Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1301,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.1301");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.d (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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 6x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1301.1 | ||
Root | \(-2.28825i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1301 |
Dual form | 2100.2.d.f.1301.3 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −1.00000 | − | 1.41421i | −0.577350 | − | 0.816497i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.23607 | + | 1.41421i | −0.845154 | + | 0.534522i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | + | 2.82843i | −0.333333 | + | 0.942809i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.82843i | − | 0.852803i | −0.904534 | − | 0.426401i | \(-0.859781\pi\) | ||
0.904534 | − | 0.426401i | \(-0.140219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.82843i | 0.784465i | 0.919866 | + | 0.392232i | \(0.128297\pi\) | ||||
−0.919866 | + | 0.392232i | \(0.871703\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.32456i | − | 1.45095i | −0.688247 | − | 0.725476i | \(-0.741620\pi\) | ||
0.688247 | − | 0.725476i | \(-0.258380\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.23607 | + | 1.74806i | 0.924386 | + | 0.381459i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.32456i | 1.31876i | 0.751809 | + | 0.659380i | \(0.229181\pi\) | ||||
−0.751809 | + | 0.659380i | \(0.770819\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000 | − | 1.41421i | 0.962250 | − | 0.272166i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.65685i | 1.05045i | 0.850963 | + | 0.525226i | \(0.176019\pi\) | ||||
−0.850963 | + | 0.525226i | \(0.823981\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.32456i | − | 1.13592i | −0.823055 | − | 0.567962i | \(-0.807732\pi\) | ||
0.823055 | − | 0.567962i | \(-0.192268\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.00000 | + | 2.82843i | −0.696311 | + | 0.492366i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.94427 | 1.47043 | 0.735215 | − | 0.677834i | \(-0.237081\pi\) | ||||
0.735215 | + | 0.677834i | \(0.237081\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.00000 | − | 2.82843i | 0.640513 | − | 0.452911i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.47214 | 0.698430 | 0.349215 | − | 0.937043i | \(-0.386448\pi\) | ||||
0.349215 | + | 0.937043i | \(0.386448\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.47214 | 0.681994 | 0.340997 | − | 0.940064i | \(-0.389235\pi\) | ||||
0.340997 | + | 0.940064i | \(0.389235\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.00000 | −0.875190 | −0.437595 | − | 0.899172i | \(-0.644170\pi\) | ||||
−0.437595 | + | 0.899172i | \(0.644170\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | − | 6.32456i | 0.428571 | − | 0.903508i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.00000 | + | 5.65685i | 0.560112 | + | 0.792118i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.32456i | 0.868744i | 0.900733 | + | 0.434372i | \(0.143030\pi\) | ||||
−0.900733 | + | 0.434372i | \(0.856970\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.94427 | + | 6.32456i | −1.18470 | + | 0.837708i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.94427 | 1.16445 | 0.582223 | − | 0.813029i | \(-0.302183\pi\) | ||||
0.582223 | + | 0.813029i | \(0.302183\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.76393 | − | 7.73877i | −0.222235 | − | 0.974993i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.47214 | 0.546358 | 0.273179 | − | 0.961963i | \(-0.411925\pi\) | ||||
0.273179 | + | 0.961963i | \(0.411925\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.94427 | − | 6.32456i | 1.07676 | − | 0.761387i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.1421i | 1.67836i | 0.543852 | + | 0.839181i | \(0.316965\pi\) | ||||
−0.543852 | + | 0.839181i | \(0.683035\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 8.48528i | − | 0.993127i | −0.868000 | − | 0.496564i | \(-0.834595\pi\) | ||
0.868000 | − | 0.496564i | \(-0.165405\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.00000 | + | 6.32456i | 0.455842 | + | 0.720750i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0000 | 1.35011 | 0.675053 | − | 0.737769i | \(-0.264121\pi\) | ||||
0.675053 | + | 0.737769i | \(0.264121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | − | 5.65685i | −0.777778 | − | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.0000 | 1.09764 | 0.548821 | − | 0.835940i | \(-0.315077\pi\) | ||||
0.548821 | + | 0.835940i | \(0.315077\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.00000 | − | 5.65685i | 0.857690 | − | 0.606478i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.47214 | 0.474045 | 0.237023 | − | 0.971504i | \(-0.423828\pi\) | ||||
0.237023 | + | 0.971504i | \(0.423828\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.00000 | − | 6.32456i | −0.419314 | − | 0.662994i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.94427 | + | 6.32456i | −0.927478 | + | 0.655826i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.48528i | 0.861550i | 0.902459 | + | 0.430775i | \(0.141760\pi\) | ||||
−0.902459 | + | 0.430775i | \(0.858240\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.00000 | + | 2.82843i | 0.804030 | + | 0.284268i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.47214 | −0.444994 | −0.222497 | − | 0.974933i | \(-0.571421\pi\) | ||||
−0.222497 | + | 0.974933i | \(0.571421\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.82843i | 0.278693i | 0.990244 | + | 0.139347i | \(0.0445002\pi\) | ||||
−0.990244 | + | 0.139347i | \(0.955500\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 18.9737i | − | 1.83425i | −0.398596 | − | 0.917127i | \(-0.630502\pi\) | ||
0.398596 | − | 0.917127i | \(-0.369498\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.94427 | − | 12.6491i | −0.848953 | − | 1.20060i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 18.9737i | − | 1.78489i | −0.451154 | − | 0.892446i | \(-0.648987\pi\) | ||
0.451154 | − | 0.892446i | \(-0.351013\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.00000 | − | 2.82843i | −0.739600 | − | 0.261488i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.94427 | − | 5.65685i | 0.819920 | − | 0.518563i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.00000 | 0.272727 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.47214 | − | 6.32456i | −0.403239 | − | 0.570266i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.47214 | 0.396838 | 0.198419 | − | 0.980117i | \(-0.436419\pi\) | ||||
0.198419 | + | 0.980117i | \(0.436419\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.47214 | − | 6.32456i | −0.393750 | − | 0.556846i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.94427 | 0.781465 | 0.390732 | − | 0.920504i | \(-0.372222\pi\) | ||||
0.390732 | + | 0.920504i | \(0.372222\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.94427 | + | 14.1421i | 0.775567 | + | 1.22628i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 6.32456i | − | 0.540343i | −0.962812 | − | 0.270172i | \(-0.912920\pi\) | ||
0.962812 | − | 0.270172i | \(-0.0870804\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 6.32456i | − | 0.536442i | −0.963357 | − | 0.268221i | \(-0.913564\pi\) | ||
0.963357 | − | 0.268221i | \(-0.0864357\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | + | 8.48528i | 0.505291 | + | 0.714590i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.00000 | 0.668994 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.9443 | + | 2.08191i | −0.985147 | + | 0.171713i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | 0.325515 | 0.162758 | − | 0.986666i | \(-0.447961\pi\) | ||||
0.162758 | + | 0.986666i | \(0.447961\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.00000 | − | 11.3137i | 0.323381 | − | 0.914659i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 2.82843i | − | 0.225733i | −0.993610 | − | 0.112867i | \(-0.963997\pi\) | ||
0.993610 | − | 0.112867i | \(-0.0360032\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.94427 | − | 6.32456i | 0.709327 | − | 0.501570i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.94427 | − | 14.1421i | −0.704907 | − | 1.11456i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.4164 | −1.05085 | −0.525427 | − | 0.850839i | \(-0.676094\pi\) | ||||
−0.525427 | + | 0.850839i | \(0.676094\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.00000 | 0.464294 | 0.232147 | − | 0.972681i | \(-0.425425\pi\) | ||||
0.232147 | + | 0.972681i | \(0.425425\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 17.8885 | + | 6.32456i | 1.36797 | + | 0.483651i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.00000 | −0.608229 | −0.304114 | − | 0.952636i | \(-0.598361\pi\) | ||||
−0.304114 | + | 0.952636i | \(0.598361\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.94427 | − | 12.6491i | −0.672293 | − | 0.950765i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.1421i | 1.05703i | 0.848923 | + | 0.528516i | \(0.177252\pi\) | ||||
−0.848923 | + | 0.528516i | \(0.822748\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.6491i | 0.940201i | 0.882613 | + | 0.470100i | \(0.155782\pi\) | ||||
−0.882613 | + | 0.470100i | \(0.844218\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.3137i | 0.827340i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.18034 | + | 10.2333i | −0.667771 | + | 0.744366i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.82843i | 0.204658i | 0.994751 | + | 0.102329i | \(0.0326294\pi\) | ||||
−0.994751 | + | 0.102329i | \(0.967371\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.9737i | 1.35182i | 0.736985 | + | 0.675909i | \(0.236249\pi\) | ||||
−0.736985 | + | 0.675909i | \(0.763751\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 18.9737i | − | 1.34501i | −0.740094 | − | 0.672504i | \(-0.765219\pi\) | ||
0.740094 | − | 0.672504i | \(-0.234781\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.47214 | − | 6.32456i | −0.315440 | − | 0.446100i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.00000 | − | 12.6491i | −0.561490 | − | 0.887794i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −17.8885 | − | 6.32456i | −1.24334 | − | 0.439587i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −17.8885 | −1.23738 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.0000 | 1.10149 | 0.550743 | − | 0.834675i | \(-0.314345\pi\) | ||||
0.550743 | + | 0.834675i | \(0.314345\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 20.0000 | − | 14.1421i | 1.37038 | − | 0.969003i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.94427 | + | 14.1421i | 0.607177 | + | 0.960031i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.0000 | + | 8.48528i | −0.810885 | + | 0.573382i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 11.3137i | − | 0.761042i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2.82843i | − | 0.189405i | −0.995506 | − | 0.0947027i | \(-0.969810\pi\) | ||
0.995506 | − | 0.0947027i | \(-0.0301901\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.00000 | 0.398234 | 0.199117 | − | 0.979976i | \(-0.436193\pi\) | ||||
0.199117 | + | 0.979976i | \(0.436193\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.6491i | 0.835877i | 0.908475 | + | 0.417938i | \(0.137247\pi\) | ||||
−0.908475 | + | 0.417938i | \(0.862753\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.94427 | − | 11.9814i | 0.325309 | − | 0.788319i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.32456i | 0.414335i | 0.978305 | + | 0.207168i | \(0.0664246\pi\) | ||||
−0.978305 | + | 0.207168i | \(0.933575\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.0000 | − | 16.9706i | −0.779484 | − | 1.10236i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.48528i | 0.548867i | 0.961606 | + | 0.274434i | \(0.0884904\pi\) | ||||
−0.961606 | + | 0.274434i | \(0.911510\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.6491i | 0.814801i | 0.913250 | + | 0.407400i | \(0.133565\pi\) | ||||
−0.913250 | + | 0.407400i | \(0.866435\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | + | 15.5563i | −0.0641500 | + | 0.997940i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.8885 | 1.13822 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.0000 | − | 14.1421i | −0.633724 | − | 0.896221i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.8328 | 1.69367 | 0.846836 | − | 0.531854i | \(-0.178504\pi\) | ||||
0.846836 | + | 0.531854i | \(0.178504\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.8885 | 1.12464 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.0000 | 1.24757 | 0.623783 | − | 0.781598i | \(-0.285595\pi\) | ||||
0.623783 | + | 0.781598i | \(0.285595\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.0000 | + | 12.6491i | −1.24274 | + | 0.785977i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.0000 | − | 5.65685i | −0.990375 | − | 0.350150i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 6.32456i | − | 0.389989i | −0.980804 | − | 0.194994i | \(-0.937531\pi\) | ||
0.980804 | − | 0.194994i | \(-0.0624689\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.47214 | − | 6.32456i | −0.273690 | − | 0.387056i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.47214 | 0.272671 | 0.136335 | − | 0.990663i | \(-0.456467\pi\) | ||||
0.136335 | + | 0.990663i | \(0.456467\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 6.32456i | − | 0.384189i | −0.981376 | − | 0.192095i | \(-0.938472\pi\) | ||
0.981376 | − | 0.192095i | \(-0.0615281\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.94427 | + | 11.9814i | −0.299241 | + | 0.725148i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.8328 | 1.61223 | 0.806114 | − | 0.591761i | \(-0.201567\pi\) | ||||
0.806114 | + | 0.591761i | \(0.201567\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 17.8885 | + | 6.32456i | 1.07096 | + | 0.378641i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.9706i | 1.01238i | 0.862422 | + | 0.506189i | \(0.168946\pi\) | ||||
−0.862422 | + | 0.506189i | \(0.831054\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 25.4558i | − | 1.51319i | −0.653882 | − | 0.756596i | \(-0.726861\pi\) | ||
0.653882 | − | 0.756596i | \(-0.273139\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.0000 | + | 6.32456i | −0.590281 | + | 0.373327i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.0000 | − | 8.48528i | 0.703452 | − | 0.497416i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −32.0000 | −1.86946 | −0.934730 | − | 0.355359i | \(-0.884359\pi\) | ||||
−0.934730 | + | 0.355359i | \(0.884359\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.00000 | − | 14.1421i | −0.232104 | − | 0.820610i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −17.8885 | −1.03452 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.0000 | + | 6.32456i | −0.576390 | + | 0.364541i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.47214 | + | 6.32456i | 0.256917 | + | 0.363336i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 8.48528i | − | 0.484281i | −0.970241 | − | 0.242140i | \(-0.922151\pi\) | ||
0.970241 | − | 0.242140i | \(-0.0778494\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.00000 | − | 2.82843i | 0.227552 | − | 0.160904i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.8885 | −1.01437 | −0.507183 | − | 0.861838i | \(-0.669313\pi\) | ||||
−0.507183 | + | 0.861838i | \(0.669313\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.4558i | 1.43885i | 0.694570 | + | 0.719425i | \(0.255594\pi\) | ||||
−0.694570 | + | 0.719425i | \(0.744406\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.9737i | 1.06567i | 0.846220 | + | 0.532834i | \(0.178873\pi\) | ||||
−0.846220 | + | 0.532834i | \(0.821127\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.0000 | 0.895828 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −26.8328 | + | 18.9737i | −1.49766 | + | 1.05901i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 25.2982i | 1.40763i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.00000 | + | 2.82843i | 0.110600 | + | 0.156412i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.4164 | − | 8.48528i | 0.739671 | − | 0.467809i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.00000 | 0.439720 | 0.219860 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.94427 | + | 25.2982i | −0.490143 | + | 1.38633i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −26.8328 | + | 18.9737i | −1.45736 | + | 1.03051i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.8885 | −0.968719 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.23607 | + | 18.3848i | 0.120736 | + | 0.992685i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.9737i | 1.01856i | 0.860601 | + | 0.509280i | \(0.170088\pi\) | ||||
−0.860601 | + | 0.509280i | \(0.829912\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.6491i | 0.677091i | 0.940950 | + | 0.338546i | \(0.109935\pi\) | ||||
−0.940950 | + | 0.338546i | \(0.890065\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.00000 | + | 14.1421i | 0.213504 | + | 0.754851i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.0000 | 1.49029 | 0.745145 | − | 0.666903i | \(-0.232380\pi\) | ||||
0.745145 | + | 0.666903i | \(0.232380\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −16.9443 | − | 6.99226i | −0.896786 | − | 0.370069i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 14.1421i | − | 0.746393i | −0.927752 | − | 0.373197i | \(-0.878262\pi\) | ||
0.927752 | − | 0.373197i | \(-0.121738\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −21.0000 | −1.10526 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.00000 | − | 4.24264i | −0.157459 | − | 0.222681i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.48528i | 0.442928i | 0.975169 | + | 0.221464i | \(0.0710835\pi\) | ||||
−0.975169 | + | 0.221464i | \(0.928916\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.47214 | + | 12.6491i | −0.232810 | + | 0.658486i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.94427 | − | 14.1421i | −0.464363 | − | 0.734223i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.8328 | 1.38935 | 0.694675 | − | 0.719323i | \(-0.255548\pi\) | ||||
0.694675 | + | 0.719323i | \(0.255548\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16.0000 | −0.824042 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.0000 | −1.23280 | −0.616399 | − | 0.787434i | \(-0.711409\pi\) | ||||
−0.616399 | + | 0.787434i | \(0.711409\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.47214 | − | 6.32456i | −0.229114 | − | 0.324017i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.0000 | −1.53293 | −0.766464 | − | 0.642287i | \(-0.777986\pi\) | ||||
−0.766464 | + | 0.642287i | \(0.777986\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.47214 | + | 12.6491i | −0.227331 | + | 0.642990i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 33.9411i | − | 1.72088i | −0.509549 | − | 0.860442i | \(-0.670188\pi\) | ||
0.509549 | − | 0.860442i | \(-0.329812\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 25.2982i | − | 1.27939i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.94427 | − | 12.6491i | −0.451179 | − | 0.638063i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.7990i | 0.993683i | 0.867841 | + | 0.496841i | \(0.165507\pi\) | ||||
−0.867841 | + | 0.496841i | \(0.834493\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.0557 | − | 26.7912i | 0.553479 | − | 1.34124i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.3137i | 0.564980i | 0.959270 | + | 0.282490i | \(0.0911603\pi\) | ||||
−0.959270 | + | 0.282490i | \(0.908840\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.8885 | 0.891092 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 25.2982i | − | 1.25399i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 37.9473i | 1.87637i | 0.346128 | + | 0.938187i | \(0.387496\pi\) | ||||
−0.346128 | + | 0.938187i | \(0.612504\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.94427 | + | 6.32456i | −0.441188 | + | 0.311967i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −20.0000 | + | 12.6491i | −0.984136 | + | 0.622422i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.94427 | + | 6.32456i | −0.438003 | + | 0.309715i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.8328 | −1.31087 | −0.655434 | − | 0.755252i | \(-0.727514\pi\) | ||||
−0.655434 | + | 0.755252i | \(0.727514\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.0000 | −1.65706 | −0.828529 | − | 0.559946i | \(-0.810822\pi\) | ||||
−0.828529 | + | 0.559946i | \(0.810822\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.00000 | − | 16.9706i | 0.291730 | − | 0.825137i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.00000 | − | 11.3137i | −0.386244 | − | 0.546231i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.82843i | 0.136241i | 0.997677 | + | 0.0681203i | \(0.0217002\pi\) | ||||
−0.997677 | + | 0.0681203i | \(0.978300\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 8.48528i | − | 0.407777i | −0.978994 | − | 0.203888i | \(-0.934642\pi\) | ||
0.978994 | − | 0.203888i | \(-0.0653579\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 40.0000 | 1.91346 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.32456i | 0.301855i | 0.988545 | + | 0.150927i | \(0.0482259\pi\) | ||||
−0.988545 | + | 0.150927i | \(0.951774\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.8885 | + | 14.8098i | 0.708978 | + | 0.705230i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 6.32456i | − | 0.300489i | −0.988649 | − | 0.150244i | \(-0.951994\pi\) | ||
0.988649 | − | 0.150244i | \(-0.0480060\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 5.65685i | − | 0.266963i | −0.991051 | − | 0.133482i | \(-0.957384\pi\) | ||
0.991051 | − | 0.133482i | \(-0.0426157\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 12.6491i | − | 0.595623i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.00000 | − | 5.65685i | −0.187936 | − | 0.265782i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −20.0000 | + | 5.65685i | −0.933520 | + | 0.264039i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.47214 | 0.208288 | 0.104144 | − | 0.994562i | \(-0.466790\pi\) | ||||
0.104144 | + | 0.994562i | \(0.466790\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −40.2492 | −1.87054 | −0.935270 | − | 0.353935i | \(-0.884843\pi\) | ||||
−0.935270 | + | 0.353935i | \(0.884843\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.0000 | −1.20314 | −0.601568 | − | 0.798821i | \(-0.705457\pi\) | ||||
−0.601568 | + | 0.798821i | \(0.705457\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.0000 | + | 6.32456i | −0.461757 | + | 0.292041i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.00000 | + | 2.82843i | −0.184310 | + | 0.130327i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 12.6491i | − | 0.581607i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −17.8885 | − | 6.32456i | −0.819060 | − | 0.289581i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.8885 | 0.817348 | 0.408674 | − | 0.912680i | \(-0.365991\pi\) | ||||
0.408674 | + | 0.912680i | \(0.365991\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.2982i | 1.15350i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −11.0557 | + | 26.7912i | −0.503053 | + | 1.21904i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.4164 | −0.607955 | −0.303978 | − | 0.952679i | \(-0.598315\pi\) | ||||
−0.303978 | + | 0.952679i | \(0.598315\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.4164 | + | 18.9737i | 0.606711 | + | 0.858019i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 2.82843i | − | 0.127645i | −0.997961 | − | 0.0638226i | \(-0.979671\pi\) | ||
0.997961 | − | 0.0638226i | \(-0.0203292\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 22.6274i | − | 1.01909i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −20.0000 | − | 31.6228i | −0.897123 | − | 1.41848i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.00000 | 0.358129 | 0.179065 | − | 0.983837i | \(-0.442693\pi\) | ||||
0.179065 | + | 0.983837i | \(0.442693\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.00000 | − | 8.48528i | −0.268060 | − | 0.379094i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 42.0000 | 1.87269 | 0.936344 | − | 0.351085i | \(-0.114187\pi\) | ||||
0.936344 | + | 0.351085i | \(0.114187\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.00000 | − | 7.07107i | −0.222058 | − | 0.314037i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.4164 | −0.594672 | −0.297336 | − | 0.954773i | \(-0.596098\pi\) | ||||
−0.297336 | + | 0.954773i | \(0.596098\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0000 | + | 18.9737i | 0.530849 | + | 0.839346i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.94427 | − | 31.6228i | −0.394899 | − | 1.39618i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.9706i | 0.746364i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.00000 | + | 11.3137i | 0.351161 | + | 0.496617i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.4164 | −0.587784 | −0.293892 | − | 0.955839i | \(-0.594951\pi\) | ||||
−0.293892 | + | 0.955839i | \(0.594951\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.7696i | 1.60782i | 0.594751 | + | 0.803910i | \(0.297251\pi\) | ||||
−0.594751 | + | 0.803910i | \(0.702749\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25.2982i | 1.10201i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.0000 | −0.739130 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.94427 | + | 25.2982i | −0.388148 | + | 1.09785i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.6491i | 0.547894i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.0000 | − | 14.1421i | 0.863064 | − | 0.610278i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −17.8885 | − | 8.48528i | −0.770514 | − | 0.365487i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.0000 | 0.601907 | 0.300954 | − | 0.953639i | \(-0.402695\pi\) | ||||
0.300954 | + | 0.953639i | \(0.402695\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.8885 | − | 12.6491i | 0.767671 | − | 0.542825i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.2492 | 1.72093 | 0.860466 | − | 0.509507i | \(-0.170172\pi\) | ||||
0.860466 | + | 0.509507i | \(0.170172\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 35.7771 | 1.52416 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −26.8328 | + | 16.9706i | −1.14105 | + | 0.721662i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 31.6228i | − | 1.33990i | −0.742406 | − | 0.669950i | \(-0.766316\pi\) | ||
0.742406 | − | 0.669950i | \(-0.233684\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.6491i | 0.535000i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.0000 | − | 11.3137i | 0.675521 | − | 0.477665i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 30.0000 | 1.26435 | 0.632175 | − | 0.774826i | \(-0.282163\pi\) | ||||
0.632175 | + | 0.774826i | \(0.282163\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.6525 | + | 2.74962i | 0.993311 | + | 0.115473i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.2843i | 1.18574i | 0.805299 | + | 0.592869i | \(0.202005\pi\) | ||||
−0.805299 | + | 0.592869i | \(0.797995\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.00000 | −0.334790 | −0.167395 | − | 0.985890i | \(-0.553535\pi\) | ||||
−0.167395 | + | 0.985890i | \(0.553535\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.00000 | − | 2.82843i | 0.167102 | − | 0.118159i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 36.7696i | − | 1.53074i | −0.643593 | − | 0.765368i | \(-0.722557\pi\) | ||
0.643593 | − | 0.765368i | \(-0.277443\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.3607 | + | 14.1421i | −0.927677 | + | 0.586715i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.8885 | 0.740868 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.0000 | 0.412744 | 0.206372 | − | 0.978474i | \(-0.433834\pi\) | ||||
0.206372 | + | 0.978474i | \(0.433834\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −40.0000 | −1.64817 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 26.8328 | − | 18.9737i | 1.10375 | − | 0.780472i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.0000 | 0.492781 | 0.246390 | − | 0.969171i | \(-0.420755\pi\) | ||||
0.246390 | + | 0.969171i | \(0.420755\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −26.8328 | + | 18.9737i | −1.09819 | + | 0.776540i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.7990i | 0.808965i | 0.914546 | + | 0.404482i | \(0.132548\pi\) | ||||
−0.914546 | + | 0.404482i | \(0.867452\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 12.6491i | − | 0.515968i | −0.966149 | − | 0.257984i | \(-0.916942\pi\) | ||
0.966149 | − | 0.257984i | \(-0.0830582\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.47214 | + | 12.6491i | −0.182119 | + | 0.515112i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.7990i | 0.803616i | 0.915724 | + | 0.401808i | \(0.131618\pi\) | ||||
−0.915724 | + | 0.401808i | \(0.868382\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.88854 | + | 23.9628i | −0.400704 | + | 0.971022i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 16.9706i | − | 0.686555i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.94427 | −0.361256 | −0.180628 | − | 0.983552i | \(-0.557813\pi\) | ||||
−0.180628 | + | 0.983552i | \(0.557813\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 6.32456i | − | 0.254617i | −0.991863 | − | 0.127309i | \(-0.959366\pi\) | ||
0.991863 | − | 0.127309i | \(-0.0406338\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.9737i | 0.762616i | 0.924448 | + | 0.381308i | \(0.124526\pi\) | ||||
−0.924448 | + | 0.381308i | \(0.875474\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.94427 | + | 31.6228i | 0.358921 | + | 1.26898i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.0000 | + | 6.32456i | −0.400642 | + | 0.253388i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17.8885 | + | 25.2982i | 0.714400 | + | 1.01031i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −35.7771 | −1.42653 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.00000 | 0.159237 | 0.0796187 | − | 0.996825i | \(-0.474630\pi\) | ||||
0.0796187 | + | 0.996825i | \(0.474630\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.0000 | − | 22.6274i | −0.635943 | − | 0.899359i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.8885 | + | 8.48528i | 0.708770 | + | 0.336199i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −40.0000 | − | 14.1421i | −1.58238 | − | 0.559454i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 28.2843i | − | 1.11716i | −0.829450 | − | 0.558581i | \(-0.811346\pi\) | ||
0.829450 | − | 0.558581i | \(-0.188654\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 31.1127i | − | 1.22697i | −0.789708 | − | 0.613483i | \(-0.789768\pi\) | ||
0.789708 | − | 0.613483i | \(-0.210232\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.0000 | −0.393141 | −0.196570 | − | 0.980490i | \(-0.562980\pi\) | ||||
−0.196570 | + | 0.980490i | \(0.562980\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 25.2982i | − | 0.993042i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.0557 | − | 26.7912i | 0.433308 | − | 1.05003i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 44.2719i | − | 1.73249i | −0.499617 | − | 0.866246i | \(-0.666526\pi\) | ||
0.499617 | − | 0.866246i | \(-0.333474\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 24.0000 | + | 8.48528i | 0.936329 | + | 0.331042i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 8.48528i | − | 0.330540i | −0.986248 | − | 0.165270i | \(-0.947151\pi\) | ||
0.986248 | − | 0.165270i | \(-0.0528495\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.2982i | 0.983987i | 0.870599 | + | 0.491993i | \(0.163732\pi\) | ||||
−0.870599 | + | 0.491993i | \(0.836268\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −16.0000 | + | 11.3137i | −0.621389 | + | 0.439388i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −35.7771 | −1.38529 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.00000 | + | 2.82843i | −0.154649 | + | 0.109353i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.7771 | 1.37911 | 0.689553 | − | 0.724236i | \(-0.257807\pi\) | ||||
0.689553 | + | 0.724236i | \(0.257807\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.0000 | −0.922395 | −0.461197 | − | 0.887298i | \(-0.652580\pi\) | ||||
−0.461197 | + | 0.887298i | \(0.652580\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.0000 | − | 18.9737i | −0.460518 | − | 0.728142i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.00000 | − | 8.48528i | −0.229920 | − | 0.325157i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 6.32456i | − | 0.242002i | −0.992652 | − | 0.121001i | \(-0.961390\pi\) | ||
0.992652 | − | 0.121001i | \(-0.0386105\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.8885 | − | 12.6491i | 0.682491 | − | 0.482594i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −17.8885 | −0.681499 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 18.9737i | − | 0.721792i | −0.932606 | − | 0.360896i | \(-0.882471\pi\) | ||
0.932606 | − | 0.360896i | \(-0.117529\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −21.8885 | + | 4.98915i | −0.831477 | + | 0.189522i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.8885 | −0.677577 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.94427 | − | 6.32456i | 0.338303 | − | 0.239217i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 45.2548i | − | 1.70925i | −0.519244 | − | 0.854626i | \(-0.673787\pi\) | ||
0.519244 | − | 0.854626i | \(-0.326213\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 56.5685i | − | 2.13352i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.0000 | − | 6.32456i | 0.376089 | − | 0.237859i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.0000 | 1.57734 | 0.788672 | − | 0.614815i | \(-0.210769\pi\) | ||||
0.788672 | + | 0.614815i | \(0.210769\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.0000 | + | 33.9411i | −0.450035 | + | 1.27289i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 40.0000 | 1.49801 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.0000 | − | 8.48528i | 0.448148 | − | 0.316889i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.8885 | 0.667130 | 0.333565 | − | 0.942727i | \(-0.391748\pi\) | ||||
0.333565 | + | 0.942727i | \(0.391748\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.00000 | − | 6.32456i | −0.148968 | − | 0.235539i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.8885 | − | 12.6491i | 0.665282 | − | 0.470425i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 25.4558i | − | 0.944105i | −0.881570 | − | 0.472052i | \(-0.843513\pi\) | ||
0.881570 | − | 0.472052i | \(-0.156487\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.0000 | − | 14.1421i | 0.851852 | − | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.8885 | −0.661632 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.4558i | 0.940233i | 0.882604 | + | 0.470117i | \(0.155788\pi\) | ||||
−0.882604 | + | 0.470117i | \(0.844212\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 12.6491i | − | 0.465936i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.00000 | 0.294285 | 0.147142 | − | 0.989115i | \(-0.452992\pi\) | ||||
0.147142 | + | 0.989115i | \(0.452992\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −17.8885 | − | 25.2982i | −0.657152 | − | 0.929353i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.9737i | 0.696076i | 0.937480 | + | 0.348038i | \(0.113152\pi\) | ||||
−0.937480 | + | 0.348038i | \(0.886848\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.0000 | + | 28.2843i | −0.365881 | + | 1.03487i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 26.8328 | + | 42.4264i | 0.980450 | + | 1.55023i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.00000 | 0.145962 | 0.0729810 | − | 0.997333i | \(-0.476749\pi\) | ||||
0.0729810 | + | 0.997333i | \(0.476749\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −26.8328 | − | 37.9473i | −0.977842 | − | 1.38288i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.94427 | 0.325085 | 0.162543 | − | 0.986702i | \(-0.448031\pi\) | ||||
0.162543 | + | 0.986702i | \(0.448031\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −17.8885 | − | 25.2982i | −0.649313 | − | 0.918267i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.47214 | −0.162115 | −0.0810574 | − | 0.996709i | \(-0.525830\pi\) | ||||
−0.0810574 | + | 0.996709i | \(0.525830\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.47214 | − | 2.82843i | 0.161902 | − | 0.102396i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25.2982i | 0.913466i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 25.2982i | − | 0.912277i | −0.889909 | − | 0.456139i | \(-0.849232\pi\) | ||
0.889909 | − | 0.456139i | \(-0.150768\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.0000 | − | 28.2843i | −0.720282 | − | 1.01863i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32.0000 | 1.15096 | 0.575480 | − | 0.817816i | \(-0.304815\pi\) | ||||
0.575480 | + | 0.817816i | \(0.304815\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 37.8885 | + | 15.6352i | 1.35924 | + | 0.560908i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 28.2843i | − | 1.01339i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 40.0000 | 1.43131 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.00000 | + | 28.2843i | 0.285897 | + | 1.01080i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 8.48528i | − | 0.302468i | −0.988498 | − | 0.151234i | \(-0.951675\pi\) | ||
0.988498 | − | 0.151234i | \(-0.0483246\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.94427 | + | 6.32456i | −0.318425 | + | 0.225160i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 26.8328 | + | 42.4264i | 0.954065 | + | 1.50851i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.0000 | 0.566749 | 0.283375 | − | 0.959009i | \(-0.408546\pi\) | ||||
0.283375 | + | 0.959009i | \(0.408546\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.0000 | 0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.47214 | + | 12.6491i | −0.158015 | + | 0.446934i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −24.0000 | −0.846942 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.47214 | − | 6.32456i | −0.157427 | − | 0.222635i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 22.6274i | − | 0.795538i | −0.917486 | − | 0.397769i | \(-0.869785\pi\) | ||
0.917486 | − | 0.397769i | \(-0.130215\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.6228i | 1.11043i | 0.831708 | + | 0.555213i | \(0.187363\pi\) | ||||
−0.831708 | + | 0.555213i | \(0.812637\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.94427 | + | 6.32456i | −0.313689 | + | 0.221812i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 28.2843i | − | 0.989541i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 21.8885 | − | 4.98915i | 0.764848 | − | 0.174335i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.3137i | 0.394851i | 0.980318 | + | 0.197426i | \(0.0632581\pi\) | ||||
−0.980318 | + | 0.197426i | \(0.936742\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.3607 | −0.779444 | −0.389722 | − | 0.920932i | \(-0.627429\pi\) | ||||
−0.389722 | + | 0.920932i | \(0.627429\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 18.9737i | − | 0.659779i | −0.944020 | − | 0.329890i | \(-0.892989\pi\) | ||
0.944020 | − | 0.329890i | \(-0.107011\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 25.2982i | − | 0.878644i | −0.898330 | − | 0.439322i | \(-0.855219\pi\) | ||
0.898330 | − | 0.439322i | \(-0.144781\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.8328 | − | 37.9473i | −0.930820 | − | 1.31638i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.0000 | + | 25.2982i | −0.415775 | + | 0.876531i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.94427 | − | 31.6228i | −0.309159 | − | 1.09304i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 35.7771 | 1.23516 | 0.617581 | − | 0.786507i | \(-0.288113\pi\) | ||||
0.617581 | + | 0.786507i | \(0.288113\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.00000 | −0.103448 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.0000 | − | 16.9706i | 0.826604 | − | 0.584497i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.70820 | + | 4.24264i | −0.230497 | + | 0.145779i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −36.0000 | + | 25.4558i | −1.23552 | + | 0.873642i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 56.5685i | 1.93914i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.7696i | 1.25897i | 0.777014 | + | 0.629483i | \(0.216733\pi\) | ||||
−0.777014 | + | 0.629483i | \(0.783267\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.0000 | −0.683187 | −0.341593 | − | 0.939848i | \(-0.610967\pi\) | ||||
−0.341593 | + | 0.939848i | \(0.610967\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.2719i | 1.51054i | 0.655415 | + | 0.755269i | \(0.272494\pi\) | ||||
−0.655415 | + | 0.755269i | \(0.727506\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.9443 | + | 7.81758i | 0.645619 | + | 0.266422i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 18.9737i | − | 0.645871i | −0.946421 | − | 0.322936i | \(-0.895330\pi\) | ||
0.946421 | − | 0.322936i | \(-0.104670\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.00000 | + | 1.41421i | 0.0339618 | + | 0.0480292i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 33.9411i | − | 1.15137i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.6491i | 0.428599i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −24.0000 | − | 8.48528i | −0.812277 | − | 0.287183i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.8328 | −0.906080 | −0.453040 | − | 0.891490i | \(-0.649660\pi\) | ||||
−0.453040 | + | 0.891490i | \(0.649660\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 32.0000 | + | 45.2548i | 1.07933 | + | 1.52641i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.3050 | 1.05469 | 0.527345 | − | 0.849651i | \(-0.323187\pi\) | ||||
0.527345 | + | 0.849651i | \(0.323187\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.2492 | −1.35449 | −0.677247 | − | 0.735756i | \(-0.736827\pi\) | ||||
−0.677247 | + | 0.735756i | \(0.736827\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −30.0000 | −1.00730 | −0.503651 | − | 0.863907i | \(-0.668010\pi\) | ||||
−0.503651 | + | 0.863907i | \(0.668010\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.0000 | + | 6.32456i | −0.335389 | + | 0.212119i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −16.0000 | + | 19.7990i | −0.536020 | + | 0.663291i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 37.9473i | 1.26986i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.8885 | + | 25.2982i | 0.597281 | + | 0.844683i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 35.7771 | 1.19323 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 25.2982i | − | 0.842806i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 18.9443 | + | 7.81758i | 0.630426 | + | 0.260153i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.4164 | −0.445485 | −0.222742 | − | 0.974877i | \(-0.571501\pi\) | ||||
−0.222742 | + | 0.974877i | \(0.571501\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.47214 | − | 12.6491i | 0.148331 | − | 0.419545i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.1421i | 0.468550i | 0.972170 | + | 0.234275i | \(0.0752716\pi\) | ||||
−0.972170 | + | 0.234275i | \(0.924728\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 28.2843i | − | 0.936073i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −20.0000 | + | 12.6491i | −0.660458 | + | 0.417710i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 52.0000 | 1.71532 | 0.857661 | − | 0.514216i | \(-0.171917\pi\) | ||||
0.857661 | + | 0.514216i | \(0.171917\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.0000 | + | 8.48528i | −0.395413 | + | 0.279600i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −40.0000 | −1.31662 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.00000 | − | 2.82843i | −0.262754 | − | 0.0928977i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.47214 | 0.146726 | 0.0733630 | − | 0.997305i | \(-0.476627\pi\) | ||||
0.0733630 | + | 0.997305i | \(0.476627\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −40.0000 | − | 18.9737i | −1.31095 | − | 0.621837i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17.8885 | + | 25.2982i | 0.585645 | + | 0.828227i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.48528i | 0.277202i | 0.990348 | + | 0.138601i | \(0.0442606\pi\) | ||||
−0.990348 | + | 0.138601i | \(0.955739\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 36.0000 | − | 25.4558i | 1.17482 | − | 0.830720i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.2492 | 1.31209 | 0.656044 | − | 0.754723i | \(-0.272229\pi\) | ||||
0.656044 | + | 0.754723i | \(0.272229\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28.2843i | 0.921063i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.9737i | 0.616561i | 0.951295 | + | 0.308281i | \(0.0997536\pi\) | ||||
−0.951295 | + | 0.308281i | \(0.900246\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.0000 | 0.779073 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26.8328 | − | 18.9737i | 0.870114 | − | 0.615263i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 18.9737i | − | 0.614617i | −0.951610 | − | 0.307309i | \(-0.900572\pi\) | ||
0.951610 | − | 0.307309i | \(-0.0994284\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16.0000 | − | 22.6274i | −0.517207 | − | 0.731441i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.94427 | + | 14.1421i | 0.288826 | + | 0.456673i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.00000 | −0.290323 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 53.6656 | + | 18.9737i | 1.72935 | + | 0.611418i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.2492 | −1.29433 | −0.647164 | − | 0.762351i | \(-0.724045\pi\) | ||||
−0.647164 | + | 0.762351i | \(0.724045\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 35.7771 | − | 25.2982i | 1.14933 | − | 0.812696i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −44.7214 | −1.43518 | −0.717588 | − | 0.696467i | \(-0.754754\pi\) | ||||
−0.717588 | + | 0.696467i | \(0.754754\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.94427 | + | 14.1421i | 0.286740 | + | 0.453376i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.9737i | 0.607021i | 0.952828 | + | 0.303511i | \(0.0981588\pi\) | ||||
−0.952828 | + | 0.303511i | \(0.901841\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 12.6491i | − | 0.404267i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00000 | − | 5.65685i | 0.0638551 | − | 0.180609i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.0000 | −0.574111 | −0.287055 | − | 0.957914i | \(-0.592676\pi\) | ||||
−0.287055 | + | 0.957914i | \(0.592676\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −25.4164 | − | 10.4884i | −0.809013 | − | 0.333849i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 28.2843i | 0.899388i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.0000 | 0.889449 | 0.444725 | − | 0.895667i | \(-0.353302\pi\) | ||||
0.444725 | + | 0.895667i | \(0.353302\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.00000 | − | 11.3137i | −0.253872 | − | 0.359030i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.48528i | 0.268732i | 0.990932 | + | 0.134366i | \(0.0428997\pi\) | ||||
−0.990932 | + | 0.134366i | \(0.957100\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 44.7214 | − | 12.6491i | 1.41492 | − | 0.400200i |
(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 | 2100.2.d.f.1301.1 | 4 | ||
3.2 | odd | 2 | 2100.2.d.i.1301.1 | 4 | |||
5.2 | odd | 4 | 420.2.f.b.209.4 | yes | 8 | ||
5.3 | odd | 4 | 420.2.f.b.209.6 | yes | 8 | ||
5.4 | even | 2 | 2100.2.d.i.1301.4 | 4 | |||
7.6 | odd | 2 | 2100.2.d.i.1301.3 | 4 | |||
15.2 | even | 4 | 420.2.f.b.209.1 | ✓ | 8 | ||
15.8 | even | 4 | 420.2.f.b.209.7 | yes | 8 | ||
15.14 | odd | 2 | inner | 2100.2.d.f.1301.4 | 4 | ||
20.3 | even | 4 | 1680.2.k.g.209.4 | 8 | |||
20.7 | even | 4 | 1680.2.k.g.209.6 | 8 | |||
21.20 | even | 2 | inner | 2100.2.d.f.1301.3 | 4 | ||
35.13 | even | 4 | 420.2.f.b.209.3 | yes | 8 | ||
35.27 | even | 4 | 420.2.f.b.209.5 | yes | 8 | ||
35.34 | odd | 2 | inner | 2100.2.d.f.1301.2 | 4 | ||
60.23 | odd | 4 | 1680.2.k.g.209.1 | 8 | |||
60.47 | odd | 4 | 1680.2.k.g.209.7 | 8 | |||
105.62 | odd | 4 | 420.2.f.b.209.8 | yes | 8 | ||
105.83 | odd | 4 | 420.2.f.b.209.2 | yes | 8 | ||
105.104 | even | 2 | 2100.2.d.i.1301.2 | 4 | |||
140.27 | odd | 4 | 1680.2.k.g.209.3 | 8 | |||
140.83 | odd | 4 | 1680.2.k.g.209.5 | 8 | |||
420.83 | even | 4 | 1680.2.k.g.209.8 | 8 | |||
420.167 | even | 4 | 1680.2.k.g.209.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.f.b.209.1 | ✓ | 8 | 15.2 | even | 4 | ||
420.2.f.b.209.2 | yes | 8 | 105.83 | odd | 4 | ||
420.2.f.b.209.3 | yes | 8 | 35.13 | even | 4 | ||
420.2.f.b.209.4 | yes | 8 | 5.2 | odd | 4 | ||
420.2.f.b.209.5 | yes | 8 | 35.27 | even | 4 | ||
420.2.f.b.209.6 | yes | 8 | 5.3 | odd | 4 | ||
420.2.f.b.209.7 | yes | 8 | 15.8 | even | 4 | ||
420.2.f.b.209.8 | yes | 8 | 105.62 | odd | 4 | ||
1680.2.k.g.209.1 | 8 | 60.23 | odd | 4 | |||
1680.2.k.g.209.2 | 8 | 420.167 | even | 4 | |||
1680.2.k.g.209.3 | 8 | 140.27 | odd | 4 | |||
1680.2.k.g.209.4 | 8 | 20.3 | even | 4 | |||
1680.2.k.g.209.5 | 8 | 140.83 | odd | 4 | |||
1680.2.k.g.209.6 | 8 | 20.7 | even | 4 | |||
1680.2.k.g.209.7 | 8 | 60.47 | odd | 4 | |||
1680.2.k.g.209.8 | 8 | 420.83 | even | 4 | |||
2100.2.d.f.1301.1 | 4 | 1.1 | even | 1 | trivial | ||
2100.2.d.f.1301.2 | 4 | 35.34 | odd | 2 | inner | ||
2100.2.d.f.1301.3 | 4 | 21.20 | even | 2 | inner | ||
2100.2.d.f.1301.4 | 4 | 15.14 | odd | 2 | inner | ||
2100.2.d.i.1301.1 | 4 | 3.2 | odd | 2 | |||
2100.2.d.i.1301.2 | 4 | 105.104 | even | 2 | |||
2100.2.d.i.1301.3 | 4 | 7.6 | odd | 2 | |||
2100.2.d.i.1301.4 | 4 | 5.4 | even | 2 |