | 0.986288i | \(-0.447227\pi\) | ||||
0.165032 | + | 0.986288i | \(0.447227\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 33.4507i | − 1.06046i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.4960i | 0.522433i | 0.965280 | + | 0.261217i | \(0.0841237\pi\) | ||||
−0.965280 | + | 0.261217i | \(0.915876\pi\) | |||||||
\(998\) | 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.e.1873.11 | 16 | ||
3.2 | odd | 2 | 1248.2.g.b.625.3 | 16 | |||
4.3 | odd | 2 | 936.2.g.e.469.14 | 16 | |||
8.3 | odd | 2 | 936.2.g.e.469.13 | 16 | |||
8.5 | even | 2 | inner | 3744.2.g.e.1873.6 | 16 | ||
12.11 | even | 2 | 312.2.g.b.157.3 | ✓ | 16 | ||
24.5 | odd | 2 | 1248.2.g.b.625.14 | 16 | |||
24.11 | even | 2 | 312.2.g.b.157.4 | yes | 16 | ||
48.5 | odd | 4 | 9984.2.a.bs.1.6 | 8 | |||
48.11 | even | 4 | 9984.2.a.bu.1.6 | 8 | |||
48.29 | odd | 4 | 9984.2.a.bv.1.3 | 8 | |||
48.35 | even | 4 | 9984.2.a.bt.1.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
312.2.g.b.157.3 | ✓ | 16 | 12.11 | even | 2 | ||
312.2.g.b.157.4 | yes | 16 | 24.11 | even | 2 | ||
936.2.g.e.469.13 | 16 | 8.3 | odd | 2 | |||
936.2.g.e.469.14 | 16 | 4.3 | odd | 2 | |||
1248.2.g.b.625.3 | 16 | 3.2 | odd | 2 | |||
1248.2.g.b.625.14 | 16 | 24.5 | odd | 2 | |||
3744.2.g.e.1873.6 | 16 | 8.5 | even | 2 | inner | ||
3744.2.g.e.1873.11 | 16 | 1.1 | even | 1 | trivial | ||
9984.2.a.bs.1.6 | 8 | 48.5 | odd | 4 | |||
9984.2.a.bt.1.3 | 8 | 48.35 | even | 4 | |||
9984.2.a.bu.1.6 | 8 | 48.11 | even | 4 | |||
9984.2.a.bv.1.3 | 8 | 48.29 | odd | 4 |