Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,2,Mod(95,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.95");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.k (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.06625543762\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.163368480538624.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{10} - 2x^{8} + 16x^{6} - 8x^{4} - 32x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 287.2 | ||
Root | \(-1.35164 + 0.416001i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.287 |
Dual form | 384.2.k.a.95.2 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −1.43726 | + | 0.966579i | −0.829804 | + | 0.558055i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.57184 | + | 1.57184i | −0.702949 | + | 0.702949i | −0.965042 | − | 0.262094i | \(-0.915587\pi\) |
0.262094 | + | 0.965042i | \(0.415587\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.24914 | −0.850095 | −0.425048 | − | 0.905171i | \(-0.639743\pi\) | ||||
−0.425048 | + | 0.905171i | \(0.639743\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.13145 | − | 2.77846i | 0.377150 | − | 0.926152i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.13145 | − | 1.13145i | −0.341145 | − | 0.341145i | 0.515653 | − | 0.856798i | \(-0.327549\pi\) |
−0.856798 | + | 0.515653i | \(0.827549\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.24914 | − | 3.24914i | 0.901149 | − | 0.901149i | −0.0943862 | − | 0.995536i | \(-0.530089\pi\) |
0.995536 | + | 0.0943862i | \(0.0300889\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.739839 | − | 3.77846i | 0.191026 | − | 0.975593i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.66400i | − | 0.403580i | −0.979429 | − | 0.201790i | \(-0.935324\pi\) | ||
0.979429 | − | 0.201790i | \(-0.0646758\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.77846 | − | 3.77846i | −0.866838 | − | 0.866838i | 0.125283 | − | 0.992121i | \(-0.460016\pi\) |
−0.992121 | + | 0.125283i | \(0.960016\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.23261 | − | 2.17397i | 0.705412 | − | 0.474400i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.26290i | − | 0.471847i | −0.971772 | − | 0.235923i | \(-0.924189\pi\) | ||
0.971772 | − | 0.235923i | \(-0.0758114\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.0586332i | 0.0117266i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.05941 | + | 5.08701i | 0.203884 | + | 0.978995i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.23584 | − | 3.23584i | −0.600881 | − | 0.600881i | 0.339665 | − | 0.940546i | \(-0.389686\pi\) |
−0.940546 | + | 0.339665i | \(0.889686\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.30777i | 0.234883i | 0.993080 | + | 0.117442i | \(0.0374693\pi\) | ||||
−0.993080 | + | 0.117442i | \(0.962531\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.71982 | + | 0.532554i | 0.473461 | + | 0.0927058i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.53529 | − | 3.53529i | 0.597573 | − | 0.597573i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.30777 | − | 2.30777i | −0.379396 | − | 0.379396i | 0.491488 | − | 0.870884i | \(-0.336453\pi\) |
−0.870884 | + | 0.491488i | \(0.836453\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.52932 | + | 7.81042i | −0.244887 | + | 1.25067i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.2143 | −1.59520 | −0.797600 | − | 0.603187i | \(-0.793897\pi\) | ||||
−0.797600 | + | 0.603187i | \(0.793897\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.77846 | − | 3.77846i | 0.576209 | − | 0.576209i | −0.357647 | − | 0.933857i | \(-0.616421\pi\) |
0.933857 | + | 0.357647i | \(0.116421\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.58884 | + | 6.14575i | 0.385921 | + | 0.916154i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.74258 | −0.545911 | −0.272955 | − | 0.962027i | \(-0.588001\pi\) | ||||
−0.272955 | + | 0.962027i | \(0.588001\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.94137 | −0.277338 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.60839 | + | 2.39161i | 0.225220 | + | 0.334892i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.972946 | − | 0.972946i | 0.133644 | − | 0.133644i | −0.637120 | − | 0.770765i | \(-0.719874\pi\) |
0.770765 | + | 0.637120i | \(0.219874\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.55691 | 0.479614 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.08281 | + | 1.77846i | 1.20305 | + | 0.235562i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.88352 | − | 3.88352i | −0.505591 | − | 0.505591i | 0.407579 | − | 0.913170i | \(-0.366373\pi\) |
−0.913170 | + | 0.407579i | \(0.866373\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.19051 | + | 4.19051i | −0.536539 | + | 0.536539i | −0.922511 | − | 0.385971i | \(-0.873866\pi\) |
0.385971 | + | 0.922511i | \(0.373866\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.54479 | + | 6.24914i | −0.320613 | + | 0.787318i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.2143i | 1.26692i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.02760 | + | 8.02760i | 0.980727 | + | 0.980727i | 0.999818 | − | 0.0190906i | \(-0.00607710\pi\) |
−0.0190906 | + | 0.999818i | \(0.506077\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.18727 | + | 3.25238i | 0.263316 | + | 0.391540i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 11.0950i | − | 1.31674i | −0.752695 | − | 0.658370i | \(-0.771246\pi\) | ||
0.752695 | − | 0.658370i | \(-0.228754\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.38101i | 0.746841i | 0.927662 | + | 0.373421i | \(0.121815\pi\) | ||||
−0.927662 | + | 0.373421i | \(0.878185\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.0566736 | − | 0.0842713i | −0.00654410 | − | 0.00973081i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.54479 | + | 2.54479i | 0.290005 | + | 0.290005i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.69223i | 0.302899i | 0.988465 | + | 0.151450i | \(0.0483941\pi\) | ||||
−0.988465 | + | 0.151450i | \(0.951606\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.43965 | − | 6.28736i | −0.715516 | − | 0.698596i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.61113 | + | 2.61113i | −0.286608 | + | 0.286608i | −0.835738 | − | 0.549129i | \(-0.814960\pi\) |
0.549129 | + | 0.835738i | \(0.314960\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.61555 | + | 2.61555i | 0.283696 | + | 0.283696i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.77846 | + | 1.52306i | 0.833938 | + | 0.163289i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.35247 | 0.779360 | 0.389680 | − | 0.920950i | \(-0.372586\pi\) | ||||
0.389680 | + | 0.920950i | \(0.372586\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.30777 | + | 7.30777i | −0.766063 | + | 0.766063i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.26407 | − | 1.87961i | −0.131078 | − | 0.194907i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.8783 | 1.21868 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.67418 | −0.576126 | −0.288063 | − | 0.957611i | \(-0.593011\pi\) | ||||
−0.288063 | + | 0.957611i | \(0.593011\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.42386 | + | 1.86351i | −0.444614 | + | 0.187289i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.3064 | + | 10.3064i | −1.02553 | + | 1.02553i | −0.0258621 | + | 0.999666i | \(0.508233\pi\) |
−0.999666 | + | 0.0258621i | \(0.991767\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.13187 | 0.801257 | 0.400629 | − | 0.916241i | \(-0.368792\pi\) | ||||
0.400629 | + | 0.916241i | \(0.368792\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.66400 | + | 8.49828i | −0.162390 | + | 0.829347i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.40384 | + | 2.40384i | 0.232388 | + | 0.232388i | 0.813689 | − | 0.581301i | \(-0.197456\pi\) |
−0.581301 | + | 0.813689i | \(0.697456\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.92332 | + | 8.92332i | −0.854699 | + | 0.854699i | −0.990708 | − | 0.136009i | \(-0.956573\pi\) |
0.136009 | + | 0.990708i | \(0.456573\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.54752 | + | 1.08623i | 0.526548 | + | 0.103100i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 15.9027i | − | 1.49600i | −0.663697 | − | 0.748002i | \(-0.731014\pi\) | ||
0.663697 | − | 0.748002i | \(-0.268986\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.55691 | + | 3.55691i | 0.331684 | + | 0.331684i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.35136 | − | 12.7038i | −0.494734 | − | 1.17447i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.74258i | 0.343081i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 8.43965i | − | 0.767241i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 14.6806 | − | 9.87290i | 1.32370 | − | 0.890209i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.95137 | − | 7.95137i | −0.711192 | − | 0.711192i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 7.42504i | − | 0.658866i | −0.944179 | − | 0.329433i | \(-0.893142\pi\) | ||
0.944179 | − | 0.329433i | \(-0.106858\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.77846 | + | 9.08281i | −0.156584 | + | 0.799697i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.88352 | − | 3.88352i | 0.339305 | − | 0.339305i | −0.516801 | − | 0.856106i | \(-0.672877\pi\) |
0.856106 | + | 0.516801i | \(0.172877\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.49828 | + | 8.49828i | 0.736894 | + | 0.736894i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.66119 | − | 6.33074i | −0.831503 | − | 0.544864i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.72911 | −0.233164 | −0.116582 | − | 0.993181i | \(-0.537194\pi\) | ||||
−0.116582 | + | 0.993181i | \(0.537194\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.0275977 | + | 0.0275977i | −0.00234080 | + | 0.00234080i | −0.708276 | − | 0.705935i | \(-0.750527\pi\) |
0.705935 | + | 0.708276i | \(0.250527\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.37907 | − | 3.61750i | 0.452999 | − | 0.304648i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.35247 | −0.614845 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.1725 | 0.844777 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.79025 | − | 1.87649i | 0.230136 | − | 0.154770i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.5693 | − | 12.5693i | 1.02972 | − | 1.02972i | 0.0301744 | − | 0.999545i | \(-0.490394\pi\) |
0.999545 | − | 0.0301744i | \(-0.00960626\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.8647 | −1.37243 | −0.686214 | − | 0.727399i | \(-0.740729\pi\) | ||||
−0.686214 | + | 0.727399i | \(0.740729\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.62336 | − | 1.88273i | −0.373777 | − | 0.152210i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.05561 | − | 2.05561i | −0.165111 | − | 0.165111i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.36641 | − | 5.36641i | 0.428286 | − | 0.428286i | −0.459758 | − | 0.888044i | \(-0.652064\pi\) |
0.888044 | + | 0.459758i | \(0.152064\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.457950 | + | 2.33881i | −0.0363178 | + | 0.185480i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.08957i | 0.401115i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.77502 | − | 8.77502i | −0.687313 | − | 0.687313i | 0.274325 | − | 0.961637i | \(-0.411546\pi\) |
−0.961637 | + | 0.274325i | \(0.911546\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.11222 | + | 3.43804i | −0.397986 | + | 0.267651i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.9678i | 1.31301i | 0.754321 | + | 0.656505i | \(0.227966\pi\) | ||||
−0.754321 | + | 0.656505i | \(0.772034\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 8.11383i | − | 0.624141i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.7734 | + | 6.22315i | −1.12975 | + | 0.475896i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.3119 | + | 16.3119i | 1.24017 | + | 1.24017i | 0.959930 | + | 0.280241i | \(0.0904144\pi\) |
0.280241 | + | 0.959930i | \(0.409586\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 0.131874i | − | 0.00996875i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.33537 | + | 1.82791i | 0.701689 | + | 0.137394i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.33873 | − | 1.33873i | 0.100062 | − | 0.100062i | −0.655304 | − | 0.755365i | \(-0.727459\pi\) |
0.755365 | + | 0.655304i | \(0.227459\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.2457 | − | 10.2457i | −0.761557 | − | 0.761557i | 0.215047 | − | 0.976604i | \(-0.431010\pi\) |
−0.976604 | + | 0.215047i | \(0.931010\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.97240 | − | 10.0733i | 0.145804 | − | 0.744641i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.25491 | 0.533391 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.88273 | + | 1.88273i | −0.137679 | + | 0.137679i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.38276 | − | 11.4414i | −0.173320 | − | 0.832239i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.5398 | −1.77563 | −0.887817 | − | 0.460197i | \(-0.847779\pi\) | ||||
−0.887817 | + | 0.460197i | \(0.847779\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.38101 | 0.603279 | 0.301639 | − | 0.953422i | \(-0.402466\pi\) | ||||
0.301639 | + | 0.953422i | \(0.402466\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.87290 | − | 14.6806i | −0.707013 | − | 1.05130i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.28995 | − | 1.28995i | 0.0919052 | − | 0.0919052i | −0.659659 | − | 0.751565i | \(-0.729299\pi\) |
0.751565 | + | 0.659659i | \(0.229299\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.0992 | 0.928579 | 0.464290 | − | 0.885683i | \(-0.346310\pi\) | ||||
0.464290 | + | 0.885683i | \(0.346310\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.2971 | − | 3.77846i | −1.36111 | − | 0.266512i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.27787 | + | 7.27787i | 0.510806 | + | 0.510806i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.0552 | − | 16.0552i | 1.12134 | − | 1.12134i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.28736 | − | 2.56035i | −0.437002 | − | 0.177957i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.55026i | 0.591434i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.47068 | − | 8.47068i | −0.583146 | − | 0.583146i | 0.352621 | − | 0.935766i | \(-0.385291\pi\) |
−0.935766 | + | 0.352621i | \(0.885291\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.7242 | + | 15.9465i | 0.734813 | + | 1.09264i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.8783i | 0.810091i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 2.94137i | − | 0.199673i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.16776 | − | 9.17120i | −0.416778 | − | 0.619732i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.40658 | − | 5.40658i | −0.363686 | − | 0.363686i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 21.5715i | − | 1.44454i | −0.691613 | − | 0.722268i | \(-0.743100\pi\) | ||
0.691613 | − | 0.722268i | \(-0.256900\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.162910 | + | 0.0663404i | 0.0108606 | + | 0.00442269i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.7523 | + | 16.7523i | −1.11189 | + | 1.11189i | −0.118994 | + | 0.992895i | \(0.537967\pi\) |
−0.992895 | + | 0.118994i | \(0.962033\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.36641 | − | 3.36641i | −0.222458 | − | 0.222458i | 0.587074 | − | 0.809533i | \(-0.300280\pi\) |
−0.809533 | + | 0.587074i | \(0.800280\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.11727 | − | 1.19779i | −0.402487 | − | 0.0788087i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.501329 | 0.0328431 | 0.0164216 | − | 0.999865i | \(-0.494773\pi\) | ||||
0.0164216 | + | 0.999865i | \(0.494773\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.88273 | − | 5.88273i | 0.383747 | − | 0.383747i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.60225 | − | 3.86944i | −0.169034 | − | 0.251347i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 30.4585 | 1.97019 | 0.985097 | − | 0.171999i | \(-0.0550225\pi\) | ||||
0.985097 | + | 0.171999i | \(0.0550225\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.4948 | −0.998111 | −0.499055 | − | 0.866570i | \(-0.666320\pi\) | ||||
−0.499055 | + | 0.866570i | \(0.666320\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.3327 | + | 2.81216i | 0.983593 | + | 0.180400i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.05152 | − | 3.05152i | 0.194954 | − | 0.194954i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −24.5535 | −1.56230 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.22901 | − | 6.27674i | 0.0778856 | − | 0.397772i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.2265 | + | 12.2265i | 0.771730 | + | 0.771730i | 0.978409 | − | 0.206679i | \(-0.0662656\pi\) |
−0.206679 | + | 0.978409i | \(0.566266\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.56035 | + | 2.56035i | −0.160968 | + | 0.160968i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.28736 | − | 1.23109i | −0.393730 | − | 0.0770941i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 7.48515i | − | 0.466911i | −0.972367 | − | 0.233455i | \(-0.924997\pi\) | ||
0.972367 | − | 0.233455i | \(-0.0750033\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.19051 | + | 5.19051i | 0.322522 | + | 0.322522i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.6518 | + | 5.32946i | −0.783129 | + | 0.329885i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 10.2659i | − | 0.633023i | −0.948589 | − | 0.316511i | \(-0.897488\pi\) | ||
0.948589 | − | 0.316511i | \(-0.102512\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.05863i | 0.187890i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.5674 | + | 7.10675i | −0.646716 | + | 0.434926i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.76963 | − | 2.76963i | −0.168867 | − | 0.168867i | 0.617614 | − | 0.786481i | \(-0.288099\pi\) |
−0.786481 | + | 0.617614i | \(0.788099\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.6854i | 1.74251i | 0.490830 | + | 0.871255i | \(0.336694\pi\) | ||||
−0.490830 | + | 0.871255i | \(0.663306\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.43965 | − | 17.5667i | 0.208177 | − | 1.06319i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.0663404 | − | 0.0663404i | 0.00400048 | − | 0.00400048i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.806055 | + | 0.806055i | 0.0484311 | + | 0.0484311i | 0.730908 | − | 0.682476i | \(-0.239097\pi\) |
−0.682476 | + | 0.730908i | \(0.739097\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.63359 | + | 1.47968i | 0.217538 | + | 0.0885861i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.3228 | 1.33167 | 0.665833 | − | 0.746101i | \(-0.268076\pi\) | ||||
0.665833 | + | 0.746101i | \(0.268076\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.08279 | − | 8.08279i | 0.480472 | − | 0.480472i | −0.424810 | − | 0.905282i | \(-0.639659\pi\) |
0.905282 | + | 0.424810i | \(0.139659\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −17.0722 | + | 11.4813i | −1.01127 | + | 0.680093i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 22.9733 | 1.35607 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.2311 | 0.837123 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.15529 | − | 5.48455i | 0.478071 | − | 0.321510i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.37953 | − | 6.37953i | 0.372696 | − | 0.372696i | −0.495762 | − | 0.868458i | \(-0.665111\pi\) |
0.868458 | + | 0.495762i | \(0.165111\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.2086 | 0.710809 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.55702 | − | 6.95436i | 0.264425 | − | 0.403533i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.35247 | − | 7.35247i | −0.425204 | − | 0.425204i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.49828 | + | 8.49828i | −0.489833 | + | 0.489833i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.85106 | − | 24.7750i | 0.278686 | − | 1.42329i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 13.1736i | − | 0.754319i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.58795 | − | 6.58795i | −0.375994 | − | 0.375994i | 0.493661 | − | 0.869655i | \(-0.335659\pi\) |
−0.869655 | + | 0.493661i | \(0.835659\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.6876 | + | 7.86010i | −0.664887 | + | 0.447146i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 9.52861i | − | 0.540318i | −0.962816 | − | 0.270159i | \(-0.912924\pi\) | ||
0.962816 | − | 0.270159i | \(-0.0870763\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.1690i | 1.42264i | 0.702870 | + | 0.711319i | \(0.251902\pi\) | ||||
−0.702870 | + | 0.711319i | \(0.748098\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.82265 | − | 13.8227i | −0.328069 | − | 0.778818i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.5287 | + | 15.5287i | 0.872178 | + | 0.872178i | 0.992709 | − | 0.120532i | \(-0.0384600\pi\) |
−0.120532 | + | 0.992709i | \(0.538460\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.32238i | 0.409975i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.77846 | − | 1.13145i | −0.322522 | − | 0.0631513i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.28736 | + | 6.28736i | −0.349838 | + | 0.349838i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.190507 | + | 0.190507i | 0.0105674 | + | 0.0105674i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.20006 | − | 21.4503i | 0.232264 | − | 1.18620i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.41758 | 0.464076 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.58795 | − | 2.58795i | 0.142247 | − | 0.142247i | −0.632397 | − | 0.774644i | \(-0.717929\pi\) |
0.774644 | + | 0.632397i | \(0.217929\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.02318 | + | 3.80092i | −0.494467 | + | 0.208289i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −25.2362 | −1.37880 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.1690 | −1.26210 | −0.631049 | − | 0.775743i | \(-0.717375\pi\) | ||||
−0.631049 | + | 0.775743i | \(0.717375\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.3713 | + | 22.8564i | 0.834852 | + | 1.24139i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.47968 | − | 1.47968i | 0.0801291 | − | 0.0801291i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1104 | 1.08586 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.55026 | − | 1.67418i | −0.460331 | − | 0.0901349i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.72235 | + | 6.72235i | 0.360875 | + | 0.360875i | 0.864135 | − | 0.503260i | \(-0.167866\pi\) |
−0.503260 | + | 0.864135i | \(0.667866\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.75086 | − | 2.75086i | 0.147250 | − | 0.147250i | −0.629638 | − | 0.776888i | \(-0.716797\pi\) |
0.776888 | + | 0.629638i | \(0.216797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 19.9706 | + | 13.0862i | 1.06595 | + | 0.698491i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.1928i | 1.23443i | 0.786796 | + | 0.617213i | \(0.211738\pi\) | ||||
−0.786796 | + | 0.617213i | \(0.788262\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.4396 | + | 17.4396i | 0.925600 | + | 0.925600i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.61750 | − | 5.37907i | −0.191458 | − | 0.284690i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.3664i | 1.44434i | 0.691713 | + | 0.722172i | \(0.256856\pi\) | ||||
−0.691713 | + | 0.722172i | \(0.743144\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.55348i | 0.502815i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.15759 | + | 12.1300i | 0.428162 | + | 0.636659i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.0299 | − | 10.0299i | −0.524991 | − | 0.524991i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.0406i | 1.35931i | 0.733533 | + | 0.679654i | \(0.237870\pi\) | ||||
−0.733533 | + | 0.679654i | \(0.762130\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.5569 | + | 28.3799i | −0.601629 | + | 1.47740i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.18829 | + | 2.18829i | −0.113611 | + | 0.113611i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.1319 | + | 13.1319i | 0.679943 | + | 0.679943i | 0.959987 | − | 0.280044i | \(-0.0903492\pi\) |
−0.280044 | + | 0.959987i | \(0.590349\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 19.1138 | + | 3.74258i | 0.987034 | + | 0.193266i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −21.0274 | −1.08297 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.4526 | + | 17.4526i | −0.896482 | + | 0.896482i | −0.995123 | − | 0.0986413i | \(-0.968550\pi\) |
0.0986413 | + | 0.995123i | \(0.468550\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.17689 | + | 10.6717i | 0.367683 | + | 0.546729i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −26.4965 | −1.35391 | −0.676953 | − | 0.736027i | \(-0.736700\pi\) | ||||
−0.676953 | + | 0.736027i | \(0.736700\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.00000 | −0.407718 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.22315 | − | 14.7734i | −0.316341 | − | 0.750975i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.35506 | + | 2.35506i | −0.119406 | + | 0.119406i | −0.764285 | − | 0.644879i | \(-0.776908\pi\) |
0.644879 | + | 0.764285i | \(0.276908\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.76547 | −0.190428 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.82791 | + | 9.33537i | −0.0922058 | + | 0.470907i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.23175 | − | 4.23175i | −0.212923 | − | 0.212923i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.68879 | + | 4.68879i | −0.235324 | + | 0.235324i | −0.814910 | − | 0.579587i | \(-0.803214\pi\) |
0.579587 | + | 0.814910i | \(0.303214\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −20.4285 | − | 4.00000i | −1.02271 | − | 0.200250i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.18714i | 0.259033i | 0.991577 | + | 0.129517i | \(0.0413426\pi\) | ||||
−0.991577 | + | 0.129517i | \(0.958657\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.24914 | + | 4.24914i | 0.211665 | + | 0.211665i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 20.0048 | − | 0.239367i | 0.994048 | − | 0.0118943i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.22225i | 0.258858i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.8793i | 0.735734i | 0.929878 | + | 0.367867i | \(0.119912\pi\) | ||||
−0.929878 | + | 0.367867i | \(0.880088\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.92245 | − | 2.63790i | 0.193480 | − | 0.130118i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.73458 | + | 8.73458i | 0.429801 | + | 0.429801i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 8.20855i | − | 0.402942i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.0129898 | − | 0.0663404i | 0.000636111 | − | 0.00324870i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.3026 | − | 25.3026i | 1.23611 | − | 1.23611i | 0.274533 | − | 0.961578i | \(-0.411477\pi\) |
0.961578 | − | 0.274533i | \(-0.0885232\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.13187 | − | 7.13187i | −0.347586 | − | 0.347586i | 0.511623 | − | 0.859210i | \(-0.329044\pi\) |
−0.859210 | + | 0.511623i | \(0.829044\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.23453 | + | 10.3986i | −0.205890 | + | 0.505597i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.0975657 | 0.00473263 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.42504 | − | 9.42504i | 0.456110 | − | 0.456110i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.5674 | − | 7.10675i | 0.510200 | − | 0.343117i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.4882 | 0.746038 | 0.373019 | − | 0.927824i | \(-0.378323\pi\) | ||||
0.373019 | + | 0.927824i | \(0.378323\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.5500 | 1.22786 | 0.613928 | − | 0.789362i | \(-0.289588\pi\) | ||||
0.613928 | + | 0.789362i | \(0.289588\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14.6205 | + | 9.83249i | −0.700999 | + | 0.471432i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.55026 | + | 8.55026i | −0.409014 | + | 0.409014i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.63703 | −0.125859 | −0.0629293 | − | 0.998018i | \(-0.520044\pi\) | ||||
−0.0629293 | + | 0.998018i | \(0.520044\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.19656 | + | 5.39400i | −0.104598 | + | 0.256857i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.8580 | − | 14.8580i | −0.705927 | − | 0.705927i | 0.259749 | − | 0.965676i | \(-0.416360\pi\) |
−0.965676 | + | 0.259749i | \(0.916360\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.5569 | + | 11.5569i | −0.547850 | + | 0.547850i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.91617 | + | 30.2147i | −0.279825 | + | 1.42910i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 31.7079i | − | 1.49639i | −0.663480 | − | 0.748194i | \(-0.730921\pi\) | ||
0.663480 | − | 0.748194i | \(-0.269079\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.5569 | + | 11.5569i | 0.544194 | + | 0.544194i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 24.2390 | − | 16.3011i | 1.13885 | − | 0.765891i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 22.9733i | − | 1.07701i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 23.8759i | − | 1.11687i | −0.829550 | − | 0.558433i | \(-0.811403\pi\) | ||
0.829550 | − | 0.558433i | \(-0.188597\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.46480 | − | 1.76286i | 0.395103 | − | 0.0822833i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.921303 | + | 0.921303i | 0.0429094 | + | 0.0429094i | 0.728236 | − | 0.685327i | \(-0.240341\pi\) |
−0.685327 | + | 0.728236i | \(0.740341\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 26.1510i | − | 1.21534i | −0.794190 | − | 0.607670i | \(-0.792105\pi\) | ||
0.794190 | − | 0.607670i | \(-0.207895\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.94137 | + | 0.967542i | 0.229150 | + | 0.0448687i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.2510 | − | 16.2510i | 0.752005 | − | 0.752005i | −0.222848 | − | 0.974853i | \(-0.571535\pi\) |
0.974853 | + | 0.222848i | \(0.0715355\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.0552 | − | 18.0552i | −0.833711 | − | 0.833711i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.52588 | + | 12.9000i | −0.116386 | + | 0.594400i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.55026 | −0.393141 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.221543 | − | 0.221543i | 0.0101651 | − | 0.0101651i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.60245 | − | 3.80413i | −0.0733712 | − | 0.174179i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.7456 | 0.536669 | 0.268335 | − | 0.963326i | \(-0.413527\pi\) | ||||
0.268335 | + | 0.963326i | \(0.413527\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.9966 | −0.683784 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.91948 | − | 7.31506i | −0.223844 | − | 0.332847i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.91891 | − | 8.91891i | 0.404987 | − | 0.404987i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.783513 | 0.0355044 | 0.0177522 | − | 0.999842i | \(-0.494349\pi\) | ||||
0.0177522 | + | 0.999842i | \(0.494349\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 21.0938 | + | 4.13026i | 0.953893 | + | 0.186777i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.0382 | + | 10.0382i | 0.453018 | + | 0.453018i | 0.896355 | − | 0.443337i | \(-0.146206\pi\) |
−0.443337 | + | 0.896355i | \(0.646206\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.38445 | + | 5.38445i | −0.242504 | + | 0.242504i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.02447 | − | 9.88273i | 0.180886 | − | 0.444196i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 24.9543i | 1.11935i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.9655 | − | 29.9655i | −1.34144 | − | 1.34144i | −0.894627 | − | 0.446815i | \(-0.852558\pi\) |
−0.446815 | − | 0.894627i | \(-0.647442\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.4008 | − | 24.3872i | −0.732732 | − | 1.08954i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 21.7131i | − | 0.968138i | −0.875030 | − | 0.484069i | \(-0.839158\pi\) | ||
0.875030 | − | 0.484069i | \(-0.160842\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 32.4001i | − | 1.44179i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.84266 | + | 11.6617i | 0.348305 | + | 0.517914i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.1276 | − | 16.1276i | −0.714842 | − | 0.714842i | 0.252702 | − | 0.967544i | \(-0.418681\pi\) |
−0.967544 | + | 0.252702i | \(0.918681\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 14.3518i | − | 0.634886i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 15.2181 | − | 23.2240i | 0.671896 | − | 1.02536i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.7820 | + | 12.7820i | −0.563243 | + | 0.563243i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.23453 | + | 4.23453i | 0.186235 | + | 0.186235i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −39.2112 | − | 7.67774i | −1.72118 | − | 0.337015i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.68847 | 0.249216 | 0.124608 | − | 0.992206i | \(-0.460233\pi\) | ||||
0.124608 | + | 0.992206i | \(0.460233\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.6612 | − | 13.6612i | 0.597362 | − | 0.597362i | −0.342248 | − | 0.939610i | \(-0.611188\pi\) |
0.939610 | + | 0.342248i | \(0.111188\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.127467 | + | 0.189538i | 0.00556311 | + | 0.00827211i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.17614 | 0.0947941 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.8793 | 0.777361 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −15.1842 | + | 6.39619i | −0.658938 | + | 0.277571i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −33.1876 | + | 33.1876i | −1.43751 | + | 1.43751i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.55691 | −0.326714 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.630120 | + | 3.21811i | −0.0271917 | + | 0.138871i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.19656 | + | 2.19656i | 0.0946124 | + | 0.0946124i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.5715 | − | 24.5715i | 1.05641 | − | 1.05641i | 0.0581016 | − | 0.998311i | \(-0.481495\pi\) |
0.998311 | − | 0.0581016i | \(-0.0185047\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.6291 | + | 4.82248i | 1.05693 | + | 0.206953i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 28.0521i | − | 1.20162i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.56990 | + | 3.56990i | 0.152638 | + | 0.152638i | 0.779295 | − | 0.626657i | \(-0.215577\pi\) |
−0.626657 | + | 0.779295i | \(0.715577\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.90180 | + | 16.3845i | 0.294562 | + | 0.699273i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.4530i | 1.04173i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 6.05520i | − | 0.257493i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.4272 | + | 7.01244i | −0.442610 | + | 0.297662i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.1602 | − | 18.1602i | −0.769473 | − | 0.769473i | 0.208540 | − | 0.978014i | \(-0.433129\pi\) |
−0.978014 | + | 0.208540i | \(0.933129\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 24.5535i | − | 1.03850i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.886172 | − | 4.52579i | 0.0374142 | − | 0.191079i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.91748 | + | 6.91748i | −0.291537 | + | 0.291537i | −0.837687 | − | 0.546150i | \(-0.816093\pi\) |
0.546150 | + | 0.837687i | \(0.316093\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 24.9966 | + | 24.9966i | 1.05161 | + | 1.05161i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 14.4837 | + | 14.1412i | 0.608257 | + | 0.593873i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −36.2961 | −1.52161 | −0.760807 | − | 0.648979i | \(-0.775196\pi\) | ||||
−0.760807 | + | 0.648979i | \(0.775196\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.5224 | + | 33.5224i | −1.40287 | + | 1.40287i | −0.612056 | + | 0.790814i | \(0.709657\pi\) |
−0.790814 | + | 0.612056i | \(0.790343\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 35.2701 | − | 23.7196i | 1.47343 | − | 0.990901i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.132681 | 0.00553317 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.9345 | −0.788253 | −0.394127 | − | 0.919056i | \(-0.628953\pi\) | ||||
−0.394127 | + | 0.919056i | \(0.628953\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.0457 | + | 8.10092i | −0.500603 | + | 0.336663i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.87279 | − | 5.87279i | 0.243644 | − | 0.243644i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.20168 | −0.0911842 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 28.3799 | + | 11.5569i | 1.17336 | + | 0.477820i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −29.6211 | − | 29.6211i | −1.22259 | − | 1.22259i | −0.966707 | − | 0.255885i | \(-0.917633\pi\) |
−0.255885 | − | 0.966707i | \(-0.582367\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.94137 | − | 4.94137i | 0.203605 | − | 0.203605i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.607159 | + | 3.10084i | −0.0249752 | + | 0.127551i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.6263i | 0.888086i | 0.896005 | + | 0.444043i | \(0.146456\pi\) | ||||
−0.896005 | + | 0.444043i | \(0.853544\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.88273 | − | 5.88273i | −0.241169 | − | 0.241169i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.8270 | + | 12.6614i | −0.770539 | + | 0.518198i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 29.8079i | − | 1.21792i | −0.793201 | − | 0.608959i | \(-0.791587\pi\) | ||
0.793201 | − | 0.608959i | \(-0.208413\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 32.8432i | − | 1.33970i | −0.742495 | − | 0.669851i | \(-0.766358\pi\) | ||
0.742495 | − | 0.669851i | \(-0.233642\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 31.3872 | − | 13.2215i | 1.27818 | − | 0.538422i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.2658 | + | 13.2658i | 0.539331 | + | 0.539331i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 6.95597i | − | 0.282334i | −0.989986 | − | 0.141167i | \(-0.954915\pi\) | ||
0.989986 | − | 0.141167i | \(-0.0450855\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −17.4948 | − | 3.42557i | −0.708927 | − | 0.138811i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.1602 | + | 12.1602i | −0.491947 | + | 0.491947i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.5389 | + | 13.5389i | 0.546830 | + | 0.546830i | 0.925522 | − | 0.378693i | \(-0.123626\pi\) |
−0.378693 | + | 0.925522i | \(0.623626\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.55691 | + | 38.5942i | −0.304724 | + | 1.55627i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.91891 | 0.359062 | 0.179531 | − | 0.983752i | \(-0.442542\pi\) | ||||
0.179531 | + | 0.983752i | \(0.442542\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.64658 | + | 1.64658i | −0.0661818 | + | 0.0661818i | −0.739423 | − | 0.673241i | \(-0.764902\pi\) |
0.673241 | + | 0.739423i | \(0.264902\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.5114 | − | 2.39734i | 0.461936 | − | 0.0962018i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16.5367 | −0.662531 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.7034 | 0.988136 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.26451 | − | 12.2890i | −0.330053 | − | 0.490774i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.84014 | + | 3.84014i | −0.153116 | + | 0.153116i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.2457 | −0.766159 | −0.383080 | − | 0.923715i | \(-0.625137\pi\) | ||||
−0.383080 | + | 0.923715i | \(0.625137\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 20.3622 | + | 3.98701i | 0.809324 | + | 0.158469i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.6710 | + | 11.6710i | 0.463149 | + | 0.463149i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.30777 | + | 6.30777i | −0.249923 | + | 0.249923i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −30.8271 | − | 12.5535i | −1.21950 | − | 0.496608i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.6343i | 0.657016i | 0.944501 | + | 0.328508i | \(0.106546\pi\) | ||||
−0.944501 | + | 0.328508i | \(0.893454\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.77502 | − | 4.77502i | −0.188308 | − | 0.188308i | 0.606656 | − | 0.794964i | \(-0.292511\pi\) |
−0.794964 | + | 0.606656i | \(0.792511\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.4813 | − | 17.0722i | −0.452075 | − | 0.672217i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 48.2095i | − | 1.89531i | −0.319293 | − | 0.947656i | \(-0.603445\pi\) | ||
0.319293 | − | 0.947656i | \(-0.396555\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.78801i | 0.344960i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.84306 | + | 4.22752i | 0.111428 | + | 0.165689i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.2281 | − | 24.2281i | −0.948121 | − | 0.948121i | 0.0505983 | − | 0.998719i | \(-0.483887\pi\) |
−0.998719 | + | 0.0505983i | \(0.983887\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.2086i | 0.477028i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 17.7294 | + | 7.21979i | 0.691689 | + | 0.281671i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.47442 | + | 9.47442i | −0.369071 | + | 0.369071i | −0.867138 | − | 0.498067i | \(-0.834043\pi\) |
0.498067 | + | 0.867138i | \(0.334043\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.0406 | − | 23.0406i | −0.896175 | − | 0.896175i | 0.0989204 | − | 0.995095i | \(-0.468461\pi\) |
−0.995095 | + | 0.0989204i | \(0.968461\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.9966 | + | 2.54479i | 0.504745 | + | 0.0988313i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −26.7159 | −1.03600 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.32238 | + | 7.32238i | −0.283524 | + | 0.283524i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.8506 | + | 31.0039i | 0.806130 | + | 1.19868i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.48269 | 0.366075 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.7846 | 1.14811 | 0.574055 | − | 0.818816i | \(-0.305369\pi\) | ||||
0.574055 | + | 0.818816i | \(0.305369\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.298267 | + | 0.0621166i | −0.0114803 | + | 0.00239087i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.59631 | − | 5.59631i | 0.215084 | − | 0.215084i | −0.591339 | − | 0.806423i | \(-0.701401\pi\) |
0.806423 | + | 0.591339i | \(0.201401\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.7620 | 0.489762 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.88503 | − | 40.2699i | 0.302155 | − | 1.54314i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.5790 | − | 19.5790i | −0.749168 | − | 0.749168i | 0.225155 | − | 0.974323i | \(-0.427711\pi\) |
−0.974323 | + | 0.225155i | \(0.927711\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.28973 | − | 4.28973i | 0.163902 | − | 0.163902i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.09231 | + | 1.58451i | 0.308741 | + | 0.0604529i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 6.32248i | − | 0.240867i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.98701 | + | 3.98701i | 0.151673 | + | 0.151673i | 0.778865 | − | 0.627192i | \(-0.215796\pi\) |
−0.627192 | + | 0.778865i | \(0.715796\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.94988 | − | 4.19129i | 0.377965 | − | 0.159214i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 0.0867582i | − | 0.00329093i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.9966i | 0.643791i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.720541 | + | 0.484574i | −0.0272534 | + | 0.0183283i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.2117 | + | 15.2117i | 0.574537 | + | 0.574537i | 0.933393 | − | 0.358856i | \(-0.116833\pi\) |
−0.358856 | + | 0.933393i | \(0.616833\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.4396i | 0.657749i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.76891 | + | 14.1412i | −0.104283 | + | 0.532587i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 23.1806 | − | 23.1806i | 0.871796 | − | 0.871796i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.3009 | − | 20.3009i | −0.762416 | − | 0.762416i | 0.214342 | − | 0.976759i | \(-0.431239\pi\) |
−0.976759 | + | 0.214342i | \(0.931239\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.48024 | + | 3.04612i | 0.280531 | + | 0.114238i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.95936 | 0.110829 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.5569 | − | 11.5569i | 0.432204 | − | 0.432204i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −43.7768 | + | 29.4405i | −1.63488 | + | 1.09948i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.52314 | −0.131391 | −0.0656954 | − | 0.997840i | \(-0.520927\pi\) | ||||
−0.0656954 | + | 0.997840i | \(0.520927\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.2897 | −0.681145 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 22.2702 | − | 14.9770i | 0.828236 | − | 0.557000i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.189728 | − | 0.189728i | 0.00704631 | − | 0.00704631i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.3664 | −0.755348 | −0.377674 | − | 0.925939i | \(-0.623276\pi\) | ||||
−0.377674 | + | 0.925939i | \(0.623276\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24.7553 | + | 10.7785i | −0.916863 | + | 0.399202i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.28736 | − | 6.28736i | −0.232547 | − | 0.232547i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.48024 | + | 2.48024i | −0.0916096 | + | 0.0916096i | −0.751426 | − | 0.659817i | \(-0.770634\pi\) |
0.659817 | + | 0.751426i | \(0.270634\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.43630 | + | 7.33537i | −0.0529787 | + | 0.270569i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 18.1656i | − | 0.669140i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.7931 | + | 15.7931i | 0.580957 | + | 0.580957i | 0.935166 | − | 0.354209i | \(-0.115250\pi\) |
−0.354209 | + | 0.935166i | \(0.615250\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 35.2898 | − | 23.7329i | 1.29640 | − | 0.871849i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.5942i | 1.41588i | 0.706271 | + | 0.707941i | \(0.250376\pi\) | ||||
−0.706271 | + | 0.707941i | \(0.749624\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 39.5139i | 1.44768i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.30055 | + | 10.2093i | 0.157349 | + | 0.373537i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.40658 | − | 5.40658i | −0.197552 | − | 0.197552i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.6527i | 0.644156i | 0.946713 | + | 0.322078i | \(0.104381\pi\) | ||||
−0.946713 | + | 0.322078i | \(0.895619\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −29.3906 | − | 5.75481i | −1.07105 | − | 0.209717i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 26.5086 | − | 26.5086i | 0.964747 | − | 0.964747i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.7440 | + | 32.7440i | 1.19010 | + | 1.19010i | 0.977039 | + | 0.213062i | \(0.0683435\pi\) |
0.213062 | + | 0.977039i | \(0.431657\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.20512 | − | 6.15468i | 0.0437429 | − | 0.223401i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.69113 | −0.242553 | −0.121277 | − | 0.992619i | \(-0.538699\pi\) | ||||
−0.121277 | + | 0.992619i | \(0.538699\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.0698 | − | 20.0698i | 0.726576 | − | 0.726576i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.2265 | − | 4.30783i | 0.369741 | − | 0.155750i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −25.2362 | −0.911227 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.03265 | −0.181482 | −0.0907411 | − | 0.995875i | \(-0.528924\pi\) | ||||
−0.0907411 | + | 0.995875i | \(0.528924\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.23499 | + | 10.7581i | 0.260562 | + | 0.387445i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.6859 | − | 10.6859i | 0.384344 | − | 0.384344i | −0.488320 | − | 0.872665i | \(-0.662390\pi\) |
0.872665 | + | 0.488320i | \(0.162390\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.0766789 | −0.00275439 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12.4772 | − | 2.44309i | −0.447616 | − | 0.0876452i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 38.5942 | + | 38.5942i | 1.38278 | + | 1.38278i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.5535 | + | 12.5535i | −0.449199 | + | 0.449199i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 13.0327 | − | 19.8888i | 0.465750 | − | 0.710769i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.8703i | 0.602126i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.0974 | + | 16.0974i | 0.573810 | + | 0.573810i | 0.933191 | − | 0.359381i | \(-0.117012\pi\) |
−0.359381 | + | 0.933191i | \(0.617012\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.92281 | + | 14.7548i | 0.353262 | + | 0.525285i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 35.7675i | 1.27175i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.2311i | 0.967005i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.95641 | − | 4.39606i | −0.104853 | − | 0.155912i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.63695 | + | 2.63695i | 0.0934055 | + | 0.0934055i | 0.752266 | − | 0.658860i | \(-0.228961\pi\) |
−0.658860 | + | 0.752266i | \(0.728961\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.22766i | 0.220319i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.31894 | − | 20.4285i | 0.293935 | − | 0.721806i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.21979 | − | 7.21979i | 0.254781 | − | 0.254781i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.00000 | − | 8.00000i | −0.281963 | − | 0.281963i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.65775 | + | 1.30362i | 0.234364 | + | 0.0458896i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.62090 | 0.232778 | 0.116389 | − | 0.993204i | \(-0.462868\pi\) | ||||
0.116389 | + | 0.993204i | \(0.462868\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.01299 | − | 4.01299i | 0.140915 | − | 0.140915i | −0.633130 | − | 0.774045i | \(-0.718230\pi\) |
0.774045 | + | 0.633130i | \(0.218230\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −27.7267 | − | 41.2284i | −0.972417 | − | 1.44594i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 27.5859 | 0.966291 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28.5535 | −0.998960 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.0360 | + | 28.5727i | 0.420571 | + | 0.998411i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.91085 | + | 7.91085i | −0.276090 | + | 0.276090i | −0.831546 | − | 0.555456i | \(-0.812544\pi\) |
0.555456 | + | 0.831546i | \(0.312544\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44.9751 | 1.56773 | 0.783866 | − | 0.620930i | \(-0.213245\pi\) | ||||
0.783866 | + | 0.620930i | \(0.213245\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.0312253 | + | 0.159472i | −0.00108713 | + | 0.00555210i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.75631 | − | 9.75631i | −0.339260 | − | 0.339260i | 0.516829 | − | 0.856089i | \(-0.327112\pi\) |
−0.856089 | + | 0.516829i | \(0.827112\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.6336 | + | 18.6336i | −0.647171 | + | 0.647171i | −0.952308 | − | 0.305137i | \(-0.901298\pi\) |
0.305137 | + | 0.952308i | \(0.401298\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.93763 | − | 0.379397i | −0.0672156 | − | 0.0131611i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.23044i | 0.111928i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26.6707 | − | 26.6707i | −0.922979 | − | 0.922979i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.65266 | + | 1.38547i | −0.229949 | + | 0.0478888i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 37.8109i | − | 1.30538i | −0.757626 | − | 0.652689i | \(-0.773641\pi\) | ||
0.757626 | − | 0.652689i | \(-0.226359\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 8.05863i | − | 0.277884i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −32.0837 | + | 21.5767i | −1.10502 | + | 0.743142i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.7536 | + | 12.7536i | 0.438739 | + | 0.438739i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.9820i | 0.652228i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.80444 | + | 19.4298i | −0.130568 | + | 0.666828i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.22225 | + | 5.22225i | −0.179017 | + | 0.179017i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.0992 | − | 24.0992i | −0.825142 | − | 0.825142i | 0.161699 | − | 0.986840i | \(-0.448303\pi\) |
−0.986840 | + | 0.161699i | \(0.948303\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13.4396 | − | 33.0033i | 0.459626 | − | 1.12869i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.794026 | 0.0271234 | 0.0135617 | − | 0.999908i | \(-0.495683\pi\) | ||||
0.0135617 | + | 0.999908i | \(0.495683\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.65775 | − | 2.65775i | 0.0906814 | − | 0.0906814i | −0.660311 | − | 0.750992i | \(-0.729576\pi\) |
0.750992 | + | 0.660311i | \(0.229576\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −33.0187 | + | 22.2055i | −1.12527 | + | 0.756762i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.4069 | 0.728699 | 0.364349 | − | 0.931262i | \(-0.381291\pi\) | ||||
0.364349 | + | 0.931262i | \(0.381291\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −51.2794 | −1.74355 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20.4538 | + | 13.7555i | −0.694648 | + | 0.467161i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.04612 | − | 3.04612i | 0.103332 | − | 0.103332i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 52.1656 | 1.76756 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.42004 | + | 15.7655i | −0.217286 | + | 0.533580i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 17.8837 | + | 17.8837i | 0.604581 | + | 0.604581i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.0923 | − | 20.0923i | 0.678470 | − | 0.678470i | −0.281184 | − | 0.959654i | \(-0.590727\pi\) |
0.959654 | + | 0.281184i | \(0.0907270\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.00274 | + | 15.3354i | −0.101280 | + | 0.517249i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.8132i | 0.364305i | 0.983270 | + | 0.182152i | \(0.0583064\pi\) | ||||
−0.983270 | + | 0.182152i | \(0.941694\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.5665 | + | 12.5665i | 0.422895 | + | 0.422895i | 0.886199 | − | 0.463304i | \(-0.153336\pi\) |
−0.463304 | + | 0.886199i | \(0.653336\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −17.5469 | + | 11.8005i | −0.589833 | + | 0.396671i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.0977i | 0.406201i | 0.979158 | + | 0.203101i | \(0.0651018\pi\) | ||||
−0.979158 | + | 0.203101i | \(0.934898\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.7000i | 0.560099i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.172302 | + | 14.4000i | 0.00577235 | + | 0.482417i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.1412 | + | 14.1412i | 0.473216 | + | 0.473216i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.20855i | 0.140676i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.6742 | + | 3.46069i | 0.590124 | + | 0.115549i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.23175 | − | 4.23175i | 0.141137 | − | 0.141137i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.61899 | − | 1.61899i | −0.0539362 | − | 0.0539362i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.00000 | − | 20.4285i | 0.133112 | − | 0.679819i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 32.2092 | 1.07067 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.3388 | + | 14.3388i | −0.476112 | + | 0.476112i | −0.903886 | − | 0.427774i | \(-0.859298\pi\) |
0.427774 | + | 0.903886i | \(0.359298\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.9748 | + | 40.2972i | 0.563018 | + | 1.33657i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.0629 | −0.929765 | −0.464882 | − | 0.885372i | \(-0.653903\pi\) | ||||
−0.464882 | + | 0.885372i | \(0.653903\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.90871 | 0.195550 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.7334 | + | 18.9340i | 0.420952 | + | 0.625937i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.73458 | + | 8.73458i | −0.288441 | + | 0.288441i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.4734 | −0.840289 | −0.420144 | − | 0.907457i | \(-0.638021\pi\) | ||||
−0.420144 | + | 0.907457i | \(0.638021\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.8364 | + | 3.10084i | 0.521827 | + | 0.102176i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −36.0494 | − | 36.0494i | −1.18658 | − | 1.18658i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.135312 | − | 0.135312i | 0.00444903 | − | 0.00444903i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.20080 | − | 22.5941i | 0.302194 | − | 0.742086i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 43.3502i | − | 1.42227i | −0.703054 | − | 0.711137i | \(-0.748181\pi\) | ||
0.703054 | − | 0.711137i | \(-0.251819\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.33537 | + | 7.33537i | 0.240407 | + | 0.240407i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.21016 | + | 13.6951i | 0.301527 | + | 0.448358i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 5.91872i | − | 0.193563i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 15.5500i | − | 0.507998i | −0.967205 | − | 0.253999i | \(-0.918254\pi\) | ||
0.967205 | − | 0.253999i | \(-0.0817459\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.3279 | − | 36.1745i | −0.793910 | − | 1.18051i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.85373 | + | 1.85373i | 0.0604299 | + | 0.0604299i | 0.736676 | − | 0.676246i | \(-0.236394\pi\) |
−0.676246 | + | 0.736676i | \(0.736394\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.1138i | 0.752690i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 21.7294 | + | 14.2387i | 0.706857 | + | 0.463186i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.2499 | + | 31.2499i | −1.01549 | + | 1.01549i | −0.0156087 | + | 0.999878i | \(0.504969\pi\) |
−0.999878 | + | 0.0156087i | \(0.995031\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.7328 | + | 20.7328i | 0.673016 | + | 0.673016i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −37.3285 | − | 7.30909i | −1.21046 | − | 0.237014i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48.9411 | 1.58536 | 0.792679 | − | 0.609639i | \(-0.208686\pi\) | ||||
0.792679 | + | 0.609639i | \(0.208686\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 38.5726 | − | 38.5726i | 1.24818 | − | 1.24818i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.07766 | − | 10.5242i | −0.228788 | − | 0.340199i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.13815 | 0.198211 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.2897 | 0.944830 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.39880 | − | 3.95915i | 0.302872 | − | 0.127582i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13.1736 | + | 13.1736i | −0.424074 | + | 0.424074i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.5129 | −0.595334 | −0.297667 | − | 0.954670i | \(-0.596209\pi\) | ||||
−0.297667 | + | 0.954670i | \(0.596209\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.95936 | − | 15.1138i | 0.0950683 | − | 0.485526i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.0663404 | + | 0.0663404i | 0.00212897 | + | 0.00212897i | 0.708170 | − | 0.706041i | \(-0.249521\pi\) |
−0.706041 | + | 0.708170i | \(0.749521\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.0620710 | − | 0.0620710i | 0.00198991 | − | 0.00198991i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.457950 | − | 0.0896687i | −0.0146661 | − | 0.00287170i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 3.42557i | − | 0.109594i | −0.998498 | − | 0.0547969i | \(-0.982549\pi\) | ||
0.998498 | − | 0.0547969i | \(-0.0174511\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.31894 | − | 8.31894i | −0.265875 | − | 0.265875i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.6968 | + | 34.8893i | 0.469232 | + | 1.11393i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.5911i | 0.975706i | 0.872926 | + | 0.487853i | \(0.162220\pi\) | ||||
−0.872926 | + | 0.487853i | \(0.837780\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.05520i | 0.129209i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.0983 | + | 8.13626i | −0.385092 | + | 0.258980i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.55026 | − | 8.55026i | −0.271882 | − | 0.271882i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 24.2975i | − | 0.771834i | −0.922533 | − | 0.385917i | \(-0.873885\pi\) | ||
0.922533 | − | 0.385917i | \(-0.126115\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.21811 | + | 6.22102i | −0.0386554 | + | 0.197418i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20.5899 | + | 20.5899i | −0.652743 | + | 0.652743i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.3078 | − | 10.3078i | −0.326450 | − | 0.326450i | 0.524785 | − | 0.851235i | \(-0.324146\pi\) |
−0.851235 | + | 0.524785i | \(0.824146\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.29478 | − | 14.1845i | 0.294074 | − | 0.448779i |
(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 | 384.2.k.a.287.2 | 12 | ||
3.2 | odd | 2 | inner | 384.2.k.a.287.5 | 12 | ||
4.3 | odd | 2 | 384.2.k.b.287.5 | 12 | |||
8.3 | odd | 2 | 48.2.k.a.11.4 | yes | 12 | ||
8.5 | even | 2 | 192.2.k.a.143.5 | 12 | |||
12.11 | even | 2 | 384.2.k.b.287.2 | 12 | |||
16.3 | odd | 4 | inner | 384.2.k.a.95.5 | 12 | ||
16.5 | even | 4 | 48.2.k.a.35.3 | yes | 12 | ||
16.11 | odd | 4 | 192.2.k.a.47.2 | 12 | |||
16.13 | even | 4 | 384.2.k.b.95.2 | 12 | |||
24.5 | odd | 2 | 192.2.k.a.143.2 | 12 | |||
24.11 | even | 2 | 48.2.k.a.11.3 | ✓ | 12 | ||
48.5 | odd | 4 | 48.2.k.a.35.4 | yes | 12 | ||
48.11 | even | 4 | 192.2.k.a.47.5 | 12 | |||
48.29 | odd | 4 | 384.2.k.b.95.5 | 12 | |||
48.35 | even | 4 | inner | 384.2.k.a.95.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.2.k.a.11.3 | ✓ | 12 | 24.11 | even | 2 | ||
48.2.k.a.11.4 | yes | 12 | 8.3 | odd | 2 | ||
48.2.k.a.35.3 | yes | 12 | 16.5 | even | 4 | ||
48.2.k.a.35.4 | yes | 12 | 48.5 | odd | 4 | ||
192.2.k.a.47.2 | 12 | 16.11 | odd | 4 | |||
192.2.k.a.47.5 | 12 | 48.11 | even | 4 | |||
192.2.k.a.143.2 | 12 | 24.5 | odd | 2 | |||
192.2.k.a.143.5 | 12 | 8.5 | even | 2 | |||
384.2.k.a.95.2 | 12 | 48.35 | even | 4 | inner | ||
384.2.k.a.95.5 | 12 | 16.3 | odd | 4 | inner | ||
384.2.k.a.287.2 | 12 | 1.1 | even | 1 | trivial | ||
384.2.k.a.287.5 | 12 | 3.2 | odd | 2 | inner | ||
384.2.k.b.95.2 | 12 | 16.13 | even | 4 | |||
384.2.k.b.95.5 | 12 | 48.29 | odd | 4 | |||
384.2.k.b.287.2 | 12 | 12.11 | even | 2 | |||
384.2.k.b.287.5 | 12 | 4.3 | odd | 2 |