Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(2017,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.2017");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.c (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: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 448) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2017.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.2017 |
Dual form | 4032.2.c.n.2017.4 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 2.73205i | − 1.22181i | −0.791704 | − | 0.610905i | \(-0.790806\pi\) | ||||
0.791704 | − | 0.610905i | \(-0.209194\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.46410i | 1.64749i | 0.566961 | + | 0.823744i | \(0.308119\pi\) | ||||
−0.566961 | + | 0.823744i | \(0.691881\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 6.73205i | − 1.86713i | −0.358402 | − | 0.933567i | \(-0.616678\pi\) | ||||
0.358402 | − | 0.933567i | \(-0.383322\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.26795i | 0.290887i | 0.989367 | + | 0.145444i | \(0.0464610\pi\) | ||||
−0.989367 | + | 0.145444i | \(0.953539\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.46410 | 0.722315 | 0.361158 | − | 0.932505i | \(-0.382382\pi\) | ||||
0.361158 | + | 0.932505i | \(0.382382\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.46410 | −0.492820 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 1.46410i | − 0.271877i | −0.990717 | − | 0.135938i | \(-0.956595\pi\) | ||||
0.990717 | − | 0.135938i | \(-0.0434049\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 2.73205i | − 0.461801i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 1.46410i | − 0.240697i | −0.992732 | − | 0.120348i | \(-0.961599\pi\) | ||||
0.992732 | − | 0.120348i | \(-0.0384012\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 5.46410i | − 0.833268i | −0.909074 | − | 0.416634i | \(-0.863210\pi\) | ||||
0.909074 | − | 0.416634i | \(-0.136790\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.92820 | −0.427122 | −0.213561 | − | 0.976930i | \(-0.568506\pi\) | ||||
−0.213561 | + | 0.976930i | \(0.568506\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 12.0000i | − 1.64833i | −0.566352 | − | 0.824163i | \(-0.691646\pi\) | ||||
0.566352 | − | 0.824163i | \(-0.308354\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.9282 | 2.01292 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 9.66025i | − 1.25766i | −0.777544 | − | 0.628829i | \(-0.783535\pi\) | ||||
0.777544 | − | 0.628829i | \(-0.216465\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.1244i | 1.42433i | 0.702013 | + | 0.712164i | \(0.252285\pi\) | ||||
−0.702013 | + | 0.712164i | \(0.747715\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −18.3923 | −2.28128 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 8.00000i | − 0.977356i | −0.872464 | − | 0.488678i | \(-0.837479\pi\) | ||||
0.872464 | − | 0.488678i | \(-0.162521\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.92820 | −0.347514 | −0.173757 | − | 0.984789i | \(-0.555591\pi\) | ||||
−0.173757 | + | 0.984789i | \(0.555591\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.9282 | 1.51313 | 0.756566 | − | 0.653917i | \(-0.226876\pi\) | ||||
0.756566 | + | 0.653917i | \(0.226876\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.46410i | 0.622692i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.9282 | −1.22952 | −0.614759 | − | 0.788715i | \(-0.710747\pi\) | ||||
−0.614759 | + | 0.788715i | \(0.710747\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 5.66025i | − 0.621294i | −0.950525 | − | 0.310647i | \(-0.899454\pi\) | ||||
0.950525 | − | 0.310647i | \(-0.100546\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.46410i | 0.592665i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.8564 | −1.25678 | −0.628388 | − | 0.777900i | \(-0.716285\pi\) | ||||
−0.628388 | + | 0.777900i | \(0.716285\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 6.73205i | − 0.705711i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.46410 | 0.355409 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.92820 | 0.906522 | 0.453261 | − | 0.891378i | \(-0.350261\pi\) | ||||
0.453261 | + | 0.891378i | \(0.350261\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.66025i | 0.165201i | 0.996583 | + | 0.0826007i | \(0.0263226\pi\) | ||||
−0.996583 | + | 0.0826007i | \(0.973677\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.85641 | 0.971181 | 0.485590 | − | 0.874187i | \(-0.338605\pi\) | ||||
0.485590 | + | 0.874187i | \(0.338605\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.07180i | 0.490309i | 0.969484 | + | 0.245155i | \(0.0788387\pi\) | ||||
−0.969484 | + | 0.245155i | \(0.921161\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 12.3923i | − 1.18697i | −0.804846 | − | 0.593484i | \(-0.797752\pi\) | ||||
0.804846 | − | 0.593484i | \(-0.202248\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.53590 | 0.614846 | 0.307423 | − | 0.951573i | \(-0.400533\pi\) | ||||
0.307423 | + | 0.951573i | \(0.400533\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 9.46410i | − 0.882532i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.00000 | −0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −18.8564 | −1.71422 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 6.92820i | − 0.619677i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.4641 | −1.01727 | −0.508637 | − | 0.860981i | \(-0.669851\pi\) | ||||
−0.508637 | + | 0.860981i | \(0.669851\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 10.7321i | − 0.937664i | −0.883287 | − | 0.468832i | \(-0.844675\pi\) | ||||
0.883287 | − | 0.468832i | \(-0.155325\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.26795i | 0.109945i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.8564 | −1.69645 | −0.848224 | − | 0.529638i | \(-0.822328\pi\) | ||||
−0.848224 | + | 0.529638i | \(0.822328\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.26795i | 0.786097i | 0.919518 | + | 0.393049i | \(0.128580\pi\) | ||||
−0.919518 | + | 0.393049i | \(0.871420\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 36.7846 | 3.07608 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.00000 | −0.332182 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 1.07180i | − 0.0878050i | −0.999036 | − | 0.0439025i | \(-0.986021\pi\) | ||||
0.999036 | − | 0.0439025i | \(-0.0139791\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.39230 | −0.194683 | −0.0973415 | − | 0.995251i | \(-0.531034\pi\) | ||||
−0.0973415 | + | 0.995251i | \(0.531034\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 10.9282i | − 0.877774i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.1962i | 0.973359i | 0.873581 | + | 0.486679i | \(0.161792\pi\) | ||||
−0.873581 | + | 0.486679i | \(0.838208\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.46410 | 0.273009 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.4641i | 1.05459i | 0.849682 | + | 0.527295i | \(0.176794\pi\) | ||||
−0.849682 | + | 0.527295i | \(0.823206\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.07180 | 0.392467 | 0.196234 | − | 0.980557i | \(-0.437129\pi\) | ||||
0.196234 | + | 0.980557i | \(0.437129\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −32.3205 | −2.48619 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.80385i | 0.289201i | 0.989490 | + | 0.144601i | \(0.0461897\pi\) | ||||
−0.989490 | + | 0.144601i | \(0.953810\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.46410 | −0.186269 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 2.92820i | − 0.218864i | −0.993994 | − | 0.109432i | \(-0.965097\pi\) | ||||
0.993994 | − | 0.109432i | \(-0.0349032\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 10.7321i | − 0.797707i | −0.917015 | − | 0.398854i | \(-0.869408\pi\) | ||||
0.917015 | − | 0.398854i | \(-0.130592\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.00000 | −0.294086 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 10.9282i | − 0.799149i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.0000 | −1.15772 | −0.578860 | − | 0.815427i | \(-0.696502\pi\) | ||||
−0.578860 | + | 0.815427i | \(0.696502\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.53590 | 0.470464 | 0.235232 | − | 0.971939i | \(-0.424415\pi\) | ||||
0.235232 | + | 0.971939i | \(0.424415\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 25.8564i | − 1.84219i | −0.389335 | − | 0.921096i | \(-0.627295\pi\) | ||||
0.389335 | − | 0.921096i | \(-0.372705\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.00000 | −0.283552 | −0.141776 | − | 0.989899i | \(-0.545281\pi\) | ||||
−0.141776 | + | 0.989899i | \(0.545281\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1.46410i | − 0.102760i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 5.46410i | − 0.381629i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.92820 | −0.479234 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 16.7846i | − 1.15550i | −0.816214 | − | 0.577750i | \(-0.803931\pi\) | ||||
0.816214 | − | 0.577750i | \(-0.196069\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.9282 | −1.01810 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.00000 | 0.271538 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.4641i | 0.905693i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.92820 | −0.463947 | −0.231973 | − | 0.972722i | \(-0.574518\pi\) | ||||
−0.231973 | + | 0.972722i | \(0.574518\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.80385i | 0.252470i | 0.992000 | + | 0.126235i | \(0.0402894\pi\) | ||||
−0.992000 | + | 0.126235i | \(0.959711\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 17.2679i | − 1.14110i | −0.821263 | − | 0.570549i | \(-0.806730\pi\) | ||||
0.821263 | − | 0.570549i | \(-0.193270\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.00000i | 0.521862i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.5359 | 0.810880 | 0.405440 | − | 0.914122i | \(-0.367118\pi\) | ||||
0.405440 | + | 0.914122i | \(0.367118\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.7846 | −1.21002 | −0.605012 | − | 0.796217i | \(-0.706832\pi\) | ||||
−0.605012 | + | 0.796217i | \(0.706832\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 2.73205i | − 0.174544i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.53590 | 0.543126 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 15.8038i | − 0.997530i | −0.866737 | − | 0.498765i | \(-0.833787\pi\) | ||||
0.866737 | − | 0.498765i | \(-0.166213\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.9282i | 1.19001i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.00000 | 0.374270 | 0.187135 | − | 0.982334i | \(-0.440080\pi\) | ||||
0.187135 | + | 0.982334i | \(0.440080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 1.46410i | − 0.0909748i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.9282 | −0.673862 | −0.336931 | − | 0.941529i | \(-0.609389\pi\) | ||||
−0.336931 | + | 0.941529i | \(0.609389\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −32.7846 | −2.01394 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.5885i | 0.767532i | 0.923430 | + | 0.383766i | \(0.125373\pi\) | ||||
−0.923430 | + | 0.383766i | \(0.874627\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.9282 | 0.906824 | 0.453412 | − | 0.891301i | \(-0.350207\pi\) | ||||
0.453412 | + | 0.891301i | \(0.350207\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 13.4641i | − 0.811916i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 4.00000i | − 0.240337i | −0.992754 | − | 0.120168i | \(-0.961657\pi\) | ||||
0.992754 | − | 0.120168i | \(-0.0383434\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.00000 | −0.119310 | −0.0596550 | − | 0.998219i | \(-0.519000\pi\) | ||||
−0.0596550 | + | 0.998219i | \(0.519000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 16.5885i | − 0.986081i | −0.870006 | − | 0.493041i | \(-0.835885\pi\) | ||||
0.870006 | − | 0.493041i | \(-0.164115\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.00000 | 0.118056 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 12.1962i | − 0.712507i | −0.934389 | − | 0.356253i | \(-0.884054\pi\) | ||||
0.934389 | − | 0.356253i | \(-0.115946\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −26.3923 | −1.53662 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 23.3205i | − 1.34866i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 5.46410i | − 0.314946i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 30.3923 | 1.74026 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.58846i | 0.490169i | 0.969502 | + | 0.245085i | \(0.0788157\pi\) | ||||
−0.969502 | + | 0.245085i | \(0.921184\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.85641 | 0.332086 | 0.166043 | − | 0.986118i | \(-0.446901\pi\) | ||||
0.166043 | + | 0.986118i | \(0.446901\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.8564 | 1.12235 | 0.561175 | − | 0.827697i | \(-0.310349\pi\) | ||||
0.561175 | + | 0.827697i | \(0.310349\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.7846i | 1.61670i | 0.588699 | + | 0.808352i | \(0.299640\pi\) | ||||
−0.588699 | + | 0.808352i | \(0.700360\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.00000 | 0.447914 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 2.53590i | − 0.141101i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.5885i | 0.920162i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.92820 | −0.161437 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.3923i | 0.901003i | 0.892776 | + | 0.450501i | \(0.148755\pi\) | ||||
−0.892776 | + | 0.450501i | \(0.851245\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −21.8564 | −1.19414 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.3923 | 0.892946 | 0.446473 | − | 0.894797i | \(-0.352680\pi\) | ||||
0.446473 | + | 0.894797i | \(0.352680\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.8564i | 1.18359i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 35.3205i | − 1.89610i | −0.318115 | − | 0.948052i | \(-0.603050\pi\) | ||||
0.318115 | − | 0.948052i | \(-0.396950\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 14.0526i | − 0.752216i | −0.926576 | − | 0.376108i | \(-0.877262\pi\) | ||||
0.926576 | − | 0.376108i | \(-0.122738\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.928203 | −0.0494033 | −0.0247016 | − | 0.999695i | \(-0.507864\pi\) | ||||
−0.0247016 | + | 0.999695i | \(0.507864\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.00000i | 0.424596i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.4641 | 1.44950 | 0.724750 | − | 0.689012i | \(-0.241955\pi\) | ||||
0.724750 | + | 0.689012i | \(0.241955\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.3923 | 0.915384 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 35.3205i | − 1.84876i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.7846 | 1.08495 | 0.542474 | − | 0.840073i | \(-0.317488\pi\) | ||||
0.542474 | + | 0.840073i | \(0.317488\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 12.0000i | − 0.623009i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 30.9282i | − 1.60140i | −0.599064 | − | 0.800701i | \(-0.704461\pi\) | ||||
0.599064 | − | 0.800701i | \(-0.295539\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.85641 | −0.507631 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.2487i | 0.731907i | 0.930633 | + | 0.365954i | \(0.119257\pi\) | ||||
−0.930633 | + | 0.365954i | \(0.880743\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.7846 | 1.67522 | 0.837608 | − | 0.546272i | \(-0.183954\pi\) | ||||
0.837608 | + | 0.546272i | \(0.183954\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.9282 | 0.760812 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 23.3205i | − 1.18240i | −0.806526 | − | 0.591198i | \(-0.798655\pi\) | ||||
0.806526 | − | 0.591198i | \(-0.201345\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.92820 | −0.350374 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 29.8564i | 1.50224i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.87564i | 0.244702i | 0.992487 | + | 0.122351i | \(0.0390433\pi\) | ||||
−0.992487 | + | 0.122351i | \(0.960957\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.4641 | −0.672365 | −0.336183 | − | 0.941797i | \(-0.609136\pi\) | ||||
−0.336183 | + | 0.941797i | \(0.609136\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 26.9282i | − 1.34139i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.00000 | 0.396545 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.07180 | −0.151891 | −0.0759453 | − | 0.997112i | \(-0.524197\pi\) | ||||
−0.0759453 | + | 0.997112i | \(0.524197\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 9.66025i | − 0.475350i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.4641 | −0.759103 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.8038i | 1.16289i | 0.813584 | + | 0.581447i | \(0.197513\pi\) | ||||
−0.813584 | + | 0.581447i | \(0.802487\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 25.8564i | − 1.26016i | −0.776529 | − | 0.630082i | \(-0.783021\pi\) | ||||
0.776529 | − | 0.630082i | \(-0.216979\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.92820 | 0.239053 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.1244i | 0.538345i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 35.4641 | 1.70825 | 0.854123 | − | 0.520071i | \(-0.174095\pi\) | ||||
0.854123 | + | 0.520071i | \(0.174095\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.8564 | 0.762010 | 0.381005 | − | 0.924573i | \(-0.375578\pi\) | ||||
0.381005 | + | 0.924573i | \(0.375578\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.39230i | 0.210112i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.9282 | 1.47612 | 0.738061 | − | 0.674734i | \(-0.235742\pi\) | ||||
0.738061 | + | 0.674734i | \(0.235742\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.0000i | 1.14027i | 0.821549 | + | 0.570137i | \(0.193110\pi\) | ||||
−0.821549 | + | 0.570137i | \(0.806890\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 32.3923i | 1.53554i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.00000 | 0.0943858 | 0.0471929 | − | 0.998886i | \(-0.484972\pi\) | ||||
0.0471929 | + | 0.998886i | \(0.484972\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.9282i | 0.514589i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −18.3923 | −0.862245 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.3205 | 0.716663 | 0.358332 | − | 0.933594i | \(-0.383346\pi\) | ||||
0.358332 | + | 0.933594i | \(0.383346\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.1962i | 1.12693i | 0.826141 | + | 0.563464i | \(0.190531\pi\) | ||||
−0.826141 | + | 0.563464i | \(0.809469\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.0000 | 0.743583 | 0.371792 | − | 0.928316i | \(-0.378744\pi\) | ||||
0.371792 | + | 0.928316i | \(0.378744\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.875644i | 0.0405200i | 0.999795 | + | 0.0202600i | \(0.00644940\pi\) | ||||
−0.999795 | + | 0.0202600i | \(0.993551\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 8.00000i | − 0.369406i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 29.8564 | 1.37280 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 3.12436i | − 0.143355i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.85641 | 0.450351 | 0.225175 | − | 0.974318i | \(-0.427705\pi\) | ||||
0.225175 | + | 0.974318i | \(0.427705\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.85641 | −0.449413 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 24.3923i | − 1.10760i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.6077 | −0.979138 | −0.489569 | − | 0.871965i | \(-0.662846\pi\) | ||||
−0.489569 | + | 0.871965i | \(0.662846\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.7846i | 1.47955i | 0.672855 | + | 0.739774i | \(0.265068\pi\) | ||||
−0.672855 | + | 0.739774i | \(0.734932\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.92820i | 0.131880i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.92820 | −0.131348 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.0718i | 0.585174i | 0.956239 | + | 0.292587i | \(0.0945161\pi\) | ||||
−0.956239 | + | 0.292587i | \(0.905484\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.9282 | −1.37902 | −0.689510 | − | 0.724276i | \(-0.742174\pi\) | ||||
−0.689510 | + | 0.724276i | \(0.742174\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.53590 | 0.201845 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.12436i | 0.138485i | 0.997600 | + | 0.0692423i | \(0.0220582\pi\) | ||||
−0.997600 | + | 0.0692423i | \(0.977942\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.9282 | 0.571910 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 26.9282i | − 1.18660i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 16.0000i | − 0.703679i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.7846 | 0.647726 | 0.323863 | − | 0.946104i | \(-0.395018\pi\) | ||||
0.323863 | + | 0.946104i | \(0.395018\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 3.41154i | − 0.149176i | −0.997214 | − | 0.0745882i | \(-0.976236\pi\) | ||||
0.997214 | − | 0.0745882i | \(-0.0237642\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.00000 | −0.348485 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.0000 | −0.478261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 13.4641i | − 0.583195i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.8564 | 0.599065 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.46410i | 0.235356i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 4.00000i | − 0.171973i | −0.996296 | − | 0.0859867i | \(-0.972596\pi\) | ||||
0.996296 | − | 0.0859867i | \(-0.0274043\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −33.8564 | −1.45025 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 46.2487i | 1.97745i | 0.149736 | + | 0.988726i | \(0.452158\pi\) | ||||
−0.149736 | + | 0.988726i | \(0.547842\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.85641 | 0.0790856 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.9282 | −0.464714 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 23.7128i | − 1.00474i | −0.864652 | − | 0.502372i | \(-0.832461\pi\) | ||||
0.864652 | − | 0.502372i | \(-0.167539\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −36.7846 | −1.55582 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 34.0526i | 1.43514i | 0.696484 | + | 0.717572i | \(0.254747\pi\) | ||||
−0.696484 | + | 0.717572i | \(0.745253\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 17.8564i | − 0.751225i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.46410 | 0.229067 | 0.114534 | − | 0.993419i | \(-0.463463\pi\) | ||||
0.114534 | + | 0.993419i | \(0.463463\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 25.1769i | − 1.05362i | −0.849983 | − | 0.526811i | \(-0.823388\pi\) | ||||
0.849983 | − | 0.526811i | \(-0.176612\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.53590 | −0.355972 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.0718 | −1.29354 | −0.646768 | − | 0.762687i | \(-0.723880\pi\) | ||||
−0.646768 | + | 0.762687i | \(0.723880\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 5.66025i | − 0.234827i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 65.5692 | 2.71560 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 33.2679i | − 1.37312i | −0.727075 | − | 0.686558i | \(-0.759121\pi\) | ||||
0.727075 | − | 0.686558i | \(-0.240879\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.07180i | 0.208980i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.1436 | −0.498678 | −0.249339 | − | 0.968416i | \(-0.580213\pi\) | ||||
−0.249339 | + | 0.968416i | \(0.580213\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.46410i | 0.224006i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.7128 | −1.13231 | −0.566157 | − | 0.824297i | \(-0.691571\pi\) | ||||
−0.566157 | + | 0.824297i | \(0.691571\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.0000 | 0.897399 | 0.448699 | − | 0.893683i | \(-0.351887\pi\) | ||||
0.448699 | + | 0.893683i | \(0.351887\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 51.5167i | 2.09445i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.7128 | −1.12483 | −0.562414 | − | 0.826856i | \(-0.690127\pi\) | ||||
−0.562414 | + | 0.826856i | \(0.690127\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.7128i | 0.797495i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.3205i | 1.58814i | 0.607826 | + | 0.794070i | \(0.292042\pi\) | ||||
−0.607826 | + | 0.794070i | \(0.707958\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.3923 | 0.981997 | 0.490999 | − | 0.871160i | \(-0.336632\pi\) | ||||
0.490999 | + | 0.871160i | \(0.336632\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.1962i | 0.972525i | 0.873813 | + | 0.486263i | \(0.161640\pi\) | ||||
−0.873813 | + | 0.486263i | \(0.838360\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.8564 | −0.475017 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2487 | −1.24995 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.92820i | 0.116755i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −49.5692 | −1.97332 | −0.986660 | − | 0.162796i | \(-0.947949\pi\) | ||||
−0.986660 | + | 0.162796i | \(0.947949\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 31.3205i | 1.24292i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 6.73205i | − 0.266734i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.2487 | 0.878771 | 0.439386 | − | 0.898299i | \(-0.355196\pi\) | ||||
0.439386 | + | 0.898299i | \(0.355196\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 14.3397i | − 0.565504i | −0.959193 | − | 0.282752i | \(-0.908753\pi\) | ||||
0.959193 | − | 0.282752i | \(-0.0912474\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.85641 | 0.0729829 | 0.0364914 | − | 0.999334i | \(-0.488382\pi\) | ||||
0.0364914 | + | 0.999334i | \(0.488382\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 52.7846 | 2.07198 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.5359i | 1.50803i | 0.656859 | + | 0.754013i | \(0.271885\pi\) | ||||
−0.656859 | + | 0.754013i | \(0.728115\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −29.3205 | −1.14565 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.32051i | 0.129349i | 0.997906 | + | 0.0646743i | \(0.0206009\pi\) | ||||
−0.997906 | + | 0.0646743i | \(0.979399\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.9808i | 1.12722i | 0.826041 | + | 0.563611i | \(0.190588\pi\) | ||||
−0.826041 | + | 0.563611i | \(0.809412\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.46410 | 0.134332 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 5.07180i | − 0.196381i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −60.7846 | −2.34656 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.14359 | 0.159724 | 0.0798619 | − | 0.996806i | \(-0.474552\pi\) | ||||
0.0798619 | + | 0.996806i | \(0.474552\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.4449i | 0.555161i | 0.960702 | + | 0.277581i | \(0.0895326\pi\) | ||||
−0.960702 | + | 0.277581i | \(0.910467\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.92820 | 0.342633 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.6410i | 1.17245i | 0.810150 | + | 0.586223i | \(0.199386\pi\) | ||||
−0.810150 | + | 0.586223i | \(0.800614\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 54.2487i | 2.07274i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −80.7846 | −3.07765 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 11.1244i | − 0.423190i | −0.977357 | − | 0.211595i | \(-0.932134\pi\) | ||||
0.977357 | − | 0.211595i | \(-0.0678658\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 25.3205 | 0.960462 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.00000 | −0.151511 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.6077i | 0.740572i | 0.928918 | + | 0.370286i | \(0.120740\pi\) | ||||
−0.928918 | + | 0.370286i | \(0.879260\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.85641 | 0.0700157 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.66025i | 0.0624403i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 48.1051i | 1.80663i | 0.428982 | + | 0.903313i | \(0.358872\pi\) | ||||
−0.428982 | + | 0.903313i | \(0.641128\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.8564 | 0.518927 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 100.497i | − 3.75839i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.0718 | −0.785845 | −0.392923 | − | 0.919572i | \(-0.628536\pi\) | ||||
−0.392923 | + | 0.919572i | \(0.628536\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.85641 | 0.367072 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.60770i | 0.133986i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.9282 | 0.405305 | 0.202652 | − | 0.979251i | \(-0.435044\pi\) | ||||
0.202652 | + | 0.979251i | \(0.435044\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.9282i | 0.404194i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 13.6603i | − 0.504553i | −0.967655 | − | 0.252276i | \(-0.918821\pi\) | ||||
0.967655 | − | 0.252276i | \(-0.0811792\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 43.7128 | 1.61018 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.32051i | 0.122147i | 0.998133 | + | 0.0610734i | \(0.0194524\pi\) | ||||
−0.998133 | + | 0.0610734i | \(0.980548\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.2487 | −1.18309 | −0.591545 | − | 0.806272i | \(-0.701482\pi\) | ||||
−0.591545 | + | 0.806272i | \(0.701482\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.92820 | −0.107281 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.07180i | 0.185319i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.2487 | 0.884848 | 0.442424 | − | 0.896806i | \(-0.354119\pi\) | ||||
0.442424 | + | 0.896806i | \(0.354119\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.53590i | 0.237866i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 10.2487i | − 0.372496i | −0.982503 | − | 0.186248i | \(-0.940367\pi\) | ||||
0.982503 | − | 0.186248i | \(-0.0596327\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.7128 | 0.787089 | 0.393544 | − | 0.919306i | \(-0.371249\pi\) | ||||
0.393544 | + | 0.919306i | \(0.371249\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 12.3923i | − 0.448632i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −65.0333 | −2.34822 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.7846 | −0.388903 | −0.194451 | − | 0.980912i | \(-0.562293\pi\) | ||||
−0.194451 | + | 0.980912i | \(0.562293\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 20.8756i | − 0.750845i | −0.926854 | − | 0.375422i | \(-0.877498\pi\) | ||||
0.926854 | − | 0.375422i | \(-0.122502\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.85641 | −0.354053 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.53590i | 0.0908580i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 16.0000i | − 0.572525i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 33.3205 | 1.18926 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 20.5885i | − 0.733899i | −0.930241 | − | 0.366950i | \(-0.880402\pi\) | ||||
0.930241 | − | 0.366950i | \(-0.119598\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.53590 | 0.232390 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 74.8897 | 2.65941 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 12.9808i | − 0.459802i | −0.973214 | − | 0.229901i | \(-0.926160\pi\) | ||||
0.973214 | − | 0.229901i | \(-0.0738403\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.85641 | 0.207185 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 70.6410i | 2.49287i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 9.46410i | − 0.333566i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.3205 | −0.819905 | −0.409953 | − | 0.912107i | \(-0.634455\pi\) | ||||
−0.409953 | + | 0.912107i | \(0.634455\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.1244i | 0.952465i | 0.879319 | + | 0.476232i | \(0.157998\pi\) | ||||
−0.879319 | + | 0.476232i | \(0.842002\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 36.7846 | 1.28851 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.92820 | 0.242387 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.92820i | 0.241796i | 0.992665 | + | 0.120898i | \(0.0385774\pi\) | ||||
−0.992665 | + | 0.120898i | \(0.961423\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.92820 | −0.102071 | −0.0510354 | − | 0.998697i | \(-0.516252\pi\) | ||||
−0.0510354 | + | 0.998697i | \(0.516252\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 13.8564i | − 0.481834i | −0.970546 | − | 0.240917i | \(-0.922552\pi\) | ||||
0.970546 | − | 0.240917i | \(-0.0774482\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.9808i | 1.42332i | 0.702524 | + | 0.711660i | \(0.252056\pi\) | ||||
−0.702524 | + | 0.711660i | \(0.747944\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.00000 | −0.0692959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 13.8564i | − 0.479521i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 39.7128 | 1.37104 | 0.685519 | − | 0.728054i | \(-0.259575\pi\) | ||||
0.685519 | + | 0.728054i | \(0.259575\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.8564 | 0.926083 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 88.3013i | 3.03766i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.8564 | −0.647914 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 5.07180i | − 0.173859i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 4.98076i | − 0.170538i | −0.996358 | − | 0.0852690i | \(-0.972825\pi\) | ||||
0.996358 | − | 0.0852690i | \(-0.0271750\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30.7846 | 1.05158 | 0.525791 | − | 0.850614i | \(-0.323769\pi\) | ||||
0.525791 | + | 0.850614i | \(0.323769\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.4449i | 1.03877i | 0.854542 | + | 0.519383i | \(0.173838\pi\) | ||||
−0.854542 | + | 0.519383i | \(0.826162\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24.0000 | −0.816970 | −0.408485 | − | 0.912765i | \(-0.633943\pi\) | ||||
−0.408485 | + | 0.912765i | \(0.633943\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.3923 | 0.353349 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 59.7128i | − 2.02562i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −53.8564 | −1.82485 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 6.92820i | − 0.234216i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.3923i | 0.688599i | 0.938860 | + | 0.344300i | \(0.111884\pi\) | ||||
−0.938860 | + | 0.344300i | \(0.888116\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 50.7846 | 1.71098 | 0.855488 | − | 0.517822i | \(-0.173257\pi\) | ||||
0.855488 | + | 0.517822i | \(0.173257\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 5.07180i | − 0.170680i | −0.996352 | − | 0.0853398i | \(-0.972802\pi\) | ||||
0.996352 | − | 0.0853398i | \(-0.0271976\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 46.6410 | 1.56605 | 0.783026 | − | 0.621989i | \(-0.213675\pi\) | ||||
0.783026 | + | 0.621989i | \(0.213675\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.4641 | −0.384494 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 3.71281i | − 0.124245i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.00000 | −0.267411 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 5.85641i | − 0.195322i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.0000i | 0.799556i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −29.3205 | −0.974647 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43.7128i | 1.45146i | 0.687980 | + | 0.725730i | \(0.258498\pi\) | ||||
−0.687980 | + | 0.725730i | \(0.741502\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.53590 | 0.150281 | 0.0751405 | − | 0.997173i | \(-0.476059\pi\) | ||||
0.0751405 | + | 0.997173i | \(0.476059\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30.9282 | 1.02357 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 10.7321i | − 0.354404i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.21539 | −0.238014 | −0.119007 | − | 0.992893i | \(-0.537971\pi\) | ||||
−0.119007 | + | 0.992893i | \(0.537971\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 19.7128i | 0.648855i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.60770i | 0.118620i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −37.7128 | −1.23732 | −0.618659 | − | 0.785660i | \(-0.712324\pi\) | ||||
−0.618659 | + | 0.785660i | \(0.712324\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.26795i | 0.0415554i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −29.8564 | −0.976409 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.64102 | 0.282290 | 0.141145 | − | 0.989989i | \(-0.454922\pi\) | ||||
0.141145 | + | 0.989989i | \(0.454922\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 44.9808i | 1.46633i | 0.680050 | + | 0.733165i | \(0.261958\pi\) | ||||
−0.680050 | + | 0.733165i | \(0.738042\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.92820 | 0.225613 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 24.3923i | − 0.792643i | −0.918112 | − | 0.396322i | \(-0.870286\pi\) | ||||
0.918112 | − | 0.396322i | \(-0.129714\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 87.0333i | − 2.82522i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.8564 | 0.643212 | 0.321606 | − | 0.946874i | \(-0.395777\pi\) | ||||
0.321606 | + | 0.946874i | \(0.395777\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 43.7128i | 1.41451i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.8564 | −0.641197 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 17.8564i | − 0.574818i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.1769 | −0.488057 | −0.244028 | − | 0.969768i | \(-0.578469\pi\) | ||||
−0.244028 | + | 0.969768i | \(0.578469\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 55.5167i | − 1.78161i | −0.454381 | − | 0.890807i | \(-0.650140\pi\) | ||||
0.454381 | − | 0.890807i | \(-0.349860\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.26795i | 0.297117i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.1436 | 0.900393 | 0.450197 | − | 0.892929i | \(-0.351354\pi\) | ||||
0.450197 | + | 0.892929i | \(0.351354\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 64.7846i | − 2.07053i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 47.7128 | 1.52180 | 0.760901 | − | 0.648868i | \(-0.224757\pi\) | ||||
0.760901 | + | 0.648868i | \(0.224757\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −70.6410 | −2.25081 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 18.9282i | − 0.601882i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.7846 | 0.787309 | 0.393655 | − | 0.919258i | \(-0.371211\pi\) | ||||
0.393655 | + | 0.919258i | \(0.371211\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.9282i | 0.346447i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 5.26795i | − 0.166838i | −0.996515 | − | 0.0834188i | \(-0.973416\pi\) | ||||
0.996515 | − | 0.0834188i | \(-0.0265839\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 4032.2.c.n.2017.1 | 4 | ||
3.2 | odd | 2 | 448.2.b.d.225.1 | yes | 4 | ||
4.3 | odd | 2 | 4032.2.c.k.2017.1 | 4 | |||
8.3 | odd | 2 | 4032.2.c.k.2017.4 | 4 | |||
8.5 | even | 2 | inner | 4032.2.c.n.2017.4 | 4 | ||
12.11 | even | 2 | 448.2.b.c.225.4 | yes | 4 | ||
21.20 | even | 2 | 3136.2.b.h.1569.4 | 4 | |||
24.5 | odd | 2 | 448.2.b.d.225.4 | yes | 4 | ||
24.11 | even | 2 | 448.2.b.c.225.1 | ✓ | 4 | ||
48.5 | odd | 4 | 1792.2.a.i.1.1 | 2 | |||
48.11 | even | 4 | 1792.2.a.q.1.2 | 2 | |||
48.29 | odd | 4 | 1792.2.a.s.1.2 | 2 | |||
48.35 | even | 4 | 1792.2.a.k.1.1 | 2 | |||
84.83 | odd | 2 | 3136.2.b.g.1569.1 | 4 | |||
168.83 | odd | 2 | 3136.2.b.g.1569.4 | 4 | |||
168.125 | even | 2 | 3136.2.b.h.1569.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
448.2.b.c.225.1 | ✓ | 4 | 24.11 | even | 2 | ||
448.2.b.c.225.4 | yes | 4 | 12.11 | even | 2 | ||
448.2.b.d.225.1 | yes | 4 | 3.2 | odd | 2 | ||
448.2.b.d.225.4 | yes | 4 | 24.5 | odd | 2 | ||
1792.2.a.i.1.1 | 2 | 48.5 | odd | 4 | |||
1792.2.a.k.1.1 | 2 | 48.35 | even | 4 | |||
1792.2.a.q.1.2 | 2 | 48.11 | even | 4 | |||
1792.2.a.s.1.2 | 2 | 48.29 | odd | 4 | |||
3136.2.b.g.1569.1 | 4 | 84.83 | odd | 2 | |||
3136.2.b.g.1569.4 | 4 | 168.83 | odd | 2 | |||
3136.2.b.h.1569.1 | 4 | 168.125 | even | 2 | |||
3136.2.b.h.1569.4 | 4 | 21.20 | even | 2 | |||
4032.2.c.k.2017.1 | 4 | 4.3 | odd | 2 | |||
4032.2.c.k.2017.4 | 4 | 8.3 | odd | 2 | |||
4032.2.c.n.2017.1 | 4 | 1.1 | even | 1 | trivial | ||
4032.2.c.n.2017.4 | 4 | 8.5 | even | 2 | inner |