Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [840,2,Mod(169,840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("840.169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 840.t (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.70743376979\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 169.4 | ||
Root | \(-0.854638 + 0.854638i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 840.169 |
Dual form | 840.2.t.e.169.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/840\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(281\) | \(337\) | \(421\) | \(631\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.17009 | − | 0.539189i | −0.970492 | − | 0.241133i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.41855 | 1.63375 | 0.816877 | − | 0.576812i | \(-0.195703\pi\) | ||||
0.816877 | + | 0.576812i | \(0.195703\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.34017i | 1.20375i | 0.798591 | + | 0.601874i | \(0.205579\pi\) | ||||
−0.798591 | + | 0.601874i | \(0.794421\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.539189 | − | 2.17009i | 0.139218 | − | 0.560314i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.07838i | − | 0.261545i | −0.991412 | − | 0.130773i | \(-0.958254\pi\) | ||
0.991412 | − | 0.130773i | \(-0.0417457\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.34017 | −0.995704 | −0.497852 | − | 0.867262i | \(-0.665878\pi\) | ||||
−0.497852 | + | 0.867262i | \(0.665878\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.34017i | 1.32202i | 0.750378 | + | 0.661009i | \(0.229871\pi\) | ||||
−0.750378 | + | 0.661009i | \(0.770129\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.41855 | + | 2.34017i | 0.883710 | + | 0.468035i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.83710 | 1.64101 | 0.820504 | − | 0.571640i | \(-0.193693\pi\) | ||||
0.820504 | + | 0.571640i | \(0.193693\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.34017 | −0.779518 | −0.389759 | − | 0.920917i | \(-0.627442\pi\) | ||||
−0.389759 | + | 0.920917i | \(0.627442\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.41855i | 0.943249i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.539189 | + | 2.17009i | −0.0911396 | + | 0.366812i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.68035i | 1.42704i | 0.700635 | + | 0.713520i | \(0.252900\pi\) | ||||
−0.700635 | + | 0.713520i | \(0.747100\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.34017 | −0.694984 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.34017 | 1.30252 | 0.651258 | − | 0.758856i | \(-0.274242\pi\) | ||||
0.651258 | + | 0.758856i | \(0.274242\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.15676i | 0.938896i | 0.882960 | + | 0.469448i | \(0.155547\pi\) | ||||
−0.882960 | + | 0.469448i | \(0.844453\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.17009 | + | 0.539189i | 0.323497 | + | 0.0803775i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.83710i | 0.997294i | 0.866805 | + | 0.498647i | \(0.166170\pi\) | ||||
−0.866805 | + | 0.498647i | \(0.833830\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.07838 | 0.151003 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.18342i | 0.849358i | 0.905344 | + | 0.424679i | \(0.139613\pi\) | ||||
−0.905344 | + | 0.424679i | \(0.860387\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.7587 | − | 2.92162i | −1.58555 | − | 0.393951i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 4.34017i | − | 0.574870i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.83710 | 0.890115 | 0.445057 | − | 0.895502i | \(-0.353183\pi\) | ||||
0.445057 | + | 0.895502i | \(0.353183\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.52359 | −0.579186 | −0.289593 | − | 0.957150i | \(-0.593520\pi\) | ||||
−0.289593 | + | 0.957150i | \(0.593520\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000i | 0.125988i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.34017 | − | 9.41855i | 0.290263 | − | 1.16823i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.34017 | −0.763267 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.0989 | −1.67323 | −0.836616 | − | 0.547790i | \(-0.815469\pi\) | ||||
−0.836616 | + | 0.547790i | \(0.815469\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 11.1773i | − | 1.30820i | −0.756408 | − | 0.654101i | \(-0.773047\pi\) | ||
0.756408 | − | 0.654101i | \(-0.226953\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.34017 | + | 4.41855i | −0.270220 | + | 0.510210i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 5.41855i | − | 0.617501i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.680346 | −0.0765449 | −0.0382724 | − | 0.999267i | \(-0.512185\pi\) | ||||
−0.0382724 | + | 0.999267i | \(0.512185\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 6.83710i | − | 0.750469i | −0.926930 | − | 0.375235i | \(-0.877562\pi\) | ||
0.926930 | − | 0.375235i | \(-0.122438\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.581449 | + | 2.34017i | −0.0630670 | + | 0.253827i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.83710i | 0.947437i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.49693 | −0.688673 | −0.344337 | − | 0.938846i | \(-0.611896\pi\) | ||||
−0.344337 | + | 0.938846i | \(0.611896\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.34017 | 0.454974 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 4.34017i | − | 0.450055i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.41855 | + | 2.34017i | 0.966323 | + | 0.240097i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.4969i | 1.06580i | 0.846178 | + | 0.532901i | \(0.178898\pi\) | ||||
−0.846178 | + | 0.532901i | \(0.821102\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.41855 | −0.544585 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.8638 | 1.87701 | 0.938507 | − | 0.345259i | \(-0.112209\pi\) | ||||
0.938507 | + | 0.345259i | \(0.112209\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.1568i | 1.00077i | 0.865802 | + | 0.500387i | \(0.166809\pi\) | ||||
−0.865802 | + | 0.500387i | \(0.833191\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.17009 | − | 0.539189i | −0.211779 | − | 0.0526194i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 14.6537i | − | 1.41663i | −0.705899 | − | 0.708313i | \(-0.749457\pi\) | ||
0.705899 | − | 0.708313i | \(-0.250543\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.8371 | 1.22957 | 0.614786 | − | 0.788694i | \(-0.289243\pi\) | ||||
0.614786 | + | 0.788694i | \(0.289243\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.68035 | −0.823902 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.50307i | 0.141397i | 0.997498 | + | 0.0706985i | \(0.0225228\pi\) | ||||
−0.997498 | + | 0.0706985i | \(0.977477\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.41855 | − | 13.7587i | 0.318781 | − | 1.28301i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 4.34017i | − | 0.401249i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.07838 | −0.0988547 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.3607 | 1.66915 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.34017i | 0.752008i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.32684 | − | 7.46081i | −0.744775 | − | 0.667315i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 19.2039i | − | 1.70407i | −0.523482 | − | 0.852037i | \(-0.675367\pi\) | ||
0.523482 | − | 0.852037i | \(-0.324633\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.15676 | −0.542072 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.00000 | −0.349482 | −0.174741 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174741 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.34017i | 0.376341i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.539189 | + | 2.17009i | −0.0464060 | + | 0.186771i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 8.65368i | − | 0.739334i | −0.929164 | − | 0.369667i | \(-0.879472\pi\) | ||
0.929164 | − | 0.369667i | \(-0.120528\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.18342 | 0.524471 | 0.262235 | − | 0.965004i | \(-0.415540\pi\) | ||||
0.262235 | + | 0.965004i | \(0.415540\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.83710 | −0.575788 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 23.5174i | 1.96663i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −19.1773 | − | 4.76487i | −1.59259 | − | 0.395701i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 1.00000i | − | 0.0824786i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.2039 | 1.08171 | 0.540854 | − | 0.841116i | \(-0.318101\pi\) | ||||
0.540854 | + | 0.841116i | \(0.318101\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.1568 | −1.47758 | −0.738788 | − | 0.673938i | \(-0.764601\pi\) | ||||
−0.738788 | + | 0.673938i | \(0.764601\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.07838i | 0.0871817i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.41855 | + | 2.34017i | 0.756516 | + | 0.187967i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 15.1773i | − | 1.21128i | −0.795739 | − | 0.605639i | \(-0.792917\pi\) | ||
0.795739 | − | 0.605639i | \(-0.207083\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.18342 | −0.490377 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.34017 | 0.499676 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2.83710i | − | 0.222219i | −0.993808 | − | 0.111109i | \(-0.964560\pi\) | ||
0.993808 | − | 0.111109i | \(-0.0354404\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.92162 | − | 11.7587i | 0.227448 | − | 0.915415i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 13.3607i | − | 1.03388i | −0.856021 | − | 0.516941i | \(-0.827071\pi\) | ||
0.856021 | − | 0.516941i | \(-0.172929\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.83710 | −0.449008 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.34017 | 0.331901 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.55479i | 0.194237i | 0.995273 | + | 0.0971184i | \(0.0309626\pi\) | ||||
−0.995273 | + | 0.0971184i | \(0.969037\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.34017 | − | 4.41855i | 0.176900 | − | 0.334011i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.83710i | 0.513908i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.9421 | 0.892598 | 0.446299 | − | 0.894884i | \(-0.352742\pi\) | ||||
0.446299 | + | 0.894884i | \(0.352742\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.15676 | 0.308969 | 0.154485 | − | 0.987995i | \(-0.450628\pi\) | ||||
0.154485 | + | 0.987995i | \(0.450628\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 4.52359i | − | 0.334393i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.68035 | − | 18.8371i | 0.344106 | − | 1.38493i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 5.84324i | − | 0.427300i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.09890 | 0.441301 | 0.220650 | − | 0.975353i | \(-0.429182\pi\) | ||||
0.220650 | + | 0.975353i | \(0.429182\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.6803i | 0.912751i | 0.889787 | + | 0.456376i | \(0.150853\pi\) | ||||
−0.889787 | + | 0.456376i | \(0.849147\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 9.41855 | + | 2.34017i | 0.674476 | + | 0.167583i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.8576i | 0.844820i | 0.906405 | + | 0.422410i | \(0.138816\pi\) | ||||
−0.906405 | + | 0.422410i | \(0.861184\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.50307 | 0.390102 | 0.195051 | − | 0.980793i | \(-0.437513\pi\) | ||||
0.195051 | + | 0.980793i | \(0.437513\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 8.83710i | − | 0.620243i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.0989 | − | 4.49693i | −1.26408 | − | 0.314079i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 6.34017i | − | 0.440672i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −23.5174 | −1.62674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.1506 | −1.31838 | −0.659191 | − | 0.751975i | \(-0.729101\pi\) | ||||
−0.659191 | + | 0.751975i | \(0.729101\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 14.0989i | − | 0.966040i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.31965 | − | 13.3607i | 0.226399 | − | 0.911192i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.34017i | 0.294630i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.1773 | 0.755290 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.68035 | 0.314834 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.3135i | 0.824574i | 0.911054 | + | 0.412287i | \(0.135270\pi\) | ||||
−0.911054 | + | 0.412287i | \(0.864730\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.41855 | − | 2.34017i | −0.294570 | − | 0.156012i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.2039i | 1.00912i | 0.863376 | + | 0.504560i | \(0.168345\pi\) | ||||
−0.863376 | + | 0.504560i | \(0.831655\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.20394 | −0.343886 | −0.171943 | − | 0.985107i | \(-0.555004\pi\) | ||||
−0.171943 | + | 0.985107i | \(0.555004\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.41855 | 0.356514 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.6598i | 0.763861i | 0.924191 | + | 0.381930i | \(0.124741\pi\) | ||||
−0.924191 | + | 0.381930i | \(0.875259\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.68649 | − | 14.8371i | 0.240480 | − | 0.967866i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 0.680346i | − | 0.0441932i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.6225 | −1.33396 | −0.666979 | − | 0.745077i | \(-0.732413\pi\) | ||||
−0.666979 | + | 0.745077i | \(0.732413\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.3545 | −1.31115 | −0.655576 | − | 0.755129i | \(-0.727574\pi\) | ||||
−0.655576 | + | 0.755129i | \(0.727574\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.17009 | + | 0.539189i | 0.138642 | + | 0.0344475i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 18.8371i | − | 1.19858i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.83710 | 0.433284 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.5236 | 0.664243 | 0.332122 | − | 0.943237i | \(-0.392236\pi\) | ||||
0.332122 | + | 0.943237i | \(0.392236\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 34.3545i | 2.15985i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.34017 | − | 0.581449i | −0.146547 | − | 0.0364118i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 22.8059i | − | 1.42259i | −0.702892 | − | 0.711297i | \(-0.748108\pi\) | ||
0.702892 | − | 0.711297i | \(-0.251892\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.68035 | 0.539370 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.83710 | −0.547003 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 28.0144i | − | 1.72744i | −0.503972 | − | 0.863720i | \(-0.668128\pi\) | ||
0.503972 | − | 0.863720i | \(-0.331872\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.33403 | − | 13.4186i | 0.204808 | − | 0.824295i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 6.49693i | − | 0.397606i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.4969 | −1.12778 | −0.563889 | − | 0.825851i | \(-0.690695\pi\) | ||||
−0.563889 | + | 0.825851i | \(0.690695\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −29.0205 | −1.76287 | −0.881435 | − | 0.472304i | \(-0.843422\pi\) | ||||
−0.881435 | + | 0.472304i | \(0.843422\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.34017i | 0.262679i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 23.9421 | + | 12.6803i | 1.44377 | + | 0.764654i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.68035i | 0.521551i | 0.965399 | + | 0.260776i | \(0.0839783\pi\) | ||||
−0.965399 | + | 0.260776i | \(0.916022\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.34017 | 0.259839 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.63317 | 0.336046 | 0.168023 | − | 0.985783i | \(-0.446262\pi\) | ||||
0.168023 | + | 0.985783i | \(0.446262\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 2.47027i | − | 0.146842i | −0.997301 | − | 0.0734210i | \(-0.976608\pi\) | ||
0.997301 | − | 0.0734210i | \(-0.0233917\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.34017 | + | 9.41855i | −0.138620 | + | 0.557907i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 8.34017i | − | 0.492305i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.8371 | 0.931594 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.4969 | −0.615341 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 7.60197i | − | 0.444112i | −0.975034 | − | 0.222056i | \(-0.928723\pi\) | ||
0.975034 | − | 0.222056i | \(-0.0712767\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.8371 | − | 3.68649i | −0.863849 | − | 0.214636i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 5.41855i | − | 0.314416i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −27.5174 | −1.59138 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.15676 | 0.354869 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18.8638i | 1.08369i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.81658 | + | 2.43907i | 0.562096 | + | 0.139661i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 6.15676i | − | 0.351385i | −0.984445 | − | 0.175692i | \(-0.943784\pi\) | ||
0.984445 | − | 0.175692i | \(-0.0562164\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.1568 | −0.577798 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.52973 | −0.0867432 | −0.0433716 | − | 0.999059i | \(-0.513810\pi\) | ||||
−0.0433716 | + | 0.999059i | \(0.513810\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.9733i | 0.676773i | 0.941007 | + | 0.338387i | \(0.109881\pi\) | ||||
−0.941007 | + | 0.338387i | \(0.890119\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.539189 | − | 2.17009i | 0.0303799 | − | 0.122271i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 23.5441i | − | 1.32237i | −0.750223 | − | 0.661184i | \(-0.770054\pi\) | ||
0.750223 | − | 0.661184i | \(-0.229946\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 47.8843 | 2.68101 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.6537 | 0.817889 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.68035i | 0.260421i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.1568 | + | 19.1773i | −0.563395 | + | 1.06376i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.8371i | 0.709893i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.83710 | 0.376942 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.16290 | −0.503638 | −0.251819 | − | 0.967774i | \(-0.581029\pi\) | ||||
−0.251819 | + | 0.967774i | \(0.581029\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 8.68035i | − | 0.475680i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 16.0000i | − | 0.871576i | −0.900049 | − | 0.435788i | \(-0.856470\pi\) | ||
0.900049 | − | 0.435788i | \(-0.143530\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.50307 | −0.0816356 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −23.5174 | −1.27354 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 13.7587 | + | 3.41855i | 0.740745 | + | 0.184049i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.0205i | 1.23581i | 0.786254 | + | 0.617903i | \(0.212018\pi\) | ||||
−0.786254 | + | 0.617903i | \(0.787982\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.78992 | 0.202870 | 0.101435 | − | 0.994842i | \(-0.467657\pi\) | ||||
0.101435 | + | 0.994842i | \(0.467657\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.34017 | 0.231661 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.5958i | 1.52200i | 0.648751 | + | 0.761001i | \(0.275292\pi\) | ||||
−0.648751 | + | 0.761001i | \(0.724708\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 30.5958 | + | 7.60197i | 1.62386 | + | 0.403471i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 1.07838i | − | 0.0570738i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.2618 | 0.594375 | 0.297187 | − | 0.954819i | \(-0.403951\pi\) | ||||
0.297187 | + | 0.954819i | \(0.403951\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.162899 | −0.00857361 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.3607i | 0.963686i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.02666 | + | 24.2557i | −0.315450 | + | 1.26960i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.3607i | 1.32382i | 0.749584 | + | 0.661909i | \(0.230253\pi\) | ||||
−0.749584 | + | 0.661909i | \(0.769747\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.34017 | −0.434172 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.18342 | 0.321027 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 21.3074i | − | 1.10325i | −0.834091 | − | 0.551627i | \(-0.814007\pi\) | ||
0.834091 | − | 0.551627i | \(-0.185993\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.46081 | − | 8.32684i | 0.385275 | − | 0.429996i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 38.3545i | 1.97536i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.84324 | 0.0946811 | 0.0473406 | − | 0.998879i | \(-0.484925\pi\) | ||||
0.0473406 | + | 0.998879i | \(0.484925\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.2039 | 0.983847 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.99386i | 0.255174i | 0.991827 | + | 0.127587i | \(0.0407232\pi\) | ||||
−0.991827 | + | 0.127587i | \(0.959277\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.92162 | + | 11.7587i | −0.148900 | + | 0.599280i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 6.15676i | − | 0.312965i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.8371 | −0.853675 | −0.426837 | − | 0.904328i | \(-0.640372\pi\) | ||||
−0.426837 | + | 0.904328i | \(0.640372\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.83710 | 0.345767 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 4.00000i | − | 0.201773i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.47641 | + | 0.366835i | 0.0742862 | + | 0.0184575i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 36.8515i | 1.84952i | 0.380548 | + | 0.924761i | \(0.375736\pi\) | ||||
−0.380548 | + | 0.924761i | \(0.624264\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.34017 | −0.217280 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.3545 | −1.21621 | −0.608104 | − | 0.793857i | \(-0.708070\pi\) | ||||
−0.608104 | + | 0.793857i | \(0.708070\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 18.8371i | − | 0.938343i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.17009 | − | 0.539189i | −0.107832 | − | 0.0267925i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 47.0349i | 2.33143i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.0410 | 1.38654 | 0.693270 | − | 0.720678i | \(-0.256169\pi\) | ||||
0.693270 | + | 0.720678i | \(0.256169\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.65368 | 0.426855 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 6.83710i | − | 0.336432i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.68649 | + | 14.8371i | −0.180963 | + | 0.728325i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.18342i | 0.302803i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.482553 | −0.0235742 | −0.0117871 | − | 0.999931i | \(-0.503752\pi\) | ||||
−0.0117871 | + | 0.999931i | \(0.503752\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.1506 | 1.03082 | 0.515409 | − | 0.856944i | \(-0.327640\pi\) | ||||
0.515409 | + | 0.856944i | \(0.327640\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 6.83710i | − | 0.332431i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.52359 | − | 4.76487i | 0.122412 | − | 0.231130i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.52359i | 0.218912i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −23.5174 | −1.13543 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.7382 | −1.38427 | −0.692135 | − | 0.721768i | \(-0.743330\pi\) | ||||
−0.692135 | + | 0.721768i | \(0.743330\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.02052i | 0.433498i | 0.976227 | + | 0.216749i | \(0.0695454\pi\) | ||||
−0.976227 | + | 0.216749i | \(0.930455\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.76487 | − | 19.1773i | 0.228458 | − | 0.919480i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 27.5174i | − | 1.31634i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.8166 | 0.850339 | 0.425170 | − | 0.905114i | \(-0.360214\pi\) | ||||
0.425170 | + | 0.905114i | \(0.360214\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.7009i | 0.555925i | 0.960592 | + | 0.277962i | \(0.0896591\pi\) | ||||
−0.960592 | + | 0.277962i | \(0.910341\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.0989 | + | 3.50307i | 0.668352 | + | 0.166062i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.2039i | 0.624525i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.7337 | −0.506553 | −0.253277 | − | 0.967394i | \(-0.581508\pi\) | ||||
−0.253277 | + | 0.967394i | \(0.581508\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 45.1917 | 2.12799 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 18.1568i | − | 0.853079i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.41855 | − | 2.34017i | −0.441548 | − | 0.109709i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 20.9939i | − | 0.982051i | −0.871145 | − | 0.491026i | \(-0.836622\pi\) | ||
0.871145 | − | 0.491026i | \(-0.163378\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.07838 | −0.0503344 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.3751 | −0.716088 | −0.358044 | − | 0.933705i | \(-0.616556\pi\) | ||||
−0.358044 | + | 0.933705i | \(0.616556\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 29.1917i | − | 1.35665i | −0.734762 | − | 0.678326i | \(-0.762706\pi\) | ||
0.734762 | − | 0.678326i | \(-0.237294\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.34017 | + | 9.41855i | −0.108523 | + | 0.436775i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 15.2039i | − | 0.703554i | −0.936084 | − | 0.351777i | \(-0.885577\pi\) | ||
0.936084 | − | 0.351777i | \(-0.114423\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.1773 | 0.699332 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 33.3607i | 1.53393i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19.1773 | − | 10.1568i | −0.879914 | − | 0.466024i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 6.18342i | − | 0.283119i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.7838 | 0.858253 | 0.429126 | − | 0.903244i | \(-0.358822\pi\) | ||||
0.429126 | + | 0.903244i | \(0.358822\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −37.6742 | −1.71780 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.34017i | 0.288488i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.65983 | − | 22.7792i | 0.257000 | − | 1.03435i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 16.5113i | − | 0.748199i | −0.927389 | − | 0.374099i | \(-0.877952\pi\) | ||
0.927389 | − | 0.374099i | \(-0.122048\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.83710 | 0.128298 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.4063 | 1.77838 | 0.889190 | − | 0.457538i | \(-0.151269\pi\) | ||||
0.889190 | + | 0.457538i | \(0.151269\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 9.52973i | − | 0.429198i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.7587 | + | 2.92162i | 0.528515 | + | 0.131317i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.0989i | 0.632422i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.5174 | 1.41091 | 0.705457 | − | 0.708752i | \(-0.250742\pi\) | ||||
0.705457 | + | 0.708752i | \(0.250742\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.3607 | 0.596912 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 20.3668i | − | 0.908112i | −0.890973 | − | 0.454056i | \(-0.849977\pi\) | ||
0.890973 | − | 0.454056i | \(-0.150023\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −40.9360 | − | 10.1711i | −1.82163 | − | 0.452609i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 5.83710i | − | 0.259235i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.1773 | −0.495424 | −0.247712 | − | 0.968834i | \(-0.579679\pi\) | ||||
−0.247712 | + | 0.968834i | \(0.579679\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.1773 | −0.494454 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.34017i | 0.191623i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.47641 | − | 22.0410i | 0.241319 | − | 0.971244i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 37.0472i | 1.62933i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.55479 | −0.112143 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.6537 | 1.43058 | 0.715292 | − | 0.698826i | \(-0.246294\pi\) | ||||
0.715292 | + | 0.698826i | \(0.246294\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.6865i | 0.685922i | 0.939350 | + | 0.342961i | \(0.111430\pi\) | ||||
−0.939350 | + | 0.342961i | \(0.888570\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.41855 | + | 2.34017i | 0.192841 | + | 0.102134i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.68035i | 0.203879i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.1978 | −0.747730 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.83710 | −0.296705 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 36.1978i | 1.56790i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.90110 | + | 31.7998i | −0.341594 | + | 1.37482i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.9421i | 0.515341i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.41855 | −0.233394 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.1978 | 1.29830 | 0.649152 | − | 0.760658i | \(-0.275124\pi\) | ||||
0.649152 | + | 0.760658i | \(0.275124\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.15676i | 0.178383i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −27.8576 | − | 6.92162i | −1.19329 | − | 0.296490i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 9.36069i | − | 0.400234i | −0.979772 | − | 0.200117i | \(-0.935868\pi\) | ||
0.979772 | − | 0.200117i | \(-0.0641323\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.52359 | 0.193062 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −38.3545 | −1.63396 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.680346i | 0.0289313i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 18.8371 | + | 4.68035i | 0.799590 | + | 0.198670i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.49079i | 0.317395i | 0.987327 | + | 0.158697i | \(0.0507294\pi\) | ||||
−0.987327 | + | 0.158697i | \(0.949271\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −26.7214 | −1.13019 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.84324 | 0.246702 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.7152i | 1.33664i | 0.743875 | + | 0.668319i | \(0.232986\pi\) | ||||
−0.743875 | + | 0.668319i | \(0.767014\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.810439 | − | 3.26180i | 0.0340954 | − | 0.137225i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 1.00000i | − | 0.0419961i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −30.6803 | −1.28619 | −0.643094 | − | 0.765788i | \(-0.722349\pi\) | ||||
−0.643094 | + | 0.765788i | \(0.722349\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.6393 | −0.445241 | −0.222621 | − | 0.974905i | \(-0.571461\pi\) | ||||
−0.222621 | + | 0.974905i | \(0.571461\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.09890i | 0.254785i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.8371 | + | 28.0144i | −0.618750 | + | 1.16828i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 30.0677i | − | 1.25173i | −0.779930 | − | 0.625867i | \(-0.784745\pi\) | ||
0.779930 | − | 0.625867i | \(-0.215255\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.6803 | −0.526977 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.83710 | −0.283651 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 33.5052i | 1.38764i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.34017 | + | 9.41855i | −0.0967542 | + | 0.389409i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 10.0410i | − | 0.414438i | −0.978295 | − | 0.207219i | \(-0.933559\pi\) | ||
0.978295 | − | 0.207219i | \(-0.0664413\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.8371 | 0.776169 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.8576 | −0.487757 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 24.2823i | − | 0.997155i | −0.866845 | − | 0.498578i | \(-0.833856\pi\) | ||
0.866845 | − | 0.498578i | \(-0.166144\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.34017 | + | 0.581449i | 0.0959377 | + | 0.0238371i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.50307i | 0.225226i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.90110 | 0.404548 | 0.202274 | − | 0.979329i | \(-0.435167\pi\) | ||||
0.202274 | + | 0.979329i | \(0.435167\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.6865 | 0.721447 | 0.360723 | − | 0.932673i | \(-0.382530\pi\) | ||||
0.360723 | + | 0.932673i | \(0.382530\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −39.8443 | − | 9.89988i | −1.61990 | − | 0.402487i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 28.3135i | − | 1.14921i | −0.818431 | − | 0.574605i | \(-0.805156\pi\) | ||
0.818431 | − | 0.574605i | \(-0.194844\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.83710 | 0.358097 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −29.6742 | −1.20049 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 23.6865i | − | 0.956688i | −0.878172 | − | 0.478344i | \(-0.841237\pi\) | ||
0.878172 | − | 0.478344i | \(-0.158763\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.49693 | − | 18.0989i | 0.181334 | − | 0.729818i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.7009i | 0.551576i | 0.961218 | + | 0.275788i | \(0.0889388\pi\) | ||||
−0.961218 | + | 0.275788i | \(0.911061\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.49693 | 0.100360 | 0.0501800 | − | 0.998740i | \(-0.484020\pi\) | ||||
0.0501800 | + | 0.998740i | \(0.484020\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.34017 | 0.254422 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.49693i | 0.260294i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.0472 | + | 20.6803i | 0.561887 | + | 0.827214i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 23.5174i | − | 0.939196i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.36069 | 0.373235 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.68035 | 0.345559 | 0.172780 | − | 0.984961i | \(-0.444725\pi\) | ||||
0.172780 | + | 0.984961i | \(0.444725\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 19.1506i | − | 0.761169i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.3545 | + | 41.6742i | −0.410908 | + | 1.65379i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 4.34017i | − | 0.171964i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.0989 | 0.557744 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.30737 | 0.130633 | 0.0653166 | − | 0.997865i | \(-0.479194\pi\) | ||||
0.0653166 | + | 0.997865i | \(0.479194\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 6.15676i | − | 0.242799i | −0.992604 | − | 0.121399i | \(-0.961262\pi\) | ||
0.992604 | − | 0.121399i | \(-0.0387382\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.3607 | + | 3.31965i | 0.526077 | + | 0.130711i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.95282i | 0.273344i | 0.990616 | + | 0.136672i | \(0.0436406\pi\) | ||||
−0.990616 | + | 0.136672i | \(0.956359\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 37.0472 | 1.45423 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.34017 | −0.170105 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 38.7480i | − | 1.51633i | −0.652064 | − | 0.758164i | \(-0.726097\pi\) | ||
0.652064 | − | 0.758164i | \(-0.273903\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.68035 | + | 2.15676i | 0.339169 | + | 0.0842714i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.1773i | 0.436067i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.22076 | −0.359190 | −0.179595 | − | 0.983741i | \(-0.557479\pi\) | ||||
−0.179595 | + | 0.983741i | \(0.557479\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.8843 | 1.00678 | 0.503391 | − | 0.864059i | \(-0.332086\pi\) | ||||
0.503391 | + | 0.864059i | \(0.332086\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.68035i | 0.181770i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.34017 | − | 9.41855i | 0.0907480 | − | 0.365236i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 56.0288i | 2.16944i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.3135 | −0.476068 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.5113 | −0.946248 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 40.0821i | − | 1.54505i | −0.634984 | − | 0.772525i | \(-0.718993\pi\) | ||
0.634984 | − | 0.772525i | \(-0.281007\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.34017 | − | 4.41855i | 0.0900733 | − | 0.170070i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 33.5897i | − | 1.29096i | −0.763779 | − | 0.645478i | \(-0.776658\pi\) | ||
0.763779 | − | 0.645478i | \(-0.223342\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.4969 | 0.402835 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.2039 | −0.582616 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 18.7070i | − | 0.715804i | −0.933759 | − | 0.357902i | \(-0.883492\pi\) | ||
0.933759 | − | 0.357902i | \(-0.116508\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.66597 | + | 18.7792i | −0.178278 | + | 0.717518i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 5.20394i | − | 0.198543i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −26.8371 | −1.02241 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.1773 | −0.729538 | −0.364769 | − | 0.931098i | \(-0.618852\pi\) | ||||
−0.364769 | + | 0.931098i | \(0.618852\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.41855i | 0.205834i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.4186 | − | 3.33403i | −0.508995 | − | 0.126467i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 8.99386i | − | 0.340667i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.6598 | −0.441015 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.4641 | 0.810689 | 0.405344 | − | 0.914164i | \(-0.367152\pi\) | ||||
0.405344 | + | 0.914164i | \(0.367152\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 37.6742i | − | 1.42091i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14.8371 | + | 3.68649i | 0.558798 | + | 0.138841i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 18.8638i | − | 0.709445i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.62702 | −0.0986599 | −0.0493299 | − | 0.998783i | \(-0.515709\pi\) | ||||
−0.0493299 | + | 0.998783i | \(0.515709\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.680346 | 0.0255150 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 27.5174i | − | 1.03054i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.6803 | − | 51.0349i | 0.474218 | − | 1.90860i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 20.6225i | − | 0.770161i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.36683 | 0.162855 | 0.0814277 | − | 0.996679i | \(-0.474052\pi\) | ||||
0.0814277 | + | 0.996679i | \(0.474052\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.1568 | 0.378257 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 20.3545i | − | 0.756994i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 39.0472 | + | 20.6803i | 1.45018 | + | 0.768049i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.1445i | 1.04382i | 0.853000 | + | 0.521910i | \(0.174780\pi\) | ||||
−0.853000 | + | 0.521910i | \(0.825220\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.63931 | 0.245564 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.7480i | 0.987962i | 0.869473 | + | 0.493981i | \(0.164459\pi\) | ||||
−0.869473 | + | 0.493981i | \(0.835541\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.539189 | + | 2.17009i | −0.0198883 | + | 0.0800448i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.0349 | −0.700210 | −0.350105 | − | 0.936710i | \(-0.613854\pi\) | ||||
−0.350105 | + | 0.936710i | \(0.613854\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18.8371 | 0.691998 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 33.6598i | − | 1.23486i | −0.786626 | − | 0.617430i | \(-0.788174\pi\) | ||
0.786626 | − | 0.617430i | \(-0.211826\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −28.6537 | − | 7.11942i | −1.04979 | − | 0.260835i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.83710i | 0.250156i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.6537 | −0.535434 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −49.8720 | −1.81985 | −0.909927 | − | 0.414767i | \(-0.863863\pi\) | ||||
−0.909927 | + | 0.414767i | \(0.863863\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.5236i | 0.383501i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 39.4017 | + | 9.78992i | 1.43398 | + | 0.356292i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 7.63317i | − | 0.277432i | −0.990332 | − | 0.138716i | \(-0.955702\pi\) | ||
0.990332 | − | 0.138716i | \(-0.0442975\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −34.3545 | −1.24699 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.5974 | 0.710406 | 0.355203 | − | 0.934789i | \(-0.384412\pi\) | ||||
0.355203 | + | 0.934789i | \(0.384412\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 12.8371i | − | 0.464734i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.581449 | − | 2.34017i | 0.0210223 | − | 0.0846091i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 29.6742i | 1.07147i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.4079 | 1.16866 | 0.584329 | − | 0.811517i | \(-0.301358\pi\) | ||||
0.584329 | + | 0.811517i | \(0.301358\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.8059 | 0.821335 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.0845i | 0.434650i | 0.976099 | + | 0.217325i | \(0.0697331\pi\) | ||||
−0.976099 | + | 0.217325i | \(0.930267\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.1773 | − | 10.1568i | −0.688868 | − | 0.364841i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.68035i | 0.311406i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −36.1978 | −1.29692 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −76.3956 | −2.73365 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 8.83710i | − | 0.315812i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.18342 | + | 32.9360i | −0.292079 | + | 1.17554i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.0472i | 0.892836i | 0.894825 | + | 0.446418i | \(0.147300\pi\) | ||||
−0.894825 | + | 0.446418i | \(0.852700\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 28.0144 | 0.997338 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.50307 | 0.0534431 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 19.6332i | − | 0.697194i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13.4186 | + | 3.33403i | 0.475907 | + | 0.118246i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 21.2762i | − | 0.753641i | −0.926286 | − | 0.376820i | \(-0.877017\pi\) | ||
0.926286 | − | 0.376820i | \(-0.122983\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.37298 | 0.260837 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.49693 | 0.229558 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 60.5646i | − | 2.13728i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.7587 | − | 3.41855i | −0.484931 | − | 0.120488i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 18.4969i | − | 0.651123i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 49.6619 | 1.74602 | 0.873010 | − | 0.487702i | \(-0.162165\pi\) | ||||
0.873010 | + | 0.487702i | \(0.162165\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.8166 | 0.906543 | 0.453271 | − | 0.891373i | \(-0.350257\pi\) | ||||
0.453271 | + | 0.891373i | \(0.350257\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 29.0205i | − | 1.01779i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.52973 | + | 6.15676i | −0.0535842 | + | 0.215662i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 26.7214i | − | 0.934863i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.34017 | −0.151658 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.8904 | 0.868682 | 0.434341 | − | 0.900749i | \(-0.356981\pi\) | ||||
0.434341 | + | 0.900749i | \(0.356981\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 18.4703i | − | 0.643833i | −0.946768 | − | 0.321917i | \(-0.895673\pi\) | ||
0.946768 | − | 0.321917i | \(-0.104327\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.6803 | + | 23.9421i | −0.441473 | + | 0.833558i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 21.6886i | − | 0.754186i | −0.926175 | − | 0.377093i | \(-0.876924\pi\) | ||
0.926175 | − | 0.377093i | \(-0.123076\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −47.5052 | −1.64992 | −0.824961 | − | 0.565189i | \(-0.808803\pi\) | ||||
−0.824961 | + | 0.565189i | \(0.808803\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.68035 | −0.301118 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.07838i | 0.0373636i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.20394 | + | 28.9939i | −0.249302 | + | 1.00337i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.34017i | 0.150018i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11.4641 | −0.395785 | −0.197893 | − | 0.980224i | \(-0.563410\pi\) | ||||
−0.197893 | + | 0.980224i | \(0.563410\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 49.0944 | 1.69291 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.63317i | 0.194017i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.6670 | + | 3.14730i | 0.435759 | + | 0.108270i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 18.3607i | − | 0.630881i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.47027 | 0.0847793 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −55.0349 | −1.88657 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 39.8043i | − | 1.36287i | −0.731877 | − | 0.681437i | \(-0.761356\pi\) | ||
0.731877 | − | 0.681437i | \(-0.238644\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.41855 | − | 2.34017i | −0.322108 | − | 0.0800322i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.9627i | 0.579433i | 0.957112 | + | 0.289717i | \(0.0935611\pi\) | ||||
−0.957112 | + | 0.289717i | \(0.906439\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.0493 | 1.40058 | 0.700292 | − | 0.713857i | \(-0.253053\pi\) | ||||
0.700292 | + | 0.713857i | \(0.253053\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.34017 | 0.284232 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 50.0554i | − | 1.70391i | −0.523618 | − | 0.851953i | \(-0.675418\pi\) | ||
0.523618 | − | 0.851953i | \(-0.324582\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.37751 | − | 5.54411i | 0.0468368 | − | 0.188505i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.8371i | 0.537856i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.68649 | −0.125056 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 10.4969i | − | 0.355267i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.46081 | + | 8.32684i | −0.252221 | + | 0.281499i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.32580i | 0.213607i | 0.994280 | + | 0.106803i | \(0.0340616\pi\) | ||||
−0.994280 | + | 0.106803i | \(0.965938\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.60197 | 0.256408 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.5380 | 0.691942 | 0.345971 | − | 0.938245i | \(-0.387550\pi\) | ||||
0.345971 | + | 0.938245i | \(0.387550\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.30737i | 0.178607i | 0.996004 | + | 0.0893036i | \(0.0284641\pi\) | ||||
−0.996004 | + | 0.0893036i | \(0.971536\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.68649 | − | 14.8371i | 0.123920 | − | 0.498744i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 3.15061i | − | 0.105787i | −0.998600 | − | 0.0528936i | \(-0.983156\pi\) | ||
0.998600 | − | 0.0528936i | \(-0.0168444\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.2039 | −0.644079 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.41855 | 0.181528 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 29.6742i | − | 0.993009i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.9155 | − | 6.43907i | −0.866259 | − | 0.215234i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 27.5174i | − | 0.918781i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −38.3545 | −1.27920 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.66806 | 0.222145 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.15676i | 0.204884i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.02052 | − | 2.24128i | −0.299852 | − | 0.0745025i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.9467i | 0.396683i | 0.980133 | + | 0.198341i | \(0.0635555\pi\) | ||||
−0.980133 | + | 0.198341i | \(0.936445\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.8638 | −0.625672 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46.0989 | 1.52732 | 0.763662 | − | 0.645616i | \(-0.223399\pi\) | ||||
0.763662 | + | 0.645616i | \(0.223399\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 37.0472i | − | 1.22608i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.43907 | + | 9.81658i | −0.0806332 | + | 0.324526i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.00000i | 0.132092i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.25726 | −0.239395 | −0.119697 | − | 0.992810i | \(-0.538192\pi\) | ||||
−0.119697 | + | 0.992810i | \(0.538192\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.15676 | 0.202872 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 61.1917i | − | 2.01415i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.3135 | + | 38.3545i | −0.667904 | + | 1.26109i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 10.1568i | − | 0.333592i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 44.9048 | 1.47328 | 0.736639 | − | 0.676286i | \(-0.236412\pi\) | ||||
0.736639 | + | 0.676286i | \(0.236412\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.34017 | 0.142243 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 1.52973i | − | 0.0500812i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.15061 | + | 12.6803i | −0.103036 | + | 0.414692i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 43.6886i | − | 1.42724i | −0.700531 | − | 0.713622i | \(-0.747054\pi\) | ||
0.700531 | − | 0.713622i | \(-0.252946\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.9733 | −0.390735 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.6660 | 0.478097 | 0.239048 | − | 0.971008i | \(-0.423165\pi\) | ||||
0.239048 | + | 0.971008i | \(0.423165\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 52.8781i | 1.72195i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.17009 | + | 0.539189i | 0.0705929 | + | 0.0175398i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.96719i | 0.0964209i | 0.998837 | + | 0.0482104i | \(0.0153518\pi\) | ||||
−0.998837 | + | 0.0482104i | \(0.984648\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 48.5113 | 1.57474 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23.5441 | 0.763470 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45.5851i | 1.47665i | 0.674446 | + | 0.738324i | \(0.264382\pi\) | ||||
−0.674446 | + | 0.738324i | \(0.735618\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.2351 | − | 3.28846i | −0.428279 | − | 0.106412i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 47.8843i | 1.54788i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.65368 | −0.279442 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.1629 | −0.392352 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.6537i | 0.472208i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.83710 | − | 27.5174i | 0.220094 | − | 0.885818i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.3668i | 1.04085i | 0.853908 | + | 0.520424i | \(0.174226\pi\) | ||||
−0.853908 | + | 0.520424i | \(0.825774\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.68035 | −0.150354 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.3197 | −0.363265 | −0.181632 | − | 0.983366i | \(-0.558138\pi\) | ||||
−0.181632 | + | 0.983366i | \(0.558138\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 6.18342i | − | 0.198231i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −19.1773 | − | 10.1568i | −0.614164 | − | 0.325277i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.6886i | 1.26975i | 0.772615 | + | 0.634875i | \(0.218948\pi\) | ||||
−0.772615 | + | 0.634875i | \(0.781052\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −35.2039 | −1.12512 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.8371 | −0.409857 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 43.5174i | − | 1.38799i | −0.719979 | − | 0.693996i | \(-0.755849\pi\) | ||
0.719979 | − | 0.693996i | \(-0.244151\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.39350 | − | 25.7321i | 0.203714 | − | 0.819892i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.83710i | 0.217627i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −39.0349 | −1.24124 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.80221 | −0.120781 | −0.0603905 | − | 0.998175i | \(-0.519235\pi\) | ||||
−0.0603905 | + | 0.998175i | \(0.519235\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 9.16290i | − | 0.290776i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.9421 | − | 2.96719i | −0.378591 | − | 0.0940664i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.8043i | 0.753890i | 0.926236 | + | 0.376945i | \(0.123025\pi\) | ||||
−0.926236 | + | 0.376945i | \(0.876975\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.68035 | 0.274634 |
(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 | 840.2.t.e.169.4 | yes | 6 | |
3.2 | odd | 2 | 2520.2.t.j.1009.6 | 6 | |||
4.3 | odd | 2 | 1680.2.t.i.1009.1 | 6 | |||
5.2 | odd | 4 | 4200.2.a.bq.1.3 | 3 | |||
5.3 | odd | 4 | 4200.2.a.bo.1.3 | 3 | |||
5.4 | even | 2 | inner | 840.2.t.e.169.1 | ✓ | 6 | |
12.11 | even | 2 | 5040.2.t.ba.1009.6 | 6 | |||
15.14 | odd | 2 | 2520.2.t.j.1009.5 | 6 | |||
20.3 | even | 4 | 8400.2.a.dk.1.1 | 3 | |||
20.7 | even | 4 | 8400.2.a.dh.1.1 | 3 | |||
20.19 | odd | 2 | 1680.2.t.i.1009.4 | 6 | |||
60.59 | even | 2 | 5040.2.t.ba.1009.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.t.e.169.1 | ✓ | 6 | 5.4 | even | 2 | inner | |
840.2.t.e.169.4 | yes | 6 | 1.1 | even | 1 | trivial | |
1680.2.t.i.1009.1 | 6 | 4.3 | odd | 2 | |||
1680.2.t.i.1009.4 | 6 | 20.19 | odd | 2 | |||
2520.2.t.j.1009.5 | 6 | 15.14 | odd | 2 | |||
2520.2.t.j.1009.6 | 6 | 3.2 | odd | 2 | |||
4200.2.a.bo.1.3 | 3 | 5.3 | odd | 4 | |||
4200.2.a.bq.1.3 | 3 | 5.2 | odd | 4 | |||
5040.2.t.ba.1009.5 | 6 | 60.59 | even | 2 | |||
5040.2.t.ba.1009.6 | 6 | 12.11 | even | 2 | |||
8400.2.a.dh.1.1 | 3 | 20.7 | even | 4 | |||
8400.2.a.dk.1.1 | 3 | 20.3 | even | 4 |