Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2400,2,Mod(2399,2400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2400.2399");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2400.o (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.1640964851\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 8 x^{14} - 16 x^{13} + 41 x^{12} - 64 x^{11} + 56 x^{10} - 100 x^{9} + 256 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2399.13 | ||
Root | \(1.47894 - 0.901513i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2400.2399 |
Dual form | 2400.2.o.l.2399.15 |
$q$-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 \(\left(\mathbb{Z}/2400\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1601\) | \(1951\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.68324 | − | 0.408305i | 0.971817 | − | 0.235735i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.40591 | −0.531383 | −0.265691 | − | 0.964058i | \(-0.585600\pi\) | ||||
−0.265691 | + | 0.964058i | \(0.585600\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.66657 | − | 1.37455i | 0.888858 | − | 0.458183i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.15156 | −1.85477 | −0.927383 | − | 0.374114i | \(-0.877947\pi\) | ||||
−0.927383 | + | 0.374114i | \(0.877947\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.52133i | − | 0.976643i | −0.872664 | − | 0.488321i | \(-0.837609\pi\) | ||
0.872664 | − | 0.488321i | \(-0.162391\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.39065 | −0.337282 | −0.168641 | − | 0.985678i | \(-0.553938\pi\) | ||||
−0.168641 | + | 0.985678i | \(0.553938\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.77238i | 0.636028i | 0.948086 | + | 0.318014i | \(0.103016\pi\) | ||||
−0.948086 | + | 0.318014i | \(0.896984\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.36647 | + | 0.574039i | −0.516407 | + | 0.125266i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.18687i | 0.873024i | 0.899698 | + | 0.436512i | \(0.143786\pi\) | ||||
−0.899698 | + | 0.436512i | \(0.856214\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.92724 | − | 3.40247i | 0.755798 | − | 0.654805i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 8.16338i | − | 1.51590i | −0.652312 | − | 0.757951i | \(-0.726201\pi\) | ||
0.652312 | − | 0.757951i | \(-0.273799\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.44858i | − | 1.15820i | −0.815257 | − | 0.579099i | \(-0.803404\pi\) | ||
0.815257 | − | 0.579099i | \(-0.196596\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10.3545 | + | 2.51171i | −1.80249 | + | 0.437233i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.73295i | − | 0.778092i | −0.921218 | − | 0.389046i | \(-0.872805\pi\) | ||
0.921218 | − | 0.389046i | \(-0.127195\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.43778 | − | 5.92724i | −0.230229 | − | 0.949118i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.02387i | 0.472249i | 0.971723 | + | 0.236124i | \(0.0758773\pi\) | ||||
−0.971723 | + | 0.236124i | \(0.924123\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.71563 | −0.871625 | −0.435813 | − | 0.900037i | \(-0.643539\pi\) | ||||
−0.435813 | + | 0.900037i | \(0.643539\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 5.49819i | − | 0.801994i | −0.916079 | − | 0.400997i | \(-0.868664\pi\) | ||
0.916079 | − | 0.400997i | \(-0.131336\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.02343 | −0.717632 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.34079 | + | 0.567809i | −0.327776 | + | 0.0795091i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.0284 | −1.65222 | −0.826111 | − | 0.563508i | \(-0.809451\pi\) | ||||
−0.826111 | + | 0.563508i | \(0.809451\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.13198 | + | 4.66657i | 0.149934 | + | 0.618103i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.86497 | −0.503177 | −0.251588 | − | 0.967834i | \(-0.580953\pi\) | ||||
−0.251588 | + | 0.967834i | \(0.580953\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.94456 | −1.01720 | −0.508598 | − | 0.861004i | \(-0.669836\pi\) | ||||
−0.508598 | + | 0.861004i | \(0.669836\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.74895 | + | 1.93249i | −0.472324 | + | 0.243470i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.89392 | 0.964395 | 0.482198 | − | 0.876062i | \(-0.339839\pi\) | ||||
0.482198 | + | 0.876062i | \(0.339839\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.70952 | + | 7.04750i | 0.205802 | + | 0.848420i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.9918 | −1.30449 | −0.652244 | − | 0.758009i | \(-0.726172\pi\) | ||||
−0.652244 | + | 0.758009i | \(0.726172\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 0.909922i | − | 0.106498i | −0.998581 | − | 0.0532491i | \(-0.983042\pi\) | ||
0.998581 | − | 0.0532491i | \(-0.0169577\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.64852 | 0.985591 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1.12153i | − | 0.126183i | −0.998008 | − | 0.0630913i | \(-0.979904\pi\) | ||
0.998008 | − | 0.0630913i | \(-0.0200959\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.22124 | − | 7.33067i | 0.580137 | − | 0.814519i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.3621i | 1.57644i | 0.615392 | + | 0.788221i | \(0.288998\pi\) | ||||
−0.615392 | + | 0.788221i | \(0.711002\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.33315 | − | 13.7409i | −0.357351 | − | 1.47318i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 14.0628i | − | 1.49065i | −0.666699 | − | 0.745327i | \(-0.732293\pi\) | ||
0.666699 | − | 0.745327i | \(-0.267707\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.95067i | 0.518971i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.63299 | − | 10.8545i | −0.273028 | − | 1.12556i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.44247i | 0.958738i | 0.877614 | + | 0.479369i | \(0.159134\pi\) | ||||
−0.877614 | + | 0.479369i | \(0.840866\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −16.4036 | + | 8.45562i | −1.64862 | + | 0.849822i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 16.9280i | − | 1.68440i | −0.539165 | − | 0.842200i | \(-0.681260\pi\) | ||
0.539165 | − | 0.842200i | \(-0.318740\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.2350 | 1.10702 | 0.553511 | − | 0.832842i | \(-0.313288\pi\) | ||||
0.553511 | + | 0.832842i | \(0.313288\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.78478i | 0.752583i | 0.926501 | + | 0.376292i | \(0.122801\pi\) | ||||
−0.926501 | + | 0.376292i | \(0.877199\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.1876 | 1.74206 | 0.871030 | − | 0.491231i | \(-0.163453\pi\) | ||||
0.871030 | + | 0.491231i | \(0.163453\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.93249 | − | 7.96667i | −0.183423 | − | 0.756163i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.09921 | −0.667838 | −0.333919 | − | 0.942602i | \(-0.608371\pi\) | ||||
−0.333919 | + | 0.942602i | \(0.608371\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.84024 | − | 9.38990i | −0.447481 | − | 0.868097i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.95512 | 0.179226 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 26.8417 | 2.44016 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.23466 | + | 5.08989i | 0.111326 | + | 0.458940i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.54476 | −0.846961 | −0.423480 | − | 0.905905i | \(-0.639192\pi\) | ||||
−0.423480 | + | 0.905905i | \(0.639192\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.62076 | + | 2.33372i | −0.847060 | + | 0.205473i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.40558 | −0.122806 | −0.0614029 | − | 0.998113i | \(-0.519557\pi\) | ||||
−0.0614029 | + | 0.998113i | \(0.519557\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 3.89771i | − | 0.337974i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.9444 | 1.02048 | 0.510241 | − | 0.860031i | \(-0.329556\pi\) | ||||
0.510241 | + | 0.860031i | \(0.329556\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 16.4091i | − | 1.39181i | −0.718136 | − | 0.695903i | \(-0.755004\pi\) | ||
0.718136 | − | 0.695903i | \(-0.244996\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.24494 | − | 9.25476i | −0.189058 | − | 0.779392i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 21.6617i | 1.81144i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.45562 | + | 2.05109i | −0.697408 | + | 0.169171i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 12.3974i | − | 1.01563i | −0.861465 | − | 0.507817i | \(-0.830453\pi\) | ||
0.861465 | − | 0.507817i | \(-0.169547\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0600i | 0.981428i | 0.871321 | + | 0.490714i | \(0.163264\pi\) | ||||
−0.871321 | + | 0.490714i | \(0.836736\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.70827 | + | 1.91151i | −0.299796 | + | 0.154537i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.45468i | 0.275714i | 0.990452 | + | 0.137857i | \(0.0440214\pi\) | ||||
−0.990452 | + | 0.137857i | \(0.955979\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −20.2466 | + | 4.91124i | −1.60566 | + | 0.389486i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 5.88635i | − | 0.463910i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.0032 | −1.33180 | −0.665898 | − | 0.746043i | \(-0.731951\pi\) | ||||
−0.665898 | + | 0.746043i | \(0.731951\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.2582i | 1.10334i | 0.834064 | + | 0.551668i | \(0.186008\pi\) | ||||
−0.834064 | + | 0.551668i | \(0.813992\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.600200 | 0.0461692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.81077 | + | 7.39276i | 0.291417 | + | 0.565338i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.0630 | 0.993164 | 0.496582 | − | 0.867990i | \(-0.334588\pi\) | ||||
0.496582 | + | 0.867990i | \(0.334588\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.50567 | + | 1.57809i | −0.488996 | + | 0.118616i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.86388 | 0.662517 | 0.331259 | − | 0.943540i | \(-0.392527\pi\) | ||||
0.331259 | + | 0.943540i | \(0.392527\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.3011 | −1.80629 | −0.903145 | − | 0.429336i | \(-0.858747\pi\) | ||||
−0.903145 | + | 0.429336i | \(0.858747\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.3726 | + | 3.24380i | −0.988530 | + | 0.239789i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.55466 | 0.625579 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.52133 | + | 4.78355i | −0.401618 | + | 0.347952i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.74947 | 0.705447 | 0.352723 | − | 0.935728i | \(-0.385256\pi\) | ||||
0.352723 | + | 0.935728i | \(0.385256\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 25.8651i | 1.86181i | 0.365257 | + | 0.930907i | \(0.380981\pi\) | ||||
−0.365257 | + | 0.930907i | \(0.619019\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.3745 | 1.59412 | 0.797058 | − | 0.603902i | \(-0.206388\pi\) | ||||
0.797058 | + | 0.603902i | \(0.206388\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 6.36971i | − | 0.451537i | −0.974181 | − | 0.225768i | \(-0.927511\pi\) | ||
0.974181 | − | 0.225768i | \(-0.0724893\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.2873 | − | 3.22312i | 0.937216 | − | 0.227342i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.4769i | 0.805524i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.75506 | + | 11.1646i | 0.400004 | + | 0.775994i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 17.0545i | − | 1.17968i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 25.4387i | − | 1.75127i | −0.482973 | − | 0.875635i | \(-0.660443\pi\) | ||
0.482973 | − | 0.875635i | \(-0.339557\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −18.5018 | + | 4.48801i | −1.26772 | + | 0.307513i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.06610i | 0.615447i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.371525 | − | 1.53161i | −0.0251054 | − | 0.103497i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.89694i | 0.329404i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.99334 | −0.267414 | −0.133707 | − | 0.991021i | \(-0.542688\pi\) | ||||
−0.133707 | + | 0.991021i | \(0.542688\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 9.59081i | − | 0.636564i | −0.947996 | − | 0.318282i | \(-0.896894\pi\) | ||
0.947996 | − | 0.318282i | \(-0.103106\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.45468 | −0.624783 | −0.312392 | − | 0.949953i | \(-0.601130\pi\) | ||||
−0.312392 | + | 0.949953i | \(0.601130\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.5575 | − | 3.53123i | 0.957814 | − | 0.232338i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.42285 | −0.0932140 | −0.0466070 | − | 0.998913i | \(-0.514841\pi\) | ||||
−0.0466070 | + | 0.998913i | \(0.514841\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.457928 | − | 1.88781i | −0.0297456 | − | 0.122626i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.6653 | 0.689883 | 0.344941 | − | 0.938624i | \(-0.387899\pi\) | ||||
0.344941 | + | 0.938624i | \(0.387899\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.53255 | 0.291967 | 0.145984 | − | 0.989287i | \(-0.453365\pi\) | ||||
0.145984 | + | 0.989287i | \(0.453365\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.79543 | − | 14.4711i | 0.371777 | − | 0.928322i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.76248 | 0.621172 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.86410 | + | 24.1748i | 0.371623 | + | 1.53201i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.1303 | −0.765659 | −0.382829 | − | 0.923819i | \(-0.625050\pi\) | ||||
−0.382829 | + | 0.923819i | \(0.625050\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 25.7558i | − | 1.61925i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.3268 | 1.01844 | 0.509218 | − | 0.860638i | \(-0.329935\pi\) | ||||
0.509218 | + | 0.860638i | \(0.329935\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.65408i | 0.413465i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.2210 | − | 21.7683i | −0.694560 | − | 1.34742i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.3933i | 0.640877i | 0.947269 | + | 0.320438i | \(0.103830\pi\) | ||||
−0.947269 | + | 0.320438i | \(0.896170\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.74191 | − | 23.6710i | −0.351399 | − | 1.44864i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.47928i | 0.577962i | 0.957335 | + | 0.288981i | \(0.0933164\pi\) | ||||
−0.957335 | + | 0.288981i | \(0.906684\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.7878i | 1.44501i | 0.691367 | + | 0.722504i | \(0.257009\pi\) | ||||
−0.691367 | + | 0.722504i | \(0.742991\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.02138 | + | 8.33315i | 0.122340 | + | 0.504345i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 21.6535i | − | 1.30103i | −0.759492 | − | 0.650517i | \(-0.774552\pi\) | ||
0.759492 | − | 0.650517i | \(-0.225448\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.86388 | − | 17.1956i | −0.530667 | − | 1.02947i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.40618i | 0.441816i | 0.975295 | + | 0.220908i | \(0.0709020\pi\) | ||||
−0.975295 | + | 0.220908i | \(0.929098\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.5907 | 0.688994 | 0.344497 | − | 0.938787i | \(-0.388050\pi\) | ||||
0.344497 | + | 0.938787i | \(0.388050\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 4.25128i | − | 0.250945i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.0661 | −0.886241 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.85541 | + | 15.8939i | 0.226008 | + | 0.931718i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 32.0550 | 1.87267 | 0.936336 | − | 0.351105i | \(-0.114194\pi\) | ||||
0.936336 | + | 0.351105i | \(0.114194\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −24.1587 | + | 20.9305i | −1.40183 | + | 1.21451i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.7434 | 0.852632 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.03564 | 0.463167 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.91179 | − | 28.4939i | −0.397072 | − | 1.63693i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.2143 | −1.43906 | −0.719528 | − | 0.694464i | \(-0.755642\pi\) | ||||
−0.719528 | + | 0.694464i | \(0.755642\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.9112 | − | 4.58732i | 1.07582 | − | 0.260964i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.3979 | −0.589608 | −0.294804 | − | 0.955558i | \(-0.595254\pi\) | ||||
−0.294804 | + | 0.955558i | \(0.595254\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 8.68972i | − | 0.491172i | −0.969375 | − | 0.245586i | \(-0.921020\pi\) | ||
0.969375 | − | 0.245586i | \(-0.0789804\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.0094 | −0.899179 | −0.449590 | − | 0.893235i | \(-0.648430\pi\) | ||||
−0.449590 | + | 0.893235i | \(0.648430\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 50.2175i | 2.81164i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.17857 | + | 13.1036i | 0.177410 | + | 0.731373i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.85541i | − | 0.214521i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 30.6141 | − | 7.42610i | 1.69296 | − | 0.410664i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.72995i | 0.426166i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 5.67620i | − | 0.311992i | −0.987758 | − | 0.155996i | \(-0.950141\pi\) | ||
0.987758 | − | 0.155996i | \(-0.0498587\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.50567 | − | 12.6208i | −0.356508 | − | 0.691613i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.4232i | 0.731210i | 0.930770 | + | 0.365605i | \(0.119138\pi\) | ||||
−0.930770 | + | 0.365605i | \(0.880862\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.9497 | + | 2.89864i | −0.649016 | + | 0.157433i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 39.6688i | 2.14819i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9038 | 0.912720 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.5685i | 1.10417i | 0.833787 | + | 0.552087i | \(0.186168\pi\) | ||||
−0.833787 | + | 0.552087i | \(0.813832\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.10932 | 0.166438 | 0.0832191 | − | 0.996531i | \(-0.473480\pi\) | ||||
0.0832191 | + | 0.996531i | \(0.473480\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.9812 | − | 13.8291i | −0.639510 | − | 0.738145i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.61137 | 0.0857645 | 0.0428823 | − | 0.999080i | \(-0.486346\pi\) | ||||
0.0428823 | + | 0.999080i | \(0.486346\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.29093 | − | 0.798286i | 0.174175 | − | 0.0422498i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.2688 | 0.700302 | 0.350151 | − | 0.936693i | \(-0.386130\pi\) | ||||
0.350151 | + | 0.936693i | \(0.386130\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.3139 | 0.595469 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 45.1810 | − | 10.9596i | 2.37139 | − | 0.575230i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.4726 | −0.703262 | −0.351631 | − | 0.936139i | \(-0.614373\pi\) | ||||
−0.351631 | + | 0.936139i | \(0.614373\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.15645 | + | 8.06337i | 0.216376 | + | 0.419762i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.9107 | 0.877962 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.03146i | 0.260519i | 0.991480 | + | 0.130259i | \(0.0415810\pi\) | ||||
−0.991480 | + | 0.130259i | \(0.958419\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −28.7460 | −1.48049 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 23.6977i | − | 1.21727i | −0.793451 | − | 0.608635i | \(-0.791718\pi\) | ||
0.793451 | − | 0.608635i | \(-0.208282\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.0661 | + | 3.89717i | −0.823091 | + | 0.199658i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 34.0338i | − | 1.73905i | −0.493892 | − | 0.869523i | \(-0.664426\pi\) | ||
0.493892 | − | 0.869523i | \(-0.335574\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −15.2411 | + | 7.85641i | −0.774751 | + | 0.399364i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 12.5779i | − | 0.637725i | −0.947801 | − | 0.318862i | \(-0.896699\pi\) | ||
0.947801 | − | 0.318862i | \(-0.103301\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 5.82247i | − | 0.294455i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.36592 | + | 0.573904i | −0.119345 | + | 0.0289496i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 32.5442i | − | 1.63335i | −0.577100 | − | 0.816673i | \(-0.695816\pi\) | ||
0.577100 | − | 0.816673i | \(-0.304184\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.59145 | − | 6.56077i | −0.0796723 | − | 0.328449i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.4987i | 1.02366i | 0.859088 | + | 0.511828i | \(0.171032\pi\) | ||||
−0.859088 | + | 0.511828i | \(0.828968\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.7076 | −1.13115 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 29.1150i | 1.44318i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.58096 | 0.0781733 | 0.0390866 | − | 0.999236i | \(-0.487555\pi\) | ||||
0.0390866 | + | 0.999236i | \(0.487555\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.1053 | − | 4.87698i | 0.991723 | − | 0.240563i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.43379 | 0.267379 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.69993 | − | 27.6205i | −0.328097 | − | 1.35258i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.7337 | 1.40373 | 0.701867 | − | 0.712308i | \(-0.252350\pi\) | ||||
0.701867 | + | 0.712308i | \(0.252350\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.1280 | −1.02972 | −0.514858 | − | 0.857275i | \(-0.672155\pi\) | ||||
−0.514858 | + | 0.857275i | \(0.672155\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.55753 | − | 14.6613i | −0.367460 | − | 0.712859i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.1693 | 0.540521 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.84458 | + | 36.4618i | 0.427021 | + | 1.76039i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.2349 | −1.26369 | −0.631845 | − | 0.775095i | \(-0.717702\pi\) | ||||
−0.631845 | + | 0.775095i | \(0.717702\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.13375i | 0.390883i | 0.980715 | + | 0.195441i | \(0.0626140\pi\) | ||||
−0.980715 | + | 0.195441i | \(0.937386\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.6076 | −0.555267 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 8.54987i | − | 0.408063i | −0.978964 | − | 0.204031i | \(-0.934596\pi\) | ||
0.978964 | − | 0.204031i | \(-0.0654045\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.3953 | + | 6.90494i | −0.637873 | + | 0.328807i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 5.28012i | − | 0.250866i | −0.992102 | − | 0.125433i | \(-0.959968\pi\) | ||
0.992102 | − | 0.125433i | \(-0.0400320\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.06191 | − | 20.8677i | −0.239420 | − | 0.987010i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 35.9522i | − | 1.69669i | −0.529446 | − | 0.848344i | \(-0.677600\pi\) | ||
0.529446 | − | 0.848344i | \(-0.322400\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 18.6015i | − | 0.875911i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.92415 | + | 20.2998i | 0.231357 | + | 0.953769i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 14.0192i | − | 0.655793i | −0.944714 | − | 0.327896i | \(-0.893660\pi\) | ||
0.944714 | − | 0.327896i | \(-0.106340\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.46141 | + | 4.73163i | −0.254917 | + | 0.220854i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.19979i | 0.0558796i | 0.999610 | + | 0.0279398i | \(0.00889467\pi\) | ||||
−0.999610 | + | 0.0279398i | \(0.991105\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.341733 | 0.0158817 | 0.00794085 | − | 0.999968i | \(-0.497472\pi\) | ||||
0.00794085 | + | 0.999968i | \(0.497472\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 10.2346i | − | 0.473601i | −0.971558 | − | 0.236801i | \(-0.923901\pi\) | ||
0.971558 | − | 0.236801i | \(-0.0760988\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.0981 | −0.512463 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.41056 | + | 5.81505i | 0.0649954 | + | 0.267943i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 35.1600 | 1.61666 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −32.0745 | + | 16.5335i | −1.46859 | + | 0.757019i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.5177 | 1.02886 | 0.514431 | − | 0.857532i | \(-0.328003\pi\) | ||||
0.514431 | + | 0.857532i | \(0.328003\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.6663 | −0.759918 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.40343 | − | 9.90813i | −0.109360 | − | 0.450836i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.1922 | 1.45877 | 0.729384 | − | 0.684105i | \(-0.239807\pi\) | ||||
0.729384 | + | 0.684105i | \(0.239807\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −28.6205 | + | 6.94251i | −1.29426 | + | 0.313951i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.9122 | 0.537592 | 0.268796 | − | 0.963197i | \(-0.413374\pi\) | ||||
0.268796 | + | 0.963197i | \(0.413374\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.3524i | 0.511286i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.4535 | 0.693182 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.37389i | 0.240569i | 0.992739 | + | 0.120284i | \(0.0383806\pi\) | ||||
−0.992739 | + | 0.120284i | \(0.961619\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.82171 | + | 24.0000i | 0.260095 | + | 1.07224i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 35.5337i | − | 1.58437i | −0.610283 | − | 0.792184i | \(-0.708944\pi\) | ||
0.610283 | − | 0.792184i | \(-0.291056\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.01028 | − | 0.245065i | 0.0448681 | − | 0.0108837i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 0.485143i | − | 0.0215036i | −0.999942 | − | 0.0107518i | \(-0.996578\pi\) | ||
0.999942 | − | 0.0107518i | \(-0.00342246\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.27926i | 0.0565913i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.43293 | + | 10.8878i | 0.416474 | + | 0.480709i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 33.8225i | 1.48751i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.9882 | − | 5.33370i | 0.965174 | − | 0.234124i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.0373i | 1.09691i | 0.836181 | + | 0.548453i | \(0.184783\pi\) | ||||
−0.836181 | + | 0.548453i | \(0.815217\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.54152 | −0.373495 | −0.186747 | − | 0.982408i | \(-0.559795\pi\) | ||||
−0.186747 | + | 0.982408i | \(0.559795\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.96770i | 0.390639i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.47008 | 0.237830 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.3062 | + | 5.31259i | −0.447253 | + | 0.230547i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.6481 | 0.461218 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.9200 | − | 3.61917i | 0.643846 | − | 0.156179i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 30.9019 | 1.33104 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.65508 | −0.200138 | −0.100069 | − | 0.994981i | \(-0.531906\pi\) | ||||
−0.100069 | + | 0.994981i | \(0.531906\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −40.9046 | + | 9.92227i | −1.75538 | + | 0.425806i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.56114 | −0.109506 | −0.0547531 | − | 0.998500i | \(-0.517437\pi\) | ||||
−0.0547531 | + | 0.998500i | \(0.517437\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −21.1848 | + | 10.9202i | −0.904144 | + | 0.466062i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.6320 | 0.964155 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.57677i | 0.0670512i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.9388 | 0.844834 | 0.422417 | − | 0.906402i | \(-0.361182\pi\) | ||||
0.422417 | + | 0.906402i | \(0.361182\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.1266i | 0.851266i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.3995 | − | 3.49291i | 0.607948 | − | 0.147471i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 31.5744i | − | 1.33070i | −0.746530 | − | 0.665352i | \(-0.768282\pi\) | ||
0.746530 | − | 0.665352i | \(-0.231718\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.34057 | + | 10.3062i | −0.308275 | + | 0.432821i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.5657i | 1.15561i | 0.816173 | + | 0.577807i | \(0.196092\pi\) | ||||
−0.816173 | + | 0.577807i | \(0.803908\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.80097i | 0.326460i | 0.986588 | + | 0.163230i | \(0.0521913\pi\) | ||||
−0.986588 | + | 0.163230i | \(0.947809\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.4107 | − | 3.98076i | 0.685565 | − | 0.166298i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.115060i | 0.00479001i | 0.999997 | + | 0.00239500i | \(0.000762354\pi\) | ||||
−0.999997 | + | 0.00239500i | \(0.999238\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.5609 | + | 43.5372i | 0.438895 | + | 1.80934i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 20.1917i | − | 0.837694i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 73.9932 | 3.06448 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.5967i | 1.01521i | 0.861589 | + | 0.507607i | \(0.169470\pi\) | ||||
−0.861589 | + | 0.507607i | \(0.830530\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.8779 | 0.736646 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 37.6616 | − | 9.13562i | 1.54919 | − | 0.375789i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.8619 | 1.22628 | 0.613140 | − | 0.789974i | \(-0.289906\pi\) | ||||
0.613140 | + | 0.789974i | \(0.289906\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.60078 | − | 10.7217i | −0.106443 | − | 0.438811i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.6643 | 0.558308 | 0.279154 | − | 0.960246i | \(-0.409946\pi\) | ||||
0.279154 | + | 0.960246i | \(0.409946\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.35657 | −0.381663 | −0.190831 | − | 0.981623i | \(-0.561118\pi\) | ||||
−0.190831 | + | 0.981623i | \(0.561118\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 21.0497 | − | 10.8506i | 0.857211 | − | 0.441869i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.9867 | −1.13594 | −0.567972 | − | 0.823048i | \(-0.692272\pi\) | ||||
−0.567972 | + | 0.823048i | \(0.692272\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.68610 | + | 19.3184i | 0.189890 | + | 0.782822i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.3610 | −0.783261 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.46171i | 0.0994277i | 0.998764 | + | 0.0497138i | \(0.0158309\pi\) | ||||
−0.998764 | + | 0.0497138i | \(0.984169\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.39313 | 0.0963440 | 0.0481720 | − | 0.998839i | \(-0.484660\pi\) | ||||
0.0481720 | + | 0.998839i | \(0.484660\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 37.4939i | − | 1.50701i | −0.657444 | − | 0.753503i | \(-0.728363\pi\) | ||
0.657444 | − | 0.753503i | \(-0.271637\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.2457 | + | 16.4429i | 0.571660 | + | 0.659830i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 19.7710i | 0.792108i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.96343 | − | 28.7067i | −0.278092 | − | 1.14644i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.58187i | 0.262436i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.3255i | 1.44609i | 0.690798 | + | 0.723047i | \(0.257259\pi\) | ||||
−0.690798 | + | 0.723047i | \(0.742741\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.3867 | − | 42.8193i | −0.412836 | − | 1.70192i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.6892i | 0.700870i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −29.3105 | + | 15.1088i | −1.15950 | + | 0.597694i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.46351i | 0.176298i | 0.996107 | + | 0.0881489i | \(0.0280951\pi\) | ||||
−0.996107 | + | 0.0881489i | \(0.971905\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.4537 | −0.688306 | −0.344153 | − | 0.938914i | \(-0.611834\pi\) | ||||
−0.344153 | + | 0.938914i | \(0.611834\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 1.84087i | − | 0.0723721i | −0.999345 | − | 0.0361860i | \(-0.988479\pi\) | ||
0.999345 | − | 0.0361860i | \(-0.0115209\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23.7756 | 0.933275 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.70173 | + | 15.2604i | 0.145082 | + | 0.598102i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.19535 | 0.359842 | 0.179921 | − | 0.983681i | \(-0.442416\pi\) | ||||
0.179921 | + | 0.983681i | \(0.442416\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.25073 | − | 2.42637i | −0.0487957 | − | 0.0946618i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.6914 | −0.883932 | −0.441966 | − | 0.897032i | \(-0.645719\pi\) | ||||
−0.441966 | + | 0.897032i | \(0.645719\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.8651 | 0.655978 | 0.327989 | − | 0.944682i | \(-0.393629\pi\) | ||||
0.327989 | + | 0.944682i | \(0.393629\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.99944 | + | 8.24271i | 0.0776520 | + | 0.320120i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 34.1790 | 1.32342 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.72173 | + | 1.63050i | −0.259877 | + | 0.0630388i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 48.8715 | 1.88666 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1.53829i | − | 0.0592966i | −0.999560 | − | 0.0296483i | \(-0.990561\pi\) | ||
0.999560 | − | 0.0296483i | \(-0.00943873\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.76238 | −0.259899 | −0.129950 | − | 0.991521i | \(-0.541482\pi\) | ||||
−0.129950 | + | 0.991521i | \(0.541482\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 13.2752i | − | 0.509457i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.91597 | − | 16.1436i | −0.150060 | − | 0.618624i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 11.0956i | − | 0.424563i | −0.977209 | − | 0.212281i | \(-0.931911\pi\) | ||
0.977209 | − | 0.212281i | \(-0.0680893\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.9145 | + | 3.86039i | −0.607175 | + | 0.147283i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 42.3559i | 1.61363i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.6949i | 0.597062i | 0.954400 | + | 0.298531i | \(0.0964965\pi\) | ||||
−0.954400 | + | 0.298531i | \(0.903503\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 23.0619 | − | 11.8878i | 0.876050 | − | 0.451581i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 4.20514i | − | 0.159281i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.39499 | + | 0.580957i | −0.0905870 | + | 0.0219738i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.45099i | 0.356959i | 0.983944 | + | 0.178479i | \(0.0571178\pi\) | ||||
−0.983944 | + | 0.178479i | \(0.942882\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.1215 | 0.494888 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 23.7992i | 0.895061i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.3011 | −0.687314 | −0.343657 | − | 0.939095i | \(-0.611666\pi\) | ||||
−0.343657 | + | 0.939095i | \(0.611666\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.54160 | − | 2.99066i | −0.0578147 | − | 0.112158i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 26.9994 | 1.01113 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 17.9523 | − | 4.35471i | 0.670440 | − | 0.162629i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.1404 | −0.378171 | −0.189086 | − | 0.981961i | \(-0.560552\pi\) | ||||
−0.189086 | + | 0.981961i | \(0.560552\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.7954 | −0.588252 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.62935 | − | 1.85066i | 0.283739 | − | 0.0688269i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34.3819 | −1.27516 | −0.637578 | − | 0.770386i | \(-0.720063\pi\) | ||||
−0.637578 | + | 0.770386i | \(0.720063\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.84645 | − | 26.7246i | 0.142461 | − | 0.989800i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.94843 | 0.293983 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.1562i | 0.929165i | 0.885530 | + | 0.464582i | \(0.153796\pi\) | ||||
−0.885530 | + | 0.464582i | \(0.846204\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −48.5599 | −1.78873 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.1626i | 0.778481i | 0.921136 | + | 0.389240i | \(0.127262\pi\) | ||||
−0.921136 | + | 0.389240i | \(0.872738\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.4326 | − | 3.98607i | 0.603666 | − | 0.146432i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 46.7087i | 1.71358i | 0.515669 | + | 0.856788i | \(0.327543\pi\) | ||||
−0.515669 | + | 0.856788i | \(0.672457\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19.7414 | + | 38.2975i | 0.722299 | + | 1.40123i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 10.9447i | − | 0.399910i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.61141i | 0.350725i | 0.984504 | + | 0.175363i | \(0.0561098\pi\) | ||||
−0.984504 | + | 0.175363i | \(0.943890\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −20.4182 | + | 4.95287i | −0.744081 | + | 0.180493i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.9388i | 1.08815i | 0.839038 | + | 0.544073i | \(0.183118\pi\) | ||||
−0.839038 | + | 0.544073i | \(0.816882\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.5162 | − | 43.3532i | −0.381715 | − | 1.57362i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 21.7438i | − | 0.788211i | −0.919065 | − | 0.394105i | \(-0.871055\pi\) | ||
0.919065 | − | 0.394105i | \(-0.128945\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −25.5701 | −0.925700 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.6099i | 0.491424i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.30972 | −0.335717 | −0.167859 | − | 0.985811i | \(-0.553685\pi\) | ||||
−0.167859 | + | 0.985811i | \(0.553685\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.4818 | − | 6.66630i | 0.989733 | − | 0.240081i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30.7908 | −1.10747 | −0.553734 | − | 0.832694i | \(-0.686798\pi\) | ||||
−0.553734 | + | 0.832694i | \(0.686798\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.71690 | + | 11.2004i | 0.0974681 | + | 0.401812i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.38331 | −0.300363 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 67.6168 | 2.41952 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −27.7756 | − | 32.0596i | −0.992620 | − | 1.14572i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.0413019 | −0.00147225 | −0.000736127 | − | 1.00000i | \(-0.500234\pi\) | ||||
−0.000736127 | 1.00000i | \(0.500234\pi\) | ||||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.24363 | + | 17.4943i | 0.151077 | + | 0.622815i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.98083 | 0.354877 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.9755i | 0.993438i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.12834 | 0.0753895 | 0.0376948 | − | 0.999289i | \(-0.487999\pi\) | ||||
0.0376948 | + | 0.999289i | \(0.487999\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.64605i | 0.270498i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19.3300 | − | 37.4995i | −0.682992 | − | 1.32498i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.59744i | 0.197529i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.87044 | + | 15.9559i | 0.136246 | + | 0.561673i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 19.9170i | − | 0.700243i | −0.936704 | − | 0.350121i | \(-0.886140\pi\) | ||
0.936704 | − | 0.350121i | \(-0.113860\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 5.43792i | − | 0.190951i | −0.995432 | − | 0.0954756i | \(-0.969563\pi\) | ||
0.995432 | − | 0.0954756i | \(-0.0304372\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.71269 | + | 40.0406i | 0.340639 | + | 1.40428i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 15.8459i | − | 0.554378i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.80493 | + | 13.2013i | 0.237784 | + | 0.461292i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 21.1720i | − | 0.738908i | −0.929249 | − | 0.369454i | \(-0.879545\pi\) | ||
0.929249 | − | 0.369454i | \(-0.120455\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.4551 | −0.434156 | −0.217078 | − | 0.976154i | \(-0.569653\pi\) | ||||
−0.217078 | + | 0.976154i | \(0.569653\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 22.3105i | − | 0.775812i | −0.921699 | − | 0.387906i | \(-0.873198\pi\) | ||
0.921699 | − | 0.387906i | \(-0.126802\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.5699 | −1.09647 | −0.548234 | − | 0.836325i | \(-0.684700\pi\) | ||||
−0.548234 | + | 0.836325i | \(0.684700\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.84124 | − | 36.4480i | −0.306699 | − | 1.26437i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.98582 | 0.242044 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −21.9411 | − | 25.3251i | −0.758394 | − | 0.875364i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.30477 | −0.286712 | −0.143356 | − | 0.989671i | \(-0.545789\pi\) | ||||
−0.143356 | + | 0.989671i | \(0.545789\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −37.6408 | −1.29796 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.02398 | + | 12.4664i | 0.104151 | + | 0.429364i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −37.7369 | −1.29666 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19.5098 | − | 4.73253i | 0.669576 | − | 0.162420i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.8163 | 0.679293 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.6348i | 0.398369i | 0.979962 | + | 0.199185i | \(0.0638294\pi\) | ||||
−0.979962 | + | 0.199185i | \(0.936171\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 51.8482 | 1.77110 | 0.885550 | − | 0.464543i | \(-0.153781\pi\) | ||||
0.885550 | + | 0.464543i | \(0.153781\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 42.9844i | − | 1.46661i | −0.679901 | − | 0.733304i | \(-0.737977\pi\) | ||
0.679901 | − | 0.733304i | \(-0.262023\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.73582 | − | 7.15591i | −0.0591565 | − | 0.243873i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 31.0656i | − | 1.05748i | −0.848783 | − | 0.528742i | \(-0.822664\pi\) | ||
0.848783 | − | 0.528742i | \(-0.177336\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −25.3598 | + | 6.15156i | −0.861264 | + | 0.208918i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.89919i | 0.234039i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 27.7971i | − | 0.941870i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.9791 | + | 25.1790i | 0.439277 | + | 0.852182i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 52.8726i | − | 1.78538i | −0.450670 | − | 0.892691i | \(-0.648815\pi\) | ||
0.450670 | − | 0.892691i | \(-0.351185\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 53.9561 | − | 13.0882i | 1.81990 | − | 0.441454i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 16.9797i | − | 0.572061i | −0.958220 | − | 0.286031i | \(-0.907664\pi\) | ||
0.958220 | − | 0.286031i | \(-0.0923359\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.5602 | −1.16304 | −0.581522 | − | 0.813531i | \(-0.697543\pi\) | ||||
−0.581522 | + | 0.813531i | \(0.697543\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 46.9163i | − | 1.57530i | −0.616125 | − | 0.787648i | \(-0.711298\pi\) | ||
0.616125 | − | 0.787648i | \(-0.288702\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.4190 | 0.450060 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −32.1188 | + | 45.0951i | −1.07602 | + | 1.51074i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.2431 | 0.510090 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 24.8166 | − | 6.01980i | 0.828603 | − | 0.200995i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −52.6422 | −1.75571 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.7272 | 0.557264 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 13.5259 | − | 3.28099i | 0.450113 | − | 0.109185i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.8545 | 1.32335 | 0.661673 | − | 0.749792i | \(-0.269847\pi\) | ||||
0.661673 | + | 0.749792i | \(0.269847\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −23.2684 | − | 45.1398i | −0.771763 | − | 1.49719i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.6627 | −1.08216 | −0.541081 | − | 0.840970i | \(-0.681985\pi\) | ||||
−0.541081 | + | 0.840970i | \(0.681985\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 88.3492i | − | 2.92393i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.97611 | 0.0652569 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 16.9449i | − | 0.558962i | −0.960151 | − | 0.279481i | \(-0.909838\pi\) | ||
0.960151 | − | 0.279481i | \(-0.0901623\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −42.4416 | + | 10.2951i | −1.39850 | + | 0.339236i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 38.7058i | 1.27402i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 29.9591 | − | 15.4431i | 0.983985 | − | 0.507218i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 57.3567i | 1.88181i | 0.338665 | + | 0.940907i | \(0.390025\pi\) | ||||
−0.338665 | + | 0.940907i | \(0.609975\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 13.9269i | − | 0.456434i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −17.5020 | + | 4.24549i | −0.572991 | + | 0.138991i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 26.7756i | − | 0.874721i | −0.899286 | − | 0.437361i | \(-0.855913\pi\) | ||
0.899286 | − | 0.437361i | \(-0.144087\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.54806 | − | 14.6269i | −0.115786 | − | 0.477330i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.1922i | 0.593049i | 0.955025 | + | 0.296524i | \(0.0958276\pi\) | ||||
−0.955025 | + | 0.296524i | \(0.904172\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.6606 | −0.412285 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.3856i | 1.11738i | 0.829376 | + | 0.558691i | \(0.188696\pi\) | ||||
−0.829376 | + | 0.558691i | \(0.811304\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.20414 | −0.104011 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −26.9477 | + | 6.53673i | −0.873838 | + | 0.211968i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42.3018 | −1.37029 | −0.685145 | − | 0.728407i | \(-0.740261\pi\) | ||||
−0.685145 | + | 0.728407i | \(0.740261\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.5041 | + | 84.5280i | 0.662802 | + | 2.73240i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.7928 | −0.542267 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.5841 | −0.341424 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.7006 | + | 20.7587i | 0.344821 | + | 0.668940i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.4110 | 0.656374 | 0.328187 | − | 0.944613i | \(-0.393562\pi\) | ||||
0.328187 | + | 0.944613i | \(0.393562\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.57418 | − | 6.48956i | −0.0505700 | − | 0.208475i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.57208 | −0.307183 | −0.153591 | − | 0.988134i | \(-0.549084\pi\) | ||||
−0.153591 | + | 0.988134i | \(0.549084\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 23.0697i | 0.739581i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.2815 | 0.360927 | 0.180464 | − | 0.983582i | \(-0.442240\pi\) | ||||
0.180464 | + | 0.983582i | \(0.442240\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 86.5082i | 2.76481i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 48.4987 | − | 24.9998i | 1.54844 | − | 0.798181i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.05349i | 0.129286i | 0.997908 | + | 0.0646432i | \(0.0205909\pi\) | ||||
−0.997908 | + | 0.0646432i | \(0.979409\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.15617 | + | 13.0113i | 0.100462 | + | 0.414155i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 23.9306i | − | 0.760949i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 48.7598i | − | 1.54891i | −0.632631 | − | 0.774453i | \(-0.718025\pi\) | ||
0.632631 | − | 0.774453i | \(-0.281975\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.31762 | − | 9.55438i | −0.0735474 | − | 0.303199i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 61.9989i | 1.96352i | 0.190113 | + | 0.981762i | \(0.439115\pi\) | ||||
−0.190113 | + | 0.981762i | \(0.560885\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16.1037 | − | 18.5874i | −0.509498 | − | 0.588080i |
(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 | 2400.2.o.l.2399.13 | 16 | ||
3.2 | odd | 2 | inner | 2400.2.o.l.2399.16 | 16 | ||
4.3 | odd | 2 | 2400.2.o.k.2399.4 | 16 | |||
5.2 | odd | 4 | 2400.2.h.f.1151.7 | ✓ | 16 | ||
5.3 | odd | 4 | 2400.2.h.g.1151.10 | yes | 16 | ||
5.4 | even | 2 | 2400.2.o.k.2399.3 | 16 | |||
12.11 | even | 2 | 2400.2.o.k.2399.1 | 16 | |||
15.2 | even | 4 | 2400.2.h.f.1151.9 | yes | 16 | ||
15.8 | even | 4 | 2400.2.h.g.1151.8 | yes | 16 | ||
15.14 | odd | 2 | 2400.2.o.k.2399.2 | 16 | |||
20.3 | even | 4 | 2400.2.h.g.1151.7 | yes | 16 | ||
20.7 | even | 4 | 2400.2.h.f.1151.10 | yes | 16 | ||
20.19 | odd | 2 | inner | 2400.2.o.l.2399.14 | 16 | ||
60.23 | odd | 4 | 2400.2.h.g.1151.9 | yes | 16 | ||
60.47 | odd | 4 | 2400.2.h.f.1151.8 | yes | 16 | ||
60.59 | even | 2 | inner | 2400.2.o.l.2399.15 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2400.2.h.f.1151.7 | ✓ | 16 | 5.2 | odd | 4 | ||
2400.2.h.f.1151.8 | yes | 16 | 60.47 | odd | 4 | ||
2400.2.h.f.1151.9 | yes | 16 | 15.2 | even | 4 | ||
2400.2.h.f.1151.10 | yes | 16 | 20.7 | even | 4 | ||
2400.2.h.g.1151.7 | yes | 16 | 20.3 | even | 4 | ||
2400.2.h.g.1151.8 | yes | 16 | 15.8 | even | 4 | ||
2400.2.h.g.1151.9 | yes | 16 | 60.23 | odd | 4 | ||
2400.2.h.g.1151.10 | yes | 16 | 5.3 | odd | 4 | ||
2400.2.o.k.2399.1 | 16 | 12.11 | even | 2 | |||
2400.2.o.k.2399.2 | 16 | 15.14 | odd | 2 | |||
2400.2.o.k.2399.3 | 16 | 5.4 | even | 2 | |||
2400.2.o.k.2399.4 | 16 | 4.3 | odd | 2 | |||
2400.2.o.l.2399.13 | 16 | 1.1 | even | 1 | trivial | ||
2400.2.o.l.2399.14 | 16 | 20.19 | odd | 2 | inner | ||
2400.2.o.l.2399.15 | 16 | 60.59 | even | 2 | inner | ||
2400.2.o.l.2399.16 | 16 | 3.2 | odd | 2 | inner |