Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [420,2,Mod(209,420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(420, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("420.209");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 420.f (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: | \(3.35371688489\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 209.6 | ||
Root | \(-1.14412 - 1.14412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 420.209 |
Dual form | 420.2.f.b.209.8 |
$q$-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 \(\left(\mathbb{Z}/420\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(241\) | \(281\) | \(337\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.41421 | − | 1.00000i | 0.816497 | − | 0.577350i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23607 | 1.00000 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.41421 | + | 2.23607i | 0.534522 | + | 0.845154i | ||||
\(8\) | 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 | ||||||||
\(13\) | −2.82843 | −0.784465 | −0.392232 | − | 0.919866i | \(-0.628297\pi\) | ||||
−0.392232 | + | 0.919866i | \(0.628297\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.16228 | − | 2.23607i | 0.816497 | − | 0.577350i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.00000i | 0.970143i | 0.874475 | + | 0.485071i | \(0.161206\pi\) | ||||
−0.874475 | + | 0.485071i | \(0.838794\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.32456i | 1.45095i | 0.688247 | + | 0.725476i | \(0.258380\pi\) | ||||
−0.688247 | + | 0.725476i | \(0.741620\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.23607 | + | 1.74806i | 0.924386 | + | 0.381459i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.32456 | −1.31876 | −0.659380 | − | 0.751809i | \(-0.729181\pi\) | ||||
−0.659380 | + | 0.751809i | \(0.729181\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.41421 | − | 5.00000i | −0.272166 | − | 0.962250i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.65685i | − | 1.05045i | −0.850963 | − | 0.525226i | \(-0.823981\pi\) | ||
0.850963 | − | 0.525226i | \(-0.176019\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.32456i | − | 1.13592i | −0.823055 | − | 0.567962i | \(-0.807732\pi\) | ||
0.823055 | − | 0.567962i | \(-0.192268\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.82843 | − | 4.00000i | −0.492366 | − | 0.696311i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.16228 | + | 5.00000i | 0.534522 | + | 0.845154i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 8.94427i | − | 1.47043i | −0.677834 | − | 0.735215i | \(-0.737081\pi\) | ||
0.677834 | − | 0.735215i | \(-0.262919\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | 4.47214i | 0.681994i | 0.940064 | + | 0.340997i | \(0.110765\pi\) | ||||
−0.940064 | + | 0.340997i | \(0.889235\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.23607 | − | 6.32456i | 0.333333 | − | 0.942809i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.00000i | 0.875190i | 0.899172 | + | 0.437595i | \(0.144170\pi\) | ||||
−0.899172 | + | 0.437595i | \(0.855830\pi\) | |||||||
\(48\) | 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 | ||||||||
\(53\) | −6.32456 | −0.868744 | −0.434372 | − | 0.900733i | \(-0.643030\pi\) | ||||
−0.434372 | + | 0.900733i | \(0.643030\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 6.32456i | − | 0.852803i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.32456 | + | 8.94427i | 0.837708 | + | 1.18470i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.94427 | −1.16445 | −0.582223 | − | 0.813029i | \(-0.697817\pi\) | ||||
−0.582223 | + | 0.813029i | \(0.697817\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.73877 | − | 1.76393i | 0.974993 | − | 0.222235i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.32456 | −0.784465 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 4.47214i | − | 0.546358i | −0.961963 | − | 0.273179i | \(-0.911925\pi\) | ||
0.961963 | − | 0.273179i | \(-0.0880752\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | 8.48528 | 0.993127 | 0.496564 | − | 0.868000i | \(-0.334595\pi\) | ||||
0.496564 | + | 0.868000i | \(0.334595\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.07107 | − | 5.00000i | 0.816497 | − | 0.577350i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.32456 | − | 4.00000i | 0.720750 | − | 0.455842i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.0000 | −1.35011 | −0.675053 | − | 0.737769i | \(-0.735879\pi\) | ||||
−0.675053 | + | 0.737769i | \(0.735879\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | − | 5.65685i | −0.777778 | − | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.0000i | 1.09764i | 0.835940 | + | 0.548821i | \(0.184923\pi\) | ||||
−0.835940 | + | 0.548821i | \(0.815077\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.94427i | 0.970143i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.65685 | − | 8.00000i | −0.606478 | − | 0.857690i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.47214 | −0.474045 | −0.237023 | − | 0.971504i | \(-0.576172\pi\) | ||||
−0.237023 | + | 0.971504i | \(0.576172\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.00000 | − | 6.32456i | −0.419314 | − | 0.662994i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.32456 | − | 8.94427i | −0.655826 | − | 0.927478i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.1421i | 1.45095i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.48528 | 0.861550 | 0.430775 | − | 0.902459i | \(-0.358240\pi\) | ||||
0.430775 | + | 0.902459i | \(0.358240\pi\) | |||||||
\(98\) | 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 | ||||||||
\(103\) | −2.82843 | −0.278693 | −0.139347 | − | 0.990244i | \(-0.544500\pi\) | ||||
−0.139347 | + | 0.990244i | \(0.544500\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.47214 | + | 3.90879i | 0.924386 | + | 0.381459i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.9737 | −1.83425 | −0.917127 | − | 0.398596i | \(-0.869498\pi\) | ||||
−0.917127 | + | 0.398596i | \(0.869498\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.94427 | − | 12.6491i | −0.848953 | − | 1.20060i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.9737 | 1.78489 | 0.892446 | − | 0.451154i | \(-0.148987\pi\) | ||||
0.892446 | + | 0.451154i | \(0.148987\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.1421 | −1.31876 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.82843 | + | 8.00000i | −0.261488 | + | 0.739600i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.94427 | + | 5.65685i | −0.819920 | + | 0.518563i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.00000 | 0.272727 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.32456 | − | 4.47214i | 0.570266 | − | 0.403239i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803 | 1.00000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 4.47214i | − | 0.396838i | −0.980117 | − | 0.198419i | \(-0.936419\pi\) | ||
0.980117 | − | 0.198419i | \(-0.0635807\pi\) | |||||||
\(128\) | 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 | ||||||||
\(133\) | −14.1421 | + | 8.94427i | −1.22628 | + | 0.775567i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.16228 | − | 11.1803i | −0.272166 | − | 0.962250i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.32456 | −0.540343 | −0.270172 | − | 0.962812i | \(-0.587080\pi\) | ||||
−0.270172 | + | 0.962812i | \(0.587080\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.32456i | 0.536442i | 0.963357 | + | 0.268221i | \(0.0864357\pi\) | ||||
−0.963357 | + | 0.268221i | \(0.913564\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | + | 8.48528i | 0.505291 | + | 0.714590i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.00000i | 0.668994i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 12.6491i | − | 1.05045i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.08191 | + | 11.9443i | 0.171713 | + | 0.985147i | ||||
\(148\) | 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 | ||||||||
\(153\) | 11.3137 | + | 4.00000i | 0.914659 | + | 0.323381i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 14.1421i | − | 1.13592i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.82843 | −0.225733 | −0.112867 | − | 0.993610i | \(-0.536003\pi\) | ||||
−0.112867 | + | 0.993610i | \(0.536003\pi\) | |||||||
\(158\) | 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 | ||||||||
\(163\) | − | 13.4164i | − | 1.05085i | −0.850839 | − | 0.525427i | \(-0.823906\pi\) | ||
0.850839 | − | 0.525427i | \(-0.176094\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.32456 | − | 8.94427i | −0.492366 | − | 0.696311i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 6.00000i | − | 0.464294i | −0.972681 | − | 0.232147i | \(-0.925425\pi\) | ||
0.972681 | − | 0.232147i | \(-0.0745750\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 17.8885 | + | 6.32456i | 1.36797 | + | 0.483651i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 8.00000i | − | 0.608229i | −0.952636 | − | 0.304114i | \(-0.901639\pi\) | ||
0.952636 | − | 0.304114i | \(-0.0983605\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.07107 | + | 11.1803i | 0.534522 | + | 0.845154i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.6491 | + | 8.94427i | −0.950765 | + | 0.672293i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 14.1421i | − | 1.05703i | −0.848923 | − | 0.528516i | \(-0.822748\pi\) | ||
0.848923 | − | 0.528516i | \(-0.177252\pi\) | |||||||
\(180\) | 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 | ||||||||
\(185\) | − | 20.0000i | − | 1.47043i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.3137 | 0.827340 | ||||||||
\(188\) | 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 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.94427 | + | 6.32456i | −0.640513 | + | 0.452911i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.9737 | 1.35182 | 0.675909 | − | 0.736985i | \(-0.263751\pi\) | ||||
0.675909 | + | 0.736985i | \(0.263751\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.9737i | 1.34501i | 0.740094 | + | 0.672504i | \(0.234781\pi\) | ||||
−0.740094 | + | 0.672504i | \(0.765219\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.47214 | − | 6.32456i | −0.315440 | − | 0.446100i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.6491 | − | 8.00000i | 0.887794 | − | 0.561490i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.0000 | 0.698430 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.32456 | + | 17.8885i | −0.439587 | + | 1.24334i | ||||
\(208\) | 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 | ||||||||
\(213\) | 14.1421 | + | 20.0000i | 0.969003 | + | 1.37038i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.0000i | 0.681994i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.1421 | − | 8.94427i | 0.960031 | − | 0.607177i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.0000 | − | 8.48528i | 0.810885 | − | 0.573382i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 11.3137i | − | 0.761042i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.82843 | 0.189405 | 0.0947027 | − | 0.995506i | \(-0.469810\pi\) | ||||
0.0947027 | + | 0.995506i | \(0.469810\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.00000 | − | 14.1421i | 0.333333 | − | 0.942809i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 6.00000i | − | 0.398234i | −0.979976 | − | 0.199117i | \(-0.936193\pi\) | ||
0.979976 | − | 0.199117i | \(-0.0638074\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 12.6491i | − | 0.835877i | −0.908475 | − | 0.417938i | \(-0.862753\pi\) | ||
0.908475 | − | 0.417938i | \(-0.137247\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.94427 | − | 11.9814i | 0.325309 | − | 0.788319i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.32456 | −0.414335 | −0.207168 | − | 0.978305i | \(-0.566425\pi\) | ||||
−0.207168 | + | 0.978305i | \(0.566425\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.4164i | 0.875190i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.9706 | + | 12.0000i | −1.10236 | + | 0.779484i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 8.48528i | − | 0.548867i | −0.961606 | − | 0.274434i | \(-0.911510\pi\) | ||
0.961606 | − | 0.274434i | \(-0.0884904\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.6491i | 0.814801i | 0.913250 | + | 0.407400i | \(0.133565\pi\) | ||||
−0.913250 | + | 0.407400i | \(0.866435\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5563 | − | 1.00000i | −0.997940 | − | 0.0641500i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.70820 | + | 14.1421i | −0.428571 | + | 0.903508i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 17.8885i | − | 1.13822i | ||||||
\(248\) | 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 | ||||||||
\(253\) | 17.8885i | 1.12464i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.94427 | + | 12.6491i | 0.560112 | + | 0.792118i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 20.0000i | − | 1.24757i | −0.781598 | − | 0.623783i | \(-0.785595\pi\) | ||
0.781598 | − | 0.623783i | \(-0.214405\pi\) | |||||||
\(258\) | 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 | ||||||||
\(263\) | 6.32456 | 0.389989 | 0.194994 | − | 0.980804i | \(-0.437531\pi\) | ||||
0.194994 | + | 0.980804i | \(0.437531\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.1421 | −0.868744 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.32456 | + | 4.47214i | −0.387056 | + | 0.273690i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.47214 | −0.272671 | −0.136335 | − | 0.990663i | \(-0.543533\pi\) | ||||
−0.136335 | + | 0.990663i | \(0.543533\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 6.32456i | − | 0.384189i | −0.981376 | − | 0.192095i | \(-0.938472\pi\) | ||
0.981376 | − | 0.192095i | \(-0.0615281\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −11.9814 | − | 4.94427i | −0.725148 | − | 0.299241i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 14.1421i | − | 0.852803i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 26.8328i | − | 1.61223i | −0.591761 | − | 0.806114i | \(-0.701567\pi\) | ||
0.591761 | − | 0.806114i | \(-0.298433\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | 25.4558 | 1.51319 | 0.756596 | − | 0.653882i | \(-0.226861\pi\) | ||||
0.756596 | + | 0.653882i | \(0.226861\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.1421 | + | 20.0000i | 0.837708 | + | 1.18470i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.32456 | + | 10.0000i | 0.373327 | + | 0.590281i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.0000 | − | 8.48528i | 0.703452 | − | 0.497416i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 32.0000i | − | 1.86946i | −0.355359 | − | 0.934730i | \(-0.615641\pi\) | ||
0.355359 | − | 0.934730i | \(-0.384359\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.0000 | −1.16445 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −14.1421 | + | 4.00000i | −0.820610 | + | 0.232104i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.8885 | 1.03452 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.0000 | + | 6.32456i | −0.576390 | + | 0.364541i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.32456 | + | 4.47214i | −0.363336 | + | 0.256917i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.48528 | −0.484281 | −0.242140 | − | 0.970241i | \(-0.577849\pi\) | ||||
−0.242140 | + | 0.970241i | \(0.577849\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | −25.4558 | −1.43885 | −0.719425 | − | 0.694570i | \(-0.755594\pi\) | ||||
−0.719425 | + | 0.694570i | \(0.755594\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 17.3044 | − | 3.94427i | 0.974993 | − | 0.222235i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.9737 | 1.06567 | 0.532834 | − | 0.846220i | \(-0.321127\pi\) | ||||
0.532834 | + | 0.846220i | \(0.321127\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.0000 | −0.895828 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −26.8328 | + | 18.9737i | −1.49766 | + | 1.05901i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −25.2982 | −1.40763 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.1421 | −0.784465 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.82843 | − | 2.00000i | 0.156412 | − | 0.110600i | ||||
\(328\) | 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 | ||||||||
\(333\) | −25.2982 | − | 8.94427i | −1.38633 | − | 0.490143i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 10.0000i | − | 0.546358i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 26.8328 | − | 18.9737i | 1.45736 | − | 1.03051i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.8885 | −0.968719 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.3848 | + | 2.23607i | −0.992685 | + | 0.120736i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −20.0000 | + | 14.1421i | −1.07676 | + | 0.761387i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.9737 | 1.01856 | 0.509280 | − | 0.860601i | \(-0.329912\pi\) | ||||
0.509280 | + | 0.860601i | \(0.329912\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 12.6491i | − | 0.677091i | −0.940950 | − | 0.338546i | \(-0.890065\pi\) | ||
0.940950 | − | 0.338546i | \(-0.109935\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.00000 | + | 14.1421i | 0.213504 | + | 0.754851i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.0000i | 1.49029i | 0.666903 | + | 0.745145i | \(0.267620\pi\) | ||||
−0.666903 | + | 0.745145i | \(0.732380\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 31.6228i | 1.67836i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.99226 | + | 16.9443i | −0.370069 | + | 0.896786i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.1421i | 0.746393i | 0.927752 | + | 0.373197i | \(0.121738\pi\) | ||||
−0.927752 | + | 0.373197i | \(0.878262\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −21.0000 | −1.10526 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.24264 | − | 3.00000i | 0.222681 | − | 0.157459i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.9737 | 0.993127 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.48528 | 0.442928 | 0.221464 | − | 0.975169i | \(-0.428916\pi\) | ||||
0.221464 | + | 0.975169i | \(0.428916\pi\) | |||||||
\(368\) | 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 | ||||||||
\(373\) | 26.8328i | 1.38935i | 0.719323 | + | 0.694675i | \(0.244452\pi\) | ||||
−0.719323 | + | 0.694675i | \(0.755548\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 15.8114 | − | 11.1803i | 0.816497 | − | 0.577350i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.0000i | 0.824042i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.0000 | 1.23280 | 0.616399 | − | 0.787434i | \(-0.288591\pi\) | ||||
0.616399 | + | 0.787434i | \(0.288591\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.47214 | − | 6.32456i | −0.229114 | − | 0.324017i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 30.0000i | − | 1.53293i | −0.642287 | − | 0.766464i | \(-0.722014\pi\) | ||
0.642287 | − | 0.766464i | \(-0.277986\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.1421 | − | 8.94427i | 0.720750 | − | 0.455842i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.6491 | + | 4.47214i | 0.642990 | + | 0.227331i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 33.9411i | 1.72088i | 0.509549 | + | 0.860442i | \(0.329812\pi\) | ||||
−0.509549 | + | 0.860442i | \(0.670188\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 25.2982i | − | 1.27939i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.6491 | − | 8.94427i | 0.638063 | − | 0.451179i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −26.8328 | −1.35011 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.7990 | 0.993683 | 0.496841 | − | 0.867841i | \(-0.334493\pi\) | ||||
0.496841 | + | 0.867841i | \(0.334493\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 17.8885i | 0.891092i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −15.6525 | − | 12.6491i | −0.777778 | − | 0.628539i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −25.2982 | −1.25399 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 37.9473i | − | 1.87637i | −0.346128 | − | 0.938187i | \(-0.612504\pi\) | ||
0.346128 | − | 0.938187i | \(-0.387496\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.94427 | + | 6.32456i | −0.441188 | + | 0.311967i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.6491 | − | 20.0000i | −0.622422 | − | 0.984136i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.3607i | 1.09764i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.32456 | + | 8.94427i | 0.309715 | + | 0.438003i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.8328 | 1.31087 | 0.655434 | − | 0.755252i | \(-0.272486\pi\) | ||||
0.655434 | + | 0.755252i | \(0.272486\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.0000 | −1.65706 | −0.828529 | − | 0.559946i | \(-0.810822\pi\) | ||||
−0.828529 | + | 0.559946i | \(0.810822\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 16.9706 | + | 6.00000i | 0.825137 | + | 0.291730i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 20.0000i | 0.970143i | ||||||||
\(426\) | 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 | ||||||||
\(433\) | 8.48528 | 0.407777 | 0.203888 | − | 0.978994i | \(-0.434642\pi\) | ||||
0.203888 | + | 0.978994i | \(0.434642\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.6491 | − | 17.8885i | −0.606478 | − | 0.857690i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 40.0000i | − | 1.91346i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 6.32456i | − | 0.301855i | −0.988545 | − | 0.150927i | \(-0.951774\pi\) | ||
0.988545 | − | 0.150927i | \(-0.0482259\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.8885 | + | 14.8098i | 0.708978 | + | 0.705230i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.32456 | 0.300489 | 0.150244 | − | 0.988649i | \(-0.451994\pi\) | ||||
0.150244 | + | 0.988649i | \(0.451994\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.0000 | −0.474045 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.65685i | 0.266963i | 0.991051 | + | 0.133482i | \(0.0426157\pi\) | ||||
−0.991051 | + | 0.133482i | \(0.957384\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 12.6491i | − | 0.595623i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.65685 | − | 4.00000i | 0.265782 | − | 0.187936i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.94427 | − | 14.1421i | −0.419314 | − | 0.662994i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(458\) | 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 | ||||||||
\(463\) | − | 40.2492i | − | 1.87054i | −0.353935 | − | 0.935270i | \(-0.615157\pi\) | ||
0.353935 | − | 0.935270i | \(-0.384843\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14.1421 | − | 20.0000i | −0.655826 | − | 0.927478i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.0000i | 1.20314i | 0.798821 | + | 0.601568i | \(0.205457\pi\) | ||||
−0.798821 | + | 0.601568i | \(0.794543\pi\) | |||||||
\(468\) | 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 | ||||||||
\(473\) | 12.6491 | 0.581607 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31.6228i | 1.45095i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.32456 | + | 17.8885i | −0.289581 | + | 0.819060i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.8885 | −0.817348 | −0.408674 | − | 0.912680i | \(-0.634009\pi\) | ||||
−0.408674 | + | 0.912680i | \(0.634009\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.2982i | 1.15350i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −26.7912 | − | 11.0557i | −1.21904 | − | 0.503053i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.9737 | 0.861550 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.4164i | 0.607955i | 0.952679 | + | 0.303978i | \(0.0983148\pi\) | ||||
−0.952679 | + | 0.303978i | \(0.901685\pi\) | |||||||
\(488\) | 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 | ||||||||
\(493\) | 22.6274 | 1.01909 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −17.8885 | − | 6.32456i | −0.804030 | − | 0.284268i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −31.6228 | + | 20.0000i | −1.41848 | + | 0.897123i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.00000 | −0.358129 | −0.179065 | − | 0.983837i | \(-0.557307\pi\) | ||||
−0.179065 | + | 0.983837i | \(0.557307\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.00000 | − | 8.48528i | −0.268060 | − | 0.379094i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 42.0000i | 1.87269i | 0.351085 | + | 0.936344i | \(0.385813\pi\) | ||||
−0.351085 | + | 0.936344i | \(0.614187\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.0000 | −0.444994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.07107 | + | 5.00000i | −0.314037 | + | 0.222058i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.4164 | 0.594672 | 0.297336 | − | 0.954773i | \(-0.403902\pi\) | ||||
0.297336 | + | 0.954773i | \(0.403902\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0000 | + | 18.9737i | 0.530849 | + | 0.839346i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 31.6228 | − | 8.94427i | 1.39618 | − | 0.394899i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.32456 | −0.278693 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.9706 | 0.746364 | ||||||||
\(518\) | 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 | ||||||||
\(523\) | −36.7696 | −1.60782 | −0.803910 | − | 0.594751i | \(-0.797251\pi\) | ||||
−0.803910 | + | 0.594751i | \(0.797251\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 21.1803 | + | 8.74032i | 0.924386 | + | 0.381459i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25.2982 | 1.10201 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.0000 | 0.739130 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.94427 | + | 25.2982i | −0.388148 | + | 1.09785i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.6491 | −0.547894 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −42.4264 | −1.83425 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14.1421 | − | 20.0000i | −0.610278 | − | 0.863064i | ||||
\(538\) | 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 | ||||||||
\(543\) | 12.6491 | + | 17.8885i | 0.542825 | + | 0.767671i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.47214 | 0.191565 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 40.2492i | − | 1.72093i | −0.509507 | − | 0.860466i | \(-0.670172\pi\) | ||
0.509507 | − | 0.860466i | \(-0.329828\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 35.7771 | 1.52416 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.9706 | − | 26.8328i | −0.721662 | − | 1.14105i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −20.0000 | − | 28.2843i | −0.848953 | − | 1.20060i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −31.6228 | −1.33990 | −0.669950 | − | 0.742406i | \(-0.733684\pi\) | ||||
−0.669950 | + | 0.742406i | \(0.733684\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 12.6491i | − | 0.535000i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.0000 | − | 11.3137i | 0.675521 | − | 0.477665i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 30.0000i | 1.26435i | 0.774826 | + | 0.632175i | \(0.217837\pi\) | ||||
−0.774826 | + | 0.632175i | \(0.782163\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 42.4264 | 1.78489 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.74962 | − | 23.6525i | 0.115473 | − | 0.993311i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 28.2843i | − | 1.18574i | −0.805299 | − | 0.592869i | \(-0.797995\pi\) | ||
0.805299 | − | 0.592869i | \(-0.202005\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.00000 | −0.334790 | −0.167395 | − | 0.985890i | \(-0.553535\pi\) | ||||
−0.167395 | + | 0.985890i | \(0.553535\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.82843 | + | 4.00000i | 0.118159 | + | 0.167102i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −31.6228 | −1.31876 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.7696 | −1.53074 | −0.765368 | − | 0.643593i | \(-0.777443\pi\) | ||||
−0.765368 | + | 0.643593i | \(0.777443\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.3607 | + | 14.1421i | −0.927677 | + | 0.586715i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.8885i | 0.740868i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.32456 | + | 17.8885i | −0.261488 | + | 0.739600i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 10.0000i | − | 0.412744i | −0.978474 | − | 0.206372i | \(-0.933834\pi\) | ||
0.978474 | − | 0.206372i | \(-0.0661657\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 40.0000 | 1.64817 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 26.8328 | − | 18.9737i | 1.10375 | − | 0.780472i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.0000i | 0.492781i | 0.969171 | + | 0.246390i | \(0.0792446\pi\) | ||||
−0.969171 | + | 0.246390i | \(0.920755\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20.0000 | + | 12.6491i | −0.819920 | + | 0.518563i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.9737 | + | 26.8328i | 0.776540 | + | 1.09819i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 19.7990i | − | 0.808965i | −0.914546 | − | 0.404482i | \(-0.867452\pi\) | ||
0.914546 | − | 0.404482i | \(-0.132548\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 12.6491i | − | 0.515968i | −0.966149 | − | 0.257984i | \(-0.916942\pi\) | ||
0.966149 | − | 0.257984i | \(-0.0830582\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.6491 | − | 4.47214i | −0.515112 | − | 0.182119i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.70820 | 0.272727 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.7990 | 0.803616 | 0.401808 | − | 0.915724i | \(-0.368382\pi\) | ||||
0.401808 | + | 0.915724i | \(0.368382\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.88854 | − | 23.9628i | 0.400704 | − | 0.971022i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 16.9706i | − | 0.686555i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 8.94427i | − | 0.361256i | −0.983552 | − | 0.180628i | \(-0.942187\pi\) | ||
0.983552 | − | 0.180628i | \(-0.0578130\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 14.1421 | − | 10.0000i | 0.570266 | − | 0.403239i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.32456 | −0.254617 | −0.127309 | − | 0.991863i | \(-0.540634\pi\) | ||||
−0.127309 | + | 0.991863i | \(0.540634\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 18.9737i | − | 0.762616i | −0.924448 | − | 0.381308i | \(-0.875474\pi\) | ||
0.924448 | − | 0.381308i | \(-0.124526\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.94427 | + | 31.6228i | 0.358921 | + | 1.26898i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.32456 | − | 10.0000i | −0.253388 | − | 0.400642i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 25.2982 | − | 17.8885i | 1.01031 | − | 0.714400i | ||||
\(628\) | 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 | ||||||||
\(633\) | 22.6274 | − | 16.0000i | 0.899359 | − | 0.635943i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 10.0000i | − | 0.396838i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.48528 | − | 17.8885i | 0.336199 | − | 0.708770i | ||||
\(638\) | 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 | ||||||||
\(643\) | 31.1127 | 1.22697 | 0.613483 | − | 0.789708i | \(-0.289768\pi\) | ||||
0.613483 | + | 0.789708i | \(0.289768\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.0000 | + | 14.1421i | 0.393750 | + | 0.556846i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.0000i | 0.393141i | 0.980490 | + | 0.196570i | \(0.0629804\pi\) | ||||
−0.980490 | + | 0.196570i | \(0.937020\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 25.2982i | 0.993042i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.0557 | − | 26.7912i | 0.433308 | − | 1.05003i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 44.2719 | 1.73249 | 0.866246 | − | 0.499617i | \(-0.166526\pi\) | ||||
0.866246 | + | 0.499617i | \(0.166526\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.0000 | 0.781465 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.48528 | − | 24.0000i | 0.331042 | − | 0.936329i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.48528i | 0.330540i | 0.986248 | + | 0.165270i | \(0.0528495\pi\) | ||||
−0.986248 | + | 0.165270i | \(0.947151\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.2982i | 0.983987i | 0.870599 | + | 0.491993i | \(0.163732\pi\) | ||||
−0.870599 | + | 0.491993i | \(0.836268\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −11.3137 | − | 16.0000i | −0.439388 | − | 0.621389i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −31.6228 | + | 20.0000i | −1.22628 | + | 0.775567i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 35.7771i | 1.38529i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.00000 | − | 2.82843i | 0.154649 | − | 0.109353i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.7771i | 1.37911i | 0.724236 | + | 0.689553i | \(0.242193\pi\) | ||||
−0.724236 | + | 0.689553i | \(0.757807\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.07107 | − | 25.0000i | −0.272166 | − | 0.962250i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.0000i | 0.922395i | 0.887298 | + | 0.461197i | \(0.152580\pi\) | ||||
−0.887298 | + | 0.461197i | \(0.847420\pi\) | |||||||
\(678\) | 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 | ||||||||
\(683\) | 6.32456 | 0.242002 | 0.121001 | − | 0.992652i | \(-0.461390\pi\) | ||||
0.121001 | + | 0.992652i | \(0.461390\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.1421 | −0.540343 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.6491 | − | 17.8885i | −0.482594 | − | 0.682491i | ||||
\(688\) | 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 | ||||||||
\(693\) | −4.98915 | − | 21.8885i | −0.189522 | − | 0.831477i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.1421i | 0.536442i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.8885i | 0.677577i | ||||||||
\(698\) | 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 | ||||||||
\(703\) | 56.5685 | 2.13352 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.4164 | + | 18.9737i | 0.505291 | + | 0.714590i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.32456 | − | 10.0000i | −0.237859 | − | 0.376089i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.0000 | −1.57734 | −0.788672 | − | 0.614815i | \(-0.789231\pi\) | ||||
−0.788672 | + | 0.614815i | \(0.789231\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.0000 | + | 33.9411i | −0.450035 | + | 1.27289i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 40.0000i | 1.49801i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.8885i | 0.668994i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.48528 | − | 12.0000i | −0.316889 | − | 0.448148i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.8885 | −0.667130 | −0.333565 | − | 0.942727i | \(-0.608252\pi\) | ||||
−0.333565 | + | 0.942727i | \(0.608252\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.00000 | − | 6.32456i | −0.148968 | − | 0.235539i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.6491 | + | 17.8885i | 0.470425 | + | 0.665282i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 28.2843i | − | 1.05045i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.4558 | −0.944105 | −0.472052 | − | 0.881570i | \(-0.656487\pi\) | ||||
−0.472052 | + | 0.881570i | \(0.656487\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.0000 | + | 14.1421i | −0.851852 | + | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.8885 | −0.661632 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.4558 | −0.940233 | −0.470117 | − | 0.882604i | \(-0.655788\pi\) | ||||
−0.470117 | + | 0.882604i | \(0.655788\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.65530 | + | 26.7082i | 0.171713 | + | 0.985147i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.6491 | −0.465936 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.00000 | −0.294285 | −0.147142 | − | 0.989115i | \(-0.547008\pi\) | ||||
−0.147142 | + | 0.989115i | \(0.547008\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −17.8885 | − | 25.2982i | −0.657152 | − | 0.929353i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.9737 | −0.696076 | −0.348038 | − | 0.937480i | \(-0.613152\pi\) | ||||
−0.348038 | + | 0.937480i | \(0.613152\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 28.2843 | + | 10.0000i | 1.03487 | + | 0.365881i | ||||
\(748\) | 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 | ||||||||
\(753\) | 37.9473 | − | 26.8328i | 1.38288 | − | 0.977842i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.94427 | 0.325515 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 8.94427i | − | 0.325085i | −0.986702 | − | 0.162543i | \(-0.948031\pi\) | ||
0.986702 | − | 0.162543i | \(-0.0519695\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | 2.82843 | + | 4.47214i | 0.102396 | + | 0.161902i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 25.2982 | + | 8.94427i | 0.914659 | + | 0.323381i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25.2982 | 0.913466 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.2982i | 0.912277i | 0.889909 | + | 0.456139i | \(0.150768\pi\) | ||||
−0.889909 | + | 0.456139i | \(0.849232\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.0000 | − | 28.2843i | −0.720282 | − | 1.01863i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32.0000i | 1.15096i | 0.817816 | + | 0.575480i | \(0.195185\pi\) | ||||
−0.817816 | + | 0.575480i | \(0.804815\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 31.6228i | − | 1.13592i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 15.6352 | − | 37.8885i | 0.560908 | − | 1.35924i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 28.2843i | 1.01339i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 40.0000 | 1.43131 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −28.2843 | + | 8.00000i | −1.01080 | + | 0.285897i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.32456 | −0.225733 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.48528 | −0.302468 | −0.151234 | − | 0.988498i | \(-0.548325\pi\) | ||||
−0.151234 | + | 0.988498i | \(0.548325\pi\) | |||||||
\(788\) | 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 | ||||||||
\(795\) | −20.0000 | + | 14.1421i | −0.709327 | + | 0.501570i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 16.0000i | − | 0.566749i | −0.959009 | − | 0.283375i | \(-0.908546\pi\) | ||
0.959009 | − | 0.283375i | \(-0.0914540\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.0000 | −0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.47214 | + | 12.6491i | −0.158015 | + | 0.446934i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 24.0000i | − | 0.846942i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.0000 | − | 31.6228i | −0.704907 | − | 1.11456i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.32456 | + | 4.47214i | −0.222635 | + | 0.157427i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.6274i | 0.795538i | 0.917486 | + | 0.397769i | \(0.130215\pi\) | ||||
−0.917486 | + | 0.397769i | \(0.869785\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.6228i | 1.11043i | 0.831708 | + | 0.555213i | \(0.187363\pi\) | ||||
−0.831708 | + | 0.555213i | \(0.812637\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.32456 | − | 8.94427i | −0.221812 | − | 0.313689i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 30.0000i | − | 1.05085i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28.2843 | −0.989541 | ||||||||
\(818\) | 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 | ||||||||
\(823\) | − | 22.3607i | − | 0.779444i | −0.920932 | − | 0.389722i | \(-0.872571\pi\) | ||
0.920932 | − | 0.389722i | \(-0.127429\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −14.1421 | − | 20.0000i | −0.492366 | − | 0.696311i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.9737 | −0.659779 | −0.329890 | − | 0.944020i | \(-0.607011\pi\) | ||||
−0.329890 | + | 0.944020i | \(0.607011\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.2982i | 0.878644i | 0.898330 | + | 0.439322i | \(0.144781\pi\) | ||||
−0.898330 | + | 0.439322i | \(0.855219\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.8328 | − | 37.9473i | −0.930820 | − | 1.31638i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −25.2982 | − | 12.0000i | −0.876531 | − | 0.415775i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 13.4164i | − | 0.464294i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −31.6228 | + | 8.94427i | −1.09304 | + | 0.309159i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35.7771 | −1.23516 | −0.617581 | − | 0.786507i | \(-0.711887\pi\) | ||||
−0.617581 | + | 0.786507i | \(0.711887\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.00000 | −0.103448 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.9706 | + | 24.0000i | 0.584497 | + | 0.826604i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.1803 | −0.384615 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.24264 | + | 6.70820i | 0.145779 | + | 0.230497i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 36.0000 | − | 25.4558i | 1.23552 | − | 0.873642i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 56.5685i | 1.93914i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −36.7696 | −1.25897 | −0.629483 | − | 0.777014i | \(-0.716733\pi\) | ||||
−0.629483 | + | 0.777014i | \(0.716733\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 40.0000 | + | 14.1421i | 1.36797 | + | 0.483651i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.0000i | 0.683187i | 0.939848 | + | 0.341593i | \(0.110967\pi\) | ||||
−0.939848 | + | 0.341593i | \(0.889033\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 44.2719i | − | 1.51054i | −0.655415 | − | 0.755269i | \(-0.727506\pi\) | ||
0.655415 | − | 0.755269i | \(-0.272494\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.9443 | + | 7.81758i | 0.645619 | + | 0.266422i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.9737 | 0.645871 | 0.322936 | − | 0.946421i | \(-0.395330\pi\) | ||||
0.322936 | + | 0.946421i | \(0.395330\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 17.8885i | − | 0.608229i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.41421 | − | 1.00000i | 0.0480292 | − | 0.0339618i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 33.9411i | 1.15137i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.6491i | 0.428599i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.48528 | − | 24.0000i | 0.287183 | − | 0.812277i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15.8114 | + | 25.0000i | 0.534522 | + | 0.845154i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.8328i | 0.906080i | 0.891490 | + | 0.453040i | \(0.149660\pi\) | ||||
−0.891490 | + | 0.453040i | \(0.850340\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | − | 40.2492i | − | 1.35449i | −0.735756 | − | 0.677247i | \(-0.763173\pi\) | ||
0.735756 | − | 0.677247i | \(-0.236827\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −28.2843 | + | 20.0000i | −0.950765 | + | 0.672293i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.0000i | 1.00730i | 0.863907 | + | 0.503651i | \(0.168010\pi\) | ||||
−0.863907 | + | 0.503651i | \(0.831990\pi\) | |||||||
\(888\) | 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 | ||||||||
\(893\) | −37.9473 | −1.26986 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 31.6228i | − | 1.05703i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 25.2982 | − | 17.8885i | 0.844683 | − | 0.597281i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −35.7771 | −1.19323 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 25.2982i | − | 0.842806i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.81758 | + | 18.9443i | −0.260153 | + | 0.630426i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 28.2843i | 0.940201i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.4164i | 0.445485i | 0.974877 | + | 0.222742i | \(0.0715008\pi\) | ||||
−0.974877 | + | 0.222742i | \(0.928499\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | 28.2843 | 0.936073 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.6491 | + | 20.0000i | 0.417710 | + | 0.660458i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −52.0000 | −1.71532 | −0.857661 | − | 0.514216i | \(-0.828083\pi\) | ||||
−0.857661 | + | 0.514216i | \(0.828083\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.0000 | + | 8.48528i | −0.395413 | + | 0.279600i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 40.0000i | − | 1.31662i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 44.7214i | − | 1.47043i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.82843 | + | 8.00000i | −0.0928977 | + | 0.262754i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.47214 | −0.146726 | −0.0733630 | − | 0.997305i | \(-0.523373\pi\) | ||||
−0.0733630 | + | 0.997305i | \(0.523373\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −40.0000 | − | 18.9737i | −1.31095 | − | 0.621837i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −25.2982 | + | 17.8885i | −0.828227 | + | 0.585645i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 25.2982 | 0.827340 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.48528 | 0.277202 | 0.138601 | − | 0.990348i | \(-0.455739\pi\) | ||||
0.138601 | + | 0.990348i | \(0.455739\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | −28.2843 | −0.921063 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 20.5279 | − | 22.8825i | 0.667771 | − | 0.744366i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.9737 | 0.616561 | 0.308281 | − | 0.951295i | \(-0.400246\pi\) | ||||
0.308281 | + | 0.951295i | \(0.400246\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24.0000 | −0.779073 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26.8328 | − | 18.9737i | 0.870114 | − | 0.615263i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.9737 | 0.614617 | 0.307309 | − | 0.951610i | \(-0.400572\pi\) | ||||
0.307309 | + | 0.951610i | \(0.400572\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.32456i | 0.204658i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −22.6274 | + | 16.0000i | −0.731441 | + | 0.517207i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.94427 | − | 14.1421i | −0.288826 | − | 0.456673i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.00000 | −0.290323 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18.9737 | + | 53.6656i | −0.611418 | + | 1.72935i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.2492i | 1.29433i | 0.762351 | + | 0.647164i | \(0.224045\pi\) | ||||
−0.762351 | + | 0.647164i | \(0.775955\pi\) | |||||||
\(968\) | 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 | ||||||||
\(973\) | −14.1421 | + | 8.94427i | −0.453376 | + | 0.286740i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −20.0000 | + | 14.1421i | −0.640513 | + | 0.452911i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.9737 | 0.607021 | 0.303511 | − | 0.952828i | \(-0.401841\pi\) | ||||
0.303511 | + | 0.952828i | \(0.401841\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.6491i | 0.404267i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00000 | − | 5.65685i | 0.0638551 | − | 0.180609i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 18.0000i | − | 0.574111i | −0.957914 | − | 0.287055i | \(-0.907324\pi\) | ||
0.957914 | − | 0.287055i | \(-0.0926764\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 42.4264 | 1.35182 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.4884 | + | 25.4164i | −0.333849 | + | 0.809013i | ||||
\(988\) | 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 | ||||||||
\(993\) | 11.3137 | − | 8.00000i | 0.359030 | − | 0.253872i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 42.4264i | 1.34501i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.48528 | 0.268732 | 0.134366 | − | 0.990932i | \(-0.457100\pi\) | ||||
0.134366 | + | 0.990932i | \(0.457100\pi\) | |||||||
\(998\) | 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 | 420.2.f.b.209.6 | yes | 8 | |
3.2 | odd | 2 | inner | 420.2.f.b.209.7 | yes | 8 | |
4.3 | odd | 2 | 1680.2.k.g.209.4 | 8 | |||
5.2 | odd | 4 | 2100.2.d.f.1301.1 | 4 | |||
5.3 | odd | 4 | 2100.2.d.i.1301.4 | 4 | |||
5.4 | even | 2 | inner | 420.2.f.b.209.4 | yes | 8 | |
7.6 | odd | 2 | inner | 420.2.f.b.209.3 | yes | 8 | |
12.11 | even | 2 | 1680.2.k.g.209.1 | 8 | |||
15.2 | even | 4 | 2100.2.d.i.1301.1 | 4 | |||
15.8 | even | 4 | 2100.2.d.f.1301.4 | 4 | |||
15.14 | odd | 2 | inner | 420.2.f.b.209.1 | ✓ | 8 | |
20.19 | odd | 2 | 1680.2.k.g.209.6 | 8 | |||
21.20 | even | 2 | inner | 420.2.f.b.209.2 | yes | 8 | |
28.27 | even | 2 | 1680.2.k.g.209.5 | 8 | |||
35.13 | even | 4 | 2100.2.d.f.1301.2 | 4 | |||
35.27 | even | 4 | 2100.2.d.i.1301.3 | 4 | |||
35.34 | odd | 2 | inner | 420.2.f.b.209.5 | yes | 8 | |
60.59 | even | 2 | 1680.2.k.g.209.7 | 8 | |||
84.83 | odd | 2 | 1680.2.k.g.209.8 | 8 | |||
105.62 | odd | 4 | 2100.2.d.f.1301.3 | 4 | |||
105.83 | odd | 4 | 2100.2.d.i.1301.2 | 4 | |||
105.104 | even | 2 | inner | 420.2.f.b.209.8 | yes | 8 | |
140.139 | even | 2 | 1680.2.k.g.209.3 | 8 | |||
420.419 | odd | 2 | 1680.2.k.g.209.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.f.b.209.1 | ✓ | 8 | 15.14 | odd | 2 | inner | |
420.2.f.b.209.2 | yes | 8 | 21.20 | even | 2 | inner | |
420.2.f.b.209.3 | yes | 8 | 7.6 | odd | 2 | inner | |
420.2.f.b.209.4 | yes | 8 | 5.4 | even | 2 | inner | |
420.2.f.b.209.5 | yes | 8 | 35.34 | odd | 2 | inner | |
420.2.f.b.209.6 | yes | 8 | 1.1 | even | 1 | trivial | |
420.2.f.b.209.7 | yes | 8 | 3.2 | odd | 2 | inner | |
420.2.f.b.209.8 | yes | 8 | 105.104 | even | 2 | inner | |
1680.2.k.g.209.1 | 8 | 12.11 | even | 2 | |||
1680.2.k.g.209.2 | 8 | 420.419 | odd | 2 | |||
1680.2.k.g.209.3 | 8 | 140.139 | even | 2 | |||
1680.2.k.g.209.4 | 8 | 4.3 | odd | 2 | |||
1680.2.k.g.209.5 | 8 | 28.27 | even | 2 | |||
1680.2.k.g.209.6 | 8 | 20.19 | odd | 2 | |||
1680.2.k.g.209.7 | 8 | 60.59 | even | 2 | |||
1680.2.k.g.209.8 | 8 | 84.83 | odd | 2 | |||
2100.2.d.f.1301.1 | 4 | 5.2 | odd | 4 | |||
2100.2.d.f.1301.2 | 4 | 35.13 | even | 4 | |||
2100.2.d.f.1301.3 | 4 | 105.62 | odd | 4 | |||
2100.2.d.f.1301.4 | 4 | 15.8 | even | 4 | |||
2100.2.d.i.1301.1 | 4 | 15.2 | even | 4 | |||
2100.2.d.i.1301.2 | 4 | 105.83 | odd | 4 | |||
2100.2.d.i.1301.3 | 4 | 35.27 | even | 4 | |||
2100.2.d.i.1301.4 | 4 | 5.3 | odd | 4 |