Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [192,2,Mod(47,192)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(192, 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("192.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.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: | \(1.53312771881\) |
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 | 47.5 | ||
Root | \(1.35164 - 0.416001i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 192.47 |
Dual form | 192.2.k.a.143.5 |
$q$-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 \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(133\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 | \(-0.0844130\pi\) |
−0.262094 | + | 0.965042i | \(0.584413\pi\) | |||||||
\(6\) | 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 | \(-0.672451\pi\) |
0.856798 | + | 0.515653i | \(0.172451\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.24914 | − | 3.24914i | −0.901149 | − | 0.901149i | 0.0943862 | − | 0.995536i | \(-0.469911\pi\) |
−0.995536 | + | 0.0943862i | \(0.969911\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.739839 | + | 3.77846i | 0.191026 | + | 0.975593i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.66400i | 0.403580i | 0.979429 | + | 0.201790i | \(0.0646758\pi\) | ||||
−0.979429 | + | 0.201790i | \(0.935324\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.77846 | − | 3.77846i | 0.866838 | − | 0.866838i | −0.125283 | − | 0.992121i | \(-0.539984\pi\) |
0.992121 | + | 0.125283i | \(0.0399840\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.23261 | − | 2.17397i | −0.705412 | − | 0.474400i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.26290i | 0.471847i | 0.971772 | + | 0.235923i | \(0.0758114\pi\) | ||||
−0.971772 | + | 0.235923i | \(0.924189\pi\) | |||||||
\(24\) | 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 | \(-0.610314\pi\) |
0.940546 | + | 0.339665i | \(0.110314\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.30777i | − | 0.234883i | −0.993080 | − | 0.117442i | \(-0.962531\pi\) | ||
0.993080 | − | 0.117442i | \(-0.0374693\pi\) | |||||||
\(32\) | 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 | \(-0.663547\pi\) |
0.870884 | + | 0.491488i | \(0.163547\pi\) | |||||||
\(38\) | 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 | \(-0.383579\pi\) |
−0.933857 | + | 0.357647i | \(0.883579\pi\) | |||||||
\(44\) | 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 | \(-0.280126\pi\) |
−0.770765 | + | 0.637120i | \(0.780126\pi\) | |||||||
\(54\) | 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 | \(-0.633627\pi\) |
0.913170 | + | 0.407579i | \(0.133627\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.19051 | + | 4.19051i | 0.536539 | + | 0.536539i | 0.922511 | − | 0.385971i | \(-0.126134\pi\) |
−0.385971 | + | 0.922511i | \(0.626134\pi\) | |||||||
\(62\) | 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 | \(-0.993923\pi\) |
0.0190906 | + | 0.999818i | \(0.493923\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.18727 | + | 3.25238i | −0.263316 | + | 0.391540i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.0950i | 1.31674i | 0.752695 | + | 0.658370i | \(0.228754\pi\) | ||||
−0.752695 | + | 0.658370i | \(0.771246\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.38101i | − | 0.746841i | −0.927662 | − | 0.373421i | \(-0.878185\pi\) | ||
0.927662 | − | 0.373421i | \(-0.121815\pi\) | |||||||
\(74\) | 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 | \(-0.951606\pi\) | ||
0.988465 | − | 0.151450i | \(-0.0483941\pi\) | |||||||
\(80\) | 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 | \(-0.185040\pi\) |
−0.549129 | + | 0.835738i | \(0.685040\pi\) | |||||||
\(84\) | 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 | 0.999666 | + | 0.0258621i | \(0.00823308\pi\) |
0.0258621 | + | 0.999666i | \(0.491767\pi\) | |||||||
\(102\) | 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 | \(-0.802544\pi\) |
0.581301 | + | 0.813689i | \(0.302544\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.92332 | + | 8.92332i | 0.854699 | + | 0.854699i | 0.990708 | − | 0.136009i | \(-0.0434275\pi\) |
−0.136009 | + | 0.990708i | \(0.543427\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.54752 | − | 1.08623i | 0.526548 | − | 0.103100i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.9027i | 1.49600i | 0.663697 | + | 0.748002i | \(0.268986\pi\) | ||||
−0.663697 | + | 0.748002i | \(0.731014\pi\) | |||||||
\(114\) | 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 | \(0.106858\pi\) | ||||
−0.944179 | + | 0.329433i | \(0.893142\pi\) | |||||||
\(128\) | 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 | \(-0.327123\pi\) |
−0.856106 | + | 0.516801i | \(0.827123\pi\) | |||||||
\(132\) | 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 | \(-0.249473\pi\) |
−0.705935 | + | 0.708276i | \(0.749473\pi\) | |||||||
\(140\) | 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 | −0.999545 | − | 0.0301744i | \(-0.990394\pi\) |
−0.0301744 | − | 0.999545i | \(-0.509606\pi\) | |||||||
\(150\) | 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 | \(-0.347936\pi\) |
−0.888044 | + | 0.459758i | \(0.847936\pi\) | |||||||
\(158\) | 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 | \(-0.588454\pi\) |
0.961637 | + | 0.274325i | \(0.0884543\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.11222 | + | 3.43804i | 0.397986 | + | 0.267651i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 16.9678i | − | 1.31301i | −0.754321 | − | 0.656505i | \(-0.772034\pi\) | ||
0.754321 | − | 0.656505i | \(-0.227966\pi\) | |||||||
\(168\) | 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 | −0.280241 | + | 0.959930i | \(0.590414\pi\) |
−0.959930 | + | 0.280241i | \(0.909586\pi\) | |||||||
\(174\) | 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 | \(-0.272541\pi\) |
−0.755365 | + | 0.655304i | \(0.772541\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.2457 | − | 10.2457i | 0.761557 | − | 0.761557i | −0.215047 | − | 0.976604i | \(-0.568990\pi\) |
0.976604 | + | 0.215047i | \(0.0689904\pi\) | |||||||
\(182\) | 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 | \(-0.270701\pi\) |
−0.751565 | + | 0.659659i | \(0.770701\pi\) | |||||||
\(198\) | 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 | \(-0.614709\pi\) |
0.935766 | + | 0.352621i | \(0.114709\pi\) | |||||||
\(212\) | 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 | \(0.256900\pi\) | ||||
−0.691613 | + | 0.722268i | \(0.743100\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.162910 | − | 0.0663404i | 0.0108606 | − | 0.00442269i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.7523 | + | 16.7523i | 1.11189 | + | 1.11189i | 0.992895 | + | 0.118994i | \(0.0379668\pi\) |
0.118994 | + | 0.992895i | \(0.462033\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.36641 | − | 3.36641i | 0.222458 | − | 0.222458i | −0.587074 | − | 0.809533i | \(-0.699720\pi\) |
0.809533 | + | 0.587074i | \(0.199720\pi\) | |||||||
\(230\) | 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 | \(-0.933734\pi\) |
0.206679 | + | 0.978409i | \(0.433734\pi\) | |||||||
\(252\) | 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 | \(0.0750033\pi\) | ||||
−0.972367 | + | 0.233455i | \(0.924997\pi\) | |||||||
\(258\) | 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 | \(0.102512\pi\) | ||||
−0.948589 | + | 0.316511i | \(0.897488\pi\) | |||||||
\(264\) | 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 | \(-0.711901\pi\) |
0.786481 | + | 0.617614i | \(0.211901\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 28.6854i | − | 1.74251i | −0.490830 | − | 0.871255i | \(-0.663306\pi\) | ||
0.490830 | − | 0.871255i | \(-0.336694\pi\) | |||||||
\(272\) | 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 | \(-0.760903\pi\) |
0.682476 | + | 0.730908i | \(0.260903\pi\) | |||||||
\(278\) | 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 | \(-0.360341\pi\) |
−0.905282 | + | 0.424810i | \(0.860341\pi\) | |||||||
\(284\) | 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 | \(-0.334889\pi\) |
−0.868458 | + | 0.495762i | \(0.834889\pi\) | |||||||
\(294\) | 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 | \(-0.664341\pi\) |
0.869655 | + | 0.493661i | \(0.164341\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.6876 | + | 7.86010i | 0.664887 | + | 0.447146i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.52861i | 0.540318i | 0.962816 | + | 0.270159i | \(0.0870763\pi\) | ||||
−0.962816 | + | 0.270159i | \(0.912924\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 25.1690i | − | 1.42264i | −0.702870 | − | 0.711319i | \(-0.748098\pi\) | ||
0.702870 | − | 0.711319i | \(-0.251902\pi\) | |||||||
\(314\) | 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 | \(-0.961540\pi\) |
0.120532 | + | 0.992709i | \(0.461540\pi\) | |||||||
\(318\) | 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 | \(-0.282071\pi\) |
−0.774644 | + | 0.632397i | \(0.782071\pi\) | |||||||
\(332\) | 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 | \(-0.832134\pi\) |
0.503260 | + | 0.864135i | \(0.332134\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.75086 | − | 2.75086i | −0.147250 | − | 0.147250i | 0.629638 | − | 0.776888i | \(-0.283203\pi\) |
−0.776888 | + | 0.629638i | \(0.783203\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 19.9706 | − | 13.0862i | 1.06595 | − | 0.698491i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 23.1928i | − | 1.23443i | −0.786796 | − | 0.617213i | \(-0.788262\pi\) | ||
0.786796 | − | 0.617213i | \(-0.211738\pi\) | |||||||
\(354\) | 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 | \(-0.743144\pi\) | ||
0.691713 | − | 0.722172i | \(-0.256856\pi\) | |||||||
\(360\) | 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 | \(-0.762130\pi\) | ||
0.733533 | − | 0.679654i | \(-0.237870\pi\) | |||||||
\(368\) | 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 | \(-0.909651\pi\) |
0.280044 | + | 0.959987i | \(0.409651\pi\) | |||||||
\(374\) | 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 | \(-0.0314496\pi\) |
−0.0986413 | + | 0.995123i | \(0.531450\pi\) | |||||||
\(380\) | 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 | \(-0.223092\pi\) |
−0.644879 | + | 0.764285i | \(0.723092\pi\) | |||||||
\(390\) | 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 | \(-0.196786\pi\) |
−0.579587 | + | 0.814910i | \(0.696786\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −20.4285 | + | 4.00000i | −1.02271 | + | 0.200250i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 5.18714i | − | 0.259033i | −0.991577 | − | 0.129517i | \(-0.958657\pi\) | ||
0.991577 | − | 0.129517i | \(-0.0413426\pi\) | |||||||
\(402\) | 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 | \(-0.880088\pi\) | ||
0.929878 | − | 0.367867i | \(-0.119912\pi\) | |||||||
\(410\) | 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 | −0.961578 | − | 0.274533i | \(-0.911477\pi\) |
−0.274533 | − | 0.961578i | \(-0.588523\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.13187 | − | 7.13187i | 0.347586 | − | 0.347586i | −0.511623 | − | 0.859210i | \(-0.670956\pi\) |
0.859210 | + | 0.511623i | \(0.170956\pi\) | |||||||
\(422\) | 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 | \(-0.583640\pi\) |
0.965676 | + | 0.259749i | \(0.0836399\pi\) | |||||||
\(444\) | 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 | \(0.269079\pi\) | ||||
−0.663480 | + | 0.748194i | \(0.730921\pi\) | |||||||
\(450\) | 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 | \(0.188597\pi\) | ||||
−0.829550 | + | 0.558433i | \(0.811403\pi\) | |||||||
\(458\) | 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 | \(-0.759659\pi\) |
0.685327 | + | 0.728236i | \(0.259659\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.1510i | 1.21534i | 0.794190 | + | 0.607670i | \(0.207895\pi\) | ||||
−0.794190 | + | 0.607670i | \(0.792105\pi\) | |||||||
\(464\) | 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 | \(-0.428465\pi\) |
−0.974853 | + | 0.222848i | \(0.928465\pi\) | |||||||
\(468\) | 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 | \(-0.853794\pi\) |
0.443337 | + | 0.896355i | \(0.353794\pi\) | |||||||
\(492\) | 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 | 0.446815 | − | 0.894627i | \(-0.352558\pi\) |
0.894627 | − | 0.446815i | \(-0.147442\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.4008 | − | 24.3872i | 0.732732 | − | 1.08954i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.7131i | 0.968138i | 0.875030 | + | 0.484069i | \(0.160842\pi\) | ||||
−0.875030 | + | 0.484069i | \(0.839158\pi\) | |||||||
\(504\) | 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 | \(-0.581319\pi\) |
0.967544 | + | 0.252702i | \(0.0813192\pi\) | |||||||
\(510\) | 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 | \(-0.388812\pi\) |
−0.939610 | + | 0.342248i | \(0.888812\pi\) | |||||||
\(524\) | 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 | −0.998311 | − | 0.0581016i | \(-0.981495\pi\) |
−0.0581016 | − | 0.998311i | \(-0.518505\pi\) | |||||||
\(542\) | 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 | \(-0.784423\pi\) |
0.626657 | + | 0.779295i | \(0.284423\pi\) | |||||||
\(548\) | 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 | \(-0.566871\pi\) |
0.978014 | + | 0.208540i | \(0.0668713\pi\) | |||||||
\(558\) | 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 | \(-0.183907\pi\) |
−0.546150 | + | 0.837687i | \(0.683907\pi\) | |||||||
\(564\) | 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 | 0.790814 | + | 0.612056i | \(0.209657\pi\) |
0.612056 | + | 0.790814i | \(0.290343\pi\) | |||||||
\(572\) | 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 | 0.255885 | − | 0.966707i | \(-0.417633\pi\) |
0.966707 | − | 0.255885i | \(-0.0823667\pi\) | |||||||
\(588\) | 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 | \(-0.853544\pi\) | ||
0.896005 | − | 0.444043i | \(-0.146456\pi\) | |||||||
\(594\) | 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 | \(0.208413\pi\) | ||||
−0.793201 | + | 0.608959i | \(0.791587\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.8432i | 1.33970i | 0.742495 | + | 0.669851i | \(0.233642\pi\) | ||||
−0.742495 | + | 0.669851i | \(0.766358\pi\) | |||||||
\(602\) | 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 | \(0.0450855\pi\) | ||||
−0.989986 | + | 0.141167i | \(0.954915\pi\) | |||||||
\(608\) | 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 | \(-0.876374\pi\) |
0.378693 | + | 0.925522i | \(0.376374\pi\) | |||||||
\(614\) | 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 | \(-0.235098\pi\) |
−0.673241 | + | 0.739423i | \(0.735098\pi\) | |||||||
\(620\) | 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 | \(-0.893454\pi\) | ||
0.944501 | − | 0.328508i | \(-0.106546\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.77502 | − | 4.77502i | 0.188308 | − | 0.188308i | −0.606656 | − | 0.794964i | \(-0.707489\pi\) |
0.794964 | + | 0.606656i | \(0.207489\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.4813 | − | 17.0722i | 0.452075 | − | 0.672217i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 48.2095i | 1.89531i | 0.319293 | + | 0.947656i | \(0.396555\pi\) | ||||
−0.319293 | + | 0.947656i | \(0.603445\pi\) | |||||||
\(648\) | 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 | \(-0.516113\pi\) |
0.998719 | + | 0.0505983i | \(0.0161128\pi\) | |||||||
\(654\) | 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 | \(-0.165957\pi\) |
−0.498067 | + | 0.867138i | \(0.665957\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.0406 | − | 23.0406i | 0.896175 | − | 0.896175i | −0.0989204 | − | 0.995095i | \(-0.531539\pi\) |
0.995095 | + | 0.0989204i | \(0.0315389\pi\) | |||||||
\(662\) | 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 | \(-0.298599\pi\) |
−0.806423 | + | 0.591339i | \(0.798599\pi\) | |||||||
\(678\) | 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 | \(-0.572289\pi\) |
0.974323 | + | 0.225155i | \(0.0722887\pi\) | |||||||
\(684\) | 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 | \(-0.784204\pi\) |
0.627192 | + | 0.778865i | \(0.284204\pi\) | |||||||
\(692\) | 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 | \(-0.883167\pi\) |
0.358856 | + | 0.933393i | \(0.383167\pi\) | |||||||
\(702\) | 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 | \(-0.568761\pi\) |
0.976759 | + | 0.214342i | \(0.0687608\pi\) | |||||||
\(710\) | 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 | \(-0.229366\pi\) |
−0.659817 | + | 0.751426i | \(0.729366\pi\) | |||||||
\(734\) | 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 | \(-0.884750\pi\) |
0.354209 | + | 0.935166i | \(0.384750\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −35.2898 | − | 23.7329i | −1.29640 | − | 0.871849i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 38.5942i | − | 1.41588i | −0.706271 | − | 0.707941i | \(-0.749624\pi\) | ||
0.706271 | − | 0.707941i | \(-0.250376\pi\) | |||||||
\(744\) | 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 | \(-0.895619\pi\) | ||
0.946713 | − | 0.322078i | \(-0.104381\pi\) | |||||||
\(752\) | 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 | −0.213062 | + | 0.977039i | \(0.568343\pi\) |
−0.977039 | + | 0.213062i | \(0.931657\pi\) | |||||||
\(758\) | 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 | \(-0.337610\pi\) |
−0.872665 | + | 0.488320i | \(0.837610\pi\) | |||||||
\(774\) | 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 | \(-0.882988\pi\) |
0.359381 | + | 0.933191i | \(0.382988\pi\) | |||||||
\(788\) | 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 | \(-0.771039\pi\) |
0.658860 | + | 0.752266i | \(0.271039\pi\) | |||||||
\(798\) | 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 | \(-0.281770\pi\) |
−0.774045 | + | 0.633130i | \(0.781770\pi\) | |||||||
\(812\) | 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 | \(-0.187456\pi\) |
−0.555456 | + | 0.831546i | \(0.687456\pi\) | |||||||
\(822\) | 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 | \(-0.672888\pi\) |
0.856089 | + | 0.516829i | \(0.172888\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.6336 | + | 18.6336i | 0.647171 | + | 0.647171i | 0.952308 | − | 0.305137i | \(-0.0987023\pi\) |
−0.305137 | + | 0.952308i | \(0.598702\pi\) | |||||||
\(830\) | 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 | \(0.226359\pi\) | ||||
−0.757626 | + | 0.652689i | \(0.773641\pi\) | |||||||
\(840\) | 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 | \(-0.551697\pi\) |
0.986840 | + | 0.161699i | \(0.0516972\pi\) | |||||||
\(854\) | 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 | \(-0.270424\pi\) |
−0.750992 | + | 0.660311i | \(0.770424\pi\) | |||||||
\(860\) | 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 | \(-0.409273\pi\) |
−0.959654 | + | 0.281184i | \(0.909273\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.00274 | − | 15.3354i | −0.101280 | − | 0.517249i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 10.8132i | − | 0.364305i | −0.983270 | − | 0.182152i | \(-0.941694\pi\) | ||
0.983270 | − | 0.182152i | \(-0.0583064\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.5665 | + | 12.5665i | −0.422895 | + | 0.422895i | −0.886199 | − | 0.463304i | \(-0.846664\pi\) |
0.463304 | + | 0.886199i | \(0.346664\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 17.5469 | + | 11.8005i | 0.589833 | + | 0.396671i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 12.0977i | − | 0.406201i | −0.979158 | − | 0.203101i | \(-0.934898\pi\) | ||
0.979158 | − | 0.203101i | \(-0.0651018\pi\) | |||||||
\(888\) | 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 | \(-0.140702\pi\) |
−0.427774 | + | 0.903886i | \(0.640702\pi\) | |||||||
\(908\) | 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 | \(0.251819\pi\) | ||||
−0.703054 | + | 0.711137i | \(0.748181\pi\) | |||||||
\(930\) | 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 | \(0.0817459\pi\) | ||||
−0.967205 | + | 0.253999i | \(0.918254\pi\) | |||||||
\(938\) | 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 | \(-0.763606\pi\) |
0.676246 | + | 0.736676i | \(0.263606\pi\) | |||||||
\(942\) | 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 | 0.999878 | + | 0.0156087i | \(0.00496860\pi\) |
0.0156087 | + | 0.999878i | \(0.495031\pi\) | |||||||
\(948\) | 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 | \(-0.750479\pi\) |
0.706041 | + | 0.708170i | \(0.250479\pi\) | |||||||
\(972\) | 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 | \(0.0174511\pi\) | ||||
−0.998498 | + | 0.0547969i | \(0.982549\pi\) | |||||||
\(978\) | 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 | \(-0.837780\pi\) | ||
0.872926 | − | 0.487853i | \(-0.162220\pi\) | |||||||
\(984\) | 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 | \(0.126115\pi\) | ||||
−0.922533 | + | 0.385917i | \(0.873885\pi\) | |||||||
\(992\) | 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 | \(-0.675854\pi\) |
0.851235 | + | 0.524785i | \(0.175854\pi\) | |||||||
\(998\) | 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 | 192.2.k.a.47.5 | 12 | ||
3.2 | odd | 2 | inner | 192.2.k.a.47.2 | 12 | ||
4.3 | odd | 2 | 48.2.k.a.35.4 | yes | 12 | ||
8.3 | odd | 2 | 384.2.k.b.95.5 | 12 | |||
8.5 | even | 2 | 384.2.k.a.95.2 | 12 | |||
12.11 | even | 2 | 48.2.k.a.35.3 | yes | 12 | ||
16.3 | odd | 4 | 384.2.k.a.287.5 | 12 | |||
16.5 | even | 4 | 48.2.k.a.11.3 | ✓ | 12 | ||
16.11 | odd | 4 | inner | 192.2.k.a.143.2 | 12 | ||
16.13 | even | 4 | 384.2.k.b.287.2 | 12 | |||
24.5 | odd | 2 | 384.2.k.a.95.5 | 12 | |||
24.11 | even | 2 | 384.2.k.b.95.2 | 12 | |||
48.5 | odd | 4 | 48.2.k.a.11.4 | yes | 12 | ||
48.11 | even | 4 | inner | 192.2.k.a.143.5 | 12 | ||
48.29 | odd | 4 | 384.2.k.b.287.5 | 12 | |||
48.35 | even | 4 | 384.2.k.a.287.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.2.k.a.11.3 | ✓ | 12 | 16.5 | even | 4 | ||
48.2.k.a.11.4 | yes | 12 | 48.5 | odd | 4 | ||
48.2.k.a.35.3 | yes | 12 | 12.11 | even | 2 | ||
48.2.k.a.35.4 | yes | 12 | 4.3 | odd | 2 | ||
192.2.k.a.47.2 | 12 | 3.2 | odd | 2 | inner | ||
192.2.k.a.47.5 | 12 | 1.1 | even | 1 | trivial | ||
192.2.k.a.143.2 | 12 | 16.11 | odd | 4 | inner | ||
192.2.k.a.143.5 | 12 | 48.11 | even | 4 | inner | ||
384.2.k.a.95.2 | 12 | 8.5 | even | 2 | |||
384.2.k.a.95.5 | 12 | 24.5 | odd | 2 | |||
384.2.k.a.287.2 | 12 | 48.35 | even | 4 | |||
384.2.k.a.287.5 | 12 | 16.3 | odd | 4 | |||
384.2.k.b.95.2 | 12 | 24.11 | even | 2 | |||
384.2.k.b.95.5 | 12 | 8.3 | odd | 2 | |||
384.2.k.b.287.2 | 12 | 16.13 | even | 4 | |||
384.2.k.b.287.5 | 12 | 48.29 | odd | 4 |