Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1520,2,Mod(609,1520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1520.609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1520 = 2^{4} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1520.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.1372611072\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.16516096.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 9x^{4} + 13x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 609.4 | ||
Root | \(1.30397i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1520.609 |
Dual form | 1520.2.d.h.609.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(401\) | \(1141\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.537080i | 0.310083i | 0.987908 | + | 0.155042i | \(0.0495512\pi\) | ||||
−0.987908 | + | 0.155042i | \(0.950449\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.07772 | + | 0.826491i | −0.929184 | + | 0.369618i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.18676i | 1.20448i | 0.798314 | + | 0.602241i | \(0.205725\pi\) | ||||
−0.798314 | + | 0.602241i | \(0.794275\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.71155 | 0.903848 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.15544 | −1.25291 | −0.626456 | − | 0.779457i | \(-0.715495\pi\) | ||||
−0.626456 | + | 0.779457i | \(0.715495\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.07086i | − | 0.574353i | −0.957878 | − | 0.287176i | \(-0.907283\pi\) | ||
0.957878 | − | 0.287176i | \(-0.0927166\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.443892 | − | 1.11590i | −0.114612 | − | 0.288124i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.79470i | 1.40542i | 0.711476 | + | 0.702710i | \(0.248027\pi\) | ||||
−0.711476 | + | 0.702710i | \(0.751973\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.71155 | −0.373490 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.60794i | − | 0.543793i | −0.962327 | − | 0.271896i | \(-0.912349\pi\) | ||
0.962327 | − | 0.271896i | \(-0.0876508\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.63383 | − | 3.43443i | 0.726765 | − | 0.686886i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.06756i | 0.590352i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.59933 | −0.466853 | −0.233427 | − | 0.972374i | \(-0.574994\pi\) | ||||
−0.233427 | + | 0.972374i | \(0.574994\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 2.23180i | − | 0.388507i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.63383 | − | 6.62119i | −0.445198 | − | 1.11919i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.30266i | 0.707353i | 0.935368 | + | 0.353677i | \(0.115069\pi\) | ||||
−0.935368 | + | 0.353677i | \(0.884931\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.11222 | 0.178097 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.599328 | −0.0935993 | −0.0467997 | − | 0.998904i | \(-0.514902\pi\) | ||||
−0.0467997 | + | 0.998904i | \(0.514902\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.18676i | 0.485976i | 0.970029 | + | 0.242988i | \(0.0781276\pi\) | ||||
−0.970029 | + | 0.242988i | \(0.921872\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.63383 | + | 2.24107i | −0.839841 | + | 0.334078i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 11.7086i | − | 1.70787i | −0.520376 | − | 0.853937i | \(-0.674208\pi\) | ||
0.520376 | − | 0.853937i | \(-0.325792\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.15544 | −0.450777 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.11222 | −0.435798 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 11.7503i | − | 1.61403i | −0.590529 | − | 0.807017i | \(-0.701081\pi\) | ||
0.590529 | − | 0.807017i | \(-0.298919\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.63383 | − | 3.43443i | 1.16418 | − | 0.463098i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.537080i | − | 0.0711380i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.71155 | −0.222824 | −0.111412 | − | 0.993774i | \(-0.535537\pi\) | ||||
−0.111412 | + | 0.993774i | \(0.535537\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.75476 | −1.12093 | −0.560466 | − | 0.828177i | \(-0.689378\pi\) | ||||
−0.560466 | + | 0.828177i | \(0.689378\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.64104i | 1.08867i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.71155 | + | 4.30266i | 0.212291 | + | 0.533679i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 4.76228i | − | 0.581805i | −0.956753 | − | 0.290902i | \(-0.906044\pi\) | ||
0.956753 | − | 0.290902i | \(-0.0939555\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.40067 | 0.168621 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.7115 | −1.62726 | −0.813631 | − | 0.581382i | \(-0.802512\pi\) | ||||
−0.813631 | + | 0.581382i | \(0.802512\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.72714i | 0.319188i | 0.987183 | + | 0.159594i | \(0.0510185\pi\) | ||||
−0.987183 | + | 0.159594i | \(0.948982\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.84456 | + | 1.95166i | 0.212992 | + | 0.225358i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 13.2424i | − | 1.50911i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.40067 | −0.157588 | −0.0787939 | − | 0.996891i | \(-0.525107\pi\) | ||||
−0.0787939 | + | 0.996891i | \(0.525107\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.48711 | 0.720790 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 7.07154i | − | 0.776203i | −0.921617 | − | 0.388101i | \(-0.873131\pi\) | ||
0.921617 | − | 0.388101i | \(-0.126869\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.78926 | − | 12.0398i | −0.519469 | − | 1.30589i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 3.22248i | − | 0.345486i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.5353 | −1.75274 | −0.876370 | − | 0.481639i | \(-0.840042\pi\) | ||||
−0.876370 | + | 0.481639i | \(0.840042\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.59933 | 0.691798 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 1.39605i | − | 0.144763i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.07772 | − | 0.826491i | 0.213169 | − | 0.0847961i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.07086i | 0.210264i | 0.994458 | + | 0.105132i | \(0.0335265\pi\) | ||||
−0.994458 | + | 0.105132i | \(0.966474\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.2677 | −1.13244 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.71155 | −0.170305 | −0.0851525 | − | 0.996368i | \(-0.527138\pi\) | ||||
−0.0851525 | + | 0.996368i | \(0.527138\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.75296i | 0.566856i | 0.958994 | + | 0.283428i | \(0.0914716\pi\) | ||||
−0.958994 | + | 0.283428i | \(0.908528\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.55611 | − | 1.41458i | 0.347041 | − | 0.138048i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.4324i | 1.49191i | 0.665996 | + | 0.745955i | \(0.268007\pi\) | ||||
−0.665996 | + | 0.745955i | \(0.731993\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.7115 | −1.12176 | −0.560881 | − | 0.827896i | \(-0.689538\pi\) | ||||
−0.560881 | + | 0.827896i | \(0.689538\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.31087 | −0.219338 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.5927i | 0.996477i | 0.867040 | + | 0.498239i | \(0.166020\pi\) | ||||
−0.867040 | + | 0.498239i | \(0.833980\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.15544 | + | 5.41856i | 0.200996 | + | 0.505283i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 5.61523i | − | 0.519128i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −18.4663 | −1.69280 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.26765 | 0.569787 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 0.321887i | − | 0.0290236i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.71155 | + | 10.1391i | −0.421413 | + | 0.906869i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.07484i | 0.539055i | 0.962993 | + | 0.269528i | \(0.0868676\pi\) | ||||
−0.962993 | + | 0.269528i | \(0.913132\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.71155 | −0.150693 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.5785 | 1.18636 | 0.593181 | − | 0.805069i | \(-0.297872\pi\) | ||||
0.593181 | + | 0.805069i | \(0.297872\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 3.18676i | − | 0.276327i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.53531 | − | 6.37352i | −0.218204 | − | 0.548545i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 7.94302i | − | 0.678618i | −0.940675 | − | 0.339309i | \(-0.889807\pi\) | ||
0.940675 | − | 0.339309i | \(-0.110193\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.26765 | 0.277159 | 0.138579 | − | 0.990351i | \(-0.455746\pi\) | ||||
0.138579 | + | 0.990351i | \(0.455746\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.28845 | 0.529583 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.60532i | 0.719613i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.4663 | − | 4.95894i | 1.03527 | − | 0.411818i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 1.69472i | − | 0.139778i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.44389 | −0.691751 | −0.345875 | − | 0.938280i | \(-0.612418\pi\) | ||||
−0.345875 | + | 0.938280i | \(0.612418\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.887783 | −0.0722468 | −0.0361234 | − | 0.999347i | \(-0.511501\pi\) | ||||
−0.0361234 | + | 0.999347i | \(0.511501\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15.7126i | 1.27029i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.40067 | − | 2.14832i | 0.433792 | − | 0.172557i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.14172i | 0.330545i | 0.986248 | + | 0.165273i | \(0.0528504\pi\) | ||||
−0.986248 | + | 0.165273i | \(0.947150\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.31087 | 0.500485 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.31087 | 0.654989 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 24.7126i | − | 1.93564i | −0.251647 | − | 0.967819i | \(-0.580972\pi\) | ||
0.251647 | − | 0.967819i | \(-0.419028\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.84456 | + | 4.63706i | 0.143599 | + | 0.360994i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.60464i | 0.278935i | 0.990227 | + | 0.139468i | \(0.0445391\pi\) | ||||
−0.990227 | + | 0.139468i | \(0.955461\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.71155 | 0.670119 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.71155 | −0.207357 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.4205i | 1.70460i | 0.523054 | + | 0.852300i | \(0.324793\pi\) | ||||
−0.523054 | + | 0.852300i | \(0.675207\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.9447 | + | 11.5801i | 0.827342 | + | 0.875376i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 0.919237i | − | 0.0690941i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.13464 | −0.383781 | −0.191890 | − | 0.981416i | \(-0.561462\pi\) | ||||
−0.191890 | + | 0.981416i | \(0.561462\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.8462 | 1.54948 | 0.774742 | − | 0.632277i | \(-0.217880\pi\) | ||||
0.774742 | + | 0.632277i | \(0.217880\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 4.70201i | − | 0.347583i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.55611 | − | 8.93972i | −0.261450 | − | 0.657261i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 24.0795i | − | 1.76087i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.77557 | −0.711068 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.26765 | 0.381154 | 0.190577 | − | 0.981672i | \(-0.438964\pi\) | ||||
0.190577 | + | 0.981672i | \(0.438964\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 2.07086i | − | 0.149064i | −0.997219 | − | 0.0745318i | \(-0.976254\pi\) | ||
0.997219 | − | 0.0745318i | \(-0.0237462\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.31087 | + | 0.919237i | −0.165485 | + | 0.0658279i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.4318i | 0.743232i | 0.928387 | + | 0.371616i | \(0.121196\pi\) | ||||
−0.928387 | + | 0.371616i | \(0.878804\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.73235 | −0.193691 | −0.0968455 | − | 0.995299i | \(-0.530875\pi\) | ||||
−0.0968455 | + | 0.995299i | \(0.530875\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.55773 | 0.180408 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 19.1206i | − | 1.34200i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.24524 | − | 0.495339i | 0.0869710 | − | 0.0345960i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 7.07154i | − | 0.491506i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.15544 | 0.287438 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.7340 | 1.08317 | 0.541585 | − | 0.840646i | \(-0.317824\pi\) | ||||
0.541585 | + | 0.840646i | \(0.317824\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 7.36420i | − | 0.504586i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.63383 | − | 6.62119i | −0.179625 | − | 0.451561i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 8.28343i | − | 0.562316i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.46469 | −0.0989748 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | 0.807207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.8219i | 1.26041i | 0.776430 | + | 0.630203i | \(0.217028\pi\) | ||||
−0.776430 | + | 0.630203i | \(0.782972\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.85328 | − | 9.31261i | 0.656886 | − | 0.620841i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.4418i | 0.958533i | 0.877669 | + | 0.479267i | \(0.159097\pi\) | ||||
−0.877669 | + | 0.479267i | \(0.840903\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.17785 | 0.276080 | 0.138040 | − | 0.990427i | \(-0.455920\pi\) | ||||
0.138040 | + | 0.990427i | \(0.455920\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.11222 | 0.467950 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 12.0847i | − | 0.791697i | −0.918316 | − | 0.395849i | \(-0.870450\pi\) | ||
0.918316 | − | 0.395849i | \(-0.129550\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.67705 | + | 24.3272i | 0.631261 | + | 1.58693i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 0.752273i | − | 0.0488654i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.3541 | −0.734435 | −0.367218 | − | 0.930135i | \(-0.619690\pi\) | ||||
−0.367218 | + | 0.930135i | \(0.619690\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.40067 | −0.219057 | −0.109528 | − | 0.993984i | \(-0.534934\pi\) | ||||
−0.109528 | + | 0.993984i | \(0.534934\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.6868i | 0.813857i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.55611 | − | 2.60794i | 0.418854 | − | 0.166615i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.07086i | 0.131766i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.79798 | 0.240687 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.04322 | −0.192086 | −0.0960432 | − | 0.995377i | \(-0.530619\pi\) | ||||
−0.0960432 | + | 0.995377i | \(0.530619\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.8371i | 0.681324i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.46631 | − | 2.57222i | 0.404936 | − | 0.161079i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.2881i | 1.07840i | 0.842177 | + | 0.539201i | \(0.181274\pi\) | ||||
−0.842177 | + | 0.539201i | \(0.818726\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.7115 | −0.851994 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.2693 | −1.00704 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 1.19336i | − | 0.0735859i | −0.999323 | − | 0.0367930i | \(-0.988286\pi\) | ||
0.999323 | − | 0.0367930i | \(-0.0117142\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.71155 | + | 24.4139i | 0.596575 | + | 1.49973i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 8.88078i | − | 0.543495i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.1089 | −1.34800 | −0.674000 | − | 0.738731i | \(-0.735425\pi\) | ||||
−0.674000 | + | 0.738731i | \(0.735425\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.08644 | 0.248234 | 0.124117 | − | 0.992268i | \(-0.460390\pi\) | ||||
0.124117 | + | 0.992268i | \(0.460390\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.54437i | 0.214515i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.1001 | + | 14.2716i | −0.910572 | + | 0.860607i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 10.0199i | − | 0.602037i | −0.953618 | − | 0.301019i | \(-0.902673\pi\) | ||
0.953618 | − | 0.301019i | \(-0.0973266\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.04820 | −0.421964 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.599328 | 0.0357529 | 0.0178765 | − | 0.999840i | \(-0.494309\pi\) | ||||
0.0178765 | + | 0.999840i | \(0.494309\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.41856i | 0.322100i | 0.986946 | + | 0.161050i | \(0.0514880\pi\) | ||||
−0.986946 | + | 0.161050i | \(0.948512\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.443892 | + | 1.11590i | 0.0262939 | + | 0.0661003i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 1.90991i | − | 0.112739i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5785 | −0.975207 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.11222 | −0.0651993 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 3.46691i | − | 0.202539i | −0.994859 | − | 0.101269i | \(-0.967710\pi\) | ||
0.994859 | − | 0.101269i | \(-0.0322904\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.55611 | − | 1.41458i | 0.207045 | − | 0.0823598i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 12.7470i | − | 0.739658i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.40067 | −0.312329 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.1554 | −0.585350 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 0.919237i | − | 0.0528088i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 18.1899 | − | 7.23573i | 1.04155 | − | 0.414317i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.5901i | 0.946846i | 0.880835 | + | 0.473423i | \(0.156982\pi\) | ||||
−0.880835 | + | 0.473423i | \(0.843018\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.08980 | −0.175772 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.15544 | 0.235633 | 0.117817 | − | 0.993035i | \(-0.462411\pi\) | ||||
0.117817 | + | 0.993035i | \(0.462411\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.919237i | 0.0519583i | 0.999662 | + | 0.0259792i | \(0.00827036\pi\) | ||||
−0.999662 | + | 0.0259792i | \(0.991730\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.14174 | − | 17.9537i | −0.402391 | − | 1.01157i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 26.7292i | − | 1.50126i | −0.660723 | − | 0.750630i | \(-0.729750\pi\) | ||
0.660723 | − | 0.750630i | \(-0.270250\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.9326 | 1.39596 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.28845 | −0.462616 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 5.79470i | − | 0.322426i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.11222 | − | 7.52514i | −0.394515 | − | 0.417420i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 6.29004i | − | 0.347840i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 37.3125 | 2.05710 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.00000 | −0.439720 | −0.219860 | − | 0.975531i | \(-0.570560\pi\) | ||||
−0.219860 | + | 0.975531i | \(0.570560\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.6669i | 0.639340i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.93598 | + | 9.89467i | 0.215045 | + | 0.540604i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.5040i | 1.22587i | 0.790133 | + | 0.612935i | \(0.210011\pi\) | ||||
−0.790133 | + | 0.612935i | \(0.789989\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.68913 | −0.308991 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.8013 | 0.584926 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.2517i | 0.661530i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.91020 | + | 1.15764i | −0.156680 | + | 0.0623254i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.4543i | 0.775946i | 0.921671 | + | 0.387973i | \(0.126825\pi\) | ||||
−0.921671 | + | 0.387973i | \(0.873175\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.3541 | 0.714828 | 0.357414 | − | 0.933946i | \(-0.383658\pi\) | ||||
0.357414 | + | 0.933946i | \(0.383658\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.35248 | 0.339070 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 17.6410i | − | 0.938937i | −0.882949 | − | 0.469469i | \(-0.844446\pi\) | ||
0.882949 | − | 0.469469i | \(-0.155554\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 28.4887 | − | 11.3325i | 1.51202 | − | 0.601465i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 9.91789i | − | 0.524910i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.4663 | 0.657947 | 0.328973 | − | 0.944339i | \(-0.393297\pi\) | ||||
0.328973 | + | 0.944339i | \(0.393297\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.36623i | 0.176681i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.25396 | − | 5.66623i | −0.117977 | − | 0.296584i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.4291i | 0.857594i | 0.903401 | + | 0.428797i | \(0.141062\pi\) | ||||
−0.903401 | + | 0.428797i | \(0.858938\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.62511 | −0.0845996 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 37.4455 | 1.94407 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.29334i | 0.274079i | 0.990566 | + | 0.137039i | \(0.0437587\pi\) | ||||
−0.990566 | + | 0.137039i | \(0.956241\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.44551 | − | 2.53048i | −0.281205 | − | 0.130673i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.4252i | 0.639928i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.5353 | 0.746629 | 0.373314 | − | 0.927705i | \(-0.378221\pi\) | ||||
0.373314 | + | 0.927705i | \(0.378221\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.26268 | −0.167152 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.453598i | 0.0231778i | 0.999933 | + | 0.0115889i | \(0.00368894\pi\) | ||||
−0.999933 | + | 0.0115889i | \(0.996311\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.9447 | + | 27.5139i | 0.557794 | + | 1.40224i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.64104i | 0.439249i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.1554 | −0.819113 | −0.409557 | − | 0.912285i | \(-0.634317\pi\) | ||||
−0.409557 | + | 0.912285i | \(0.634317\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.1122 | 0.764258 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.29276i | 0.367871i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.91020 | − | 1.15764i | 0.146428 | − | 0.0582473i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.7563i | 1.64399i | 0.569495 | + | 0.821995i | \(0.307139\pi\) | ||||
−0.569495 | + | 0.821995i | \(0.692861\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.71155 | 0.0856844 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.0864 | 0.603568 | 0.301784 | − | 0.953376i | \(-0.402418\pi\) | ||||
0.301784 | + | 0.953376i | \(0.402418\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.38284i | 0.268138i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −13.4784 | + | 5.36154i | −0.669747 | + | 0.266417i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 17.8794i | − | 0.886251i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.1346 | 0.946147 | 0.473073 | − | 0.881023i | \(-0.343145\pi\) | ||||
0.473073 | + | 0.881023i | \(0.343145\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.26604 | 0.210428 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 5.45428i | − | 0.268388i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.84456 | + | 14.6927i | 0.286898 | + | 0.721235i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.75499i | 0.0859423i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.04484 | 0.393016 | 0.196508 | − | 0.980502i | \(-0.437040\pi\) | ||||
0.196508 | + | 0.980502i | \(0.437040\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.3591 | −1.43087 | −0.715437 | − | 0.698678i | \(-0.753772\pi\) | ||||
−0.715437 | + | 0.698678i | \(0.753772\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 31.7484i | − | 1.54366i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 19.9015 | + | 21.0569i | 0.965364 | + | 1.02141i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 27.8993i | − | 1.35014i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.62175 | −0.223140 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.0448 | 1.54355 | 0.771773 | − | 0.635898i | \(-0.219370\pi\) | ||||
0.771773 | + | 0.635898i | \(0.219370\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 0.482831i | − | 0.0232034i | −0.999933 | − | 0.0116017i | \(-0.996307\pi\) | ||
0.999933 | − | 0.0116017i | \(-0.00369301\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.66335 | + | 6.69541i | 0.127698 | + | 0.321020i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.60794i | 0.124755i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.3591 | −1.30578 | −0.652889 | − | 0.757454i | \(-0.726443\pi\) | ||||
−0.652889 | + | 0.757454i | \(0.726443\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.55611 | −0.407434 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.3815i | 1.11089i | 0.831554 | + | 0.555444i | \(0.187452\pi\) | ||||
−0.831554 | + | 0.555444i | \(0.812548\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 34.3557 | − | 13.6663i | 1.62862 | − | 0.647844i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 4.53505i | − | 0.214500i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.1346 | −1.09179 | −0.545895 | − | 0.837853i | \(-0.683810\pi\) | ||||
−0.545895 | + | 0.837853i | \(0.683810\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.49047 | 0.117272 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 0.476811i | − | 0.0224025i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.7115 | + | 5.45428i | −0.642807 | + | 0.255701i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.2503i | 0.994049i | 0.867736 | + | 0.497025i | \(0.165574\pi\) | ||||
−0.867736 | + | 0.497025i | \(0.834426\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −17.7756 | −0.829692 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.5785 | 1.47076 | 0.735379 | − | 0.677656i | \(-0.237004\pi\) | ||||
0.735379 | + | 0.677656i | \(0.237004\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 15.6119i | − | 0.725547i | −0.931877 | − | 0.362774i | \(-0.881830\pi\) | ||
0.931877 | − | 0.362774i | \(-0.118170\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.15382 | + | 2.90059i | 0.0535071 | + | 0.134512i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 29.8264i | 1.38020i | 0.723713 | + | 0.690101i | \(0.242434\pi\) | ||||
−0.723713 | + | 0.690101i | \(0.757566\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.1762 | 0.700774 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.22443 | −0.102496 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 13.2424i | − | 0.608885i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.63383 | + | 3.43443i | −0.166731 | + | 0.157582i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 31.8616i | − | 1.45884i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.53531 | 0.207223 | 0.103612 | − | 0.994618i | \(-0.466960\pi\) | ||||
0.103612 | + | 0.994618i | \(0.466960\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.91020 | 0.406270 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.46360i | 0.203101i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.71155 | − | 4.30266i | −0.0777173 | − | 0.195374i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 39.2550i | − | 1.77881i | −0.457116 | − | 0.889407i | \(-0.651118\pi\) | ||
0.457116 | − | 0.889407i | \(-0.348882\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.2726 | 0.600209 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.8910 | −1.75513 | −0.877564 | − | 0.479460i | \(-0.840832\pi\) | ||||
−0.877564 | + | 0.479460i | \(0.840832\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 34.7682i | − | 1.56588i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 23.4110 | − | 9.31261i | 1.05225 | − | 0.418571i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 43.6954i | − | 1.96001i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.73235 | 0.211849 | 0.105924 | − | 0.994374i | \(-0.466220\pi\) | ||||
0.105924 | + | 0.994374i | \(0.466220\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.93598 | −0.0864931 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.85567i | 0.0827400i | 0.999144 | + | 0.0413700i | \(0.0131722\pi\) | ||||
−0.999144 | + | 0.0413700i | \(0.986828\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.55611 | − | 1.41458i | 0.158245 | − | 0.0629478i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.67880i | 0.207793i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.8878 | −1.01448 | −0.507242 | − | 0.861804i | \(-0.669335\pi\) | ||||
−0.507242 | + | 0.861804i | \(0.669335\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.69074 | −0.384456 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 3.06756i | − | 0.135436i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.75476 | − | 11.9530i | −0.209520 | − | 0.526713i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 48.6543i | 2.13982i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.0416 | −0.528568 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.7340 | −1.30267 | −0.651334 | − | 0.758791i | \(-0.725790\pi\) | ||||
−0.651334 | + | 0.758791i | \(0.725790\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.6497i | 1.34022i | 0.742263 | + | 0.670109i | \(0.233752\pi\) | ||||
−0.742263 | + | 0.670109i | \(0.766248\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.21946 | + | 5.87818i | −0.271439 | + | 0.256545i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 15.0623i | − | 0.656125i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.1987 | 0.704289 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.64093 | −0.201399 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.24112i | 0.0537590i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.7548 | − | 32.0643i | −0.551437 | − | 1.38626i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 2.75771i | − | 0.119004i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.1122 | 0.564783 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.21946 | 0.0954220 | 0.0477110 | − | 0.998861i | \(-0.484807\pi\) | ||||
0.0477110 | + | 0.998861i | \(0.484807\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.1961i | 0.480469i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.3333 | − | 9.67948i | 1.04232 | − | 0.414623i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.4297i | 0.616970i | 0.951229 | + | 0.308485i | \(0.0998220\pi\) | ||||
−0.951229 | + | 0.308485i | \(0.900178\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −23.7389 | −1.01315 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.00000 | 0.255609 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 4.46360i | − | 0.189812i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.80134 | − | 1.90991i | 0.203806 | − | 0.0810714i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.4610i | 0.824588i | 0.911051 | + | 0.412294i | \(0.135272\pi\) | ||||
−0.911051 | + | 0.412294i | \(0.864728\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.59933 | 0.279122 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.9326 | 0.546016 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 12.3649i | − | 0.521118i | −0.965458 | − | 0.260559i | \(-0.916093\pi\) | ||
0.965458 | − | 0.260559i | \(-0.0839068\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.75476 | − | 22.0086i | −0.368316 | − | 0.925911i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 20.6729i | 0.868179i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.0898 | −0.632597 | −0.316299 | − | 0.948660i | \(-0.602440\pi\) | ||||
−0.316299 | + | 0.948660i | \(0.602440\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.1571 | −0.718000 | −0.359000 | − | 0.933337i | \(-0.616882\pi\) | ||||
−0.359000 | + | 0.933337i | \(0.616882\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.82915i | 0.118190i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.95678 | − | 9.47680i | −0.373524 | − | 0.395210i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 22.5165i | − | 0.937374i | −0.883364 | − | 0.468687i | \(-0.844727\pi\) | ||
0.883364 | − | 0.468687i | \(-0.155273\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.11222 | 0.0462222 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22.5353 | 0.934922 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 48.8278i | 2.02224i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.64093 | + | 11.6669i | 0.191879 | + | 0.482365i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 7.49544i | − | 0.309370i | −0.987964 | − | 0.154685i | \(-0.950564\pi\) | ||
0.987964 | − | 0.154685i | \(-0.0494363\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.59933 | 0.107103 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.60269 | −0.230464 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 27.8094i | − | 1.14199i | −0.820952 | − | 0.570997i | \(-0.806557\pi\) | ||
0.820952 | − | 0.570997i | \(-0.193443\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 38.3678 | − | 15.2622i | 1.57293 | − | 0.625690i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 1.46749i | − | 0.0600603i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −45.4903 | −1.85869 | −0.929343 | − | 0.369219i | \(-0.879625\pi\) | ||||
−0.929343 | + | 0.369219i | \(0.879625\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.5993 | −0.677101 | −0.338550 | − | 0.940948i | \(-0.609937\pi\) | ||||
−0.338550 | + | 0.940948i | \(0.609937\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 12.9131i | − | 0.525863i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.0224 | + | 5.18016i | −0.529437 | + | 0.210603i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.08417i | 0.206360i | 0.994663 | + | 0.103180i | \(0.0329018\pi\) | ||||
−0.994663 | + | 0.103180i | \(0.967098\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.2693 | 0.416132 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.2469 | −0.980923 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 4.63706i | − | 0.187289i | −0.995606 | − | 0.0936445i | \(-0.970148\pi\) | ||
0.995606 | − | 0.0936445i | \(-0.0298517\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.266037 | + | 0.668791i | 0.0107276 | + | 0.0269683i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 40.2874i | 1.62191i | 0.585108 | + | 0.810955i | \(0.301052\pi\) | ||||
−0.585108 | + | 0.810955i | \(0.698948\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −43.3815 | −1.74365 | −0.871825 | − | 0.489818i | \(-0.837063\pi\) | ||||
−0.871825 | + | 0.489818i | \(0.837063\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.00000 | 0.321029 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 52.6940i | − | 2.11114i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.40939 | − | 24.9602i | 0.0563757 | − | 0.998410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.23180i | 0.0891296i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −24.9326 | −0.994129 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.53369 | −0.299911 | −0.149956 | − | 0.988693i | \(-0.547913\pi\) | ||||
−0.149956 | + | 0.988693i | \(0.547913\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.45040i | 0.335873i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.02080 | − | 12.6218i | −0.199244 | − | 0.500881i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.53446i | 0.258905i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −37.1795 | −1.47080 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.3075 | −0.920591 | −0.460296 | − | 0.887766i | \(-0.652257\pi\) | ||||
−0.460296 | + | 0.887766i | \(0.652257\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.87419i | 0.0739110i | 0.999317 | + | 0.0369555i | \(0.0117660\pi\) | ||||
−0.999317 | + | 0.0369555i | \(0.988234\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.55611 | − | 1.41458i | 0.140022 | − | 0.0556989i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 47.0371i | 1.84922i | 0.380917 | + | 0.924609i | \(0.375608\pi\) | ||||
−0.380917 | + | 0.924609i | \(0.624392\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.11222 | 0.279179 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.44887 | 0.174365 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 24.1630i | − | 0.945571i | −0.881178 | − | 0.472785i | \(-0.843249\pi\) | ||
0.881178 | − | 0.472785i | \(-0.156751\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −28.2124 | + | 11.2225i | −1.10235 | + | 0.438500i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.39477i | 0.288497i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.2885 | 0.400781 | 0.200391 | − | 0.979716i | \(-0.435779\pi\) | ||||
0.200391 | + | 0.979716i | \(0.435779\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.93598 | 0.230883 | 0.115441 | − | 0.993314i | \(-0.463172\pi\) | ||||
0.115441 | + | 0.993314i | \(0.463172\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.44496i | 0.250302i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.63383 | + | 6.62119i | 0.102135 | + | 0.256759i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.6476i | 0.605879i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.1089 | −0.390831 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 36.3799 | 1.40443 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.7053i | 1.56907i | 0.620082 | + | 0.784537i | \(0.287099\pi\) | ||||
−0.620082 | + | 0.784537i | \(0.712901\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.5353 | + | 11.1470i | 0.405504 | + | 0.429047i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.8761i | 0.725469i | 0.931893 | + | 0.362734i | \(0.118157\pi\) | ||||
−0.931893 | + | 0.362734i | \(0.881843\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.59933 | −0.253259 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.75638 | −0.297225 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 19.6576i | − | 0.752179i | −0.926583 | − | 0.376089i | \(-0.877269\pi\) | ||
0.926583 | − | 0.376089i | \(-0.122731\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.56483 | + | 16.5034i | 0.250829 | + | 0.630561i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.24384i | 0.0856079i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −24.3333 | −0.927025 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 48.2451 | 1.83533 | 0.917665 | − | 0.397354i | \(-0.130072\pi\) | ||||
0.917665 | + | 0.397354i | \(0.130072\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 35.9073i | − | 1.36401i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.78926 | + | 2.70068i | −0.257531 | + | 0.102443i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 3.47293i | − | 0.131546i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.49047 | 0.245492 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.512889 | 0.0193715 | 0.00968577 | − | 0.999953i | \(-0.496917\pi\) | ||||
0.00968577 | + | 0.999953i | \(0.496917\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 4.30266i | − | 0.162278i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.0656 | + | 5.19735i | −0.492080 | + | 0.195743i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 5.45428i | − | 0.205129i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.84618 | 0.332225 | 0.166113 | − | 0.986107i | \(-0.446878\pi\) | ||||
0.166113 | + | 0.986107i | \(0.446878\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.79798 | −0.142436 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.77889i | 0.253871i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.11222 | − | 17.8794i | −0.265982 | − | 0.668653i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 6.09806i | − | 0.227736i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.84456 | 0.292553 | 0.146276 | − | 0.989244i | \(-0.453271\pi\) | ||||
0.146276 | + | 0.989244i | \(0.453271\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.3333 | −0.682767 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 1.82643i | − | 0.0679258i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −21.8030 | + | 20.6066i | −0.809742 | + | 0.765309i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.91130i | 0.107974i | 0.998542 | + | 0.0539870i | \(0.0171930\pi\) | ||||
−0.998542 | + | 0.0539870i | \(0.982807\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 12.6475 | 0.468427 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.4663 | −0.683001 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.7775i | 1.24760i | 0.781584 | + | 0.623800i | \(0.214412\pi\) | ||||
−0.781584 | + | 0.623800i | \(0.785588\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.40067 | + | 3.52116i | 0.0516646 | + | 0.129880i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.7893i | 0.728950i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.8030 | −1.31703 | −0.658517 | − | 0.752566i | \(-0.728816\pi\) | ||||
−0.658517 | + | 0.752566i | \(0.728816\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.11222 | −0.0408583 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 5.66948i | − | 0.207993i | −0.994578 | − | 0.103996i | \(-0.966837\pi\) | ||
0.994578 | − | 0.103996i | \(-0.0331631\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.5440 | − | 6.97880i | 0.642763 | − | 0.255683i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 19.1748i | − | 0.701569i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −49.1795 | −1.79698 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.4679 | 1.00232 | 0.501159 | − | 0.865355i | \(-0.332907\pi\) | ||||
0.501159 | + | 0.865355i | \(0.332907\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 1.63445i | − | 0.0595628i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.84456 | − | 0.733744i | 0.0671305 | − | 0.0267037i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 41.6370i | − | 1.51332i | −0.653806 | − | 0.756662i | \(-0.726829\pi\) | ||
0.653806 | − | 0.756662i | \(-0.273171\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.82040 | −0.211267 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.46967 | −0.343275 | −0.171638 | − | 0.985160i | \(-0.554906\pi\) | ||||
−0.171638 | + | 0.985160i | \(0.554906\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 37.3219i | − | 1.35114i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12.9863 | − | 32.6463i | −0.469521 | − | 1.18033i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.54437i | 0.127980i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.90858 | −0.0688253 | −0.0344127 | − | 0.999408i | \(-0.510956\pi\) | ||||
−0.0344127 | + | 0.999408i | \(0.510956\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.28510 | −0.334395 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.4007i | 1.02150i | 0.859729 | + | 0.510751i | \(0.170633\pi\) | ||||
−0.859729 | + | 0.510751i | \(0.829367\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.44551 | + | 8.92721i | −0.339293 | + | 0.320675i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 7.36420i | − | 0.264189i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.599328 | 0.0214732 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 56.9775 | 2.03881 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 18.4053i | − | 0.657753i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.42309 | − | 8.60532i | −0.122175 | − | 0.307137i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 15.6708i | − | 0.558605i | −0.960203 | − | 0.279303i | \(-0.909897\pi\) | ||
0.960203 | − | 0.279303i | \(-0.0901033\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.640931 | 0.0228178 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −33.7564 | −1.20024 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.1299i | 0.643811i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.1122 | + | 5.21588i | −0.465042 | + | 0.184988i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 36.9225i | − | 1.30786i | −0.756554 | − | 0.653932i | \(-0.773118\pi\) | ||
0.756554 | − | 0.653932i | \(-0.226882\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 67.8478 | 2.40028 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −44.8362 | −1.58421 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 11.3325i | − | 0.399914i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.2677 | + | 6.86886i | −0.608605 | + | 0.242095i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 11.8742i | − | 0.417993i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43.0465 | −1.51343 | −0.756716 | − | 0.653743i | \(-0.773198\pi\) | ||||
−0.756716 | + | 0.653743i | \(0.773198\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.2469 | −1.13234 | −0.566170 | − | 0.824288i | \(-0.691575\pi\) | ||||
−0.566170 | + | 0.824288i | \(0.691575\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.19475i | 0.0769731i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.4247 | + | 51.3458i | 0.715446 | + | 1.79856i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 3.18676i | − | 0.111491i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 17.8944 | 0.625280 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.18121 | 0.180826 | 0.0904128 | − | 0.995904i | \(-0.471181\pi\) | ||||
0.0904128 | + | 0.995904i | \(0.471181\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 25.8517i | − | 0.901133i | −0.892743 | − | 0.450567i | \(-0.851222\pi\) | ||
0.892743 | − | 0.450567i | \(-0.148778\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.66497 | − | 8.10998i | −0.266860 | − | 0.282353i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.97816i | 0.346974i | 0.984836 | + | 0.173487i | \(0.0555035\pi\) | ||||
−0.984836 | + | 0.173487i | \(0.944496\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.9808 | −0.763425 | −0.381713 | − | 0.924281i | \(-0.624666\pi\) | ||||
−0.381713 | + | 0.924281i | \(0.624666\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.38149 | 0.186682 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 18.2848i | − | 0.633531i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.97920 | − | 7.48942i | −0.103099 | − | 0.259182i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 7.97359i | − | 0.275607i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.1089 | −0.556140 | −0.278070 | − | 0.960561i | \(-0.589695\pi\) | ||||
−0.278070 | + | 0.960561i | \(0.589695\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.321887i | 0.0110864i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −18.1001 | + | 7.20001i | −0.622664 | + | 0.247688i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19.9735i | 0.686298i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.91020 | −0.0998779 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.2211 | 0.384653 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 44.9615i | − | 1.53945i | −0.638373 | − | 0.769727i | \(-0.720392\pi\) | ||
0.638373 | − | 0.769727i | \(-0.279608\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.63383 | − | 2.24107i | 0.192673 | − | 0.0766429i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 46.2431i | − | 1.57963i | −0.613343 | − | 0.789817i | \(-0.710176\pi\) | ||
0.613343 | − | 0.789817i | \(-0.289824\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.7772 | −0.367713 | −0.183856 | − | 0.982953i | \(-0.558858\pi\) | ||||
−0.183856 | + | 0.982953i | \(0.558858\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.02578 | 0.0349584 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.7966i | 0.776007i | 0.921658 | + | 0.388003i | \(0.126835\pi\) | ||||
−0.921658 | + | 0.388003i | \(0.873165\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.5303 | − | 46.5835i | −0.630050 | − | 1.58389i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 8.90400i | − | 0.302396i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.82040 | 0.197444 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.86201 | −0.334161 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.61523i | 0.190047i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −32.3109 | − | 15.0146i | −1.09231 | − | 0.507585i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 4.94644i | − | 0.167029i | −0.996507 | − | 0.0835146i | \(-0.973385\pi\) | ||
0.996507 | − | 0.0835146i | \(-0.0266145\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.86201 | 0.0628039 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.53033 | 0.0852490 | 0.0426245 | − | 0.999091i | \(-0.486428\pi\) | ||||
0.0426245 | + | 0.999091i | \(0.486428\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.7430i | 1.00093i | 0.865757 | + | 0.500465i | \(0.166838\pi\) | ||||
−0.865757 | + | 0.500465i | \(0.833162\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.759740 | + | 1.90991i | 0.0255384 | + | 0.0642011i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 45.5450i | − | 1.52925i | −0.644474 | − | 0.764626i | \(-0.722924\pi\) | ||
0.644474 | − | 0.764626i | \(-0.277076\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.3591 | −0.649282 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −26.9568 | −0.903086 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.7086i | 0.391813i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.6683 | − | 4.24373i | 0.356603 | − | 0.141852i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 2.90059i | − | 0.0968480i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.5960 | 0.520155 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 68.0897 | 2.26840 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 5.45428i | − | 0.181507i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −43.3125 | + | 17.2292i | −1.43976 | + | 0.572717i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 33.2034i | − | 1.10250i | −0.834340 | − | 0.551250i | \(-0.814151\pi\) | ||
0.834340 | − | 0.551250i | \(-0.185849\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.64093 | −0.153930 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −55.7788 | −1.84803 | −0.924017 | − | 0.382351i | \(-0.875114\pi\) | ||||
−0.924017 | + | 0.382351i | \(0.875114\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 29.3853i | 0.972513i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.88617 | + | 9.76945i | 0.128473 | + | 0.322968i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 43.2715i | 1.42895i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.5769 | −0.942665 | −0.471333 | − | 0.881956i | \(-0.656227\pi\) | ||||
−0.471333 | + | 0.881956i | \(0.656227\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.91020 | −0.293601 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 28.3947i | 0.934622i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.7772 | + | 15.6351i | 0.485871 | + | 0.514080i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.5994i | 0.512352i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 54.4937 | 1.78788 | 0.893940 | − | 0.448186i | \(-0.147930\pi\) | ||||
0.893940 | + | 0.448186i | \(0.147930\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.15544 | 0.103415 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.23180i | 0.0730659i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.9015 | + | 50.0304i | 0.650848 | + | 1.63617i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 37.1484i | − | 1.21359i | −0.794860 | − | 0.606793i | \(-0.792456\pi\) | ||
0.794860 | − | 0.606793i | \(-0.207544\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.493704 | −0.0161114 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.3973 | 1.05612 | 0.528061 | − | 0.849206i | \(-0.322919\pi\) | ||||
0.528061 | + | 0.849206i | \(0.322919\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.56301i | 0.0508986i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 20.3109 | − | 8.07941i | 0.660713 | − | 0.262823i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 35.4662i | − | 1.15250i | −0.817275 | − | 0.576249i | \(-0.804516\pi\) | ||
0.817275 | − | 0.576249i | \(-0.195484\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.64752 | 0.183326 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.3557 | 0.465516 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.3411i | 0.464553i | 0.972650 | + | 0.232277i | \(0.0746175\pi\) | ||||
−0.972650 | + | 0.232277i | \(0.925383\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.9447 | + | 4.35367i | −0.354162 | + | 0.140881i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.3908i | 0.432864i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 25.3125 | 0.817383 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.2435 | −0.782048 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 41.8458i | 1.34846i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.71155 | + | 4.30266i | 0.0550966 | + | 0.138508i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.9351i | 0.898331i | 0.893449 | + | 0.449165i | \(0.148279\pi\) | ||||
−0.893449 | + | 0.449165i | \(0.851721\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.11222 | 0.0999788 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.5993 | 1.36708 | 0.683539 | − | 0.729914i | \(-0.260440\pi\) | ||||
0.683539 | + | 0.729914i | \(0.260440\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.4132i | 0.333833i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.04160 | − | 3.81983i | 0.129435 | − | 0.122332i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.5597i | 1.26563i | 0.774304 | + | 0.632813i | \(0.218100\pi\) | ||||
−0.774304 | + | 0.632813i | \(0.781900\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 68.7114 | 2.19603 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −31.7564 | −1.01390 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 39.7689i | − | 1.26843i | −0.773157 | − | 0.634215i | \(-0.781323\pi\) | ||
0.773157 | − | 0.634215i | \(-0.218677\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.62175 | − | 21.6742i | −0.274712 | − | 0.690599i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 20.0398i | 0.637874i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.31087 | 0.264270 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −55.2019 | −1.75355 | −0.876773 | − | 0.480905i | \(-0.840308\pi\) | ||||
−0.876773 | + | 0.480905i | \(0.840308\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 4.29664i | − | 0.136350i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.67705 | − | 2.25826i | 0.179974 | − | 0.0715916i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 11.6543i | − | 0.369097i | −0.982823 | − | 0.184548i | \(-0.940918\pi\) | ||
0.982823 | − | 0.184548i | \(-0.0590823\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −13.1987 | −0.417587 |
(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 | 1520.2.d.h.609.4 | 6 | ||
4.3 | odd | 2 | 95.2.b.b.39.1 | ✓ | 6 | ||
5.2 | odd | 4 | 7600.2.a.ck.1.4 | 6 | |||
5.3 | odd | 4 | 7600.2.a.ck.1.3 | 6 | |||
5.4 | even | 2 | inner | 1520.2.d.h.609.3 | 6 | ||
12.11 | even | 2 | 855.2.c.d.514.6 | 6 | |||
20.3 | even | 4 | 475.2.a.j.1.1 | 6 | |||
20.7 | even | 4 | 475.2.a.j.1.6 | 6 | |||
20.19 | odd | 2 | 95.2.b.b.39.6 | yes | 6 | ||
60.23 | odd | 4 | 4275.2.a.br.1.6 | 6 | |||
60.47 | odd | 4 | 4275.2.a.br.1.1 | 6 | |||
60.59 | even | 2 | 855.2.c.d.514.1 | 6 | |||
76.75 | even | 2 | 1805.2.b.e.1084.6 | 6 | |||
380.227 | odd | 4 | 9025.2.a.bx.1.1 | 6 | |||
380.303 | odd | 4 | 9025.2.a.bx.1.6 | 6 | |||
380.379 | even | 2 | 1805.2.b.e.1084.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.b.b.39.1 | ✓ | 6 | 4.3 | odd | 2 | ||
95.2.b.b.39.6 | yes | 6 | 20.19 | odd | 2 | ||
475.2.a.j.1.1 | 6 | 20.3 | even | 4 | |||
475.2.a.j.1.6 | 6 | 20.7 | even | 4 | |||
855.2.c.d.514.1 | 6 | 60.59 | even | 2 | |||
855.2.c.d.514.6 | 6 | 12.11 | even | 2 | |||
1520.2.d.h.609.3 | 6 | 5.4 | even | 2 | inner | ||
1520.2.d.h.609.4 | 6 | 1.1 | even | 1 | trivial | ||
1805.2.b.e.1084.1 | 6 | 380.379 | even | 2 | |||
1805.2.b.e.1084.6 | 6 | 76.75 | even | 2 | |||
4275.2.a.br.1.1 | 6 | 60.47 | odd | 4 | |||
4275.2.a.br.1.6 | 6 | 60.23 | odd | 4 | |||
7600.2.a.ck.1.3 | 6 | 5.3 | odd | 4 | |||
7600.2.a.ck.1.4 | 6 | 5.2 | odd | 4 | |||
9025.2.a.bx.1.1 | 6 | 380.227 | odd | 4 | |||
9025.2.a.bx.1.6 | 6 | 380.303 | odd | 4 |