Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1352,2,Mod(361,1352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1352, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1352.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1352 = 2^{3} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1352.o (of order \(6\), 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: | \(10.7957743533\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - x^{2} + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 104) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 361.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1352.361 |
Dual form | 1352.2.o.b.1161.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1352\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(1015\) | \(1185\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | 0.684819 | − | 0.728714i | \(-0.259881\pi\) |
−0.973494 | + | 0.228714i | \(0.926548\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000i | 0.894427i | 0.894427 | + | 0.447214i | \(0.147584\pi\) | ||||
−0.894427 | + | 0.447214i | \(0.852416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.866025 | − | 0.500000i | −0.327327 | − | 0.188982i | 0.327327 | − | 0.944911i | \(-0.393852\pi\) |
−0.654654 | + | 0.755929i | \(0.727186\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | − | 1.73205i | 0.333333 | − | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.866025 | + | 0.500000i | −0.261116 | + | 0.150756i | −0.624844 | − | 0.780750i | \(-0.714837\pi\) |
0.363727 | + | 0.931505i | \(0.381504\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.73205 | − | 1.00000i | 0.447214 | − | 0.258199i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.50000 | − | 2.59808i | 0.363803 | − | 0.630126i | −0.624780 | − | 0.780801i | \(-0.714811\pi\) |
0.988583 | + | 0.150675i | \(0.0481447\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.06218 | − | 3.50000i | −1.39076 | − | 0.802955i | −0.397360 | − | 0.917663i | \(-0.630073\pi\) |
−0.993399 | + | 0.114708i | \(0.963407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000i | 0.218218i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.500000 | + | 0.866025i | 0.104257 | + | 0.180579i | 0.913434 | − | 0.406986i | \(-0.133420\pi\) |
−0.809177 | + | 0.587565i | \(0.800087\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.50000 | − | 2.59808i | −0.278543 | − | 0.482451i | 0.692480 | − | 0.721437i | \(-0.256518\pi\) |
−0.971023 | + | 0.238987i | \(0.923185\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.00000i | 1.43684i | 0.695608 | + | 0.718421i | \(0.255135\pi\) | ||||
−0.695608 | + | 0.718421i | \(0.744865\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.866025 | + | 0.500000i | 0.150756 | + | 0.0870388i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000 | − | 1.73205i | 0.169031 | − | 0.292770i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.866025 | − | 0.500000i | 0.142374 | − | 0.0821995i | −0.427121 | − | 0.904194i | \(-0.640472\pi\) |
0.569495 | + | 0.821995i | \(0.307139\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.52628 | − | 5.50000i | 1.48775 | − | 0.858956i | 0.487852 | − | 0.872926i | \(-0.337780\pi\) |
0.999902 | + | 0.0139704i | \(0.00444706\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.50000 | − | 9.52628i | 0.838742 | − | 1.45274i | −0.0522047 | − | 0.998636i | \(-0.516625\pi\) |
0.890947 | − | 0.454108i | \(-0.150042\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.46410 | + | 2.00000i | 0.516398 | + | 0.298142i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 12.0000i | − | 1.75038i | −0.483779 | − | 0.875190i | \(-0.660736\pi\) | ||
0.483779 | − | 0.875190i | \(-0.339264\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | − | 5.19615i | −0.428571 | − | 0.742307i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.00000 | −0.420084 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00000 | − | 1.73205i | −0.134840 | − | 0.233550i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.00000i | 0.927173i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.79423 | − | 4.50000i | −1.01472 | − | 0.585850i | −0.102151 | − | 0.994769i | \(-0.532573\pi\) |
−0.912571 | + | 0.408919i | \(0.865906\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.50000 | − | 7.79423i | 0.576166 | − | 0.997949i | −0.419748 | − | 0.907641i | \(-0.637882\pi\) |
0.995914 | − | 0.0903080i | \(-0.0287851\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.73205 | + | 1.00000i | −0.218218 | + | 0.125988i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.59808 | + | 1.50000i | −0.317406 | + | 0.183254i | −0.650236 | − | 0.759733i | \(-0.725330\pi\) |
0.332830 | + | 0.942987i | \(0.391996\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.500000 | − | 0.866025i | 0.0601929 | − | 0.104257i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.33013 | + | 2.50000i | 0.513892 | + | 0.296695i | 0.734432 | − | 0.678682i | \(-0.237449\pi\) |
−0.220540 | + | 0.975378i | \(0.570782\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.00000i | 0.234082i | 0.993127 | + | 0.117041i | \(0.0373409\pi\) | ||||
−0.993127 | + | 0.117041i | \(0.962659\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.500000 | − | 0.866025i | −0.0577350 | − | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.0000 | −1.35011 | −0.675053 | − | 0.737769i | \(-0.735879\pi\) | ||||
−0.675053 | + | 0.737769i | \(0.735879\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 4.00000i | − | 0.439057i | −0.975606 | − | 0.219529i | \(-0.929548\pi\) | ||
0.975606 | − | 0.219529i | \(-0.0704519\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.19615 | + | 3.00000i | 0.563602 | + | 0.325396i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.50000 | + | 2.59808i | −0.160817 | + | 0.278543i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.866025 | − | 0.500000i | 0.0917985 | − | 0.0529999i | −0.453398 | − | 0.891308i | \(-0.649788\pi\) |
0.545197 | + | 0.838308i | \(0.316455\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.92820 | − | 4.00000i | 0.718421 | − | 0.414781i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.00000 | − | 12.1244i | 0.718185 | − | 1.24393i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.866025 | + | 0.500000i | 0.0879316 | + | 0.0507673i | 0.543321 | − | 0.839525i | \(-0.317167\pi\) |
−0.455389 | + | 0.890292i | \(0.650500\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.00000i | 0.201008i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.50000 | − | 14.7224i | −0.845782 | − | 1.46494i | −0.884941 | − | 0.465704i | \(-0.845801\pi\) |
0.0391591 | − | 0.999233i | \(-0.487532\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000 | 0.788263 | 0.394132 | − | 0.919054i | \(-0.371045\pi\) | ||||
0.394132 | + | 0.919054i | \(0.371045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.00000 | −0.195180 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.50000 | − | 14.7224i | −0.821726 | − | 1.42327i | −0.904396 | − | 0.426694i | \(-0.859678\pi\) |
0.0826699 | − | 0.996577i | \(-0.473655\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000i | 0.957826i | 0.877862 | + | 0.478913i | \(0.158969\pi\) | ||||
−0.877862 | + | 0.478913i | \(0.841031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.866025 | − | 0.500000i | −0.0821995 | − | 0.0474579i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.50000 | + | 9.52628i | −0.517396 | + | 0.896157i | 0.482399 | + | 0.875951i | \(0.339765\pi\) |
−0.999796 | + | 0.0202056i | \(0.993568\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.73205 | + | 1.00000i | −0.161515 | + | 0.0932505i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.59808 | + | 1.50000i | −0.238165 | + | 0.137505i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.00000 | + | 8.66025i | −0.454545 | + | 0.787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.52628 | − | 5.50000i | −0.858956 | − | 0.495918i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0000i | 1.07331i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.50000 | + | 11.2583i | 0.576782 | + | 0.999015i | 0.995846 | + | 0.0910585i | \(0.0290250\pi\) |
−0.419064 | + | 0.907957i | \(0.637642\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.0000 | −0.968496 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.0000 | 1.04844 | 0.524222 | − | 0.851581i | \(-0.324356\pi\) | ||||
0.524222 | + | 0.851581i | \(0.324356\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.50000 | + | 6.06218i | 0.303488 | + | 0.525657i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 10.0000i | − | 0.860663i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.79423 | − | 4.50000i | −0.665906 | − | 0.384461i | 0.128618 | − | 0.991694i | \(-0.458946\pi\) |
−0.794524 | + | 0.607233i | \(0.792279\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.50000 | − | 7.79423i | 0.381685 | − | 0.661098i | −0.609618 | − | 0.792695i | \(-0.708677\pi\) |
0.991303 | + | 0.131597i | \(0.0420106\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.3923 | + | 6.00000i | −0.875190 | + | 0.505291i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.19615 | − | 3.00000i | 0.431517 | − | 0.249136i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.00000 | + | 5.19615i | −0.247436 | + | 0.428571i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.866025 | + | 0.500000i | 0.0709476 | + | 0.0409616i | 0.535054 | − | 0.844818i | \(-0.320291\pi\) |
−0.464107 | + | 0.885779i | \(0.653625\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 16.0000i | − | 1.30206i | −0.759051 | − | 0.651031i | \(-0.774337\pi\) | ||
0.759051 | − | 0.651031i | \(-0.225663\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.00000 | − | 5.19615i | −0.242536 | − | 0.420084i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.0000 | −1.28515 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0000 | 0.798087 | 0.399043 | − | 0.916932i | \(-0.369342\pi\) | ||||
0.399043 | + | 0.916932i | \(0.369342\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.00000 | + | 5.19615i | 0.237915 | + | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.00000i | − | 0.0788110i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.33013 | − | 2.50000i | −0.339162 | − | 0.195815i | 0.320740 | − | 0.947167i | \(-0.396069\pi\) |
−0.659901 | + | 0.751352i | \(0.729402\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.00000 | + | 1.73205i | −0.0778499 | + | 0.134840i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.06218 | − | 3.50000i | 0.469105 | − | 0.270838i | −0.246760 | − | 0.969077i | \(-0.579366\pi\) |
0.715865 | + | 0.698239i | \(0.246033\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.1244 | + | 7.00000i | −0.927173 | + | 0.535303i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.50000 | + | 7.79423i | −0.342129 | + | 0.592584i | −0.984828 | − | 0.173534i | \(-0.944481\pi\) |
0.642699 | + | 0.766119i | \(0.277815\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.866025 | − | 0.500000i | −0.0654654 | − | 0.0377964i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.00000i | 0.676481i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.50000 | + | 7.79423i | 0.336346 | + | 0.582568i | 0.983742 | − | 0.179585i | \(-0.0574756\pi\) |
−0.647397 | + | 0.762153i | \(0.724142\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.0000 | 1.04061 | 0.520306 | − | 0.853980i | \(-0.325818\pi\) | ||||
0.520306 | + | 0.853980i | \(0.325818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.00000 | −0.665299 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.00000 | + | 1.73205i | 0.0735215 | + | 0.127343i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.00000i | 0.219382i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.33013 | + | 2.50000i | 0.314970 | + | 0.181848i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.50000 | + | 6.06218i | −0.253251 | + | 0.438644i | −0.964419 | − | 0.264378i | \(-0.914833\pi\) |
0.711168 | + | 0.703022i | \(0.248167\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.33013 | − | 2.50000i | 0.311689 | − | 0.179954i | −0.335993 | − | 0.941865i | \(-0.609072\pi\) |
0.647682 | + | 0.761911i | \(0.275738\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.2583 | + | 6.50000i | −0.802123 | + | 0.463106i | −0.844213 | − | 0.536008i | \(-0.819932\pi\) |
0.0420901 | + | 0.999114i | \(0.486598\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.50000 | − | 2.59808i | 0.106332 | − | 0.184173i | −0.807950 | − | 0.589252i | \(-0.799423\pi\) |
0.914282 | + | 0.405079i | \(0.132756\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.59808 | + | 1.50000i | 0.183254 | + | 0.105802i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.00000i | 0.210559i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.0000 | + | 19.0526i | 0.768273 | + | 1.33069i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.00000 | 0.139010 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.00000 | 0.484200 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.500000 | − | 0.866025i | −0.0344214 | − | 0.0596196i | 0.848301 | − | 0.529514i | \(-0.177626\pi\) |
−0.882723 | + | 0.469894i | \(0.844292\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 5.00000i | − | 0.342594i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 19.0526 | + | 11.0000i | 1.29937 | + | 0.750194i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.00000 | − | 6.92820i | 0.271538 | − | 0.470317i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.73205 | − | 1.00000i | 0.117041 | − | 0.0675737i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.866025 | − | 0.500000i | 0.0579934 | − | 0.0334825i | −0.470723 | − | 0.882281i | \(-0.656007\pi\) |
0.528716 | + | 0.848799i | \(0.322674\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | − | 1.73205i | 0.0666667 | − | 0.115470i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.866025 | + | 0.500000i | 0.0574801 | + | 0.0331862i | 0.528465 | − | 0.848955i | \(-0.322768\pi\) |
−0.470985 | + | 0.882141i | \(0.656101\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.00000i | 0.396491i | 0.980152 | + | 0.198246i | \(0.0635244\pi\) | ||||
−0.980152 | + | 0.198246i | \(0.936476\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.500000 | − | 0.866025i | −0.0328976 | − | 0.0569803i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 26.0000 | 1.70332 | 0.851658 | − | 0.524097i | \(-0.175597\pi\) | ||||
0.851658 | + | 0.524097i | \(0.175597\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 24.0000 | 1.56559 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.00000 | + | 10.3923i | 0.389742 | + | 0.675053i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 24.0000i | − | 1.55243i | −0.630468 | − | 0.776215i | \(-0.717137\pi\) | ||
0.630468 | − | 0.776215i | \(-0.282863\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.52628 | + | 5.50000i | 0.613642 | + | 0.354286i | 0.774389 | − | 0.632709i | \(-0.218057\pi\) |
−0.160748 | + | 0.986996i | \(0.551391\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.00000 | + | 13.8564i | −0.513200 | + | 0.888889i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.3923 | − | 6.00000i | 0.663940 | − | 0.383326i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.46410 | + | 2.00000i | −0.219529 | + | 0.126745i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.50000 | + | 11.2583i | −0.410276 | + | 0.710620i | −0.994920 | − | 0.100671i | \(-0.967901\pi\) |
0.584643 | + | 0.811290i | \(0.301234\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.866025 | − | 0.500000i | −0.0544466 | − | 0.0314347i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 6.00000i | − | 0.375735i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.50000 | − | 11.2583i | −0.405459 | − | 0.702275i | 0.588916 | − | 0.808194i | \(-0.299555\pi\) |
−0.994375 | + | 0.105919i | \(0.966222\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.00000 | −0.0621370 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.00000 | −0.371391 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.5000 | + | 26.8468i | 0.955771 | + | 1.65544i | 0.732594 | + | 0.680666i | \(0.238309\pi\) |
0.223177 | + | 0.974778i | \(0.428357\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 12.0000i | − | 0.737154i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.866025 | − | 0.500000i | −0.0529999 | − | 0.0305995i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.50000 | − | 4.33013i | 0.152428 | − | 0.264013i | −0.779692 | − | 0.626164i | \(-0.784624\pi\) |
0.932119 | + | 0.362151i | \(0.117958\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.06218 | − | 3.50000i | 0.368251 | − | 0.212610i | −0.304443 | − | 0.952531i | \(-0.598470\pi\) |
0.672694 | + | 0.739921i | \(0.265137\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.866025 | + | 0.500000i | −0.0522233 | + | 0.0301511i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.5000 | + | 18.1865i | −0.630884 | + | 1.09272i | 0.356488 | + | 0.934300i | \(0.383974\pi\) |
−0.987371 | + | 0.158423i | \(0.949359\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.8564 | + | 8.00000i | 0.829561 | + | 0.478947i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 14.0000i | − | 0.835170i | −0.908638 | − | 0.417585i | \(-0.862877\pi\) | ||
0.908638 | − | 0.417585i | \(-0.137123\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.5000 | + | 21.6506i | 0.743048 | + | 1.28700i | 0.951101 | + | 0.308879i | \(0.0999539\pi\) |
−0.208053 | + | 0.978117i | \(0.566713\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −14.0000 | −0.829288 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.0000 | −0.649309 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 1.00000i | − | 0.0586210i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.79423 | − | 4.50000i | −0.455344 | − | 0.262893i | 0.254741 | − | 0.967009i | \(-0.418010\pi\) |
−0.710084 | + | 0.704117i | \(0.751343\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.00000 | − | 15.5885i | 0.524000 | − | 0.907595i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.33013 | − | 2.50000i | 0.251259 | − | 0.145065i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.52628 | + | 5.50000i | −0.549086 | + | 0.317015i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.50000 | + | 14.7224i | −0.488312 | + | 0.845782i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.5885 | + | 9.00000i | 0.892592 | + | 0.515339i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.0000i | 1.14146i | 0.821138 | + | 0.570730i | \(0.193340\pi\) | ||||
−0.821138 | + | 0.570730i | \(0.806660\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.00000 | − | 6.92820i | −0.227552 | − | 0.394132i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.00000 | −0.453638 | −0.226819 | − | 0.973937i | \(-0.572833\pi\) | ||||
−0.226819 | + | 0.973937i | \(0.572833\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 30.0000 | 1.69570 | 0.847850 | − | 0.530236i | \(-0.177897\pi\) | ||||
0.847850 | + | 0.530236i | \(0.177897\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.00000 | − | 3.46410i | −0.112687 | − | 0.195180i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 2.00000i | − | 0.112331i | −0.998421 | − | 0.0561656i | \(-0.982113\pi\) | ||
0.998421 | − | 0.0561656i | \(-0.0178875\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.59808 | + | 1.50000i | 0.145464 | + | 0.0839839i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.50000 | + | 14.7224i | −0.474424 | + | 0.821726i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.1865 | + | 10.5000i | −1.01193 | + | 0.584236i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.66025 | − | 5.00000i | 0.478913 | − | 0.276501i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.00000 | + | 10.3923i | −0.330791 | + | 0.572946i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.3827 | − | 13.5000i | −1.28523 | − | 0.742027i | −0.307429 | − | 0.951571i | \(-0.599469\pi\) |
−0.977799 | + | 0.209544i | \(0.932802\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 2.00000i | − | 0.109599i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.00000 | − | 5.19615i | −0.163908 | − | 0.283896i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.00000 | −0.326841 | −0.163420 | − | 0.986557i | \(-0.552253\pi\) | ||||
−0.163420 | + | 0.986557i | \(0.552253\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.0000 | 0.597438 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.00000 | − | 6.92820i | −0.216612 | − | 0.375183i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.0000i | 0.701934i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.73205 | + | 1.00000i | 0.0932505 | + | 0.0538382i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.5000 | + | 23.3827i | −0.724718 | + | 1.25525i | 0.234372 | + | 0.972147i | \(0.424697\pi\) |
−0.959090 | + | 0.283101i | \(0.908637\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.79423 | − | 4.50000i | 0.417215 | − | 0.240879i | −0.276670 | − | 0.960965i | \(-0.589231\pi\) |
0.693885 | + | 0.720086i | \(0.255897\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.6506 | + | 12.5000i | −1.15235 | + | 0.665308i | −0.949458 | − | 0.313894i | \(-0.898366\pi\) |
−0.202889 | + | 0.979202i | \(0.565033\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.00000 | + | 8.66025i | −0.265372 | + | 0.459639i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.59808 | + | 1.50000i | 0.137505 | + | 0.0793884i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.0000i | 1.26667i | 0.773877 | + | 0.633336i | \(0.218315\pi\) | ||||
−0.773877 | + | 0.633336i | \(0.781685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | + | 25.9808i | 0.789474 | + | 1.36741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.0000 | 0.524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.00000 | −0.209370 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.50000 | + | 12.9904i | 0.391497 | + | 0.678092i | 0.992647 | − | 0.121044i | \(-0.0386241\pi\) |
−0.601150 | + | 0.799136i | \(0.705291\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 22.0000i | − | 1.14527i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.19615 | + | 3.00000i | 0.269771 | + | 0.155752i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.50000 | + | 9.52628i | −0.284779 | + | 0.493252i | −0.972556 | − | 0.232671i | \(-0.925254\pi\) |
0.687776 | + | 0.725923i | \(0.258587\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.3923 | − | 6.00000i | 0.536656 | − | 0.309839i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.9904 | + | 7.50000i | −0.667271 | + | 0.385249i | −0.795042 | − | 0.606555i | \(-0.792551\pi\) |
0.127771 | + | 0.991804i | \(0.459218\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.50000 | − | 11.2583i | 0.333005 | − | 0.576782i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.5788 | + | 16.5000i | 1.46031 | + | 0.843111i | 0.999025 | − | 0.0441413i | \(-0.0140552\pi\) |
0.461285 | + | 0.887252i | \(0.347389\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.00000i | 0.101929i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.0000 | − | 19.0526i | −0.559161 | − | 0.968496i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.00000 | −0.304212 | −0.152106 | − | 0.988364i | \(-0.548606\pi\) | ||||
−0.152106 | + | 0.988364i | \(0.548606\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.00000 | 0.151717 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.00000 | − | 10.3923i | −0.302660 | − | 0.524222i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 24.0000i | − | 1.20757i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.4545 | + | 9.50000i | 0.825827 | + | 0.476791i | 0.852422 | − | 0.522855i | \(-0.175133\pi\) |
−0.0265948 | + | 0.999646i | \(0.508466\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.50000 | − | 6.06218i | 0.175219 | − | 0.303488i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.3827 | + | 13.5000i | −1.16768 | + | 0.674158i | −0.953131 | − | 0.302556i | \(-0.902160\pi\) |
−0.214544 | + | 0.976714i | \(0.568827\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.73205 | − | 1.00000i | 0.0860663 | − | 0.0496904i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.500000 | + | 0.866025i | −0.0247841 | + | 0.0429273i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.3109 | − | 17.5000i | −1.49878 | − | 0.865319i | −0.498778 | − | 0.866730i | \(-0.666218\pi\) |
−0.999999 | + | 0.00141047i | \(0.999551\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.00000i | 0.443937i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.50000 | + | 7.79423i | 0.221431 | + | 0.383529i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.00000 | 0.392705 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.00000 | −0.440732 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.5000 | − | 18.1865i | −0.512959 | − | 0.888470i | −0.999887 | − | 0.0150285i | \(-0.995216\pi\) |
0.486928 | − | 0.873442i | \(-0.338117\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 22.0000i | − | 1.07221i | −0.844150 | − | 0.536107i | \(-0.819894\pi\) | ||
0.844150 | − | 0.536107i | \(-0.180106\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −20.7846 | − | 12.0000i | −1.01058 | − | 0.583460i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.50000 | − | 2.59808i | 0.0727607 | − | 0.126025i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.79423 | + | 4.50000i | −0.377189 | + | 0.217770i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.52628 | + | 5.50000i | −0.458865 | + | 0.264926i | −0.711567 | − | 0.702618i | \(-0.752014\pi\) |
0.252702 | + | 0.967544i | \(0.418681\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.50000 | − | 16.4545i | 0.456541 | − | 0.790752i | −0.542234 | − | 0.840227i | \(-0.682422\pi\) |
0.998775 | + | 0.0494752i | \(0.0157549\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.19615 | − | 3.00000i | −0.249136 | − | 0.143839i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 7.00000i | − | 0.334855i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.5000 | − | 30.3109i | −0.835229 | − | 1.44666i | −0.893843 | − | 0.448379i | \(-0.852001\pi\) |
0.0586141 | − | 0.998281i | \(-0.481332\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.0000 | −0.571429 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.0000 | 0.570137 | 0.285069 | − | 0.958507i | \(-0.407984\pi\) | ||||
0.285069 | + | 0.958507i | \(0.407984\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.00000 | + | 1.73205i | 0.0474045 | + | 0.0821071i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 1.00000i | − | 0.0472984i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.1865 | − | 10.5000i | −0.858276 | − | 0.495526i | 0.00515887 | − | 0.999987i | \(-0.498358\pi\) |
−0.863434 | + | 0.504461i | \(0.831691\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.50000 | + | 9.52628i | −0.258985 | + | 0.448575i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13.8564 | + | 8.00000i | −0.651031 | + | 0.375873i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.06218 | − | 3.50000i | 0.283577 | − | 0.163723i | −0.351465 | − | 0.936201i | \(-0.614316\pi\) |
0.635042 | + | 0.772478i | \(0.280983\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.50000 | + | 12.9904i | −0.350070 | + | 0.606339i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.59808 | − | 1.50000i | −0.121004 | − | 0.0698620i | 0.438276 | − | 0.898840i | \(-0.355589\pi\) |
−0.559281 | + | 0.828978i | \(0.688923\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 24.0000i | − | 1.11537i | −0.830051 | − | 0.557687i | \(-0.811689\pi\) | ||
0.830051 | − | 0.557687i | \(-0.188311\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.00000 | + | 13.8564i | 0.370991 | + | 0.642575i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.00000 | 0.370196 | 0.185098 | − | 0.982720i | \(-0.440740\pi\) | ||||
0.185098 | + | 0.982720i | \(0.440740\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.00000 | 0.138527 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.00000 | − | 8.66025i | −0.230388 | − | 0.399043i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.0000i | 0.505781i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.06218 | − | 3.50000i | −0.278152 | − | 0.160591i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.00000 | + | 10.3923i | −0.274721 | + | 0.475831i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.3827 | − | 13.5000i | 1.06838 | − | 0.616831i | 0.140643 | − | 0.990060i | \(-0.455083\pi\) |
0.927739 | + | 0.373230i | \(0.121750\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.866025 | + | 0.500000i | −0.0394055 | + | 0.0227508i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.00000 | + | 1.73205i | −0.0454077 | + | 0.0786484i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.2583 | + | 6.50000i | 0.510164 | + | 0.294543i | 0.732901 | − | 0.680335i | \(-0.238166\pi\) |
−0.222737 | + | 0.974879i | \(0.571499\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.00000i | 0.226108i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.50000 | − | 2.59808i | −0.0676941 | − | 0.117250i | 0.830192 | − | 0.557478i | \(-0.188231\pi\) |
−0.897886 | + | 0.440228i | \(0.854898\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.00000 | −0.405340 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.00000 | −0.179787 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.50000 | − | 4.33013i | −0.112140 | − | 0.194233i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.0000i | 1.61158i | 0.592200 | + | 0.805791i | \(0.298259\pi\) | ||||
−0.592200 | + | 0.805791i | \(0.701741\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.06218 | − | 3.50000i | −0.270838 | − | 0.156368i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.5000 | − | 21.6506i | 0.557347 | − | 0.965354i | −0.440369 | − | 0.897817i | \(-0.645152\pi\) |
0.997717 | − | 0.0675374i | \(-0.0215142\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 29.4449 | − | 17.0000i | 1.31028 | − | 0.756490i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.866025 | + | 0.500000i | −0.0383859 | + | 0.0221621i | −0.519070 | − | 0.854732i | \(-0.673722\pi\) |
0.480684 | + | 0.876894i | \(0.340388\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.00000 | − | 1.73205i | 0.0442374 | − | 0.0766214i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 30.3109 | + | 17.5000i | 1.33826 | + | 0.772644i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.0000i | 0.705044i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.00000 | + | 10.3923i | 0.263880 | + | 0.457053i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.00000 | 0.395056 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −42.0000 | −1.84005 | −0.920027 | − | 0.391856i | \(-0.871833\pi\) | ||||
−0.920027 | + | 0.391856i | \(0.871833\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.50000 | + | 16.4545i | 0.415406 | + | 0.719504i | 0.995471 | − | 0.0950659i | \(-0.0303062\pi\) |
−0.580065 | + | 0.814570i | \(0.696973\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.00000i | 0.0436436i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.7846 | + | 12.0000i | 0.905392 | + | 0.522728i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | − | 19.0526i | 0.478261 | − | 0.828372i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −15.5885 | + | 9.00000i | −0.676481 | + | 0.390567i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 29.4449 | − | 17.0000i | 1.27301 | − | 0.734974i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.50000 | − | 7.79423i | 0.194189 | − | 0.336346i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.19615 | + | 3.00000i | 0.223814 | + | 0.129219i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 30.0000i | − | 1.28980i | −0.764267 | − | 0.644900i | \(-0.776899\pi\) | ||
0.764267 | − | 0.644900i | \(-0.223101\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.00000 | − | 12.1244i | −0.300399 | − | 0.520306i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −20.0000 | −0.856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0000 | 0.513083 | 0.256541 | − | 0.966533i | \(-0.417417\pi\) | ||||
0.256541 | + | 0.966533i | \(0.417417\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.00000 | − | 15.5885i | −0.384111 | − | 0.665299i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.0000i | 0.894630i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.3923 | + | 6.00000i | 0.441926 | + | 0.255146i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.00000 | − | 1.73205i | 0.0424476 | − | 0.0735215i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.4545 | + | 9.50000i | −0.697199 | + | 0.402528i | −0.806303 | − | 0.591502i | \(-0.798535\pi\) |
0.109104 | + | 0.994030i | \(0.465202\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.59808 | − | 1.50000i | 0.109691 | − | 0.0633300i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.50000 | + | 7.79423i | −0.189652 | + | 0.328488i | −0.945134 | − | 0.326682i | \(-0.894069\pi\) |
0.755482 | + | 0.655169i | \(0.227403\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.0526 | − | 11.0000i | −0.801547 | − | 0.462773i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.50000 | − | 14.7224i | −0.356339 | − | 0.617196i | 0.631008 | − | 0.775777i | \(-0.282642\pi\) |
−0.987346 | + | 0.158580i | \(0.949308\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.0000 | 0.836974 | 0.418487 | − | 0.908223i | \(-0.362561\pi\) | ||||
0.418487 | + | 0.908223i | \(0.362561\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.00000 | 0.292429 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.500000 | + | 0.866025i | 0.0208514 | + | 0.0361158i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.0000i | 0.915872i | 0.888985 | + | 0.457936i | \(0.151411\pi\) | ||||
−0.888985 | + | 0.457936i | \(0.848589\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.33013 | − | 2.50000i | −0.179954 | − | 0.103896i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.00000 | + | 3.46410i | −0.0829740 | + | 0.143715i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.19615 | − | 3.00000i | 0.215203 | − | 0.124247i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.1865 | − | 10.5000i | 0.750639 | − | 0.433381i | −0.0752860 | − | 0.997162i | \(-0.523987\pi\) |
0.825925 | + | 0.563781i | \(0.190654\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.0000 | − | 48.4974i | 1.15372 | − | 1.99830i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.2583 | + | 6.50000i | 0.463106 | + | 0.267374i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 14.0000i | − | 0.574911i | −0.957794 | − | 0.287456i | \(-0.907191\pi\) | ||
0.957794 | − | 0.287456i | \(-0.0928094\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.00000 | − | 5.19615i | −0.122988 | − | 0.213021i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.00000 | −0.122782 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −44.0000 | −1.79779 | −0.898896 | − | 0.438163i | \(-0.855629\pi\) | ||||
−0.898896 | + | 0.438163i | \(0.855629\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.5000 | + | 18.1865i | 0.428304 | + | 0.741844i | 0.996723 | − | 0.0808953i | \(-0.0257779\pi\) |
−0.568419 | + | 0.822739i | \(0.692445\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.00000i | 0.244339i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −17.3205 | − | 10.0000i | −0.704179 | − | 0.406558i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.50000 | − | 11.2583i | 0.263827 | − | 0.456962i | −0.703429 | − | 0.710766i | \(-0.748349\pi\) |
0.967256 | + | 0.253804i | \(0.0816819\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.59808 | − | 1.50000i | 0.105279 | − | 0.0607831i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.7750 | − | 19.5000i | 1.36416 | − | 0.787598i | 0.373985 | − | 0.927435i | \(-0.377991\pi\) |
0.990174 | + | 0.139837i | \(0.0446580\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.0000 | − | 19.0526i | 0.443563 | − | 0.768273i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −40.7032 | − | 23.5000i | −1.63865 | − | 0.946074i | −0.981299 | − | 0.192489i | \(-0.938344\pi\) |
−0.657350 | − | 0.753586i | \(-0.728323\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.0000i | 0.803868i | 0.915669 | + | 0.401934i | \(0.131662\pi\) | ||||
−0.915669 | + | 0.401934i | \(0.868338\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.50000 | − | 4.33013i | −0.100322 | − | 0.173762i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.00000 | −0.0400642 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.50000 | − | 6.06218i | −0.139777 | − | 0.242100i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 3.00000i | − | 0.119618i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.3827 | + | 13.5000i | 0.930850 | + | 0.537427i | 0.887080 | − | 0.461615i | \(-0.152730\pi\) |
0.0437697 | + | 0.999042i | \(0.486063\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.500000 | + | 0.866025i | −0.0198732 | + | 0.0344214i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22.5167 | + | 13.0000i | −0.893546 | + | 0.515889i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.66025 | − | 5.00000i | 0.342594 | − | 0.197797i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.50000 | − | 9.52628i | 0.217237 | − | 0.376265i | −0.736725 | − | 0.676192i | \(-0.763629\pi\) |
0.953962 | + | 0.299927i | \(0.0969622\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.4545 | − | 9.50000i | −0.648901 | − | 0.374643i | 0.139134 | − | 0.990274i | \(-0.455568\pi\) |
−0.788035 | + | 0.615630i | \(0.788902\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 22.0000i | − | 0.866249i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.50000 | − | 2.59808i | −0.0589711 | − | 0.102141i | 0.835033 | − | 0.550200i | \(-0.185449\pi\) |
−0.894004 | + | 0.448059i | \(0.852115\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.00000 | 0.353281 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.00000 | −0.313545 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.50000 | + | 7.79423i | 0.176099 | + | 0.305012i | 0.940541 | − | 0.339680i | \(-0.110319\pi\) |
−0.764442 | + | 0.644692i | \(0.776986\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.0000i | 0.937758i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.46410 | + | 2.00000i | 0.135147 | + | 0.0780274i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.5000 | − | 25.1147i | 0.564840 | − | 0.978331i | −0.432225 | − | 0.901766i | \(-0.642271\pi\) |
0.997065 | − | 0.0765653i | \(-0.0243954\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.6506 | − | 12.5000i | 0.842112 | − | 0.486194i | −0.0158695 | − | 0.999874i | \(-0.505052\pi\) |
0.857982 | + | 0.513680i | \(0.171718\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.1244 | + | 7.00000i | −0.470162 | + | 0.271448i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.50000 | − | 2.59808i | 0.0580802 | − | 0.100598i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.866025 | − | 0.500000i | −0.0334825 | − | 0.0193311i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.00000i | 0.347441i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.5000 | + | 33.7750i | 0.751670 | + | 1.30193i | 0.947013 | + | 0.321195i | \(0.104085\pi\) |
−0.195343 | + | 0.980735i | \(0.562582\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.00000 | −0.192450 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.00000 | −0.230599 | −0.115299 | − | 0.993331i | \(-0.536783\pi\) | ||||
−0.115299 | + | 0.993331i | \(0.536783\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.500000 | − | 0.866025i | −0.0191882 | − | 0.0332350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 1.00000i | − | 0.0383201i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.79423 | − | 4.50000i | −0.298238 | − | 0.172188i | 0.343413 | − | 0.939184i | \(-0.388417\pi\) |
−0.641651 | + | 0.766997i | \(0.721750\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.00000 | − | 15.5885i | 0.343872 | − | 0.595604i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.19615 | − | 3.00000i | 0.198246 | − | 0.114457i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.6506 | − | 12.5000i | 0.823629 | − | 0.475522i | −0.0280373 | − | 0.999607i | \(-0.508926\pi\) |
0.851666 | + | 0.524084i | \(0.175592\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.00000 | − | 1.73205i | 0.0379869 | − | 0.0657952i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.5885 | + | 9.00000i | 0.591304 | + | 0.341389i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 33.0000i | − | 1.24996i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.0000 | − | 22.5167i | −0.491705 | − | 0.851658i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.0000 | 0.830929 | 0.415464 | − | 0.909610i | \(-0.363619\pi\) | ||||
0.415464 | + | 0.909610i | \(0.363619\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.00000 | −0.264010 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.0000 | − | 20.7846i | −0.451946 | − | 0.782794i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17.0000i | 0.639351i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.1147 | − | 14.5000i | −0.943204 | − | 0.544559i | −0.0522406 | − | 0.998635i | \(-0.516636\pi\) |
−0.890963 | + | 0.454076i | \(0.849970\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.0000 | + | 20.7846i | −0.450035 | + | 0.779484i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.92820 | + | 4.00000i | −0.259463 | + | 0.149801i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20.7846 | + | 12.0000i | −0.776215 | + | 0.448148i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.5000 | − | 33.7750i | 0.727227 | − | 1.25959i | −0.230823 | − | 0.972996i | \(-0.574142\pi\) |
0.958051 | − | 0.286599i | \(-0.0925247\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.92820 | − | 4.00000i | −0.258020 | − | 0.148968i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 11.0000i | − | 0.409094i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.50000 | − | 2.59808i | −0.0557086 | − | 0.0964901i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.00000 | 0.296704 | 0.148352 | − | 0.988935i | \(-0.452603\pi\) | ||||
0.148352 | + | 0.988935i | \(0.452603\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.5000 | − | 28.5788i | −0.610275 | − | 1.05703i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.0000i | 1.69905i | 0.527549 | + | 0.849524i | \(0.323111\pi\) | ||||
−0.527549 | + | 0.849524i | \(0.676889\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −10.3923 | − | 6.00000i | −0.383326 | − | 0.221313i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.50000 | − | 2.59808i | 0.0552532 | − | 0.0957014i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.52628 | − | 5.50000i | 0.350430 | − | 0.202321i | −0.314445 | − | 0.949276i | \(-0.601818\pi\) |
0.664875 | + | 0.746955i | \(0.268485\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.1147 | − | 14.5000i | 0.921370 | − | 0.531953i | 0.0372984 | − | 0.999304i | \(-0.488125\pi\) |
0.884072 | + | 0.467351i | \(0.154791\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.00000 | + | 1.73205i | −0.0366372 | + | 0.0634574i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.92820 | − | 4.00000i | −0.253490 | − | 0.146352i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.0000i | 0.621166i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.50000 | + | 14.7224i | 0.310169 | + | 0.537229i | 0.978399 | − | 0.206726i | \(-0.0662809\pi\) |
−0.668229 | + | 0.743955i | \(0.732948\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.0000 | 0.473746 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 32.0000 | 1.16460 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.5000 | − | 40.7032i | −0.854122 | − | 1.47938i | −0.877457 | − | 0.479655i | \(-0.840762\pi\) |
0.0233351 | − | 0.999728i | \(-0.492572\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.00000i | 0.0362977i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.59808 | + | 1.50000i | 0.0941802 | + | 0.0543750i | 0.546350 | − | 0.837557i | \(-0.316017\pi\) |
−0.452170 | + | 0.891932i | \(0.649350\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.00000 | − | 8.66025i | 0.181012 | − | 0.313522i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.3923 | − | 6.00000i | 0.375735 | − | 0.216930i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.33013 | + | 2.50000i | −0.156148 | + | 0.0901523i | −0.576038 | − | 0.817423i | \(-0.695402\pi\) |
0.419890 | + | 0.907575i | \(0.362069\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.50000 | + | 11.2583i | −0.234092 | + | 0.405459i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.59808 | − | 1.50000i | −0.0934463 | − | 0.0539513i | 0.452549 | − | 0.891740i | \(-0.350515\pi\) |
−0.545995 | + | 0.837788i | \(0.683848\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.00000i | 0.287368i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.500000 | + | 0.866025i | 0.0179374 | + | 0.0310685i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −77.0000 | −2.75881 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.00000 | −0.178914 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.50000 | + | 12.9904i | 0.268028 | + | 0.464238i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.0000i | 0.713831i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.1865 | − | 10.5000i | −0.648280 | − | 0.374285i | 0.139517 | − | 0.990220i | \(-0.455445\pi\) |
−0.787797 | + | 0.615935i | \(0.788778\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.5000 | − | 26.8468i | 0.551815 | − | 0.955771i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.52628 | − | 5.50000i | 0.338716 | − | 0.195557i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.3923 | + | 6.00000i | −0.368577 | + | 0.212798i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.5000 | − | 19.9186i | 0.407351 | − | 0.705552i | −0.587241 | − | 0.809412i | \(-0.699786\pi\) |
0.994592 | + | 0.103860i | \(0.0331193\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31.1769 | − | 18.0000i | −1.10296 | − | 0.636794i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 2.00000i | − | 0.0706665i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.00000 | − | 1.73205i | −0.0352892 | − | 0.0611227i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.00000 | 0.0704907 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.00000 | −0.176008 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.5000 | − | 23.3827i | −0.474635 | − | 0.822091i | 0.524943 | − | 0.851137i | \(-0.324086\pi\) |
−0.999578 | + | 0.0290457i | \(0.990753\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.0000i | 1.12367i | 0.827249 | + | 0.561836i | \(0.189905\pi\) | ||||
−0.827249 | + | 0.561836i | \(0.810095\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.06218 | − | 3.50000i | −0.212610 | − | 0.122750i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.00000 | − | 8.66025i | 0.175142 | − | 0.303355i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −66.6840 | + | 38.5000i | −2.33298 | + | 1.34694i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.33013 | + | 2.50000i | −0.151122 | + | 0.0872506i | −0.573654 | − | 0.819097i | \(-0.694475\pi\) |
0.422532 | + | 0.906348i | \(0.361141\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.5000 | + | 25.1147i | −0.505438 | + | 0.875445i | 0.494542 | + | 0.869154i | \(0.335336\pi\) |
−0.999980 | + | 0.00629095i | \(0.997998\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.866025 | + | 0.500000i | 0.0301511 | + | 0.0174078i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 20.0000i | − | 0.695468i | −0.937593 | − | 0.347734i | \(-0.886951\pi\) | ||
0.937593 | − | 0.347734i | \(-0.113049\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.50000 | + | 2.59808i | 0.0520972 | + | 0.0902349i | 0.890898 | − | 0.454204i | \(-0.150076\pi\) |
−0.838801 | + | 0.544438i | \(0.816743\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.0000 | 0.728482 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.0000 | −0.623663 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.00000 | + | 12.1244i | 0.242245 | + | 0.419581i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 40.0000i | − | 1.38260i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.3827 | + | 13.5000i | 0.807260 | + | 0.466072i | 0.846003 | − | 0.533177i | \(-0.179002\pi\) |
−0.0387435 | + | 0.999249i | \(0.512336\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0000 | − | 17.3205i | 0.344828 | − | 0.597259i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.1244 | + | 7.00000i | −0.417585 | + | 0.241093i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.66025 | − | 5.00000i | 0.297570 | − | 0.171802i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.5000 | − | 21.6506i | 0.428999 | − | 0.743048i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.866025 | + | 0.500000i | 0.0296870 | + | 0.0171398i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 10.0000i | − | 0.342393i | −0.985237 | − | 0.171197i | \(-0.945237\pi\) | ||
0.985237 | − | 0.171197i | \(-0.0547634\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −14.0000 | − | 24.2487i | −0.478790 | − | 0.829288i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.0000 | 0.614868 | 0.307434 | − | 0.951569i | \(-0.400530\pi\) | ||||
0.307434 | + | 0.951569i | \(0.400530\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.0000 | 0.682391 | 0.341196 | − | 0.939992i | \(-0.389168\pi\) | ||||
0.341196 | + | 0.939992i | \(0.389168\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.50000 | + | 9.52628i | 0.187439 | + | 0.324655i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 16.0000i | − | 0.544646i | −0.962206 | − | 0.272323i | \(-0.912208\pi\) | ||
0.962206 | − | 0.272323i | \(-0.0877920\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.5885 | − | 9.00000i | −0.530023 | − | 0.306009i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.00000 | − | 6.92820i | 0.135847 | − | 0.235294i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.3923 | − | 6.00000i | 0.352535 | − | 0.203536i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.73205 | − | 1.00000i | 0.0586210 | − | 0.0338449i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.00000 | − | 10.3923i | 0.202837 | − | 0.351324i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.866025 | + | 0.500000i | 0.0292436 | + | 0.0168838i | 0.514551 | − | 0.857460i | \(-0.327959\pi\) |
−0.485307 | + | 0.874344i | \(0.661292\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.00000i | 0.303562i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.5000 | − | 38.9711i | −0.758044 | − | 1.31297i | −0.943847 | − | 0.330384i | \(-0.892822\pi\) |
0.185802 | − | 0.982587i | \(-0.440512\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.0000 | 0.403832 | 0.201916 | − | 0.979403i | \(-0.435283\pi\) | ||||
0.201916 | + | 0.979403i | \(0.435283\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −18.0000 | −0.605063 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.5000 | + | 23.3827i | 0.453286 | + | 0.785114i | 0.998588 | − | 0.0531258i | \(-0.0169184\pi\) |
−0.545302 | + | 0.838240i | \(0.683585\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 13.0000i | − | 0.436006i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.866025 | + | 0.500000i | 0.0290129 | + | 0.0167506i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −42.0000 | + | 72.7461i | −1.40548 | + | 2.43436i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.5885 | + | 9.00000i | −0.521065 | + | 0.300837i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20.7846 | − | 12.0000i | 0.693206 | − | 0.400222i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.00000 | + | 15.5885i | −0.299833 | + | 0.519327i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.52628 | + | 5.50000i | 0.317015 | + | 0.183029i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 28.0000i | 0.930751i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.5000 | + | 21.6506i | 0.415056 | + | 0.718898i | 0.995434 | − | 0.0954492i | \(-0.0304288\pi\) |
−0.580379 | + | 0.814347i | \(0.697095\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −34.0000 | −1.12771 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.0000 | −0.530104 | −0.265052 | − | 0.964234i | \(-0.585389\pi\) | ||||
−0.265052 | + | 0.964234i | \(0.585389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.00000 | + | 3.46410i | 0.0661903 | + | 0.114645i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 18.0000i | − | 0.595062i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.3923 | − | 6.00000i | −0.343184 | − | 0.198137i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.50000 | + | 12.9904i | −0.247402 | + | 0.428513i | −0.962804 | − | 0.270200i | \(-0.912910\pi\) |
0.715402 | + | 0.698713i | \(0.246244\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.3205 | − | 10.0000i | 0.570730 | − | 0.329511i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.866025 | − | 0.500000i | 0.0284747 | − | 0.0164399i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.00000 | − | 13.8564i | 0.262754 | − | 0.455104i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.33013 | + | 2.50000i | 0.142067 | + | 0.0820223i | 0.569349 | − | 0.822096i | \(-0.307195\pi\) |
−0.427282 | + | 0.904118i | \(0.640529\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 42.0000i | 1.37649i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.00000 | + | 6.92820i | 0.130954 | + | 0.226819i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.00000 | −0.196221 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.00000 | −0.0653372 | −0.0326686 | − | 0.999466i | \(-0.510401\pi\) | ||||
−0.0326686 | + | 0.999466i | \(0.510401\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.0000 | − | 25.9808i | −0.489506 | − | 0.847850i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.0000i | 0.456387i | 0.973616 | + | 0.228193i | \(0.0732819\pi\) | ||||
−0.973616 | + | 0.228193i | \(0.926718\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.52628 | + | 5.50000i | 0.310218 | + | 0.179105i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.00000 | + | 8.66025i | −0.162650 | + | 0.281718i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33.7750 | − | 19.5000i | 1.09754 | − | 0.633665i | 0.161966 | − | 0.986796i | \(-0.448217\pi\) |
0.935574 | + | 0.353131i | \(0.114883\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.73205 | + | 1.00000i | −0.0561656 | + | 0.0324272i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.50000 | + | 7.79423i | −0.145769 | + | 0.252480i | −0.929660 | − | 0.368419i | \(-0.879899\pi\) |
0.783890 | + | 0.620899i | \(0.213232\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.1244 | − | 7.00000i | −0.392335 | − | 0.226515i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 3.00000i | − | 0.0969762i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.50000 | + | 7.79423i | 0.145313 | + | 0.251689i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −33.0000 | −1.06452 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −34.0000 | −1.09563 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.00000 | + | 8.66025i | 0.160956 | + | 0.278783i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 16.0000i | − | 0.514525i | −0.966342 | − | 0.257263i | \(-0.917179\pi\) | ||
0.966342 | − | 0.257263i | \(-0.0828206\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.1865 | + | 10.5000i | 0.584236 | + | 0.337309i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.5000 | + | 23.3827i | −0.433236 | + | 0.750386i | −0.997150 | − | 0.0754473i | \(-0.975962\pi\) |
0.563914 | + | 0.825833i | \(0.309295\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.79423 | + | 4.50000i | −0.249871 | + | 0.144263i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.79423 | + | 4.50000i | −0.249359 | + | 0.143968i | −0.619471 | − | 0.785020i | \(-0.712653\pi\) |
0.370111 | + | 0.928987i | \(0.379319\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.500000 | + | 0.866025i | −0.0159801 | + | 0.0276783i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.3205 | + | 10.0000i | 0.553001 | + | 0.319275i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 32.0000i | − | 1.02064i | −0.859984 | − | 0.510321i | \(-0.829527\pi\) | ||
0.859984 | − | 0.510321i | \(-0.170473\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.0000 | − | 22.5167i | −0.414214 | − | 0.717440i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12.0000 | 0.381964 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.0000 | 0.349780 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.50000 | − | 11.2583i | −0.206479 | − | 0.357633i | 0.744124 | − | 0.668042i | \(-0.232867\pi\) |
−0.950603 | + | 0.310409i | \(0.899534\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.0000i | 0.856819i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.19615 | + | 3.00000i | 0.164729 | + | 0.0951064i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.5000 | − | 21.6506i | 0.395879 | − | 0.685682i | −0.597334 | − | 0.801993i | \(-0.703773\pi\) |
0.993213 | + | 0.116310i | \(0.0371066\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.33013 | + | 2.50000i | −0.136999 | + | 0.0790965i |
(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 | 1352.2.o.b.361.2 | 4 | ||
13.2 | odd | 12 | 1352.2.a.c.1.1 | 1 | |||
13.3 | even | 3 | 1352.2.f.a.337.2 | 2 | |||
13.4 | even | 6 | inner | 1352.2.o.b.1161.1 | 4 | ||
13.5 | odd | 4 | 104.2.i.a.81.1 | yes | 2 | ||
13.6 | odd | 12 | 104.2.i.a.9.1 | ✓ | 2 | ||
13.7 | odd | 12 | 1352.2.i.a.529.1 | 2 | |||
13.8 | odd | 4 | 1352.2.i.a.1329.1 | 2 | |||
13.9 | even | 3 | inner | 1352.2.o.b.1161.2 | 4 | ||
13.10 | even | 6 | 1352.2.f.a.337.1 | 2 | |||
13.11 | odd | 12 | 1352.2.a.a.1.1 | 1 | |||
13.12 | even | 2 | inner | 1352.2.o.b.361.1 | 4 | ||
39.5 | even | 4 | 936.2.t.c.289.1 | 2 | |||
39.32 | even | 12 | 936.2.t.c.217.1 | 2 | |||
52.3 | odd | 6 | 2704.2.f.c.337.2 | 2 | |||
52.11 | even | 12 | 2704.2.a.c.1.1 | 1 | |||
52.15 | even | 12 | 2704.2.a.e.1.1 | 1 | |||
52.19 | even | 12 | 208.2.i.c.113.1 | 2 | |||
52.23 | odd | 6 | 2704.2.f.c.337.1 | 2 | |||
52.31 | even | 4 | 208.2.i.c.81.1 | 2 | |||
104.5 | odd | 4 | 832.2.i.g.705.1 | 2 | |||
104.19 | even | 12 | 832.2.i.d.321.1 | 2 | |||
104.45 | odd | 12 | 832.2.i.g.321.1 | 2 | |||
104.83 | even | 4 | 832.2.i.d.705.1 | 2 | |||
156.71 | odd | 12 | 1872.2.t.d.1153.1 | 2 | |||
156.83 | odd | 4 | 1872.2.t.d.289.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
104.2.i.a.9.1 | ✓ | 2 | 13.6 | odd | 12 | ||
104.2.i.a.81.1 | yes | 2 | 13.5 | odd | 4 | ||
208.2.i.c.81.1 | 2 | 52.31 | even | 4 | |||
208.2.i.c.113.1 | 2 | 52.19 | even | 12 | |||
832.2.i.d.321.1 | 2 | 104.19 | even | 12 | |||
832.2.i.d.705.1 | 2 | 104.83 | even | 4 | |||
832.2.i.g.321.1 | 2 | 104.45 | odd | 12 | |||
832.2.i.g.705.1 | 2 | 104.5 | odd | 4 | |||
936.2.t.c.217.1 | 2 | 39.32 | even | 12 | |||
936.2.t.c.289.1 | 2 | 39.5 | even | 4 | |||
1352.2.a.a.1.1 | 1 | 13.11 | odd | 12 | |||
1352.2.a.c.1.1 | 1 | 13.2 | odd | 12 | |||
1352.2.f.a.337.1 | 2 | 13.10 | even | 6 | |||
1352.2.f.a.337.2 | 2 | 13.3 | even | 3 | |||
1352.2.i.a.529.1 | 2 | 13.7 | odd | 12 | |||
1352.2.i.a.1329.1 | 2 | 13.8 | odd | 4 | |||
1352.2.o.b.361.1 | 4 | 13.12 | even | 2 | inner | ||
1352.2.o.b.361.2 | 4 | 1.1 | even | 1 | trivial | ||
1352.2.o.b.1161.1 | 4 | 13.4 | even | 6 | inner | ||
1352.2.o.b.1161.2 | 4 | 13.9 | even | 3 | inner | ||
1872.2.t.d.289.1 | 2 | 156.83 | odd | 4 | |||
1872.2.t.d.1153.1 | 2 | 156.71 | odd | 12 | |||
2704.2.a.c.1.1 | 1 | 52.11 | even | 12 | |||
2704.2.a.e.1.1 | 1 | 52.15 | even | 12 | |||
2704.2.f.c.337.1 | 2 | 52.23 | odd | 6 | |||
2704.2.f.c.337.2 | 2 | 52.3 | odd | 6 |