Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(2591,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.2591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.h (of order \(2\), degree \(1\), 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: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.8 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.2591 |
Dual form | 6048.2.h.a.2591.1 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.24969i | 1.45331i | 0.687005 | + | 0.726653i | \(0.258925\pi\) | ||||
−0.687005 | + | 0.726653i | \(0.741075\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.07812 | −1.83262 | −0.916310 | − | 0.400469i | \(-0.868847\pi\) | ||||
−0.916310 | + | 0.400469i | \(0.868847\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.0963763 | 0.0267300 | 0.0133650 | − | 0.999911i | \(-0.495746\pi\) | ||||
0.0133650 | + | 0.999911i | \(0.495746\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 3.41421i | − 0.828068i | −0.910261 | − | 0.414034i | \(-0.864119\pi\) | ||||
0.910261 | − | 0.414034i | \(-0.135881\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 5.89898i | − 1.35332i | −0.736296 | − | 0.676659i | \(-0.763427\pi\) | ||||
0.736296 | − | 0.676659i | \(-0.236573\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.54222 | 1.57266 | 0.786331 | − | 0.617806i | \(-0.211978\pi\) | ||||
0.786331 | + | 0.617806i | \(0.211978\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.56048 | −1.11210 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.81382i | 1.07960i | 0.841794 | + | 0.539799i | \(0.181500\pi\) | ||||
−0.841794 | + | 0.539799i | \(0.818500\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.07055i | 0.192277i | 0.995368 | + | 0.0961384i | \(0.0306492\pi\) | ||||
−0.995368 | + | 0.0961384i | \(0.969351\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.24969 | 0.549298 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.82843 | 1.28699 | 0.643493 | − | 0.765452i | \(-0.277485\pi\) | ||||
0.643493 | + | 0.765452i | \(0.277485\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 0.614014i | − 0.0958929i | −0.998850 | − | 0.0479465i | \(-0.984732\pi\) | ||||
0.998850 | − | 0.0479465i | \(-0.0152677\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 7.75323i | − 1.18236i | −0.806541 | − | 0.591178i | \(-0.798663\pi\) | ||||
0.806541 | − | 0.591178i | \(-0.201337\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.585786 | 0.0854457 | 0.0427229 | − | 0.999087i | \(-0.486397\pi\) | ||||
0.0427229 | + | 0.999087i | \(0.486397\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.39836i | 1.01624i | 0.861286 | + | 0.508121i | \(0.169660\pi\) | ||||
−0.861286 | + | 0.508121i | \(0.830340\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 19.7520i | − 2.66336i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.01461 | −1.17360 | −0.586801 | − | 0.809731i | \(-0.699613\pi\) | ||||
−0.586801 | + | 0.809731i | \(0.699613\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.92820 | −1.14314 | −0.571570 | − | 0.820554i | \(-0.693665\pi\) | ||||
−0.571570 | + | 0.820554i | \(0.693665\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.313193i | 0.0388468i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.4887i | 1.28140i | 0.767793 | + | 0.640698i | \(0.221355\pi\) | ||||
−0.767793 | + | 0.640698i | \(0.778645\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.19980 | 1.09182 | 0.545908 | − | 0.837845i | \(-0.316185\pi\) | ||||
0.545908 | + | 0.837845i | \(0.316185\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.8238 | 1.38387 | 0.691935 | − | 0.721960i | \(-0.256759\pi\) | ||||
0.691935 | + | 0.721960i | \(0.256759\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.07812i | 0.692666i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 11.0951i | − 1.24830i | −0.781305 | − | 0.624150i | \(-0.785445\pi\) | ||||
0.781305 | − | 0.624150i | \(-0.214555\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.6118 | 1.71361 | 0.856807 | − | 0.515637i | \(-0.172445\pi\) | ||||
0.856807 | + | 0.515637i | \(0.172445\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.0951 | 1.20344 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.01362i | 0.319443i | 0.987162 | + | 0.159721i | \(0.0510596\pi\) | ||||
−0.987162 | + | 0.159721i | \(0.948940\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 0.0963763i | − 0.0101030i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 19.1698 | 1.96678 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.5851 | 1.88703 | 0.943513 | − | 0.331335i | \(-0.107499\pi\) | ||||
0.943513 | + | 0.331335i | \(0.107499\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 0.858380i | − 0.0854120i | −0.999088 | − | 0.0427060i | \(-0.986402\pi\) | ||||
0.999088 | − | 0.0427060i | \(-0.0135979\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.3843i | 1.61439i | 0.590285 | + | 0.807195i | \(0.299015\pi\) | ||||
−0.590285 | + | 0.807195i | \(0.700985\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.34366 | −0.516591 | −0.258296 | − | 0.966066i | \(-0.583161\pi\) | ||||
−0.258296 | + | 0.966066i | \(0.583161\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.85425 | −0.177605 | −0.0888025 | − | 0.996049i | \(-0.528304\pi\) | ||||
−0.0888025 | + | 0.996049i | \(0.528304\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.0413286i | 0.00388787i | 0.999998 | + | 0.00194393i | \(0.000618774\pi\) | ||||
−0.999998 | + | 0.00194393i | \(0.999381\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 24.5099i | 2.28556i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.41421 | −0.312980 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 25.9435 | 2.35850 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1.82138i | − 0.162909i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 7.63103i | − 0.677144i | −0.940940 | − | 0.338572i | \(-0.890056\pi\) | ||||
0.940940 | − | 0.338572i | \(-0.109944\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.05594 | 0.0922579 | 0.0461290 | − | 0.998935i | \(-0.485311\pi\) | ||||
0.0461290 | + | 0.998935i | \(0.485311\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.89898 | −0.511506 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.7420i | 1.77211i | 0.463580 | + | 0.886055i | \(0.346565\pi\) | ||||
−0.463580 | + | 0.886055i | \(0.653435\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 2.53590i | − 0.215092i | −0.994200 | − | 0.107546i | \(-0.965701\pi\) | ||||
0.994200 | − | 0.107546i | \(-0.0342993\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.585786 | −0.0489859 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.8931 | −1.56899 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 12.6848i | − 1.03918i | −0.854415 | − | 0.519591i | \(-0.826084\pi\) | ||||
0.854415 | − | 0.519591i | \(-0.173916\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.47896 | −0.279437 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.7532 | 1.09763 | 0.548814 | − | 0.835945i | \(-0.315080\pi\) | ||||
0.548814 | + | 0.835945i | \(0.315080\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 7.54222i | − 0.594410i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.70158i | 0.446582i | 0.974752 | + | 0.223291i | \(0.0716801\pi\) | ||||
−0.974752 | + | 0.223291i | \(0.928320\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.95544 | 0.692992 | 0.346496 | − | 0.938051i | \(-0.387371\pi\) | ||||
0.346496 | + | 0.938051i | \(0.387371\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9907 | −0.999286 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.82138i | 0.138477i | 0.997600 | + | 0.0692384i | \(0.0220569\pi\) | ||||
−0.997600 | + | 0.0692384i | \(0.977943\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.56048i | 0.420333i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.11563 | −0.307617 | −0.153808 | − | 0.988101i | \(-0.549154\pi\) | ||||
−0.153808 | + | 0.988101i | \(0.549154\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.4548 | −1.44606 | −0.723032 | − | 0.690814i | \(-0.757252\pi\) | ||||
−0.723032 | + | 0.690814i | \(0.757252\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 25.4400i | 1.87038i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.7520i | 1.51754i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.80071 | −0.419725 | −0.209862 | − | 0.977731i | \(-0.567302\pi\) | ||||
−0.209862 | + | 0.977731i | \(0.567302\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.1210 | −1.52032 | −0.760160 | − | 0.649736i | \(-0.774879\pi\) | ||||
−0.760160 | + | 0.649736i | \(0.774879\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.3971i | 1.45323i | 0.687043 | + | 0.726617i | \(0.258909\pi\) | ||||
−0.687043 | + | 0.726617i | \(0.741091\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.8956i | 1.12681i | 0.826182 | + | 0.563404i | \(0.190508\pi\) | ||||
−0.826182 | + | 0.563404i | \(0.809492\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.81382 | 0.408050 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.99536 | 0.139362 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 35.8547i | 2.48012i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 8.19275i | − 0.564012i | −0.959413 | − | 0.282006i | \(-0.909000\pi\) | ||||
0.959413 | − | 0.282006i | \(-0.0909999\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 25.1956 | 1.71832 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.07055 | 0.0726738 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 0.329049i | − 0.0221343i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 5.61088i | − 0.375732i | −0.982195 | − | 0.187866i | \(-0.939843\pi\) | ||||
0.982195 | − | 0.187866i | \(-0.0601571\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.9988 | 0.862758 | 0.431379 | − | 0.902171i | \(-0.358027\pi\) | ||||
0.431379 | + | 0.902171i | \(0.358027\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.60521 | 0.502566 | 0.251283 | − | 0.967914i | \(-0.419147\pi\) | ||||
0.251283 | + | 0.967914i | \(0.419147\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.898979i | 0.0588941i | 0.999566 | + | 0.0294471i | \(0.00937464\pi\) | ||||
−0.999566 | + | 0.0294471i | \(0.990625\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.90362i | 0.124179i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.7712 | 0.696734 | 0.348367 | − | 0.937358i | \(-0.386736\pi\) | ||||
0.348367 | + | 0.937358i | \(0.386736\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.3463 | −0.988544 | −0.494272 | − | 0.869307i | \(-0.664565\pi\) | ||||
−0.494272 | + | 0.869307i | \(0.664565\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 3.24969i | − 0.207615i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 0.568522i | − 0.0361742i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.6982 | 0.864622 | 0.432311 | − | 0.901725i | \(-0.357698\pi\) | ||||
0.432311 | + | 0.901725i | \(0.357698\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −45.8425 | −2.88209 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 23.3419i | − 1.45603i | −0.685561 | − | 0.728015i | \(-0.740443\pi\) | ||||
0.685561 | − | 0.728015i | \(-0.259557\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 7.82843i | − 0.486435i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 27.3543 | 1.68674 | 0.843368 | − | 0.537336i | \(-0.180569\pi\) | ||||
0.843368 | + | 0.537336i | \(0.180569\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −24.0424 | −1.47691 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.47720i | 0.577835i | 0.957354 | + | 0.288918i | \(0.0932954\pi\) | ||||
−0.957354 | + | 0.288918i | \(0.906705\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 21.6544i | − 1.31541i | −0.753276 | − | 0.657705i | \(-0.771528\pi\) | ||||
0.753276 | − | 0.657705i | \(-0.228472\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 33.7972 | 2.03805 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.37519 | −0.322964 | −0.161482 | − | 0.986876i | \(-0.551627\pi\) | ||||
−0.161482 | + | 0.986876i | \(0.551627\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.0958i | 1.25847i | 0.777215 | + | 0.629235i | \(0.216632\pi\) | ||||
−0.777215 | + | 0.629235i | \(0.783368\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.2326i | 1.79714i | 0.438827 | + | 0.898571i | \(0.355394\pi\) | ||||
−0.438827 | + | 0.898571i | \(0.644606\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.614014 | −0.0362441 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.34315 | 0.314303 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 24.6009i | − 1.43720i | −0.695423 | − | 0.718600i | \(-0.744783\pi\) | ||||
0.695423 | − | 0.718600i | \(-0.255217\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 29.2947i | − 1.70560i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.726891 | 0.0420372 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.75323 | −0.446889 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 29.0139i | − 1.66133i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.6143i | 1.00530i | 0.864490 | + | 0.502650i | \(0.167642\pi\) | ||||
−0.864490 | + | 0.502650i | \(0.832358\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.34242 | −0.132826 | −0.0664131 | − | 0.997792i | \(-0.521156\pi\) | ||||
−0.0664131 | + | 0.997792i | \(0.521156\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.97418 | 0.563774 | 0.281887 | − | 0.959448i | \(-0.409040\pi\) | ||||
0.281887 | + | 0.959448i | \(0.409040\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.0144i | 1.57345i | 0.617307 | + | 0.786723i | \(0.288224\pi\) | ||||
−0.617307 | + | 0.786723i | \(0.711776\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 35.3370i | − 1.97849i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.1404 | −1.12064 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.535898 | −0.0297263 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 0.585786i | − 0.0322955i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 28.1810i | − 1.54897i | −0.632594 | − | 0.774483i | \(-0.718010\pi\) | ||||
0.632594 | − | 0.774483i | \(-0.281990\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −34.0850 | −1.86226 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.12096 | 0.224483 | 0.112241 | − | 0.993681i | \(-0.464197\pi\) | ||||
0.112241 | + | 0.993681i | \(0.464197\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 6.50694i | − 0.352371i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.4619 | −0.883719 | −0.441860 | − | 0.897084i | \(-0.645681\pi\) | ||||
−0.441860 | + | 0.897084i | \(0.645681\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.4032 | 1.14569 | 0.572843 | − | 0.819665i | \(-0.305841\pi\) | ||||
0.572843 | + | 0.819665i | \(0.305841\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.7118i | 0.889479i | 0.895660 | + | 0.444740i | \(0.146704\pi\) | ||||
−0.895660 | + | 0.444740i | \(0.853296\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 29.8965i | 1.58674i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.9973 | 1.26653 | 0.633264 | − | 0.773936i | \(-0.281715\pi\) | ||||
0.633264 | + | 0.773936i | \(0.281715\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.7980 | −0.831472 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 38.4236i | 2.01118i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.8661i | 1.08920i | 0.838695 | + | 0.544602i | \(0.183319\pi\) | ||||
−0.838695 | + | 0.544602i | \(0.816681\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.39836 | 0.384104 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.3184 | 1.20738 | 0.603689 | − | 0.797220i | \(-0.293697\pi\) | ||||
0.603689 | + | 0.797220i | \(0.293697\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.560314i | 0.0288576i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.8117i | 0.606725i | 0.952875 | + | 0.303363i | \(0.0981093\pi\) | ||||
−0.952875 | + | 0.303363i | \(0.901891\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.69818 | 0.291164 | 0.145582 | − | 0.989346i | \(-0.453495\pi\) | ||||
0.145582 | + | 0.989346i | \(0.453495\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −19.7520 | −1.00665 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 3.72940i | − 0.189088i | −0.995521 | − | 0.0945440i | \(-0.969861\pi\) | ||||
0.995521 | − | 0.0945440i | \(-0.0301393\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 25.7507i | − 1.30227i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 36.0557 | 1.81416 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.4947 | 1.68105 | 0.840525 | − | 0.541773i | \(-0.182247\pi\) | ||||
0.840525 | + | 0.541773i | \(0.182247\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.79744i | 0.339448i | 0.985492 | + | 0.169724i | \(0.0542876\pi\) | ||||
−0.985492 | + | 0.169724i | \(0.945712\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.103176i | 0.00513956i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −47.5821 | −2.35856 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.411329 | 0.0203389 | 0.0101695 | − | 0.999948i | \(-0.496763\pi\) | ||||
0.0101695 | + | 0.999948i | \(0.496763\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.01461i | 0.443580i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 50.7334i | 2.49041i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.1396 | 0.983886 | 0.491943 | − | 0.870627i | \(-0.336287\pi\) | ||||
0.491943 | + | 0.870627i | \(0.336287\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.03047 | −0.293907 | −0.146954 | − | 0.989143i | \(-0.546947\pi\) | ||||
−0.146954 | + | 0.989143i | \(0.546947\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 18.9847i | 0.920891i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.92820i | 0.432066i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.8255 | 0.665949 | 0.332974 | − | 0.942936i | \(-0.391948\pi\) | ||||
0.332974 | + | 0.942936i | \(0.391948\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.55923 | −0.315217 | −0.157608 | − | 0.987502i | \(-0.550378\pi\) | ||||
−0.157608 | + | 0.987502i | \(0.550378\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 44.4914i | − 2.12831i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 10.9799i | − 0.524040i | −0.965062 | − | 0.262020i | \(-0.915611\pi\) | ||||
0.965062 | − | 0.262020i | \(-0.0843886\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.9204 | −0.851425 | −0.425713 | − | 0.904858i | \(-0.639977\pi\) | ||||
−0.425713 | + | 0.904858i | \(0.639977\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.79331 | −0.464248 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 9.14537i | − 0.431597i | −0.976438 | − | 0.215798i | \(-0.930765\pi\) | ||||
0.976438 | − | 0.215798i | \(-0.0692354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.73205i | 0.175735i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.313193 | 0.0146827 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.3629 | 1.13965 | 0.569823 | − | 0.821767i | \(-0.307012\pi\) | ||||
0.569823 | + | 0.821767i | \(0.307012\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 19.4651i | − 0.906580i | −0.891363 | − | 0.453290i | \(-0.850250\pi\) | ||||
0.891363 | − | 0.453290i | \(-0.149750\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.07860i | 0.143075i | 0.997438 | + | 0.0715373i | \(0.0227905\pi\) | ||||
−0.997438 | + | 0.0715373i | \(0.977210\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 31.8829 | 1.47537 | 0.737683 | − | 0.675148i | \(-0.235920\pi\) | ||||
0.737683 | + | 0.675148i | \(0.235920\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.4887 | 0.484322 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 47.1250i | 2.16681i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 32.8011i | 1.50502i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.5851 | −1.12332 | −0.561660 | − | 0.827368i | \(-0.689837\pi\) | ||||
−0.561660 | + | 0.827368i | \(0.689837\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.754475 | 0.0344011 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 60.3957i | 2.74243i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 35.5298i | − 1.61001i | −0.593269 | − | 0.805004i | \(-0.702163\pi\) | ||||
0.593269 | − | 0.805004i | \(-0.297837\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.2772 | 1.59204 | 0.796019 | − | 0.605271i | \(-0.206935\pi\) | ||||
0.796019 | + | 0.605271i | \(0.206935\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.8496 | 0.893981 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 9.19980i | − 0.412667i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 35.4169i | 1.58548i | 0.609562 | + | 0.792739i | \(0.291346\pi\) | ||||
−0.609562 | + | 0.792739i | \(0.708654\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.90074 | −0.307689 | −0.153844 | − | 0.988095i | \(-0.549165\pi\) | ||||
−0.153844 | + | 0.988095i | \(0.549165\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.78947 | 0.124130 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 34.0285i | 1.50829i | 0.656710 | + | 0.754143i | \(0.271948\pi\) | ||||
−0.656710 | + | 0.754143i | \(0.728052\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 11.8238i | − 0.523053i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −53.2438 | −2.34620 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.56048 | −0.156590 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.4125i | 1.11334i | 0.830733 | + | 0.556671i | \(0.187921\pi\) | ||||
−0.830733 | + | 0.556671i | \(0.812079\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.46750i | 0.282804i | 0.989952 | + | 0.141402i | \(0.0451610\pi\) | ||||
−0.989952 | + | 0.141402i | \(0.954839\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.65509 | 0.159218 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 33.8850 | 1.47326 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 0.0591764i | − 0.00256322i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 17.3652i | − 0.750765i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.07812 | 0.261803 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.6823 | −1.27614 | −0.638072 | − | 0.769977i | \(-0.720268\pi\) | ||||
−0.638072 | + | 0.769977i | \(0.720268\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 6.02574i | − 0.258114i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 0.327058i | − 0.0139840i | −0.999976 | − | 0.00699199i | \(-0.997774\pi\) | ||||
0.999976 | − | 0.00699199i | \(-0.00222564\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 34.2956 | 1.46104 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.0951 | −0.471813 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.19632i | 0.0506895i | 0.999679 | + | 0.0253448i | \(0.00806836\pi\) | ||||
−0.999679 | + | 0.0253448i | \(0.991932\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 0.747228i | − 0.0316044i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.1156 | 0.679193 | 0.339596 | − | 0.940571i | \(-0.389709\pi\) | ||||
0.339596 | + | 0.940571i | \(0.389709\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.134305 | −0.00565026 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 32.6098i | − 1.36707i | −0.729916 | − | 0.683537i | \(-0.760441\pi\) | ||||
0.729916 | − | 0.683537i | \(-0.239559\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 36.9189i | − 1.54501i | −0.635010 | − | 0.772504i | \(-0.719004\pi\) | ||||
0.635010 | − | 0.772504i | \(-0.280996\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −41.9383 | −1.74895 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 43.5866 | 1.81454 | 0.907268 | − | 0.420554i | \(-0.138164\pi\) | ||||
0.907268 | + | 0.420554i | \(0.138164\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 15.6118i | − 0.647686i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 44.9681i | − 1.86239i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.6120 | 1.05712 | 0.528560 | − | 0.848896i | \(-0.322732\pi\) | ||||
0.528560 | + | 0.848896i | \(0.322732\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.31517 | 0.260212 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 24.4984i | − 1.00603i | −0.864278 | − | 0.503014i | \(-0.832224\pi\) | ||||
0.864278 | − | 0.503014i | \(-0.167776\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 11.0951i | − 0.454856i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.9534 | −1.55073 | −0.775367 | − | 0.631510i | \(-0.782435\pi\) | ||||
−0.775367 | + | 0.631510i | \(0.782435\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.4181 | 0.669709 | 0.334855 | − | 0.942270i | \(-0.391313\pi\) | ||||
0.334855 | + | 0.942270i | \(0.391313\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 84.3083i | 3.42762i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.921404i | 0.0373986i | 0.999825 | + | 0.0186993i | \(0.00595252\pi\) | ||||
−0.999825 | + | 0.0186993i | \(0.994047\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.0564559 | 0.00228396 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.7614 | 1.40400 | 0.702000 | − | 0.712177i | \(-0.252291\pi\) | ||||
0.702000 | + | 0.712177i | \(0.252291\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 47.4692i | − 1.91104i | −0.294929 | − | 0.955519i | \(-0.595296\pi\) | ||||
0.294929 | − | 0.955519i | \(-0.404704\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.2138i | 1.05362i | 0.849982 | + | 0.526811i | \(0.176612\pi\) | ||||
−0.849982 | + | 0.526811i | \(0.823388\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.01362 | 0.120738 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.8835 | −0.875339 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 26.7279i | − 1.06571i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 5.00568i | − 0.199273i | −0.995024 | − | 0.0996364i | \(-0.968232\pi\) | ||||
0.995024 | − | 0.0996364i | \(-0.0317680\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 24.7985 | 0.984097 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.0963763 | −0.00381857 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.17011i | 0.362198i | 0.983465 | + | 0.181099i | \(0.0579654\pi\) | ||||
−0.983465 | + | 0.181099i | \(0.942035\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 38.4655i | − 1.51693i | −0.651714 | − | 0.758465i | \(-0.725950\pi\) | ||||
0.651714 | − | 0.758465i | \(-0.274050\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.65310 | −0.143618 | −0.0718091 | − | 0.997418i | \(-0.522877\pi\) | ||||
−0.0718091 | + | 0.997418i | \(0.522877\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 54.7919 | 2.15077 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 48.3662i | − 1.89272i | −0.323121 | − | 0.946358i | \(-0.604732\pi\) | ||||
0.323121 | − | 0.946358i | \(-0.395268\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.43148i | 0.134079i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.6738 | −0.805338 | −0.402669 | − | 0.915346i | \(-0.631917\pi\) | ||||
−0.402669 | + | 0.915346i | \(0.631917\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.9729 | 1.28250 | 0.641249 | − | 0.767333i | \(-0.278416\pi\) | ||||
0.641249 | + | 0.767333i | \(0.278416\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 19.1698i | − 0.743375i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 43.8491i | 1.69784i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 54.2667 | 2.09494 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.0000 | −0.385472 | −0.192736 | − | 0.981251i | \(-0.561736\pi\) | ||||
−0.192736 | + | 0.981251i | \(0.561736\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 15.7446i | − 0.605114i | −0.953131 | − | 0.302557i | \(-0.902160\pi\) | ||||
0.953131 | − | 0.302557i | \(-0.0978402\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 18.5851i | − 0.713229i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.4490 | 1.31816 | 0.659078 | − | 0.752075i | \(-0.270947\pi\) | ||||
0.659078 | + | 0.752075i | \(0.270947\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −67.4051 | −2.57542 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.713026i | 0.0271641i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 14.1504i | − 0.538306i | −0.963097 | − | 0.269153i | \(-0.913256\pi\) | ||||
0.963097 | − | 0.269153i | \(-0.0867438\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.24088 | 0.312594 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.09638 | −0.0794059 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.9289i | 0.563858i | 0.959435 | + | 0.281929i | \(0.0909743\pi\) | ||||
−0.959435 | + | 0.281929i | \(0.909026\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 46.1797i | − 1.74170i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.858380 | −0.0322827 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −44.6389 | −1.67645 | −0.838224 | − | 0.545326i | \(-0.816406\pi\) | ||||
−0.838224 | + | 0.545326i | \(0.816406\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.07434i | 0.302386i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 1.90362i | − 0.0711915i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.2268 | −0.866214 | −0.433107 | − | 0.901343i | \(-0.642583\pi\) | ||||
−0.433107 | + | 0.901343i | \(0.642583\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.3843 | 0.610182 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 32.3276i | − 1.20062i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.7153i | 1.25043i | 0.780452 | + | 0.625216i | \(0.214989\pi\) | ||||
−0.780452 | + | 0.625216i | \(0.785011\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26.4712 | −0.979072 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.2984 | 0.675867 | 0.337934 | − | 0.941170i | \(-0.390272\pi\) | ||||
0.337934 | + | 0.941170i | \(0.390272\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 63.7514i | − 2.34831i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 14.3246i | − 0.526938i | −0.964668 | − | 0.263469i | \(-0.915133\pi\) | ||||
0.964668 | − | 0.263469i | \(-0.0848666\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −48.2374 | −1.76966 | −0.884829 | − | 0.465916i | \(-0.845725\pi\) | ||||
−0.884829 | + | 0.465916i | \(0.845725\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 41.2218 | 1.51025 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.34366i | 0.195253i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 39.4689i | − 1.44024i | −0.693850 | − | 0.720120i | \(-0.744087\pi\) | ||||
0.693850 | − | 0.720120i | \(-0.255913\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.3112 | 1.28341 | 0.641704 | − | 0.766952i | \(-0.278228\pi\) | ||||
0.641704 | + | 0.766952i | \(0.278228\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 32.5093i | − 1.17846i | −0.807965 | − | 0.589231i | \(-0.799431\pi\) | ||||
0.807965 | − | 0.589231i | \(-0.200569\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.85425i | 0.0671284i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.868795 | −0.0313704 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −39.2362 | −1.41489 | −0.707447 | − | 0.706766i | \(-0.750153\pi\) | ||||
−0.707447 | + | 0.706766i | \(0.750153\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 7.29301i | − 0.262311i | −0.991362 | − | 0.131156i | \(-0.958131\pi\) | ||||
0.991362 | − | 0.131156i | \(-0.0418688\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 5.95278i | − 0.213830i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.62206 | −0.129774 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −55.9175 | −2.00088 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 44.6937i | 1.59519i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 21.3044i | − 0.759421i | −0.925105 | − | 0.379710i | \(-0.876024\pi\) | ||||
0.925105 | − | 0.379710i | \(-0.123976\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.0413286 | 0.00146948 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.860467 | −0.0305561 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 9.71735i | − 0.344206i | −0.985079 | − | 0.172103i | \(-0.944944\pi\) | ||||
0.985079 | − | 0.172103i | \(-0.0550562\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 2.00000i | − 0.0707549i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −71.8663 | −2.53611 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24.5099 | 0.863859 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.1981i | 1.09687i | 0.836195 | + | 0.548433i | \(0.184775\pi\) | ||||
−0.836195 | + | 0.548433i | \(0.815225\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 9.29945i | − 0.326548i | −0.986581 | − | 0.163274i | \(-0.947795\pi\) | ||||
0.986581 | − | 0.163274i | \(-0.0522054\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.5284 | −0.649020 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −45.7361 | −1.60011 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 46.4539i | 1.62125i | 0.585565 | + | 0.810626i | \(0.300873\pi\) | ||||
−0.585565 | + | 0.810626i | \(0.699127\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.9282i | 0.590080i | 0.955485 | + | 0.295040i | \(0.0953330\pi\) | ||||
−0.955485 | + | 0.295040i | \(0.904667\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.0242 | 0.452895 | 0.226447 | − | 0.974023i | \(-0.427289\pi\) | ||||
0.226447 | + | 0.974023i | \(0.427289\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44.9632 | 1.56164 | 0.780819 | − | 0.624758i | \(-0.214802\pi\) | ||||
0.780819 | + | 0.624758i | \(0.214802\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.41421i | 0.118295i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29.1024i | 1.00713i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.08392 | 0.140993 | 0.0704963 | − | 0.997512i | \(-0.477542\pi\) | ||||
0.0704963 | + | 0.997512i | \(0.477542\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.80045 | −0.165533 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 42.2158i | − 1.45227i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 25.9435i | − 0.891429i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 59.0437 | 2.02399 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.1515 | 1.47748 | 0.738740 | − | 0.673990i | \(-0.235421\pi\) | ||||
0.738740 | + | 0.673990i | \(0.235421\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 0.542431i | − 0.0185291i | −0.999957 | − | 0.00926455i | \(-0.997051\pi\) | ||||
0.999957 | − | 0.00926455i | \(-0.00294904\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 38.6159i | − 1.31756i | −0.752337 | − | 0.658778i | \(-0.771074\pi\) | ||||
0.752337 | − | 0.658778i | \(-0.228926\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.6834 | 1.07851 | 0.539257 | − | 0.842141i | \(-0.318705\pi\) | ||||
0.539257 | + | 0.842141i | \(0.318705\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.91891 | −0.201249 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 67.4375i | 2.28766i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.01086i | 0.0342517i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.82138 | −0.0615738 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.4999 | −0.894838 | −0.447419 | − | 0.894324i | \(-0.647657\pi\) | ||||
−0.447419 | + | 0.894324i | \(0.647657\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.8866i | 0.838451i | 0.907882 | + | 0.419226i | \(0.137698\pi\) | ||||
−0.907882 | + | 0.419226i | \(0.862302\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.8978i | 1.51093i | 0.655187 | + | 0.755466i | \(0.272590\pi\) | ||||
−0.655187 | + | 0.755466i | \(0.727410\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.7844 | 0.630718 | 0.315359 | − | 0.948972i | \(-0.397875\pi\) | ||||
0.315359 | + | 0.948972i | \(0.397875\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.63103 | −0.255937 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 3.45554i | − 0.115635i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 13.3745i | − 0.447061i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.22399 | −0.207582 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.2596 | 0.841518 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 63.2221i | − 2.10157i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 54.7660i | 1.81848i | 0.416276 | + | 0.909238i | \(0.363335\pi\) | ||||
−0.416276 | + | 0.909238i | \(0.636665\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.32405 | −0.242657 | −0.121328 | − | 0.992612i | \(-0.538715\pi\) | ||||
−0.121328 | + | 0.992612i | \(0.538715\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −94.8902 | −3.14041 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 1.05594i | − 0.0348702i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.4838i | 1.00557i | 0.864412 | + | 0.502784i | \(0.167691\pi\) | ||||
−0.864412 | + | 0.502784i | \(0.832309\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.886643 | 0.0291842 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −43.5298 | −1.43125 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 20.7385i | − 0.680408i | −0.940352 | − | 0.340204i | \(-0.889504\pi\) | ||||
0.940352 | − | 0.340204i | \(-0.110496\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.89898i | 0.193331i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −67.4375 | −2.20544 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.5402 | 1.25905 | 0.629527 | − | 0.776979i | \(-0.283249\pi\) | ||||
0.629527 | + | 0.776979i | \(0.283249\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 44.2505i | − 1.44253i | −0.692662 | − | 0.721263i | \(-0.743562\pi\) | ||||
0.692662 | − | 0.721263i | \(-0.256438\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 4.63103i | − 0.150807i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.9046 | 0.581820 | 0.290910 | − | 0.956750i | \(-0.406042\pi\) | ||||
0.290910 | + | 0.956750i | \(0.406042\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.13953 | 0.0369908 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.8668i | 0.708334i | 0.935182 | + | 0.354167i | \(0.115235\pi\) | ||||
−0.935182 | + | 0.354167i | \(0.884765\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 18.8505i | − 0.609988i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20.7420 | 0.669795 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.8539 | 0.963030 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 68.6365i | − 2.20949i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 42.8761i | − 1.37880i | −0.724379 | − | 0.689402i | \(-0.757874\pi\) | ||||
0.724379 | − | 0.689402i | \(-0.242126\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.19045 | −0.230753 | −0.115376 | − | 0.993322i | \(-0.536807\pi\) | ||||
−0.115376 | + | 0.993322i | \(0.536807\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.53590 | −0.0812972 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.78834i | 0.0572142i | 0.999591 | + | 0.0286071i | \(0.00910716\pi\) | ||||
−0.999591 | + | 0.0286071i | \(0.990893\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 18.3171i | − 0.585417i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −32.6201 | −1.04042 | −0.520211 | − | 0.854038i | \(-0.674147\pi\) | ||||
−0.520211 | + | 0.854038i | \(0.674147\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −66.2843 | −2.11199 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 58.4766i | − 1.85945i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 21.3866i | − 0.679369i | −0.940539 | − | 0.339684i | \(-0.889680\pi\) | ||||
0.940539 | − | 0.339684i | \(-0.110320\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −51.6557 | −1.63760 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.0560 | 0.635179 | 0.317589 | − | 0.948228i | \(-0.397127\pi\) | ||||
0.317589 | + | 0.948228i | \(0.397127\pi\) | |||||||
\(998\) | 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 | 6048.2.h.a.2591.8 | yes | 8 | |
3.2 | odd | 2 | 6048.2.h.g.2591.1 | yes | 8 | ||
4.3 | odd | 2 | 6048.2.h.g.2591.8 | yes | 8 | ||
12.11 | even | 2 | inner | 6048.2.h.a.2591.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.h.a.2591.1 | ✓ | 8 | 12.11 | even | 2 | inner | |
6048.2.h.a.2591.8 | yes | 8 | 1.1 | even | 1 | trivial | |
6048.2.h.g.2591.1 | yes | 8 | 3.2 | odd | 2 | ||
6048.2.h.g.2591.8 | yes | 8 | 4.3 | odd | 2 |