Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [352,2,Mod(351,352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("352.351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 352 = 2^{5} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 352.e (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: | \(2.81073415115\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.653473922154496.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{10} + 13x^{8} - 28x^{6} + 52x^{4} - 64x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{15} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 351.10 | ||
Root | \(1.35489 + 0.405301i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 352.351 |
Dual form | 352.2.e.a.351.4 |
$q$-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 \(\left(\mathbb{Z}/352\mathbb{Z}\right)^\times\).
\(n\) | \(133\) | \(287\) | \(321\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.34292i | 0.775337i | 0.921799 | + | 0.387669i | \(0.126719\pi\) | ||||
−0.921799 | + | 0.387669i | \(0.873281\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.48929 | 1.11324 | 0.556622 | − | 0.830766i | \(-0.312097\pi\) | ||||
0.556622 | + | 0.830766i | \(0.312097\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.62121 | 0.612758 | 0.306379 | − | 0.951910i | \(-0.400882\pi\) | ||||
0.306379 | + | 0.951910i | \(0.400882\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.19656 | 0.398853 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.31339 | − | 0.146365i | −0.999026 | − | 0.0441309i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.20722i | 0.334823i | 0.985887 | + | 0.167412i | \(0.0535408\pi\) | ||||
−0.985887 | + | 0.167412i | \(0.946459\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.34292i | 0.863139i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 5.41957i | − | 1.31444i | −0.753700 | − | 0.657219i | \(-0.771733\pi\) | ||
0.753700 | − | 0.657219i | \(-0.228267\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.59114 | 0.594448 | 0.297224 | − | 0.954808i | \(-0.403939\pi\) | ||||
0.297224 | + | 0.954808i | \(0.403939\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.17715i | 0.475094i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.63565i | 0.758086i | 0.925379 | + | 0.379043i | \(0.123747\pi\) | ||||
−0.925379 | + | 0.379043i | \(0.876253\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.19656 | 0.239312 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.63565i | 1.08458i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.86920i | 1.83266i | 0.400419 | + | 0.916332i | \(0.368865\pi\) | ||||
−0.400419 | + | 0.916332i | \(0.631135\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.949808i | − | 0.170591i | −0.996356 | − | 0.0852953i | \(-0.972817\pi\) | ||
0.996356 | − | 0.0852953i | \(-0.0271834\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.196558 | − | 4.44963i | 0.0342163 | − | 0.774582i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.03565 | 0.682149 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.48929 | 0.409237 | 0.204618 | − | 0.978842i | \(-0.434405\pi\) | ||||
0.204618 | + | 0.978842i | \(0.434405\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.62121 | −0.259601 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.83401i | − | 1.22347i | −0.791064 | − | 0.611733i | \(-0.790473\pi\) | ||
0.791064 | − | 0.611733i | \(-0.209527\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.62679 | −1.01058 | −0.505288 | − | 0.862951i | \(-0.668614\pi\) | ||||
−0.505288 | + | 0.862951i | \(0.668614\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.97858 | 0.444020 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 5.66442i | − | 0.826241i | −0.910676 | − | 0.413121i | \(-0.864439\pi\) | ||
0.910676 | − | 0.413121i | \(-0.135561\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.37169 | −0.624527 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.27806 | 1.01913 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.37169 | −1.01258 | −0.506290 | − | 0.862363i | \(-0.668983\pi\) | ||||
−0.506290 | + | 0.862363i | \(0.668983\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.24799 | − | 0.364346i | −1.11216 | − | 0.0491284i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.47970i | 0.460897i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 12.0288i | − | 1.56601i | −0.622014 | − | 0.783006i | \(-0.713685\pi\) | ||
0.622014 | − | 0.783006i | \(-0.286315\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 0.969933i | − | 0.124187i | −0.998070 | − | 0.0620936i | \(-0.980222\pi\) | ||
0.998070 | − | 0.0620936i | \(-0.0197777\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.93987 | 0.244400 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.00512i | 0.372740i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 8.61423i | − | 1.05240i | −0.850362 | − | 0.526198i | \(-0.823617\pi\) | ||
0.850362 | − | 0.526198i | \(-0.176383\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.88240 | −0.587772 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 14.3215i | − | 1.69965i | −0.527065 | − | 0.849825i | \(-0.676708\pi\) | ||
0.527065 | − | 0.849825i | \(-0.323292\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.83401i | 0.916901i | 0.888720 | + | 0.458451i | \(0.151595\pi\) | ||||
−0.888720 | + | 0.458451i | \(0.848405\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.60688i | 0.185547i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.37169 | − | 0.237289i | −0.612161 | − | 0.0270415i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.3137 | 1.27289 | 0.636446 | − | 0.771321i | \(-0.280404\pi\) | ||||
0.636446 | + | 0.771321i | \(0.280404\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.97858 | −0.442064 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.38438 | 0.371484 | 0.185742 | − | 0.982599i | \(-0.440531\pi\) | ||||
0.185742 | + | 0.982599i | \(0.440531\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 13.4909i | − | 1.46329i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −13.2536 | −1.42093 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.5468 | −1.54196 | −0.770980 | − | 0.636859i | \(-0.780233\pi\) | ||||
−0.770980 | + | 0.636859i | \(0.780233\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.95715i | 0.205166i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.27552 | 0.132265 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.45009 | 0.661765 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.15371 | 0.624815 | 0.312407 | − | 0.949948i | \(-0.398865\pi\) | ||||
0.312407 | + | 0.949948i | \(0.398865\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.96467 | − | 0.175135i | −0.398464 | − | 0.0176017i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.1065i | 1.00563i | 0.864393 | + | 0.502817i | \(0.167703\pi\) | ||||
−0.864393 | + | 0.502817i | \(0.832297\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.2927i | 1.21124i | 0.795754 | + | 0.605619i | \(0.207075\pi\) | ||||
−0.795754 | + | 0.605619i | \(0.792925\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.41957i | 0.528895i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.1473 | −1.65769 | −0.828844 | − | 0.559480i | \(-0.811001\pi\) | ||||
−0.828844 | + | 0.559480i | \(0.811001\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 12.2836i | − | 1.17656i | −0.808658 | − | 0.588280i | \(-0.799805\pi\) | ||
0.808658 | − | 0.588280i | \(-0.200195\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.34292i | 0.317296i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.782020 | 0.0735662 | 0.0367831 | − | 0.999323i | \(-0.488289\pi\) | ||||
0.0367831 | + | 0.999323i | \(0.488289\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.05019i | 0.843935i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.44451i | 0.133545i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 8.78623i | − | 0.805432i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9572 | + | 0.969933i | 0.996105 | + | 0.0881757i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.5205 | 0.948599 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.46787 | −0.846832 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.1172 | 1.60764 | 0.803820 | − | 0.594872i | \(-0.202797\pi\) | ||||
0.803820 | + | 0.594872i | \(0.202797\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 8.89927i | − | 0.783537i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.59114 | 0.226389 | 0.113194 | − | 0.993573i | \(-0.463892\pi\) | ||||
0.113194 | + | 0.993573i | \(0.463892\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.20077 | 0.364253 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 14.0288i | 1.20740i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.17513 | −0.783885 | −0.391942 | − | 0.919990i | \(-0.628197\pi\) | ||||
−0.391942 | + | 0.919990i | \(0.628197\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.83355 | −0.494795 | −0.247398 | − | 0.968914i | \(-0.579575\pi\) | ||||
−0.247398 | + | 0.968914i | \(0.579575\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.60688 | 0.640615 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.176696 | − | 4.00000i | 0.0147760 | − | 0.334497i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 24.5673i | 2.04020i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 5.87085i | − | 0.484219i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 1.20722i | − | 0.0988994i | −0.998777 | − | 0.0494497i | \(-0.984253\pi\) | ||
0.998777 | − | 0.0494497i | \(-0.0157468\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.3249 | −1.73539 | −0.867697 | − | 0.497094i | \(-0.834400\pi\) | ||||
−0.867697 | + | 0.497094i | \(0.834400\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 6.48482i | − | 0.524267i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 2.36435i | − | 0.189909i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.90383 | 0.471177 | 0.235588 | − | 0.971853i | \(-0.424298\pi\) | ||||
0.235588 | + | 0.971853i | \(0.424298\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 9.89962i | − | 0.785091i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.89414i | 0.464524i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.4507i | 1.44517i | 0.691284 | + | 0.722583i | \(0.257045\pi\) | ||||
−0.691284 | + | 0.722583i | \(0.742955\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.489289 | − | 11.0764i | 0.0380911 | − | 0.862298i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.69250 | 0.750028 | 0.375014 | − | 0.927019i | \(-0.377638\pi\) | ||||
0.375014 | + | 0.927019i | \(0.377638\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.5426 | 0.887894 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.10045 | 0.237097 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 18.7685i | − | 1.42694i | −0.700686 | − | 0.713470i | \(-0.747123\pi\) | ||
0.700686 | − | 0.713470i | \(-0.252877\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.93987 | 0.146640 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.1537 | 1.21419 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 17.4005i | − | 1.30057i | −0.759690 | − | 0.650286i | \(-0.774649\pi\) | ||
0.759690 | − | 0.650286i | \(-0.225351\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.8610 | 1.17894 | 0.589469 | − | 0.807791i | \(-0.299337\pi\) | ||||
0.589469 | + | 0.807791i | \(0.299337\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.30255 | 0.0962869 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.19656 | 0.455580 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.793237 | + | 17.9572i | −0.0580073 | + | 1.31316i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.13655i | 0.664587i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.0502i | 1.08899i | 0.838763 | + | 0.544497i | \(0.183279\pi\) | ||||
−0.838763 | + | 0.544497i | \(0.816721\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.1528i | 1.59460i | 0.603586 | + | 0.797298i | \(0.293738\pi\) | ||||
−0.603586 | + | 0.797298i | \(0.706262\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.03565 | −0.288999 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3.38438i | − | 0.241127i | −0.992706 | − | 0.120563i | \(-0.961530\pi\) | ||
0.992706 | − | 0.120563i | \(-0.0384701\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.07896i | 0.360038i | 0.983663 | + | 0.180019i | \(0.0576159\pi\) | ||||
−0.983663 | + | 0.180019i | \(0.942384\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.5682 | 0.815961 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 16.0000i | 1.12298i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 19.5011i | − | 1.36202i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.35027i | 0.302365i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.58546 | − | 0.379253i | −0.593869 | − | 0.0262335i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.9405 | 1.23507 | 0.617537 | − | 0.786542i | \(-0.288130\pi\) | ||||
0.617537 | + | 0.786542i | \(0.288130\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 19.2327 | 1.31780 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.4960 | −1.12502 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1.53983i | − | 0.104531i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.5205 | −0.710908 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.54262 | 0.440104 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.0502i | 1.00784i | 0.863752 | + | 0.503918i | \(0.168109\pi\) | ||||
−0.863752 | + | 0.503918i | \(0.831891\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.43175 | 0.0954500 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.1473 | 1.13810 | 0.569052 | − | 0.822302i | \(-0.307310\pi\) | ||||
0.569052 | + | 0.822302i | \(0.307310\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.0533 | −1.32516 | −0.662581 | − | 0.748991i | \(-0.730539\pi\) | ||||
−0.662581 | + | 0.748991i | \(0.730539\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.318660 | − | 7.21377i | 0.0209663 | − | 0.474631i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.76875i | 0.443436i | 0.975111 | + | 0.221718i | \(0.0711664\pi\) | ||||
−0.975111 | + | 0.221718i | \(0.928834\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 14.1004i | − | 0.919808i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.1934i | 0.986920i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.9207 | −1.61198 | −0.805992 | − | 0.591926i | \(-0.798368\pi\) | ||||
−0.805992 | + | 0.591926i | \(0.798368\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 17.3240i | − | 1.11593i | −0.829863 | − | 0.557967i | \(-0.811582\pi\) | ||
0.829863 | − | 0.557967i | \(-0.188418\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.5640i | 0.741833i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.8824 | −0.695251 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.12808i | 0.199035i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.54496i | 0.288025i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 5.98592i | − | 0.377828i | −0.981994 | − | 0.188914i | \(-0.939503\pi\) | ||
0.981994 | − | 0.188914i | \(-0.0604968\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.532134 | − | 12.0464i | 0.0334550 | − | 0.757348i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 18.1172 | 1.13454 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.5426 | −0.782387 | −0.391193 | − | 0.920308i | \(-0.627938\pi\) | ||||
−0.391193 | + | 0.920308i | \(0.627938\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.03565 | 0.250763 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.8091i | 0.730963i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.8146 | 1.03684 | 0.518418 | − | 0.855128i | \(-0.326521\pi\) | ||||
0.518418 | + | 0.855128i | \(0.326521\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.3503 | −1.12725 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 19.5353i | − | 1.19554i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.3717 | −0.937229 | −0.468614 | − | 0.883403i | \(-0.655247\pi\) | ||||
−0.468614 | + | 0.883403i | \(0.655247\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.318660 | 0.0193572 | 0.00967862 | − | 0.999953i | \(-0.496919\pi\) | ||||
0.00967862 | + | 0.999953i | \(0.496919\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.62831 | −0.159072 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.96467 | − | 0.175135i | −0.239078 | − | 0.0105610i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.2836i | 0.738052i | 0.929419 | + | 0.369026i | \(0.120309\pi\) | ||||
−0.929419 | + | 0.369026i | \(0.879691\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 1.13650i | − | 0.0680405i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 13.2536i | − | 0.790642i | −0.918543 | − | 0.395321i | \(-0.870633\pi\) | ||
0.918543 | − | 0.395321i | \(-0.129367\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.6981 | −0.873710 | −0.436855 | − | 0.899532i | \(-0.643908\pi\) | ||||
−0.436855 | + | 0.899532i | \(0.643908\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.66198i | 0.513091i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 12.7005i | − | 0.749689i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.3717 | −0.727747 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.26396i | 0.484442i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.9456i | 1.22366i | 0.790991 | + | 0.611828i | \(0.209566\pi\) | ||||
−0.790991 | + | 0.611828i | \(0.790434\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 29.9431i | − | 1.74335i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.824865 | − | 18.6731i | 0.0478635 | − | 1.08353i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.38904 | −0.253825 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.7434 | −0.619238 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.5722 | −0.779705 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 2.41444i | − | 0.138251i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.651273 | −0.0371701 | −0.0185850 | − | 0.999827i | \(-0.505916\pi\) | ||||
−0.0185850 | + | 0.999827i | \(0.505916\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.5082 | −0.939118 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.9933i | 1.41724i | 0.705591 | + | 0.708619i | \(0.250682\pi\) | ||||
−0.705591 | + | 0.708619i | \(0.749318\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.11087 | 0.458453 | 0.229227 | − | 0.973373i | \(-0.426380\pi\) | ||||
0.229227 | + | 0.973373i | \(0.426380\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.82889 | 0.272077 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.4464 | 0.699062 | 0.349531 | − | 0.936925i | \(-0.386341\pi\) | ||||
0.349531 | + | 0.936925i | \(0.386341\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.44451 | − | 32.7005i | 0.0808770 | − | 1.83088i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 23.0274i | − | 1.28527i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 14.0428i | − | 0.781365i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.44451i | 0.0801270i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.4960 | 0.912230 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 9.18319i | − | 0.506286i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.71462i | 0.369069i | 0.982826 | + | 0.184534i | \(0.0590777\pi\) | ||||
−0.982826 | + | 0.184534i | \(0.940922\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.97858 | 0.163225 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 21.4433i | − | 1.17157i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.590680i | 0.0321764i | 0.999871 | + | 0.0160882i | \(0.00512125\pi\) | ||||
−0.999871 | + | 0.0160882i | \(0.994879\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.05019i | 0.0570386i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.139019 | + | 3.14709i | −0.00752831 | + | 0.170424i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.4359 | −0.995442 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.1537 | −0.654334 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.3184 | −0.661285 | −0.330642 | − | 0.943756i | \(-0.607265\pi\) | ||||
−0.330642 | + | 0.943756i | \(0.607265\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.0566i | 0.966548i | 0.875469 | + | 0.483274i | \(0.160552\pi\) | ||||
−0.875469 | + | 0.483274i | \(0.839448\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.80348 | −0.363143 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.1537 | 1.17912 | 0.589562 | − | 0.807723i | \(-0.299301\pi\) | ||||
0.589562 | + | 0.807723i | \(0.299301\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 35.6503i | − | 1.89212i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11.7992 | 0.624482 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 31.3708 | 1.65569 | 0.827843 | − | 0.560960i | \(-0.189568\pi\) | ||||
0.827843 | + | 0.560960i | \(0.189568\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.2860 | −0.646632 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.30255 | + | 14.7146i | −0.0683659 | + | 0.772317i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.5011i | 1.02073i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.7936i | 1.34641i | 0.739454 | + | 0.673207i | \(0.235084\pi\) | ||||
−0.739454 | + | 0.673207i | \(0.764916\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 9.37384i | − | 0.487983i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.9510 | −0.620467 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 16.4007i | − | 0.849194i | −0.905382 | − | 0.424597i | \(-0.860416\pi\) | ||
0.905382 | − | 0.424597i | \(-0.139584\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 12.7146i | − | 0.656580i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.9143 | −0.613618 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 15.9431i | − | 0.818941i | −0.912323 | − | 0.409470i | \(-0.865713\pi\) | ||
0.912323 | − | 0.409470i | \(-0.134287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 24.3300i | 1.24646i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.7507i | 0.600434i | 0.953871 | + | 0.300217i | \(0.0970591\pi\) | ||||
−0.953871 | + | 0.300217i | \(0.902941\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.3717 | − | 0.590680i | −0.681485 | − | 0.0301038i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.92933 | −0.403071 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.71148 | −0.0867755 | −0.0433877 | − | 0.999058i | \(-0.513815\pi\) | ||||
−0.0433877 | + | 0.999058i | \(0.513815\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.7037 | 0.996457 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.47970i | 0.175528i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 28.1631 | 1.41704 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.62831 | −0.232288 | −0.116144 | − | 0.993232i | \(-0.537053\pi\) | ||||
−0.116144 | + | 0.993232i | \(0.537053\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.64131i | 0.282419i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.2008 | 0.709153 | 0.354576 | − | 0.935027i | \(-0.384625\pi\) | ||||
0.354576 | + | 0.935027i | \(0.384625\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.14663 | 0.0571176 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.90383 | −0.492125 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.24799 | − | 0.364346i | −0.408838 | − | 0.0180600i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.89927i | 0.440040i | 0.975495 | + | 0.220020i | \(0.0706123\pi\) | ||||
−0.975495 | + | 0.220020i | \(0.929388\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 12.3215i | − | 0.607775i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 19.5011i | − | 0.959587i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.42469 | 0.413552 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 7.83401i | − | 0.383633i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 7.12181i | − | 0.347923i | −0.984752 | − | 0.173962i | \(-0.944343\pi\) | ||
0.984752 | − | 0.173962i | \(-0.0556568\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.37169 | 0.164326 | 0.0821631 | − | 0.996619i | \(-0.473817\pi\) | ||||
0.0821631 | + | 0.996619i | \(0.473817\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 6.77781i | − | 0.329548i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 6.48482i | − | 0.314560i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 1.57246i | − | 0.0760967i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.37169 | + | 0.237289i | 0.259348 | + | 0.0114564i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.9461 | −1.10527 | −0.552637 | − | 0.833422i | \(-0.686378\pi\) | ||||
−0.552637 | + | 0.833422i | \(0.686378\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.1537 | 0.680184 | 0.340092 | − | 0.940392i | \(-0.389542\pi\) | ||||
0.340092 | + | 0.940392i | \(0.389542\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −32.9920 | −1.58184 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.42048i | 0.450643i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.2536 | −0.632559 | −0.316279 | − | 0.948666i | \(-0.602434\pi\) | ||||
−0.316279 | + | 0.948666i | \(0.602434\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.23098 | −0.249094 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.5008i | 0.736467i | 0.929733 | + | 0.368234i | \(0.120037\pi\) | ||||
−0.929733 | + | 0.368234i | \(0.879963\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −36.2113 | −1.71658 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.62121 | 0.0766804 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.9614 | −0.847649 | −0.423825 | − | 0.905744i | \(-0.639313\pi\) | ||||
−0.423825 | + | 0.905744i | \(0.639313\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.14663 | + | 25.9572i | −0.0539926 | + | 1.22227i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 28.6377i | − | 1.34551i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.87192i | 0.228399i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.88902i | 0.135143i | 0.997714 | + | 0.0675713i | \(0.0215250\pi\) | ||||
−0.997714 | + | 0.0675713i | \(0.978475\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 30.5428 | 1.42562 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.0524i | 0.887358i | 0.896186 | + | 0.443679i | \(0.146327\pi\) | ||||
−0.896186 | + | 0.443679i | \(0.853673\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.00735i | 0.0468154i | 0.999726 | + | 0.0234077i | \(0.00745158\pi\) | ||||
−0.999726 | + | 0.0234077i | \(0.992548\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.17513 | 0.147243 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 36.0863i | 1.66988i | 0.550345 | + | 0.834938i | \(0.314496\pi\) | ||||
−0.550345 | + | 0.834938i | \(0.685504\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 13.9654i | − | 0.644864i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.92839i | 0.365321i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21.9572 | + | 0.969933i | 1.00959 | + | 0.0445976i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.10045 | 0.142258 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.82065 | −0.403870 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.9950 | −0.502377 | −0.251188 | − | 0.967938i | \(-0.580821\pi\) | ||||
−0.251188 | + | 0.967938i | \(0.580821\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.00512i | 0.137022i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.91538 | −0.360162 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.3184 | 0.695571 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.4647i | 0.474202i | 0.971485 | + | 0.237101i | \(0.0761973\pi\) | ||||
−0.971485 | + | 0.237101i | \(0.923803\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −24.7778 | −1.12049 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.2939 | 0.825592 | 0.412796 | − | 0.910824i | \(-0.364552\pi\) | ||||
0.412796 | + | 0.910824i | \(0.364552\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 53.4868 | 2.40892 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.86920 | − | 0.435961i | −0.443587 | − | 0.0195950i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 23.2181i | − | 1.04147i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 7.12181i | − | 0.318816i | −0.987213 | − | 0.159408i | \(-0.949041\pi\) | ||
0.987213 | − | 0.159408i | \(-0.0509585\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.0163i | 0.581525i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.4960 | 0.735520 | 0.367760 | − | 0.929921i | \(-0.380125\pi\) | ||||
0.367760 | + | 0.929921i | \(0.380125\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.1580i | 1.11951i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.5008i | 0.688417i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.4464 | 1.26087 | 0.630433 | − | 0.776244i | \(-0.282877\pi\) | ||||
0.630433 | + | 0.776244i | \(0.282877\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.7005i | 0.561839i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14.6028i | 0.644728i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 30.6002i | 1.34840i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.829076 | + | 18.7685i | −0.0364627 | + | 0.825436i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 25.2046 | 1.10636 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 40.2259 | 1.76233 | 0.881165 | − | 0.472808i | \(-0.156760\pi\) | ||||
0.881165 | + | 0.472808i | \(0.156760\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.8857 | 1.61290 | 0.806449 | − | 0.591304i | \(-0.201387\pi\) | ||||
0.806449 | + | 0.591304i | \(0.201387\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.60509i | 0.113695i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.14755 | −0.224231 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.78202 | 0.425305 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 14.3931i | − | 0.624608i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.45738 | 0.409645 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −42.6845 | −1.84541 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 23.3675 | 1.00838 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 14.4851 | + | 0.639865i | 0.623919 | + | 0.0275609i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 27.4304i | − | 1.17933i | −0.807649 | − | 0.589663i | \(-0.799260\pi\) | ||
0.807649 | − | 0.589663i | \(-0.200740\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21.3001i | 0.914074i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 30.5775i | − | 1.30980i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.141965 | 0.00606997 | 0.00303499 | − | 0.999995i | \(-0.499034\pi\) | ||||
0.00303499 | + | 0.999995i | \(0.499034\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 1.16058i | − | 0.0495324i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 25.5725i | 1.08942i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.3418 | 0.779975 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.32150i | 0.353228i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.33774i | 0.141424i | 0.997497 | + | 0.0707122i | \(0.0225272\pi\) | ||||
−0.997497 | + | 0.0707122i | \(0.977473\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 8.00000i | − | 0.338364i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.1151 | − | 1.06526i | −1.01814 | − | 0.0449752i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.7805 | −1.38154 | −0.690768 | − | 0.723077i | \(-0.742727\pi\) | ||||
−0.690768 | + | 0.723077i | \(0.742727\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.94667 | 0.0818971 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.45009 | −0.270878 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.2027i | 0.595409i | 0.954658 | + | 0.297705i | \(0.0962211\pi\) | ||||
−0.954658 | + | 0.297705i | \(0.903779\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.28272 | −0.346621 | −0.173311 | − | 0.984867i | \(-0.555446\pi\) | ||||
−0.173311 | + | 0.984867i | \(0.555446\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.2113 | −0.844337 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.35027i | 0.181419i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 46.2688 | 1.92619 | 0.963097 | − | 0.269153i | \(-0.0867437\pi\) | ||||
0.963097 | + | 0.269153i | \(0.0867437\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −29.7496 | −1.23635 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.48677 | 0.227630 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.4253 | + | 1.07896i | 1.01159 | + | 0.0446860i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.59580i | 0.148668i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 18.2499i | − | 0.753253i | −0.926365 | − | 0.376627i | \(-0.877084\pi\) | ||
0.926365 | − | 0.376627i | \(-0.122916\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 2.46108i | − | 0.101407i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.54496 | 0.186955 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 38.2954i | 1.57261i | 0.617842 | + | 0.786303i | \(0.288007\pi\) | ||||
−0.617842 | + | 0.786303i | \(0.711993\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 21.8715i | − | 0.896643i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.82065 | −0.279151 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 30.8353i | − | 1.25990i | −0.776636 | − | 0.629949i | \(-0.783076\pi\) | ||
0.776636 | − | 0.629949i | \(-0.216924\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 36.9462i | − | 1.50707i | −0.657408 | − | 0.753534i | \(-0.728347\pi\) | ||
0.657408 | − | 0.753534i | \(-0.271653\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 10.3074i | − | 0.419751i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 27.2755 | + | 2.41444i | 1.10891 | + | 0.0981611i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.48482 | −0.263211 | −0.131605 | − | 0.991302i | \(-0.542013\pi\) | ||||
−0.131605 | + | 0.991302i | \(0.542013\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −21.4868 | −0.870688 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.83821 | 0.276645 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 35.9018i | − | 1.45006i | −0.688718 | − | 0.725029i | \(-0.741826\pi\) | ||
0.688718 | − | 0.725029i | \(-0.258174\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 26.1885 | 1.05602 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.62831 | −0.347363 | −0.173681 | − | 0.984802i | \(-0.555566\pi\) | ||||
−0.173681 | + | 0.984802i | \(0.555566\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.6289i | 0.748760i | 0.927275 | + | 0.374380i | \(0.122144\pi\) | ||||
−0.927275 | + | 0.374380i | \(0.877856\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −20.4893 | −0.822207 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −23.5834 | −0.944849 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.5510 | −1.18204 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.509308 | − | 11.5296i | 0.0203398 | − | 0.460448i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 13.4909i | − | 0.537916i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 5.15058i | − | 0.205041i | −0.994731 | − | 0.102521i | \(-0.967309\pi\) | ||
0.994731 | − | 0.102521i | \(-0.0326908\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 24.0927i | 0.957599i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 45.0989 | 1.78970 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 5.27760i | − | 0.209106i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 17.1365i | − | 0.677909i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.38890 | −0.331342 | −0.165671 | − | 0.986181i | \(-0.552979\pi\) | ||||
−0.165671 | + | 0.986181i | \(0.552979\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 16.6142i | − | 0.655201i | −0.944816 | − | 0.327601i | \(-0.893760\pi\) | ||
0.944816 | − | 0.327601i | \(-0.106240\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 22.1528i | − | 0.872267i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.67850i | 0.0659886i | 0.999456 | + | 0.0329943i | \(0.0105043\pi\) | ||||
−0.999456 | + | 0.0329943i | \(0.989496\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.76060 | + | 39.8560i | −0.0691095 | + | 1.56449i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.06788 | 0.0810465 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.53213 | 0.333888 | 0.166944 | − | 0.985966i | \(-0.446610\pi\) | ||||
0.166944 | + | 0.985966i | \(0.446610\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.45009 | 0.252026 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.37384i | 0.365708i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.2939 | −0.712629 | −0.356314 | − | 0.934366i | \(-0.615967\pi\) | ||||
−0.356314 | + | 0.934366i | \(0.615967\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.916828 | 0.0356605 | 0.0178302 | − | 0.999841i | \(-0.494324\pi\) | ||||
0.0178302 | + | 0.999841i | \(0.494324\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.78623i | 0.341229i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.4569 | 0.405502 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −35.8810 | −1.38932 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −20.2113 | −0.781412 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.141965 | + | 3.21377i | −0.00548049 | + | 0.124066i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.0428i | 1.23516i | 0.786508 | + | 0.617580i | \(0.211887\pi\) | ||||
−0.786508 | + | 0.617580i | \(0.788113\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.74338i | 0.259553i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 16.8752i | − | 0.648568i | −0.945960 | − | 0.324284i | \(-0.894877\pi\) | ||
0.945960 | − | 0.324284i | \(-0.105123\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.97643 | 0.382860 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.0274i | 0.882414i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 8.29273i | − | 0.317313i | −0.987334 | − | 0.158656i | \(-0.949284\pi\) | ||
0.987334 | − | 0.158656i | \(-0.0507162\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.8396 | −0.872655 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 26.9301i | − | 1.02745i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 8.89927i | − | 0.339035i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.0435i | 0.534238i | 0.963663 | + | 0.267119i | \(0.0860718\pi\) | ||||
−0.963663 | + | 0.267119i | \(0.913928\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.42754 | − | 0.283929i | −0.244162 | − | 0.0107856i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.5214 | −0.550828 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −42.4569 | −1.60817 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.08991 | −0.343812 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 4.80302i | − | 0.181408i | −0.995878 | − | 0.0907039i | \(-0.971088\pi\) | ||
0.995878 | − | 0.0907039i | \(-0.0289117\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.45009 | 0.243270 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 18.9357 | 0.713161 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.3847i | 0.616210i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.20329 | 0.0451904 | 0.0225952 | − | 0.999745i | \(-0.492807\pi\) | ||||
0.0225952 | + | 0.999745i | \(0.492807\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.5375 | 0.507696 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.45317 | 0.129322 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.439846 | − | 9.95715i | 0.0164493 | − | 0.372376i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 33.4665i | − | 1.24983i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28.1354i | 1.04927i | 0.851326 | + | 0.524637i | \(0.175799\pi\) | ||||
−0.851326 | + | 0.524637i | \(0.824201\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.9290i | 0.742196i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 23.2647 | 0.865225 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11.8091i | 0.438578i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.7637i | 0.547557i | 0.961793 | + | 0.273778i | \(0.0882734\pi\) | ||||
−0.961793 | + | 0.273778i | \(0.911727\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.4653 | −1.01724 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 35.9143i | 1.32834i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 46.2248i | − | 1.70735i | −0.520806 | − | 0.853675i | \(-0.674368\pi\) | ||
0.520806 | − | 0.853675i | \(-0.325632\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 14.6142i | − | 0.539054i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.26083 | + | 28.5423i | −0.0464431 | + | 1.05137i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.0515 | −0.553677 | −0.276839 | − | 0.960916i | \(-0.589287\pi\) | ||||
−0.276839 | + | 0.960916i | \(0.589287\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.20077 | −0.154319 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 41.4167 | 1.51943 | 0.759715 | − | 0.650256i | \(-0.225338\pi\) | ||||
0.759715 | + | 0.650256i | \(0.225338\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 3.00512i | − | 0.110099i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.04960 | 0.148167 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −27.7992 | −1.01576 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 44.3080i | − | 1.61682i | −0.588618 | − | 0.808412i | \(-0.700328\pi\) | ||
0.588618 | − | 0.808412i | \(-0.299672\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.03863 | 0.292944 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −53.0838 | −1.93192 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.3717 | −0.849459 | −0.424729 | − | 0.905320i | \(-0.639631\pi\) | ||||
−0.424729 | + | 0.905320i | \(0.639631\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 16.1773 | + | 0.714615i | 0.587200 | + | 0.0259389i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 36.4717i | − | 1.32210i | −0.750343 | − | 0.661049i | \(-0.770112\pi\) | ||
0.750343 | − | 0.661049i | \(-0.229888\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 19.9143i | − | 0.720946i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 16.1426i | − | 0.583637i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.5214 | 0.524337 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.590680i | 0.0213005i | 0.999943 | + | 0.0106502i | \(0.00339014\pi\) | ||||
−0.999943 | + | 0.0106502i | \(0.996610\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 16.8438i | − | 0.606614i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.57246 | 0.272362 | 0.136181 | − | 0.990684i | \(-0.456517\pi\) | ||||
0.136181 | + | 0.990684i | \(0.456517\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.13650i | − | 0.0408243i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.41957i | 0.194426i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 20.2990i | − | 0.727287i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.09617 | + | 47.4528i | −0.0750070 | + | 1.69799i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −55.6194 | −1.98767 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.6963 | 0.524534 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 44.4476 | 1.58439 | 0.792194 | − | 0.610270i | \(-0.208939\pi\) | ||||
0.792194 | + | 0.610270i | \(0.208939\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.5808i | 0.803897i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.26781 | 0.0450783 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.17092 | 0.0415807 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 24.6430i | − | 0.873997i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.4977 | −0.655223 | −0.327611 | − | 0.944813i | \(-0.606244\pi\) | ||||
−0.327611 | + | 0.944813i | \(0.606244\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30.6987 | −1.08604 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.4061 | −0.615015 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.14663 | − | 25.9572i | 0.0404636 | − | 0.916008i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.6722i | 0.517128i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 20.6430i | − | 0.726668i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 15.2680i | − | 0.536794i | −0.963308 | − | 0.268397i | \(-0.913506\pi\) | ||
0.963308 | − | 0.268397i | \(-0.0864939\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.8202 | −0.766212 | −0.383106 | − | 0.923704i | \(-0.625146\pi\) | ||||
−0.383106 | + | 0.923704i | \(0.625146\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.427936i | 0.0150084i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 45.9290i | 1.60882i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.1709 | −0.600735 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.34185i | 0.0818308i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 9.39462i | − | 0.327875i | −0.986471 | − | 0.163937i | \(-0.947581\pi\) | ||
0.986471 | − | 0.163937i | \(-0.0524195\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 33.8511i | − | 1.17998i | −0.807412 | − | 0.589988i | \(-0.799133\pi\) | ||
0.807412 | − | 0.589988i | \(-0.200867\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.235192 | − | 5.32424i | 0.00818835 | − | 0.185366i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.94453 | 0.102391 | 0.0511957 | − | 0.998689i | \(-0.483697\pi\) | ||||
0.0511957 | + | 0.998689i | \(0.483697\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.55356 | −0.123420 | −0.0617101 | − | 0.998094i | \(-0.519655\pi\) | ||||
−0.0617101 | + | 0.998094i | \(0.519655\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.4960 | −0.572239 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 23.6927i | 0.820902i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.1274 | 0.834964 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.35279 | 0.185019 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 41.4496i | − | 1.43100i | −0.698614 | − | 0.715499i | \(-0.746199\pi\) | ||
0.698614 | − | 0.715499i | \(-0.253801\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −68.4011 | −2.35866 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.7985 | 0.613014 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 28.7329 | 0.988442 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.7638 | + | 1.57246i | 0.610371 | + | 0.0540304i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 19.7384i | − | 0.677420i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.05019i | 0.310237i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.5871i | 0.602171i | 0.953597 | + | 0.301085i | \(0.0973490\pi\) | ||||
−0.953597 | + | 0.301085i | \(0.902651\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.71791 | 0.263947 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 19.2638i | − | 0.658040i | −0.944323 | − | 0.329020i | \(-0.893282\pi\) | ||
0.944323 | − | 0.329020i | \(-0.106718\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 15.5584i | − | 0.530845i | −0.964132 | − | 0.265423i | \(-0.914489\pi\) | ||
0.964132 | − | 0.265423i | \(-0.0855115\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.0558 | 0.581262 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.8223i | 0.538599i | 0.963056 | + | 0.269299i | \(0.0867921\pi\) | ||||
−0.963056 | + | 0.269299i | \(0.913208\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 46.7201i | − | 1.58853i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 16.6142i | − | 0.564249i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −37.4868 | − | 1.65594i | −1.27165 | − | 0.0561738i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.3993 | 0.352366 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.36327 | 0.249209 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15.3494 | −0.518903 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.4007i | 0.553811i | 0.960897 | + | 0.276905i | \(0.0893089\pi\) | ||||
−0.960897 | + | 0.276905i | \(0.910691\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −28.1284 | −0.948746 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.49602 | 0.252547 | 0.126274 | − | 0.991995i | \(-0.459698\pi\) | ||||
0.126274 | + | 0.991995i | \(0.459698\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.8353i | 0.364638i | 0.983239 | + | 0.182319i | \(0.0583604\pi\) | ||||
−0.983239 | + | 0.182319i | \(0.941640\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 40.2113 | 1.35169 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.6163 | −0.423612 | −0.211806 | − | 0.977312i | \(-0.567935\pi\) | ||||
−0.211806 | + | 0.977312i | \(0.567935\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29.3717 | 0.985095 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.1826 | + | 0.582326i | 0.441633 | + | 0.0195087i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 14.6773i | − | 0.491157i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 43.3148i | − | 1.44785i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 5.89414i | − | 0.196800i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.37384 | 0.312635 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 39.9514i | 1.33097i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 14.4275i | − | 0.480118i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 39.4826 | 1.31244 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 8.29273i | − | 0.275356i | −0.990477 | − | 0.137678i | \(-0.956036\pi\) | ||
0.990477 | − | 0.137678i | \(-0.0439639\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.0930i | 0.401099i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.2499i | 0.472120i | 0.971739 | + | 0.236060i | \(0.0758562\pi\) | ||||
−0.971739 | + | 0.236060i | \(0.924144\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.2138 | − | 0.495356i | −0.371122 | − | 0.0163939i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.24241 | 0.107191 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.20077 | 0.138722 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.76875 | −0.223281 | −0.111640 | − | 0.993749i | \(-0.535610\pi\) | ||||
−0.111640 | + | 0.993749i | \(0.535610\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 0.874609i | − | 0.0288193i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17.2892 | 0.569082 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.97858 | 0.0979350 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.7090i | 0.483106i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 42.1151 | 1.38175 | 0.690875 | − | 0.722974i | \(-0.257225\pi\) | ||||
0.690875 | + | 0.722974i | \(0.257225\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.3277 | −0.371249 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −33.5640 | −1.09884 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.97460 | + | 44.7005i | −0.0645762 | + | 1.46186i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 56.0194i | − | 1.83007i | −0.403369 | − | 0.915037i | \(-0.632161\pi\) | ||
0.403369 | − | 0.915037i | \(-0.367839\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.8923i | 0.355456i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.21326i | 0.267745i | 0.990999 | + | 0.133872i | \(0.0427412\pi\) | ||||
−0.990999 | + | 0.133872i | \(0.957259\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28.4817 | 0.927493 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 22.7435i | 0.739847i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 3.91369i | − | 0.127178i | −0.997976 | − | 0.0635890i | \(-0.979745\pi\) | ||
0.997976 | − | 0.0635890i | \(-0.0202547\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.45738 | −0.307000 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.7146i | 0.542009i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.3514i | 1.30711i | 0.756879 | + | 0.653555i | \(0.226723\pi\) | ||||
−0.756879 | + | 0.653555i | \(0.773277\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 37.4643i | 1.21232i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 43.9143 | + | 1.93987i | 1.41955 | + | 0.0627070i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.8748 | −0.480332 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.0979 | 0.970899 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −20.5177 | −0.661173 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 55.1448i | 1.77517i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.93987 | −0.0623819 | −0.0311909 | − | 0.999513i | \(-0.509930\pi\) | ||||
−0.0311909 | + | 0.999513i | \(0.509930\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.8585 | 0.605821 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.7146i | 1.24241i | 0.783648 | + | 0.621206i | \(0.213357\pi\) | ||||
−0.783648 | + | 0.621206i | \(0.786643\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.45738 | −0.303190 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.93987 | −0.0621254 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.9315 | −0.989587 | −0.494794 | − | 0.869011i | \(-0.664756\pi\) | ||||
−0.494794 | + | 0.869011i | \(0.664756\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 48.1994 | + | 2.12915i | 1.54046 | + | 0.0680480i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 14.6981i | − | 0.469274i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 39.5500i | 1.26145i | 0.776007 | + | 0.630724i | \(0.217242\pi\) | ||||
−0.776007 | + | 0.630724i | \(0.782758\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 8.42469i | − | 0.268433i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12.3323 | 0.392542 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 24.0927i | − | 0.766103i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 7.23688i | − | 0.229887i | −0.993372 | − | 0.114944i | \(-0.963331\pi\) | ||
0.993372 | − | 0.114944i | \(-0.0366687\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.01721 | −0.286153 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.6430i | 0.400810i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 3.81231i | − | 0.120737i | −0.998176 | − | 0.0603686i | \(-0.980772\pi\) | ||
0.998176 | − | 0.0603686i | \(-0.0192276\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14.0288i | 0.443851i |
(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 | 352.2.e.a.351.10 | yes | 12 | |
3.2 | odd | 2 | 3168.2.o.e.703.4 | 12 | |||
4.3 | odd | 2 | inner | 352.2.e.a.351.3 | ✓ | 12 | |
8.3 | odd | 2 | 704.2.e.d.703.9 | 12 | |||
8.5 | even | 2 | 704.2.e.d.703.4 | 12 | |||
11.10 | odd | 2 | inner | 352.2.e.a.351.9 | yes | 12 | |
12.11 | even | 2 | 3168.2.o.e.703.1 | 12 | |||
16.3 | odd | 4 | 2816.2.g.d.1407.10 | 12 | |||
16.5 | even | 4 | 2816.2.g.d.1407.11 | 12 | |||
16.11 | odd | 4 | 2816.2.g.i.1407.4 | 12 | |||
16.13 | even | 4 | 2816.2.g.i.1407.1 | 12 | |||
33.32 | even | 2 | 3168.2.o.e.703.2 | 12 | |||
44.43 | even | 2 | inner | 352.2.e.a.351.4 | yes | 12 | |
88.21 | odd | 2 | 704.2.e.d.703.3 | 12 | |||
88.43 | even | 2 | 704.2.e.d.703.10 | 12 | |||
132.131 | odd | 2 | 3168.2.o.e.703.3 | 12 | |||
176.21 | odd | 4 | 2816.2.g.d.1407.12 | 12 | |||
176.43 | even | 4 | 2816.2.g.i.1407.3 | 12 | |||
176.109 | odd | 4 | 2816.2.g.i.1407.2 | 12 | |||
176.131 | even | 4 | 2816.2.g.d.1407.9 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
352.2.e.a.351.3 | ✓ | 12 | 4.3 | odd | 2 | inner | |
352.2.e.a.351.4 | yes | 12 | 44.43 | even | 2 | inner | |
352.2.e.a.351.9 | yes | 12 | 11.10 | odd | 2 | inner | |
352.2.e.a.351.10 | yes | 12 | 1.1 | even | 1 | trivial | |
704.2.e.d.703.3 | 12 | 88.21 | odd | 2 | |||
704.2.e.d.703.4 | 12 | 8.5 | even | 2 | |||
704.2.e.d.703.9 | 12 | 8.3 | odd | 2 | |||
704.2.e.d.703.10 | 12 | 88.43 | even | 2 | |||
2816.2.g.d.1407.9 | 12 | 176.131 | even | 4 | |||
2816.2.g.d.1407.10 | 12 | 16.3 | odd | 4 | |||
2816.2.g.d.1407.11 | 12 | 16.5 | even | 4 | |||
2816.2.g.d.1407.12 | 12 | 176.21 | odd | 4 | |||
2816.2.g.i.1407.1 | 12 | 16.13 | even | 4 | |||
2816.2.g.i.1407.2 | 12 | 176.109 | odd | 4 | |||
2816.2.g.i.1407.3 | 12 | 176.43 | even | 4 | |||
2816.2.g.i.1407.4 | 12 | 16.11 | odd | 4 | |||
3168.2.o.e.703.1 | 12 | 12.11 | even | 2 | |||
3168.2.o.e.703.2 | 12 | 33.32 | even | 2 | |||
3168.2.o.e.703.3 | 12 | 132.131 | odd | 2 | |||
3168.2.o.e.703.4 | 12 | 3.2 | odd | 2 |