Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(1249,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.f (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: | \(12.7760643234\) |
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: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 320) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.4 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.1249 |
Dual form | 1600.2.f.i.1249.3 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 2.73205 | 1.57735 | 0.788675 | − | 0.614810i | \(-0.210767\pi\) | ||||
0.788675 | + | 0.614810i | \(0.210767\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.73205i | 1.78855i | 0.447521 | + | 0.894274i | \(0.352307\pi\) | ||||
−0.447521 | + | 0.894274i | \(0.647693\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.46410 | 1.48803 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 3.46410i | − 1.04447i | −0.852803 | − | 0.522233i | \(-0.825099\pi\) | ||||
0.852803 | − | 0.522233i | \(-0.174901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.46410 | 0.960769 | 0.480384 | − | 0.877058i | \(-0.340497\pi\) | ||||
0.480384 | + | 0.877058i | \(0.340497\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.46410i | 0.840168i | 0.907485 | + | 0.420084i | \(0.137999\pi\) | ||||
−0.907485 | + | 0.420084i | \(0.862001\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 2.00000i | − 0.458831i | −0.973329 | − | 0.229416i | \(-0.926318\pi\) | ||||
0.973329 | − | 0.229416i | \(-0.0736815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.9282i | 2.82117i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.19615i | 0.457929i | 0.973435 | + | 0.228965i | \(0.0735340\pi\) | ||||
−0.973435 | + | 0.228965i | \(0.926466\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.53590 | 0.455461 | 0.227730 | − | 0.973724i | \(-0.426870\pi\) | ||||
0.227730 | + | 0.973724i | \(0.426870\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 9.46410i | − 1.64749i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | −0.986394 | −0.493197 | − | 0.869918i | \(-0.664172\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.46410 | 1.51547 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.46410 | 1.47804 | 0.739022 | − | 0.673681i | \(-0.235288\pi\) | ||||
0.739022 | + | 0.673681i | \(0.235288\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.196152 | −0.0299130 | −0.0149565 | − | 0.999888i | \(-0.504761\pi\) | ||||
−0.0149565 | + | 0.999888i | \(0.504761\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.19615i | 0.320342i | 0.987089 | + | 0.160171i | \(0.0512045\pi\) | ||||
−0.987089 | + | 0.160171i | \(0.948795\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15.3923 | −2.19890 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.46410i | 1.32524i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.3923 | 1.42749 | 0.713746 | − | 0.700404i | \(-0.246997\pi\) | ||||
0.713746 | + | 0.700404i | \(0.246997\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 5.46410i | − 0.723738i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.00000i | 0.781133i | 0.920575 | + | 0.390567i | \(0.127721\pi\) | ||||
−0.920575 | + | 0.390567i | \(0.872279\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.928203i | 0.118844i | 0.998233 | + | 0.0594221i | \(0.0189258\pi\) | ||||
−0.998233 | + | 0.0594221i | \(0.981074\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 21.1244i | 2.66142i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.196152 | 0.0239638 | 0.0119819 | − | 0.999928i | \(-0.496186\pi\) | ||||
0.0119819 | + | 0.999928i | \(0.496186\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.00000i | 0.722315i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −16.3923 | −1.94541 | −0.972704 | − | 0.232048i | \(-0.925457\pi\) | ||||
−0.972704 | + | 0.232048i | \(0.925457\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.39230i | 0.748163i | 0.927396 | + | 0.374081i | \(0.122042\pi\) | ||||
−0.927396 | + | 0.374081i | \(0.877958\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 16.3923 | 1.86808 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.0000 | −1.35011 | −0.675053 | − | 0.737769i | \(-0.735879\pi\) | ||||
−0.675053 | + | 0.737769i | \(0.735879\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.46410 | −0.273789 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.26795 | 0.139176 | 0.0695878 | − | 0.997576i | \(-0.477832\pi\) | ||||
0.0695878 | + | 0.997576i | \(0.477832\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.9282 | 1.37039 | 0.685193 | − | 0.728361i | \(-0.259718\pi\) | ||||
0.685193 | + | 0.728361i | \(0.259718\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.3923i | 1.71838i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.92820 | 0.718421 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 14.3923i | − 1.46132i | −0.682743 | − | 0.730659i | \(-0.739213\pi\) | ||||
0.682743 | − | 0.730659i | \(-0.260787\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 15.4641i | − 1.55420i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 12.0000i | − 1.19404i | −0.802225 | − | 0.597022i | \(-0.796350\pi\) | ||||
0.802225 | − | 0.597022i | \(-0.203650\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.19615i | 0.216393i | 0.994130 | + | 0.108197i | \(0.0345076\pi\) | ||||
−0.994130 | + | 0.108197i | \(0.965492\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.2679 | 1.28266 | 0.641331 | − | 0.767265i | \(-0.278383\pi\) | ||||
0.641331 | + | 0.767265i | \(0.278383\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 12.9282i | − 1.23830i | −0.785274 | − | 0.619149i | \(-0.787478\pi\) | ||||
0.785274 | − | 0.619149i | \(-0.212522\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −16.3923 | −1.55589 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 12.9282i | − 1.21618i | −0.793867 | − | 0.608092i | \(-0.791935\pi\) | ||||
0.793867 | − | 0.608092i | \(-0.208065\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 15.4641 | 1.42966 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.3923 | −1.50268 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 25.8564 | 2.33139 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 14.1962i | − 1.25970i | −0.776715 | − | 0.629852i | \(-0.783115\pi\) | ||||
0.776715 | − | 0.629852i | \(-0.216885\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.535898 | −0.0471832 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 10.3923i | − 0.907980i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | − | 0.453990i | \(-0.150000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.46410 | 0.820642 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.928203i | 0.0793018i | 0.999214 | + | 0.0396509i | \(0.0126246\pi\) | ||||
−0.999214 | + | 0.0396509i | \(0.987375\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0000i | 0.848189i | 0.905618 | + | 0.424094i | \(0.139408\pi\) | ||||
−0.905618 | + | 0.424094i | \(0.860592\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000i | 0.505291i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 12.0000i | − 1.00349i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −42.0526 | −3.46844 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 18.0000i | − 1.47462i | −0.675556 | − | 0.737309i | \(-0.736096\pi\) | ||||
0.675556 | − | 0.737309i | \(-0.263904\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.46410 | −0.770178 | −0.385089 | − | 0.922880i | \(-0.625829\pi\) | ||||
−0.385089 | + | 0.922880i | \(0.625829\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15.4641i | 1.25020i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.9282 | −1.03178 | −0.515891 | − | 0.856654i | \(-0.672539\pi\) | ||||
−0.515891 | + | 0.856654i | \(0.672539\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 28.3923 | 2.25166 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.3923 | −0.819028 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.1962 | −1.26858 | −0.634290 | − | 0.773095i | \(-0.718708\pi\) | ||||
−0.634290 | + | 0.773095i | \(0.718708\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.19615i | 0.169943i | 0.996383 | + | 0.0849717i | \(0.0270800\pi\) | ||||
−0.996383 | + | 0.0849717i | \(0.972920\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 8.92820i | − 0.682757i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.00000 | −0.456172 | −0.228086 | − | 0.973641i | \(-0.573247\pi\) | ||||
−0.228086 | + | 0.973641i | \(0.573247\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.3923i | 1.23212i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.85641i | 0.587215i | 0.955926 | + | 0.293608i | \(0.0948559\pi\) | ||||
−0.955926 | + | 0.293608i | \(0.905144\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 6.92820i | − 0.514969i | −0.966282 | − | 0.257485i | \(-0.917106\pi\) | ||||
0.966282 | − | 0.257485i | \(-0.0828937\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.53590i | 0.187459i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.0000 | 0.877527 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 18.9282i | 1.37682i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.39230 | 0.317816 | 0.158908 | − | 0.987293i | \(-0.449203\pi\) | ||||
0.158908 | + | 0.987293i | \(0.449203\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 14.3923i | − 1.03598i | −0.855386 | − | 0.517990i | \(-0.826680\pi\) | ||||
0.855386 | − | 0.517990i | \(-0.173320\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.3923 | 0.740421 | 0.370211 | − | 0.928948i | \(-0.379286\pi\) | ||||
0.370211 | + | 0.928948i | \(0.379286\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.92820 | 0.491127 | 0.245564 | − | 0.969380i | \(-0.421027\pi\) | ||||
0.245564 | + | 0.969380i | \(0.421027\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.535898 | 0.0377994 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.80385i | 0.681415i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.92820 | −0.479234 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.3923i | 0.990807i | 0.868663 | + | 0.495404i | \(0.164980\pi\) | ||||
−0.868663 | + | 0.495404i | \(0.835020\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −44.7846 | −3.06859 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.0000i | 0.814613i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.4641i | 1.18011i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000i | 0.807207i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 9.12436i | − 0.611012i | −0.952190 | − | 0.305506i | \(-0.901174\pi\) | ||||
0.952190 | − | 0.305506i | \(-0.0988256\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.5885 | 0.835525 | 0.417763 | − | 0.908556i | \(-0.362814\pi\) | ||||
0.417763 | + | 0.908556i | \(0.362814\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.07180i | 0.335154i | 0.985859 | + | 0.167577i | \(0.0535942\pi\) | ||||
−0.985859 | + | 0.167577i | \(0.946406\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 44.7846 | 2.94661 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 22.3923i | − 1.46697i | −0.679706 | − | 0.733484i | \(-0.737893\pi\) | ||||
0.679706 | − | 0.733484i | \(-0.262107\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −32.7846 | −2.12959 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.7846 | −1.34444 | −0.672222 | − | 0.740349i | \(-0.734660\pi\) | ||||
−0.672222 | + | 0.740349i | \(0.734660\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.392305 | 0.0252706 | 0.0126353 | − | 0.999920i | \(-0.495978\pi\) | ||||
0.0126353 | + | 0.999920i | \(0.495978\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −18.7321 | −1.20166 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 6.92820i | − 0.440831i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.46410 | 0.219529 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 8.53590i | − 0.538781i | −0.963031 | − | 0.269391i | \(-0.913178\pi\) | ||||
0.963031 | − | 0.269391i | \(-0.0868223\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.60770 | 0.478292 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 6.00000i | − 0.374270i | −0.982334 | − | 0.187135i | \(-0.940080\pi\) | ||||
0.982334 | − | 0.187135i | \(-0.0599201\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 28.3923i | − 1.76421i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.80385i | 0.604531i | 0.953224 | + | 0.302266i | \(0.0977429\pi\) | ||||
−0.953224 | + | 0.302266i | \(0.902257\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 35.3205 | 2.16158 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.7846i | 1.63309i | 0.577284 | + | 0.816543i | \(0.304112\pi\) | ||||
−0.577284 | + | 0.816543i | \(0.695888\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.3923 | 0.995762 | 0.497881 | − | 0.867245i | \(-0.334112\pi\) | ||||
0.497881 | + | 0.867245i | \(0.334112\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 44.7846i | 2.71049i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.85641 | −0.472046 | −0.236023 | − | 0.971748i | \(-0.575844\pi\) | ||||
−0.236023 | + | 0.971748i | \(0.575844\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.3205 | 0.677741 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.60770 | −0.453837 | −0.226919 | − | 0.973914i | \(-0.572865\pi\) | ||||
−0.226919 | + | 0.973914i | \(0.572865\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.5885 | −1.22386 | −0.611928 | − | 0.790913i | \(-0.709606\pi\) | ||||
−0.611928 | + | 0.790913i | \(0.709606\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 44.7846i | 2.64355i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.00000 | 0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 39.3205i | − 2.30501i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.0000 | 1.75262 | 0.876309 | − | 0.481749i | \(-0.159998\pi\) | ||||
0.876309 | + | 0.481749i | \(0.159998\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 13.8564i | − 0.804030i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.60770i | 0.439964i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 0.928203i | − 0.0535007i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 32.7846i | − 1.88343i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.8038 | −1.35856 | −0.679279 | − | 0.733880i | \(-0.737707\pi\) | ||||
−0.679279 | + | 0.733880i | \(0.737707\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.00000i | 0.341328i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.3923 | 1.60998 | 0.804990 | − | 0.593288i | \(-0.202171\pi\) | ||||
0.804990 | + | 0.593288i | \(0.202171\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.0000i | 1.24351i | 0.783210 | + | 0.621757i | \(0.213581\pi\) | ||||
−0.783210 | + | 0.621757i | \(0.786419\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.60770 | −0.0902972 | −0.0451486 | − | 0.998980i | \(-0.514376\pi\) | ||||
−0.0451486 | + | 0.998980i | \(0.514376\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 36.2487 | 2.02321 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.92820 | 0.385496 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 35.3205i | − 1.95323i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.3923 | −0.572946 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 26.3923i | − 1.45065i | −0.688405 | − | 0.725326i | \(-0.741689\pi\) | ||||
0.688405 | − | 0.725326i | \(-0.258311\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −26.7846 | −1.46779 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000i | 0.762629i | 0.924445 | + | 0.381314i | \(0.124528\pi\) | ||||
−0.924445 | + | 0.381314i | \(0.875472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 35.3205i | − 1.91835i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 8.78461i | − 0.475713i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 39.7128i | − 2.14429i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.0526 | −0.539650 | −0.269825 | − | 0.962909i | \(-0.586966\pi\) | ||||
−0.269825 | + | 0.962909i | \(0.586966\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 32.7846i | − 1.75492i | −0.479650 | − | 0.877460i | \(-0.659236\pi\) | ||||
0.479650 | − | 0.877460i | \(-0.340764\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.8564 | 0.739600 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.7846i | 1.42560i | 0.701367 | + | 0.712800i | \(0.252573\pi\) | ||||
−0.701367 | + | 0.712800i | \(0.747427\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −44.7846 | −2.37025 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −32.7846 | −1.73031 | −0.865153 | − | 0.501508i | \(-0.832779\pi\) | ||||
−0.865153 | + | 0.501508i | \(0.832779\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.73205 | −0.143395 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 28.0526i | − 1.46433i | −0.681126 | − | 0.732166i | \(-0.738510\pi\) | ||||
0.681126 | − | 0.732166i | \(-0.261490\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 42.2487 | 2.19938 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 49.1769i | 2.55314i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.8564 | −1.02813 | −0.514063 | − | 0.857753i | \(-0.671860\pi\) | ||||
−0.514063 | + | 0.857753i | \(0.671860\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.00000i | 0.102733i | 0.998680 | + | 0.0513665i | \(0.0163577\pi\) | ||||
−0.998680 | + | 0.0513665i | \(0.983642\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 38.7846i | − 1.98700i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 14.1962i | − 0.725390i | −0.931908 | − | 0.362695i | \(-0.881857\pi\) | ||||
0.931908 | − | 0.362695i | \(-0.118143\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.875644 | −0.0445115 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.7846i | 0.749609i | 0.927104 | + | 0.374805i | \(0.122290\pi\) | ||||
−0.927104 | + | 0.374805i | \(0.877710\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.60770 | −0.384738 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 28.3923i | − 1.43220i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.5359 | 1.03067 | 0.515334 | − | 0.856990i | \(-0.327668\pi\) | ||||
0.515334 | + | 0.856990i | \(0.327668\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 25.8564 | 1.29444 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.8564 | −1.59083 | −0.795417 | − | 0.606063i | \(-0.792748\pi\) | ||||
−0.795417 | + | 0.606063i | \(0.792748\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.78461 | 0.437593 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.7846i | 1.03025i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.3923 | −1.20612 | −0.603061 | − | 0.797695i | \(-0.706052\pi\) | ||||
−0.603061 | + | 0.797695i | \(0.706052\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.53590i | 0.125087i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −28.3923 | −1.39709 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 27.3205i | 1.33789i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.9282i | 0.631584i | 0.948828 | + | 0.315792i | \(0.102270\pi\) | ||||
−0.948828 | + | 0.315792i | \(0.897730\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 6.00000i | − 0.292422i | −0.989253 | − | 0.146211i | \(-0.953292\pi\) | ||||
0.989253 | − | 0.146211i | \(-0.0467079\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.80385i | 0.476679i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.39230 | −0.212559 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 32.7846i | − 1.58286i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.60770 | −0.366450 | −0.183225 | − | 0.983071i | \(-0.558654\pi\) | ||||
−0.183225 | + | 0.983071i | \(0.558654\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.60770i | 0.269489i | 0.990880 | + | 0.134744i | \(0.0430213\pi\) | ||||
−0.990880 | + | 0.134744i | \(0.956979\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.39230 | 0.210112 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.07180 | 0.242064 | 0.121032 | − | 0.992649i | \(-0.461380\pi\) | ||||
0.121032 | + | 0.992649i | \(0.461380\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −68.7128 | −3.27204 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.6603 | −0.839064 | −0.419532 | − | 0.907741i | \(-0.637806\pi\) | ||||
−0.419532 | + | 0.907741i | \(0.637806\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 49.1769i | − 2.32599i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.46410 | 0.446639 | 0.223319 | − | 0.974745i | \(-0.428311\pi\) | ||||
0.223319 | + | 0.974745i | \(0.428311\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 32.7846i | − 1.54377i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −25.8564 | −1.21484 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.7846i | 0.878707i | 0.898314 | + | 0.439353i | \(0.144792\pi\) | ||||
−0.898314 | + | 0.439353i | \(0.855208\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.8564i | 0.646762i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 12.0000i | − 0.558896i | −0.960161 | − | 0.279448i | \(-0.909849\pi\) | ||||
0.960161 | − | 0.279448i | \(-0.0901514\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.1962i | 1.21744i | 0.793386 | + | 0.608719i | \(0.208316\pi\) | ||||
−0.793386 | + | 0.608719i | \(0.791684\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −28.9808 | −1.34107 | −0.670535 | − | 0.741878i | \(-0.733935\pi\) | ||||
−0.670535 | + | 0.741878i | \(0.733935\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.928203i | 0.0428604i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −35.3205 | −1.62748 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.679492i | 0.0312431i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 46.3923 | 2.12416 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.7846 | −0.947697 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −28.3923 | −1.29189 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.8756i | 0.674080i | 0.941490 | + | 0.337040i | \(0.109426\pi\) | ||||
−0.941490 | + | 0.337040i | \(0.890574\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −44.2487 | −2.00100 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 1.60770i | − 0.0725543i | −0.999342 | − | 0.0362771i | \(-0.988450\pi\) | ||||
0.999342 | − | 0.0362771i | \(-0.0115499\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 77.5692i | − 3.47946i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 43.5692i | 1.95043i | 0.221268 | + | 0.975213i | \(0.428980\pi\) | ||||
−0.221268 | + | 0.975213i | \(0.571020\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.00000i | 0.268060i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.19615i | 0.0979216i | 0.998801 | + | 0.0489608i | \(0.0155909\pi\) | ||||
−0.998801 | + | 0.0489608i | \(0.984409\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.73205 | −0.121335 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 32.7846i | 1.45315i | 0.687086 | + | 0.726576i | \(0.258890\pi\) | ||||
−0.687086 | + | 0.726576i | \(0.741110\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30.2487 | −1.33812 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 8.00000i | − 0.353209i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.60770 | 0.334586 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.3923 | −0.719542 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.14359 | 0.181534 | 0.0907671 | − | 0.995872i | \(-0.471068\pi\) | ||||
0.0907671 | + | 0.995872i | \(0.471068\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.9808 | 1.61706 | 0.808528 | − | 0.588458i | \(-0.200265\pi\) | ||||
0.808528 | + | 0.588458i | \(0.200265\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.78461i | 0.382664i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.1769 | 0.790301 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 26.7846i | 1.16235i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 32.7846 | 1.42006 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 21.4641i | 0.926244i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 53.3205i | 2.29668i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 39.7128i | − 1.70739i | −0.520776 | − | 0.853694i | \(-0.674357\pi\) | ||||
0.520776 | − | 0.853694i | \(-0.325643\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 18.9282i | − 0.812287i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.1962 | −0.521470 | −0.260735 | − | 0.965410i | \(-0.583965\pi\) | ||||
−0.260735 | + | 0.965410i | \(0.583965\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.14359i | 0.176844i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 56.7846i | − 2.41473i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.7846 | 1.13490 | 0.567450 | − | 0.823408i | \(-0.307930\pi\) | ||||
0.567450 | + | 0.823408i | \(0.307930\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.679492 | −0.0287394 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 32.7846 | 1.38417 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.8038 | 0.666053 | 0.333026 | − | 0.942918i | \(-0.391930\pi\) | ||||
0.333026 | + | 0.942918i | \(0.391930\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 11.6603i | − 0.489685i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.24871 | −0.261960 | −0.130980 | − | 0.991385i | \(-0.541812\pi\) | ||||
−0.130980 | + | 0.991385i | \(0.541812\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.60770i | 0.402070i | 0.979584 | + | 0.201035i | \(0.0644304\pi\) | ||||
−0.979584 | + | 0.201035i | \(0.935570\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.0000 | 0.501307 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.00000i | 0.0832611i | 0.999133 | + | 0.0416305i | \(0.0132552\pi\) | ||||
−0.999133 | + | 0.0416305i | \(0.986745\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 39.3205i | − 1.63410i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.00000i | 0.248922i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 36.0000i | − 1.49097i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 31.5167 | 1.30083 | 0.650416 | − | 0.759578i | \(-0.274595\pi\) | ||||
0.650416 | + | 0.759578i | \(0.274595\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 5.07180i | − 0.208980i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 28.3923 | 1.16790 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.9282i | 0.530898i | 0.964125 | + | 0.265449i | \(0.0855201\pi\) | ||||
−0.964125 | + | 0.265449i | \(0.914480\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.9282 | 0.774680 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.0000 | 0.490307 | 0.245153 | − | 0.969484i | \(-0.421162\pi\) | ||||
0.245153 | + | 0.969484i | \(0.421162\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.392305 | 0.0160024 | 0.00800122 | − | 0.999968i | \(-0.497453\pi\) | ||||
0.00800122 | + | 0.999968i | \(0.497453\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.875644 | 0.0356590 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.19615i | 0.0891391i | 0.999006 | + | 0.0445695i | \(0.0141916\pi\) | ||||
−0.999006 | + | 0.0445695i | \(0.985808\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.60770i | 0.307774i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.3923 | −1.38909 | −0.694546 | − | 0.719448i | \(-0.744395\pi\) | ||||
−0.694546 | + | 0.719448i | \(0.744395\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 34.3923i | − 1.38458i | −0.721618 | − | 0.692291i | \(-0.756601\pi\) | ||||
0.721618 | − | 0.692291i | \(-0.243399\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 34.7846i | − 1.39811i | −0.715067 | − | 0.699056i | \(-0.753604\pi\) | ||||
0.715067 | − | 0.699056i | \(-0.246396\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.78461i | 0.352514i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 61.1769i | 2.45100i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −18.9282 | −0.755920 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 20.7846i | − 0.828737i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.5359 | −0.578665 | −0.289332 | − | 0.957229i | \(-0.593433\pi\) | ||||
−0.289332 | + | 0.957229i | \(0.593433\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 39.3205i | 1.56285i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −53.3205 | −2.11264 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −73.1769 | −2.89483 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.3923 | 0.647457 | 0.323729 | − | 0.946150i | \(-0.395064\pi\) | ||||
0.323729 | + | 0.946150i | \(0.395064\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.5885 | −0.811929 | −0.405965 | − | 0.913889i | \(-0.633064\pi\) | ||||
−0.405965 | + | 0.913889i | \(0.633064\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 5.41154i | − 0.212750i | −0.994326 | − | 0.106375i | \(-0.966076\pi\) | ||||
0.994326 | − | 0.106375i | \(-0.0339244\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.7846 | 0.815867 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 32.7846i | 1.28493i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 43.1769 | 1.68964 | 0.844822 | − | 0.535048i | \(-0.179707\pi\) | ||||
0.844822 | + | 0.535048i | \(0.179707\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 28.5359i | 1.11329i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 28.6410i | − 1.11570i | −0.829943 | − | 0.557848i | \(-0.811627\pi\) | ||||
0.829943 | − | 0.557848i | \(-0.188373\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 47.5692i | 1.85023i | 0.379689 | + | 0.925114i | \(0.376031\pi\) | ||||
−0.379689 | + | 0.925114i | \(0.623969\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 32.7846i | 1.27325i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 24.9282i | − 0.963780i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.21539 | 0.124129 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.1769i | 0.893404i | 0.894683 | + | 0.446702i | \(0.147402\pi\) | ||||
−0.894683 | + | 0.446702i | \(0.852598\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.1769 | 0.737029 | 0.368514 | − | 0.929622i | \(-0.379867\pi\) | ||||
0.368514 | + | 0.929622i | \(0.379867\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 68.1051 | 2.61363 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 34.3923 | 1.31792 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.66025 | 0.216584 | 0.108292 | − | 0.994119i | \(-0.465462\pi\) | ||||
0.108292 | + | 0.994119i | \(0.465462\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.8564i | 0.528655i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 36.0000 | 1.37149 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 26.3923i | − 1.00401i | −0.864865 | − | 0.502005i | \(-0.832596\pi\) | ||||
0.864865 | − | 0.502005i | \(-0.167404\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 73.1769 | 2.77976 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 32.7846i | 1.24181i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 61.1769i | − 2.31392i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.7846i | 1.01164i | 0.862639 | + | 0.505820i | \(0.168810\pi\) | ||||
−0.862639 | + | 0.505820i | \(0.831190\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.0000i | 0.452589i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 56.7846 | 2.13561 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 37.8564i | − 1.42173i | −0.703330 | − | 0.710864i | \(-0.748304\pi\) | ||||
0.703330 | − | 0.710864i | \(-0.251696\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −53.5692 | −2.00900 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.56922i | 0.208569i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −56.7846 | −2.12066 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.21539 | 0.119914 | 0.0599569 | − | 0.998201i | \(-0.480904\pi\) | ||||
0.0599569 | + | 0.998201i | \(0.480904\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.3923 | −0.387030 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.07180 | 0.0398606 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 4.05256i | − 0.150301i | −0.997172 | − | 0.0751505i | \(-0.976056\pi\) | ||||
0.997172 | − | 0.0751505i | \(-0.0239437\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.7846 | −1.62165 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 0.679492i | − 0.0251319i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.78461 | 0.102852 | 0.0514260 | − | 0.998677i | \(-0.483623\pi\) | ||||
0.0514260 | + | 0.998677i | \(0.483623\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 0.679492i | − 0.0250294i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.00000i | 0.0735712i | 0.999323 | + | 0.0367856i | \(0.0117119\pi\) | ||||
−0.999323 | + | 0.0367856i | \(0.988288\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 18.9282i | − 0.695345i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 5.41154i | − 0.198530i | −0.995061 | − | 0.0992651i | \(-0.968351\pi\) | ||||
0.995061 | − | 0.0992651i | \(-0.0316492\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.66025 | 0.207098 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 62.7846i | 2.29410i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.6077 | 0.715495 | 0.357747 | − | 0.933818i | \(-0.383545\pi\) | ||||
0.357747 | + | 0.933818i | \(0.383545\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 23.3205i | − 0.849847i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.9282 | −1.34218 | −0.671089 | − | 0.741377i | \(-0.734173\pi\) | ||||
−0.671089 | + | 0.741377i | \(0.734173\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.7846 | 0.754434 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33.7128 | 1.22209 | 0.611044 | − | 0.791596i | \(-0.290750\pi\) | ||||
0.611044 | + | 0.791596i | \(0.290750\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 61.1769 | 2.21475 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.7846i | 0.750489i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.7846 | −1.25437 | −0.627183 | − | 0.778872i | \(-0.715792\pi\) | ||||
−0.627183 | + | 0.778872i | \(0.715792\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 16.3923i | − 0.590354i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.6077 | −0.921045 | −0.460522 | − | 0.887648i | \(-0.652338\pi\) | ||||
−0.460522 | + | 0.887648i | \(0.652338\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 77.5692i | − 2.78278i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 18.9282i | − 0.678173i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 56.7846i | 2.03191i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.1962 | 0.577330 | 0.288665 | − | 0.957430i | \(-0.406789\pi\) | ||||
0.288665 | + | 0.957430i | \(0.406789\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 26.7846i | 0.953557i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 61.1769 | 2.17520 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.21539i | 0.114182i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.3923 | 0.793176 | 0.396588 | − | 0.917997i | \(-0.370194\pi\) | ||||
0.396588 | + | 0.917997i | \(0.370194\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.60770 | −0.269141 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 57.7128 | 2.03918 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 22.1436 | 0.781430 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 73.1769i | 2.57595i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 47.5692 | 1.67244 | 0.836222 | − | 0.548391i | \(-0.184759\pi\) | ||||
0.836222 | + | 0.548391i | \(0.184759\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.6077i | 0.618290i | 0.951015 | + | 0.309145i | \(0.100043\pi\) | ||||
−0.951015 | + | 0.309145i | \(0.899957\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 44.7846 | 1.57066 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.392305i | 0.0137250i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 73.1769i | 2.55701i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 9.21539i | − 0.321619i | −0.986985 | − | 0.160810i | \(-0.948589\pi\) | ||||
0.986985 | − | 0.160810i | \(-0.0514105\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 48.8372i | 1.70236i | 0.524877 | + | 0.851178i | \(0.324111\pi\) | ||||
−0.524877 | + | 0.851178i | \(0.675889\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.26795 | −0.0440909 | −0.0220455 | − | 0.999757i | \(-0.507018\pi\) | ||||
−0.0220455 | + | 0.999757i | \(0.507018\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.21539i | 0.320064i | 0.987112 | + | 0.160032i | \(0.0511597\pi\) | ||||
−0.987112 | + | 0.160032i | \(0.948840\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21.4641 | −0.744581 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 53.3205i | − 1.84745i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.1436 | 0.350614 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32.7846 | −1.13185 | −0.565925 | − | 0.824457i | \(-0.691481\pi\) | ||||
−0.565925 | + | 0.824457i | \(0.691481\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −20.7846 | −0.715860 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 4.73205i | − 0.162595i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −56.2487 | −1.93045 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 13.1769i | − 0.451699i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.46410 | 0.118609 | 0.0593043 | − | 0.998240i | \(-0.481112\pi\) | ||||
0.0593043 | + | 0.998240i | \(0.481112\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 43.8564i | 1.49811i | 0.662510 | + | 0.749053i | \(0.269491\pi\) | ||||
−0.662510 | + | 0.749053i | \(0.730509\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.5692i | 1.07713i | 0.842585 | + | 0.538564i | \(0.181033\pi\) | ||||
−0.842585 | + | 0.538564i | \(0.818967\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 122.354i | 4.16981i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.9808i | 0.373789i | 0.982380 | + | 0.186895i | \(0.0598423\pi\) | ||||
−0.982380 | + | 0.186895i | \(0.940158\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.6603 | 0.463927 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 41.5692i | 1.41014i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.679492 | 0.0230237 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 64.2487i | − 2.17449i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.8564 | 0.670503 | 0.335252 | − | 0.942129i | \(-0.391179\pi\) | ||||
0.335252 | + | 0.942129i | \(0.391179\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 81.9615 | 2.76449 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.3923 | −0.956561 | −0.478281 | − | 0.878207i | \(-0.658740\pi\) | ||||
−0.478281 | + | 0.878207i | \(0.658740\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.1962 | −0.545044 | −0.272522 | − | 0.962150i | \(-0.587858\pi\) | ||||
−0.272522 | + | 0.962150i | \(0.587858\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 51.3731i | 1.72494i | 0.506109 | + | 0.862469i | \(0.331083\pi\) | ||||
−0.506109 | + | 0.862469i | \(0.668917\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 67.1769 | 2.25304 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.53590i | 0.285963i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.39230 | 0.146983 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20.7846i | 0.693978i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.0000i | 1.19933i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 2.53590i | − 0.0843894i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.5885 | −1.08208 | −0.541041 | − | 0.840996i | \(-0.681970\pi\) | ||||
−0.541041 | + | 0.840996i | \(0.681970\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 53.5692i | − 1.77678i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.1769 | −0.834148 | −0.417074 | − | 0.908872i | \(-0.636944\pi\) | ||||
−0.417074 | + | 0.908872i | \(0.636944\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 4.39230i | − 0.145364i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 49.1769 | 1.62396 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.7128 | −0.518318 | −0.259159 | − | 0.965835i | \(-0.583445\pi\) | ||||
−0.259159 | + | 0.965835i | \(0.583445\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −65.0333 | −2.14292 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −56.7846 | −1.86909 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.80385i | 0.322001i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.3923 | −0.931521 | −0.465761 | − | 0.884911i | \(-0.654219\pi\) | ||||
−0.465761 | + | 0.884911i | \(0.654219\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30.7846i | 1.00892i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 77.5692 | 2.53950 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.3923i | 0.992873i | 0.868073 | + | 0.496437i | \(0.165359\pi\) | ||||
−0.868073 | + | 0.496437i | \(0.834641\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 60.1051i | 1.96146i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 20.7846i | − 0.677559i | −0.940866 | − | 0.338779i | \(-0.889986\pi\) | ||||
0.940866 | − | 0.338779i | \(-0.110014\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.7846i | 0.676840i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 56.1962 | 1.82613 | 0.913065 | − | 0.407815i | \(-0.133709\pi\) | ||||
0.913065 | + | 0.407815i | \(0.133709\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.1436i | 0.718811i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.39230 | −0.142430 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.0718i | 0.358651i | 0.983790 | + | 0.179325i | \(0.0573915\pi\) | ||||
−0.983790 | + | 0.179325i | \(0.942609\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.39230 | −0.141835 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.5692 | −0.792555 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 59.2295 | 1.90864 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.19615i | 0.0706235i | 0.999376 | + | 0.0353118i | \(0.0112424\pi\) | ||||
−0.999376 | + | 0.0353118i | \(0.988758\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.9282 | 0.608061 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 57.0333i | − 1.83029i | −0.403129 | − | 0.915143i | \(-0.632077\pi\) | ||||
0.403129 | − | 0.915143i | \(-0.367923\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −47.3205 | −1.51703 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.3205i | 0.938046i | 0.883186 | + | 0.469023i | \(0.155394\pi\) | ||||
−0.883186 | + | 0.469023i | \(0.844606\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 44.7846i | − 1.43132i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 57.7128i | − 1.84263i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 42.5885i | 1.35836i | 0.733971 | + | 0.679180i | \(0.237665\pi\) | ||||
−0.733971 | + | 0.679180i | \(0.762335\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −28.3923 | −0.903737 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 0.430781i | − 0.0136980i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.1051 | 1.01985 | 0.509926 | − | 0.860218i | \(-0.329673\pi\) | ||||
0.509926 | + | 0.860218i | \(0.329673\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 72.1051i | − 2.28819i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.3923 | 1.46926 | 0.734630 | − | 0.678468i | \(-0.237356\pi\) | ||||
0.734630 | + | 0.678468i | \(0.237356\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −24.0000 | −0.759326 |
(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 | 1600.2.f.i.1249.4 | 4 | ||
4.3 | odd | 2 | 1600.2.f.d.1249.1 | 4 | |||
5.2 | odd | 4 | 320.2.d.a.161.1 | ✓ | 4 | ||
5.3 | odd | 4 | 1600.2.d.h.801.4 | 4 | |||
5.4 | even | 2 | 1600.2.f.e.1249.1 | 4 | |||
8.3 | odd | 2 | 1600.2.f.h.1249.3 | 4 | |||
8.5 | even | 2 | 1600.2.f.e.1249.2 | 4 | |||
15.2 | even | 4 | 2880.2.k.e.1441.1 | 4 | |||
20.3 | even | 4 | 1600.2.d.b.801.1 | 4 | |||
20.7 | even | 4 | 320.2.d.b.161.4 | yes | 4 | ||
20.19 | odd | 2 | 1600.2.f.h.1249.4 | 4 | |||
40.3 | even | 4 | 1600.2.d.b.801.4 | 4 | |||
40.13 | odd | 4 | 1600.2.d.h.801.1 | 4 | |||
40.19 | odd | 2 | 1600.2.f.d.1249.2 | 4 | |||
40.27 | even | 4 | 320.2.d.b.161.1 | yes | 4 | ||
40.29 | even | 2 | inner | 1600.2.f.i.1249.3 | 4 | ||
40.37 | odd | 4 | 320.2.d.a.161.4 | yes | 4 | ||
60.47 | odd | 4 | 2880.2.k.l.1441.2 | 4 | |||
80.3 | even | 4 | 6400.2.a.ck.1.2 | 2 | |||
80.13 | odd | 4 | 6400.2.a.y.1.1 | 2 | |||
80.27 | even | 4 | 1280.2.a.m.1.2 | 2 | |||
80.37 | odd | 4 | 1280.2.a.b.1.1 | 2 | |||
80.43 | even | 4 | 6400.2.a.bf.1.1 | 2 | |||
80.53 | odd | 4 | 6400.2.a.cd.1.2 | 2 | |||
80.67 | even | 4 | 1280.2.a.c.1.1 | 2 | |||
80.77 | odd | 4 | 1280.2.a.p.1.2 | 2 | |||
120.77 | even | 4 | 2880.2.k.e.1441.3 | 4 | |||
120.107 | odd | 4 | 2880.2.k.l.1441.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
320.2.d.a.161.1 | ✓ | 4 | 5.2 | odd | 4 | ||
320.2.d.a.161.4 | yes | 4 | 40.37 | odd | 4 | ||
320.2.d.b.161.1 | yes | 4 | 40.27 | even | 4 | ||
320.2.d.b.161.4 | yes | 4 | 20.7 | even | 4 | ||
1280.2.a.b.1.1 | 2 | 80.37 | odd | 4 | |||
1280.2.a.c.1.1 | 2 | 80.67 | even | 4 | |||
1280.2.a.m.1.2 | 2 | 80.27 | even | 4 | |||
1280.2.a.p.1.2 | 2 | 80.77 | odd | 4 | |||
1600.2.d.b.801.1 | 4 | 20.3 | even | 4 | |||
1600.2.d.b.801.4 | 4 | 40.3 | even | 4 | |||
1600.2.d.h.801.1 | 4 | 40.13 | odd | 4 | |||
1600.2.d.h.801.4 | 4 | 5.3 | odd | 4 | |||
1600.2.f.d.1249.1 | 4 | 4.3 | odd | 2 | |||
1600.2.f.d.1249.2 | 4 | 40.19 | odd | 2 | |||
1600.2.f.e.1249.1 | 4 | 5.4 | even | 2 | |||
1600.2.f.e.1249.2 | 4 | 8.5 | even | 2 | |||
1600.2.f.h.1249.3 | 4 | 8.3 | odd | 2 | |||
1600.2.f.h.1249.4 | 4 | 20.19 | odd | 2 | |||
1600.2.f.i.1249.3 | 4 | 40.29 | even | 2 | inner | ||
1600.2.f.i.1249.4 | 4 | 1.1 | even | 1 | trivial | ||
2880.2.k.e.1441.1 | 4 | 15.2 | even | 4 | |||
2880.2.k.e.1441.3 | 4 | 120.77 | even | 4 | |||
2880.2.k.l.1441.2 | 4 | 60.47 | odd | 4 | |||
2880.2.k.l.1441.4 | 4 | 120.107 | odd | 4 | |||
6400.2.a.y.1.1 | 2 | 80.13 | odd | 4 | |||
6400.2.a.bf.1.1 | 2 | 80.43 | even | 4 | |||
6400.2.a.cd.1.2 | 2 | 80.53 | odd | 4 | |||
6400.2.a.ck.1.2 | 2 | 80.3 | even | 4 |