Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [288,2,Mod(97,288)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(288, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("288.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 288 = 2^{5} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 288.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.29969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 193.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 288.193 |
Dual form | 288.2.i.b.97.1 |
$q$-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 \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.50000 | − | 0.866025i | 0.866025 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.00000 | + | 3.46410i | −0.894427 | + | 1.54919i | −0.0599153 | + | 0.998203i | \(0.519083\pi\) |
−0.834512 | + | 0.550990i | \(0.814250\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | + | 1.73205i | 0.377964 | + | 0.654654i | 0.990766 | − | 0.135583i | \(-0.0432908\pi\) |
−0.612801 | + | 0.790237i | \(0.709957\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.50000 | + | 4.33013i | 0.753778 | + | 1.30558i | 0.945979 | + | 0.324227i | \(0.105104\pi\) |
−0.192201 | + | 0.981356i | \(0.561563\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | − | 1.73205i | 0.277350 | − | 0.480384i | −0.693375 | − | 0.720577i | \(-0.743877\pi\) |
0.970725 | + | 0.240192i | \(0.0772105\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.92820i | 1.78885i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.00000 | −0.727607 | −0.363803 | − | 0.931476i | \(-0.618522\pi\) | ||||
−0.363803 | + | 0.931476i | \(0.618522\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | 0.114708 | − | 0.993399i | \(-0.463407\pi\) | ||||
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.00000 | + | 1.73205i | 0.654654 | + | 0.377964i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.00000 | − | 5.19615i | 0.625543 | − | 1.08347i | −0.362892 | − | 0.931831i | \(-0.618211\pi\) |
0.988436 | − | 0.151642i | \(-0.0484560\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.50000 | − | 9.52628i | −1.10000 | − | 1.90526i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | + | 1.73205i | 0.185695 | + | 0.321634i | 0.943811 | − | 0.330487i | \(-0.107213\pi\) |
−0.758115 | + | 0.652121i | \(0.773880\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | − | 3.46410i | 0.359211 | − | 0.622171i | −0.628619 | − | 0.777714i | \(-0.716379\pi\) |
0.987829 | + | 0.155543i | \(0.0497126\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.50000 | + | 4.33013i | 1.30558 | + | 0.753778i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.00000 | −1.35225 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.00000 | −1.31519 | −0.657596 | − | 0.753371i | \(-0.728427\pi\) | ||||
−0.657596 | + | 0.753371i | \(0.728427\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 3.46410i | − | 0.554700i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.500000 | + | 0.866025i | −0.0780869 | + | 0.135250i | −0.902424 | − | 0.430848i | \(-0.858214\pi\) |
0.824338 | + | 0.566099i | \(0.191548\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.50000 | + | 6.06218i | 0.533745 | + | 0.924473i | 0.999223 | + | 0.0394140i | \(0.0125491\pi\) |
−0.465478 | + | 0.885059i | \(0.654118\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.00000 | + | 10.3923i | 0.894427 | + | 1.54919i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.00000 | − | 1.73205i | −0.145865 | − | 0.252646i | 0.783830 | − | 0.620975i | \(-0.213263\pi\) |
−0.929695 | + | 0.368329i | \(0.879930\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.50000 | − | 2.59808i | 0.214286 | − | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.50000 | + | 2.59808i | −0.630126 | + | 0.363803i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.00000 | −0.549442 | −0.274721 | − | 0.961524i | \(-0.588586\pi\) | ||||
−0.274721 | + | 0.961524i | \(0.588586\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −20.0000 | −2.69680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.50000 | − | 0.866025i | 0.198680 | − | 0.114708i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.50000 | + | 4.33013i | −0.325472 | + | 0.563735i | −0.981608 | − | 0.190909i | \(-0.938857\pi\) |
0.656136 | + | 0.754643i | \(0.272190\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.00000 | 0.755929 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.00000 | + | 6.92820i | 0.496139 | + | 0.859338i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.50000 | − | 11.2583i | 0.794101 | − | 1.37542i | −0.129307 | − | 0.991605i | \(-0.541275\pi\) |
0.923408 | − | 0.383819i | \(-0.125391\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 10.3923i | − | 1.25109i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.00000 | 0.351123 | 0.175562 | − | 0.984468i | \(-0.443826\pi\) | ||||
0.175562 | + | 0.984468i | \(0.443826\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −16.5000 | − | 9.52628i | −1.90526 | − | 1.10000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.00000 | + | 8.66025i | −0.569803 | + | 0.986928i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | − | 6.92820i | −0.450035 | − | 0.779484i | 0.548352 | − | 0.836247i | \(-0.315255\pi\) |
−0.998388 | + | 0.0567635i | \(0.981922\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.00000 | − | 10.3923i | −0.658586 | − | 1.14070i | −0.980982 | − | 0.194099i | \(-0.937822\pi\) |
0.322396 | − | 0.946605i | \(-0.395512\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.00000 | − | 10.3923i | 0.650791 | − | 1.12720i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.00000 | + | 1.73205i | 0.321634 | + | 0.185695i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.0000 | −1.06000 | −0.529999 | − | 0.847998i | \(-0.677808\pi\) | ||||
−0.529999 | + | 0.847998i | \(0.677808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | 0.419314 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 6.92820i | − | 0.718421i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.00000 | + | 3.46410i | −0.205196 | + | 0.355409i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.50000 | + | 9.52628i | 0.558440 | + | 0.967247i | 0.997627 | + | 0.0688512i | \(0.0219334\pi\) |
−0.439187 | + | 0.898396i | \(0.644733\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15.0000 | 1.50756 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | − | 10.3923i | −0.597022 | − | 1.03407i | −0.993258 | − | 0.115924i | \(-0.963017\pi\) |
0.396236 | − | 0.918149i | \(-0.370316\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.00000 | + | 5.19615i | −0.295599 | + | 0.511992i | −0.975124 | − | 0.221660i | \(-0.928852\pi\) |
0.679525 | + | 0.733652i | \(0.262186\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −12.0000 | + | 6.92820i | −1.17108 | + | 0.676123i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.00000 | 0.483368 | 0.241684 | − | 0.970355i | \(-0.422300\pi\) | ||||
0.241684 | + | 0.970355i | \(0.422300\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.00000 | 0.766261 | 0.383131 | − | 0.923694i | \(-0.374846\pi\) | ||||
0.383131 | + | 0.923694i | \(0.374846\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.0000 | + | 6.92820i | −1.13899 | + | 0.657596i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.00000 | − | 1.73205i | 0.0940721 | − | 0.162938i | −0.815149 | − | 0.579252i | \(-0.803345\pi\) |
0.909221 | + | 0.416314i | \(0.136678\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.0000 | + | 20.7846i | 1.11901 | + | 1.93817i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.00000 | − | 5.19615i | −0.277350 | − | 0.480384i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.00000 | − | 5.19615i | −0.275010 | − | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | + | 12.1244i | −0.636364 | + | 1.10221i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.73205i | 0.156174i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 24.0000 | 2.14663 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.00000 | 0.177471 | 0.0887357 | − | 0.996055i | \(-0.471717\pi\) | ||||
0.0887357 | + | 0.996055i | \(0.471717\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.5000 | + | 6.06218i | 0.924473 | + | 0.533745i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.00000 | + | 13.8564i | −0.698963 | + | 1.21064i | 0.269863 | + | 0.962899i | \(0.413022\pi\) |
−0.968826 | + | 0.247741i | \(0.920312\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.00000 | + | 1.73205i | 0.0867110 | + | 0.150188i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 18.0000 | + | 10.3923i | 1.54919 | + | 0.894427i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.50000 | + | 2.59808i | 0.128154 | + | 0.221969i | 0.922961 | − | 0.384893i | \(-0.125762\pi\) |
−0.794808 | + | 0.606861i | \(0.792428\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.50000 | − | 11.2583i | 0.551323 | − | 0.954919i | −0.446857 | − | 0.894606i | \(-0.647457\pi\) |
0.998179 | − | 0.0603135i | \(-0.0192101\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.00000 | − | 1.73205i | −0.252646 | − | 0.145865i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.0000 | 0.836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.00000 | −0.664364 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 5.19615i | − | 0.428571i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.00000 | − | 15.5885i | 0.737309 | − | 1.27706i | −0.216394 | − | 0.976306i | \(-0.569430\pi\) |
0.953703 | − | 0.300750i | \(-0.0972370\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.00000 | + | 15.5885i | 0.732410 | + | 1.26857i | 0.955851 | + | 0.293853i | \(0.0949377\pi\) |
−0.223441 | + | 0.974717i | \(0.571729\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.50000 | + | 7.79423i | −0.363803 | + | 0.630126i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.00000 | + | 13.8564i | 0.642575 | + | 1.11297i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | + | 17.3205i | −0.798087 | + | 1.38233i | 0.122774 | + | 0.992435i | \(0.460821\pi\) |
−0.920860 | + | 0.389892i | \(0.872512\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.00000 | + | 3.46410i | −0.475831 | + | 0.274721i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.0000 | 0.945732 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.0000 | −1.56652 | −0.783260 | − | 0.621694i | \(-0.786445\pi\) | ||||
−0.783260 | + | 0.621694i | \(0.786445\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −30.0000 | + | 17.3205i | −2.33550 | + | 1.34840i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.00000 | − | 13.8564i | 0.619059 | − | 1.07224i | −0.370599 | − | 0.928793i | \(-0.620848\pi\) |
0.989658 | − | 0.143448i | \(-0.0458190\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.50000 | + | 7.79423i | 0.346154 | + | 0.599556i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.50000 | − | 2.59808i | 0.114708 | − | 0.198680i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.00000 | − | 15.5885i | −0.684257 | − | 1.18517i | −0.973670 | − | 0.227964i | \(-0.926793\pi\) |
0.289412 | − | 0.957205i | \(-0.406540\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.0000 | − | 19.0526i | 0.831522 | − | 1.44024i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.66025i | 0.650945i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16.0000 | − | 27.7128i | 1.17634 | − | 2.03749i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.50000 | − | 12.9904i | −0.548454 | − | 0.949951i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.00000 | − | 5.19615i | 0.654654 | − | 0.377964i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.00000 | + | 5.19615i | 0.217072 | + | 0.375980i | 0.953912 | − | 0.300088i | \(-0.0970159\pi\) |
−0.736839 | + | 0.676068i | \(0.763683\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.50000 | − | 2.59808i | 0.107972 | − | 0.187014i | −0.806976 | − | 0.590584i | \(-0.798898\pi\) |
0.914949 | + | 0.403570i | \(0.132231\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 12.0000 | + | 6.92820i | 0.859338 | + | 0.496139i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.00000 | 0.284988 | 0.142494 | − | 0.989796i | \(-0.454488\pi\) | ||||
0.142494 | + | 0.989796i | \(0.454488\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.00000 | 0.141776 | 0.0708881 | − | 0.997484i | \(-0.477417\pi\) | ||||
0.0708881 | + | 0.997484i | \(0.477417\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 22.5167i | − | 1.58820i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.00000 | + | 3.46410i | −0.140372 | + | 0.243132i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.00000 | − | 3.46410i | −0.139686 | − | 0.241943i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.00000 | − | 15.5885i | −0.625543 | − | 1.08347i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.50000 | + | 4.33013i | 0.172929 | + | 0.299521i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.0000 | + | 24.2487i | −0.963800 | + | 1.66935i | −0.250994 | + | 0.967989i | \(0.580757\pi\) |
−0.712806 | + | 0.701361i | \(0.752576\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.0000 | − | 6.92820i | 0.822226 | − | 0.474713i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −28.0000 | −1.90958 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.00000 | 0.543075 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.50000 | − | 2.59808i | 0.304082 | − | 0.175562i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.00000 | + | 5.19615i | −0.201802 | + | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.00000 | + | 12.1244i | 0.468755 | + | 0.811907i | 0.999362 | − | 0.0357107i | \(-0.0113695\pi\) |
−0.530607 | + | 0.847618i | \(0.678036\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −33.0000 | −2.20000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.50000 | − | 2.59808i | −0.0995585 | − | 0.172440i | 0.811943 | − | 0.583736i | \(-0.198410\pi\) |
−0.911502 | + | 0.411296i | \(0.865076\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.00000 | + | 12.1244i | −0.462573 | + | 0.801200i | −0.999088 | − | 0.0426906i | \(-0.986407\pi\) |
0.536515 | + | 0.843891i | \(0.319740\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17.3205i | 1.13961i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21.0000 | −1.37576 | −0.687878 | − | 0.725826i | \(-0.741458\pi\) | ||||
−0.687878 | + | 0.725826i | \(0.741458\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.00000 | 0.521862 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.0000 | − | 6.92820i | −0.779484 | − | 0.450035i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.00000 | + | 5.19615i | −0.194054 | + | 0.336111i | −0.946590 | − | 0.322440i | \(-0.895497\pi\) |
0.752536 | + | 0.658551i | \(0.228830\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.5000 | + | 19.9186i | 0.740780 | + | 1.28307i | 0.952141 | + | 0.305661i | \(0.0988773\pi\) |
−0.211360 | + | 0.977408i | \(0.567789\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.5000 | − | 7.79423i | −0.866025 | − | 0.500000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.00000 | + | 10.3923i | 0.383326 | + | 0.663940i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.00000 | − | 1.73205i | 0.0636285 | − | 0.110208i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18.0000 | − | 10.3923i | −1.14070 | − | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.0000 | −1.32551 | −0.662754 | − | 0.748837i | \(-0.730613\pi\) | ||||
−0.662754 | + | 0.748837i | \(0.730613\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 30.0000 | 1.88608 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 20.7846i | − | 1.30158i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.50000 | − | 4.33013i | 0.155946 | − | 0.270106i | −0.777457 | − | 0.628936i | \(-0.783491\pi\) |
0.933403 | + | 0.358830i | \(0.116824\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.00000 | − | 13.8564i | −0.497096 | − | 0.860995i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.00000 | 0.371391 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.00000 | − | 5.19615i | −0.184988 | − | 0.320408i | 0.758585 | − | 0.651575i | \(-0.225891\pi\) |
−0.943572 | + | 0.331166i | \(0.892558\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.00000 | − | 13.8564i | 0.491436 | − | 0.851192i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.0000 | + | 8.66025i | −0.917985 | + | 0.529999i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.0000 | −0.728948 | −0.364474 | − | 0.931214i | \(-0.618751\pi\) | ||||
−0.364474 | + | 0.931214i | \(0.618751\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.00000 | − | 3.46410i | 0.363137 | − | 0.209657i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 27.5000 | − | 47.6314i | 1.65831 | − | 2.87228i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.00000 | + | 12.1244i | 0.420589 | + | 0.728482i | 0.995997 | − | 0.0893846i | \(-0.0284900\pi\) |
−0.575408 | + | 0.817867i | \(0.695157\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.00000 | − | 10.3923i | −0.359211 | − | 0.622171i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.00000 | + | 15.5885i | 0.536895 | + | 0.929929i | 0.999069 | + | 0.0431402i | \(0.0137362\pi\) |
−0.462174 | + | 0.886789i | \(0.652930\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.0000 | − | 24.2487i | 0.832214 | − | 1.44144i | −0.0640654 | − | 0.997946i | \(-0.520407\pi\) |
0.896279 | − | 0.443491i | \(-0.146260\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.92820i | 0.410391i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.00000 | −0.118056 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.5000 | + | 9.52628i | 0.967247 | + | 0.558440i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.0000 | + | 25.9808i | −0.876309 | + | 1.51781i | −0.0209480 | + | 0.999781i | \(0.506668\pi\) |
−0.855361 | + | 0.518032i | \(0.826665\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.0000 | − | 17.3205i | −0.582223 | − | 1.00844i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 22.5000 | − | 12.9904i | 1.30558 | − | 0.753778i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.00000 | − | 10.3923i | −0.346989 | − | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.00000 | + | 12.1244i | −0.403473 | + | 0.698836i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −18.0000 | − | 10.3923i | −1.03407 | − | 0.597022i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.00000 | −0.513657 | −0.256829 | − | 0.966457i | \(-0.582678\pi\) | ||||
−0.256829 | + | 0.966457i | \(0.582678\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.3923i | 0.591198i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.00000 | + | 15.5885i | −0.510343 | + | 0.883940i | 0.489585 | + | 0.871956i | \(0.337148\pi\) |
−0.999928 | + | 0.0119847i | \(0.996185\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.50000 | − | 11.2583i | −0.367402 | − | 0.636358i | 0.621757 | − | 0.783210i | \(-0.286419\pi\) |
−0.989158 | + | 0.146852i | \(0.953086\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −12.0000 | + | 20.7846i | −0.676123 | + | 1.17108i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.00000 | − | 15.5885i | −0.505490 | − | 0.875535i | −0.999980 | − | 0.00635137i | \(-0.997978\pi\) |
0.494489 | − | 0.869184i | \(-0.335355\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.00000 | + | 8.66025i | −0.279946 | + | 0.484881i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.50000 | − | 4.33013i | 0.418609 | − | 0.241684i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.00000 | −0.166924 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −22.0000 | −1.22034 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.0000 | − | 6.92820i | 0.663602 | − | 0.383131i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.00000 | − | 3.46410i | 0.110264 | − | 0.190982i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.00000 | + | 3.46410i | 0.109930 | + | 0.190404i | 0.915742 | − | 0.401768i | \(-0.131604\pi\) |
−0.805812 | + | 0.592172i | \(0.798271\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.0000 | + | 20.7846i | −0.657596 | + | 1.13899i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 26.0000 | + | 45.0333i | 1.42053 | + | 2.46043i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.5000 | − | 21.6506i | 0.680918 | − | 1.17939i | −0.293783 | − | 0.955872i | \(-0.594914\pi\) |
0.974701 | − | 0.223513i | \(-0.0717525\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 3.46410i | − | 0.188144i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.0000 | 1.08306 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 36.0000 | + | 20.7846i | 1.93817 | + | 1.11901i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.500000 | − | 0.866025i | 0.0268414 | − | 0.0464907i | −0.852293 | − | 0.523065i | \(-0.824788\pi\) |
0.879134 | + | 0.476575i | \(0.158122\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.00000 | − | 13.8564i | −0.428230 | − | 0.741716i | 0.568486 | − | 0.822693i | \(-0.307529\pi\) |
−0.996716 | + | 0.0809766i | \(0.974196\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.00000 | − | 5.19615i | −0.480384 | − | 0.277350i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.5000 | − | 30.3109i | −0.931431 | − | 1.61329i | −0.780878 | − | 0.624684i | \(-0.785228\pi\) |
−0.150553 | − | 0.988602i | \(-0.548106\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.0000 | + | 27.7128i | −0.849192 | + | 1.47084i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.00000 | − | 5.19615i | −0.476331 | − | 0.275010i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.0000 | −0.738892 | −0.369446 | − | 0.929252i | \(-0.620452\pi\) | ||||
−0.369446 | + | 0.929252i | \(0.620452\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 24.2487i | 1.27273i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.00000 | + | 10.3923i | −0.314054 | + | 0.543958i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.50000 | + | 2.59808i | 0.0780869 | + | 0.135250i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.00000 | − | 6.92820i | −0.207670 | − | 0.359694i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.0000 | − | 19.0526i | 0.569558 | − | 0.986504i | −0.427051 | − | 0.904227i | \(-0.640448\pi\) |
0.996610 | − | 0.0822766i | \(-0.0262191\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 36.0000 | − | 20.7846i | 1.85903 | − | 1.07331i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.00000 | 0.206010 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.00000 | 0.0513665 | 0.0256833 | − | 0.999670i | \(-0.491824\pi\) | ||||
0.0256833 | + | 0.999670i | \(0.491824\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.00000 | − | 1.73205i | 0.153695 | − | 0.0887357i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.0000 | + | 17.3205i | −0.510976 | + | 0.885037i | 0.488943 | + | 0.872316i | \(0.337383\pi\) |
−0.999919 | + | 0.0127209i | \(0.995951\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −20.0000 | − | 34.6410i | −1.01929 | − | 1.76547i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 21.0000 | 1.06749 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.00000 | + | 5.19615i | 0.152106 | + | 0.263455i | 0.932002 | − | 0.362454i | \(-0.118061\pi\) |
−0.779895 | + | 0.625910i | \(0.784728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00000 | + | 15.5885i | −0.455150 | + | 0.788342i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 27.7128i | 1.39793i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 32.0000 | 1.61009 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.0000 | −1.60603 | −0.803017 | − | 0.595956i | \(-0.796773\pi\) | ||||
−0.803017 | + | 0.595956i | \(0.796773\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.00000 | + | 1.73205i | 0.150188 | + | 0.0867110i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.50000 | + | 4.33013i | −0.124844 | + | 0.216236i | −0.921672 | − | 0.387970i | \(-0.873176\pi\) |
0.796828 | + | 0.604206i | \(0.206510\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.00000 | − | 6.92820i | −0.199254 | − | 0.345118i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 36.0000 | 1.78885 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.0000 | − | 34.6410i | −0.991363 | − | 1.71709i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.5000 | + | 21.6506i | −0.618085 | + | 1.07056i | 0.371750 | + | 0.928333i | \(0.378758\pi\) |
−0.989835 | + | 0.142222i | \(0.954575\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.50000 | + | 2.59808i | 0.221969 | + | 0.128154i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.0000 | −0.492068 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 48.0000 | 2.35623 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 22.5167i | − | 1.10265i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.00000 | + | 3.46410i | −0.0977064 | + | 0.169232i | −0.910735 | − | 0.412991i | \(-0.864484\pi\) |
0.813029 | + | 0.582224i | \(0.197817\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.00000 | − | 6.92820i | −0.194948 | − | 0.337660i | 0.751935 | − | 0.659237i | \(-0.229121\pi\) |
−0.946883 | + | 0.321577i | \(0.895787\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.00000 | −0.291730 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 16.5000 | + | 28.5788i | 0.800368 | + | 1.38628i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 15.0000 | − | 8.66025i | 0.724207 | − | 0.418121i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.0000 | 1.44505 | 0.722525 | − | 0.691345i | \(-0.242982\pi\) | ||||
0.722525 | + | 0.691345i | \(0.242982\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.00000 | 0.0480569 | 0.0240285 | − | 0.999711i | \(-0.492351\pi\) | ||||
0.0240285 | + | 0.999711i | \(0.492351\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.0000 | + | 6.92820i | −0.575356 | + | 0.332182i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.00000 | − | 5.19615i | 0.143509 | − | 0.248566i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.00000 | + | 6.92820i | 0.190910 | + | 0.330665i | 0.945552 | − | 0.325471i | \(-0.105523\pi\) |
−0.754642 | + | 0.656136i | \(0.772190\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.50000 | − | 7.79423i | −0.214286 | − | 0.371154i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.5000 | + | 23.3827i | 0.641404 | + | 1.11094i | 0.985119 | + | 0.171871i | \(0.0549812\pi\) |
−0.343715 | + | 0.939074i | \(0.611685\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 20.0000 | − | 34.6410i | 0.948091 | − | 1.64214i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 31.1769i | − | 1.47462i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −31.0000 | −1.46298 | −0.731490 | − | 0.681852i | \(-0.761175\pi\) | ||||
−0.731490 | + | 0.681852i | \(0.761175\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.00000 | −0.235441 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 27.0000 | + | 15.5885i | 1.26857 | + | 0.732410i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.00000 | + | 13.8564i | −0.375046 | + | 0.649598i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.50000 | + | 6.06218i | 0.163723 | + | 0.283577i | 0.936201 | − | 0.351465i | \(-0.114316\pi\) |
−0.772478 | + | 0.635042i | \(0.780983\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 15.5885i | 0.727607i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.00000 | + | 15.5885i | 0.419172 | + | 0.726027i | 0.995856 | − | 0.0909401i | \(-0.0289872\pi\) |
−0.576685 | + | 0.816967i | \(0.695654\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.00000 | − | 13.8564i | 0.371792 | − | 0.643962i | −0.618050 | − | 0.786139i | \(-0.712077\pi\) |
0.989841 | + | 0.142177i | \(0.0454103\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 24.0000 | + | 13.8564i | 1.11297 | + | 0.642575i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.00000 | 0.323921 | 0.161961 | − | 0.986797i | \(-0.448218\pi\) | ||||
0.161961 | + | 0.986797i | \(0.448218\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.0000 | 1.20057 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 34.6410i | 1.59617i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −17.5000 | + | 30.3109i | −0.804651 | + | 1.39370i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.50000 | − | 9.52628i | −0.252357 | − | 0.437096i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.00000 | + | 10.3923i | −0.274721 | + | 0.475831i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.00000 | − | 15.5885i | −0.411220 | − | 0.712255i | 0.583803 | − | 0.811895i | \(-0.301564\pi\) |
−0.995023 | + | 0.0996406i | \(0.968231\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.00000 | + | 13.8564i | −0.364769 | + | 0.631798i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 18.0000 | − | 10.3923i | 0.819028 | − | 0.472866i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −44.0000 | −1.99794 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.0000 | 0.996915 | 0.498458 | − | 0.866914i | \(-0.333900\pi\) | ||||
0.498458 | + | 0.866914i | \(0.333900\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −30.0000 | + | 17.3205i | −1.35665 | + | 0.783260i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.50000 | + | 6.06218i | −0.157953 | + | 0.273582i | −0.934130 | − | 0.356932i | \(-0.883823\pi\) |
0.776178 | + | 0.630514i | \(0.217156\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.00000 | − | 5.19615i | −0.135113 | − | 0.234023i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −30.0000 | + | 51.9615i | −1.34840 | + | 2.33550i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.00000 | + | 13.8564i | 0.358849 | + | 0.621545i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.5000 | + | 18.1865i | −0.470045 | + | 0.814141i | −0.999413 | − | 0.0342508i | \(-0.989095\pi\) |
0.529369 | + | 0.848392i | \(0.322429\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 27.7128i | − | 1.23812i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.0000 | 1.07011 | 0.535054 | − | 0.844818i | \(-0.320291\pi\) | ||||
0.535054 | + | 0.844818i | \(0.320291\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 48.0000 | 2.13597 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.5000 | + | 7.79423i | 0.599556 | + | 0.346154i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.0000 | + | 20.7846i | −0.531891 | + | 0.921262i | 0.467416 | + | 0.884037i | \(0.345185\pi\) |
−0.999307 | + | 0.0372243i | \(0.988148\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.00000 | + | 5.19615i | 0.132712 | + | 0.229864i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 5.19615i | − | 0.229416i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.0000 | − | 20.7846i | −0.528783 | − | 0.915879i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.00000 | − | 8.66025i | 0.219900 | − | 0.380878i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −27.0000 | − | 15.5885i | −1.18517 | − | 0.684257i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.00000 | −0.131432 | −0.0657162 | − | 0.997838i | \(-0.520933\pi\) | ||||
−0.0657162 | + | 0.997838i | \(0.520933\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.0000 | −0.524723 | −0.262362 | − | 0.964970i | \(-0.584501\pi\) | ||||
−0.262362 | + | 0.964970i | \(0.584501\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 38.1051i | − | 1.66304i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.00000 | + | 10.3923i | −0.261364 | + | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | − | 11.2583i | −0.282609 | − | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.50000 | + | 12.9904i | 0.325472 | + | 0.563735i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.00000 | + | 1.73205i | 0.0433148 | + | 0.0750234i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.0000 | + | 17.3205i | −0.432338 | + | 0.748831i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.0000 | − | 10.3923i | 0.776757 | − | 0.448461i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.0000 | 0.646096 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.0000 | −1.37579 | −0.687894 | − | 0.725811i | \(-0.741464\pi\) | ||||
−0.687894 | + | 0.725811i | \(0.741464\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.00000 | − | 1.73205i | 0.128742 | − | 0.0743294i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.0000 | + | 27.7128i | −0.685365 | + | 1.18709i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.5000 | − | 28.5788i | −0.705489 | − | 1.22194i | −0.966515 | − | 0.256611i | \(-0.917394\pi\) |
0.261026 | − | 0.965332i | \(-0.415939\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.00000 | + | 1.73205i | 0.0426014 | + | 0.0737878i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.00000 | − | 13.8564i | 0.340195 | − | 0.589234i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 55.4256i | − | 2.35269i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.0000 | 0.423714 | 0.211857 | − | 0.977301i | \(-0.432049\pi\) | ||||
0.211857 | + | 0.977301i | \(0.432049\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.0000 | 0.592137 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22.5000 | − | 12.9904i | −0.949951 | − | 0.548454i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.50000 | + | 12.9904i | −0.316087 | + | 0.547479i | −0.979668 | − | 0.200625i | \(-0.935703\pi\) |
0.663581 | + | 0.748105i | \(0.269036\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.00000 | + | 6.92820i | 0.168281 | + | 0.291472i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.00000 | − | 15.5885i | 0.377964 | − | 0.654654i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.50000 | + | 9.52628i | 0.230572 | + | 0.399362i | 0.957977 | − | 0.286846i | \(-0.0926069\pi\) |
−0.727405 | + | 0.686209i | \(0.759274\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.50000 | + | 11.2583i | −0.272017 | + | 0.471146i | −0.969378 | − | 0.245573i | \(-0.921024\pi\) |
0.697362 | + | 0.716720i | \(0.254357\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.00000 | + | 5.19615i | 0.375980 | + | 0.217072i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −66.0000 | −2.75239 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.00000 | 0.124892 | 0.0624458 | − | 0.998048i | \(-0.480110\pi\) | ||||
0.0624458 | + | 0.998048i | \(0.480110\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 5.19615i | − | 0.215945i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.0000 | − | 20.7846i | 0.497844 | − | 0.862291i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.0000 | − | 17.3205i | −0.414158 | − | 0.717342i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 24.0000 | 0.992278 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.50000 | − | 7.79423i | −0.185735 | − | 0.321702i | 0.758089 | − | 0.652151i | \(-0.226133\pi\) |
−0.943824 | + | 0.330449i | \(0.892800\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.00000 | − | 3.46410i | 0.0824086 | − | 0.142736i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.00000 | − | 3.46410i | 0.246807 | − | 0.142494i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.00000 | 0.246390 | 0.123195 | − | 0.992382i | \(-0.460686\pi\) | ||||
0.123195 | + | 0.992382i | \(0.460686\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 24.0000 | 0.983904 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.00000 | − | 1.73205i | 0.122782 | − | 0.0708881i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.0000 | − | 34.6410i | 0.817178 | − | 1.41539i | −0.0905757 | − | 0.995890i | \(-0.528871\pi\) |
0.907754 | − | 0.419504i | \(-0.137796\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.50000 | − | 16.4545i | −0.387513 | − | 0.671192i | 0.604601 | − | 0.796528i | \(-0.293332\pi\) |
−0.992114 | + | 0.125336i | \(0.959999\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −19.5000 | − | 33.7750i | −0.794101 | − | 1.37542i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −28.0000 | − | 48.4974i | −1.13836 | − | 1.97170i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.0000 | + | 17.3205i | −0.405887 | + | 0.703018i | −0.994424 | − | 0.105453i | \(-0.966371\pi\) |
0.588537 | + | 0.808470i | \(0.299704\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.92820i | 0.280745i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.00000 | −0.161823 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.0000 | 0.484675 | 0.242338 | − | 0.970192i | \(-0.422086\pi\) | ||||
0.242338 | + | 0.970192i | \(0.422086\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.00000 | − | 3.46410i | −0.241943 | − | 0.139686i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.5000 | − | 38.9711i | 0.905816 | − | 1.56892i | 0.0859976 | − | 0.996295i | \(-0.472592\pi\) |
0.819818 | − | 0.572624i | \(-0.194074\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.5000 | − | 18.1865i | −0.422031 | − | 0.730978i | 0.574107 | − | 0.818780i | \(-0.305349\pi\) |
−0.996138 | + | 0.0878015i | \(0.972016\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −27.0000 | − | 15.5885i | −1.08347 | − | 0.625543i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.0000 | − | 17.3205i | −0.400642 | − | 0.693932i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.5000 | + | 35.5070i | −0.820000 | + | 1.42028i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.50000 | + | 4.33013i | 0.299521 | + | 0.172929i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24.0000 | 0.956943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.0000 | −1.11466 | −0.557331 | − | 0.830290i | \(-0.688175\pi\) | ||||
−0.557331 | + | 0.830290i | \(0.688175\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 48.4974i | 1.92760i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.00000 | + | 6.92820i | −0.158735 | + | 0.274937i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.00000 | − | 5.19615i | −0.118864 | − | 0.205879i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.0000 | − | 20.7846i | 0.474713 | − | 0.822226i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.50000 | − | 4.33013i | −0.0987441 | − | 0.171030i | 0.812421 | − | 0.583071i | \(-0.198149\pi\) |
−0.911165 | + | 0.412042i | \(0.864816\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.50000 | − | 12.9904i | 0.295771 | − | 0.512291i | −0.679393 | − | 0.733775i | \(-0.737757\pi\) |
0.975164 | + | 0.221484i | \(0.0710901\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −42.0000 | + | 24.2487i | −1.65375 | + | 0.954792i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.00000 | 0.235884 | 0.117942 | − | 0.993020i | \(-0.462370\pi\) | ||||
0.117942 | + | 0.993020i | \(0.462370\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.0000 | −0.981336 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.0000 | − | 6.92820i | 0.470317 | − | 0.271538i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.0000 | − | 19.0526i | 0.430463 | − | 0.745584i | −0.566450 | − | 0.824096i | \(-0.691684\pi\) |
0.996913 | + | 0.0785119i | \(0.0250169\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −32.0000 | − | 55.4256i | −1.25034 | − | 2.16566i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.50000 | − | 7.79423i | 0.175562 | − | 0.304082i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.00000 | + | 10.3923i | 0.233727 | + | 0.404827i | 0.958902 | − | 0.283738i | \(-0.0915745\pi\) |
−0.725175 | + | 0.688565i | \(0.758241\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.0000 | + | 27.7128i | −0.622328 | + | 1.07790i | 0.366723 | + | 0.930330i | \(0.380480\pi\) |
−0.989051 | + | 0.147573i | \(0.952854\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.3923i | 0.403604i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.00000 | −0.310227 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.0000 | 0.464642 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 21.0000 | + | 12.1244i | 0.811907 | + | 0.468755i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.00000 | − | 1.73205i | −0.0385472 | − | 0.0667657i | 0.846108 | − | 0.533011i | \(-0.178940\pi\) |
−0.884655 | + | 0.466246i | \(0.845606\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −49.5000 | + | 28.5788i | −1.90526 | + | 1.10000i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.0000 | + | 24.2487i | 0.538064 | + | 0.931954i | 0.999008 | + | 0.0445248i | \(0.0141774\pi\) |
−0.460945 | + | 0.887429i | \(0.652489\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.0000 | + | 19.0526i | −0.422141 | + | 0.731170i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.50000 | − | 2.59808i | −0.172440 | − | 0.0995585i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.0000 | −0.573959 | −0.286980 | − | 0.957937i | \(-0.592651\pi\) | ||||
−0.286980 | + | 0.957937i | \(0.592651\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.0000 | −0.458496 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.2487i | 0.925146i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.00000 | + | 6.92820i | −0.152388 | + | 0.263944i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.00000 | + | 6.92820i | 0.152167 | + | 0.263561i | 0.932024 | − | 0.362397i | \(-0.118041\pi\) |
−0.779857 | + | 0.625958i | \(0.784708\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15.0000 | + | 25.9808i | 0.569803 | + | 0.986928i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 26.0000 | + | 45.0333i | 0.986236 | + | 1.70821i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.50000 | − | 2.59808i | 0.0568166 | − | 0.0984092i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −31.5000 | + | 18.1865i | −1.19144 | + | 0.687878i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.0000 | 1.58632 | 0.793159 | − | 0.609015i | \(-0.208435\pi\) | ||||
0.793159 | + | 0.609015i | \(0.208435\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.00000 | −0.301726 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.0000 | − | 6.92820i | 0.451946 | − | 0.260931i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.0000 | − | 20.7846i | 0.451306 | − | 0.781686i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.0000 | + | 17.3205i | 0.375558 | + | 0.650485i | 0.990410 | − | 0.138157i | \(-0.0441178\pi\) |
−0.614852 | + | 0.788642i | \(0.710784\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −24.0000 | −0.900070 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12.0000 | − | 20.7846i | −0.449404 | − | 0.778390i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −20.0000 | + | 34.6410i | −0.747958 | + | 1.29550i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.3923i | 0.388108i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.0000 | 1.19340 | 0.596699 | − | 0.802465i | \(-0.296479\pi\) | ||||
0.596699 | + | 0.802465i | \(0.296479\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.0000 | −0.446903 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 34.5000 | + | 19.9186i | 1.28307 | + | 0.740780i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11.0000 | − | 19.0526i | 0.408530 | − | 0.707594i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.0000 | + | 25.9808i | 0.556319 | + | 0.963573i | 0.997800 | + | 0.0663022i | \(0.0211201\pi\) |
−0.441480 | + | 0.897271i | \(0.645547\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.5000 | − | 18.1865i | −0.388357 | − | 0.672653i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.0000 | − | 29.4449i | 0.627909 | − | 1.08757i | −0.360061 | − | 0.932929i | \(-0.617244\pi\) |
0.987971 | − | 0.154642i | \(-0.0494225\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 18.0000 | + | 10.3923i | 0.663940 | + | 0.383326i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 65.0000 | 2.39431 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 49.0000 | 1.80249 | 0.901247 | − | 0.433306i | \(-0.142653\pi\) | ||||
0.901247 | + | 0.433306i | \(0.142653\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 3.46410i | − | 0.127257i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.00000 | − | 5.19615i | 0.110059 | − | 0.190628i | −0.805735 | − | 0.592277i | \(-0.798229\pi\) |
0.915794 | + | 0.401648i | \(0.131563\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 36.0000 | + | 62.3538i | 1.31894 | + | 2.28447i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −36.0000 | −1.31717 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.00000 | + | 8.66025i | 0.182696 | + | 0.316439i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.0000 | − | 45.0333i | 0.948753 | − | 1.64329i | 0.200698 | − | 0.979653i | \(-0.435679\pi\) |
0.748056 | − | 0.663636i | \(-0.230988\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −31.5000 | + | 18.1865i | −1.14792 | + | 0.662754i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −72.0000 | −2.62035 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.0000 | 0.654221 | 0.327111 | − | 0.944986i | \(-0.393925\pi\) | ||||
0.327111 | + | 0.944986i | \(0.393925\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 45.0000 | − | 25.9808i | 1.63340 | − | 0.943042i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.0000 | − | 25.9808i | 0.543750 | − | 0.941802i | −0.454935 | − | 0.890525i | \(-0.650337\pi\) |
0.998684 | − | 0.0512772i | \(-0.0163292\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.00000 | + | 13.8564i | 0.289619 | + | 0.501636i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −18.0000 | − | 31.1769i | −0.650791 | − | 1.12720i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.00000 | + | 8.66025i | 0.180540 | + | 0.312704i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.00000 | + | 8.66025i | −0.180305 | + | 0.312297i | −0.941984 | − | 0.335657i | \(-0.891042\pi\) |
0.761680 | + | 0.647954i | \(0.224375\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 8.66025i | − | 0.311891i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −42.0000 | −1.51064 | −0.755318 | − | 0.655359i | \(-0.772517\pi\) | ||||
−0.755318 | + | 0.655359i | \(0.772517\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −44.0000 | −1.58053 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −24.0000 | − | 13.8564i | −0.860995 | − | 0.497096i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.500000 | + | 0.866025i | −0.0179144 | + | 0.0310286i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.0000 | + | 34.6410i | 0.715656 | + | 1.23955i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.00000 | − | 5.19615i | 0.321634 | − | 0.185695i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −40.0000 | − | 69.2820i | −1.42766 | − | 2.47278i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.0000 | − | 31.1769i | 0.641631 | − | 1.11134i | −0.343438 | − | 0.939175i | \(-0.611592\pi\) |
0.985069 | − | 0.172162i | \(-0.0550751\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.00000 | − | 5.19615i | −0.320408 | − | 0.184988i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.00000 | 0.142224 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 27.7128i | − | 0.982872i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.0000 | + | 20.7846i | −0.425062 | + | 0.736229i | −0.996426 | − | 0.0844678i | \(-0.973081\pi\) |
0.571364 | + | 0.820696i | \(0.306414\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.00000 | + | 5.19615i | 0.106132 | + | 0.183827i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.0000 | + | 25.9808i | −0.529999 | + | 0.917985i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.50000 | + | 12.9904i | 0.264669 | + | 0.458421i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −24.0000 | + | 41.5692i | −0.845889 | + | 1.46512i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.0000 | 0.597688 | 0.298844 | − | 0.954302i | \(-0.403399\pi\) | ||||
0.298844 | + | 0.954302i | \(0.403399\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 55.0000 | 1.93131 | 0.965656 | − | 0.259825i | \(-0.0836650\pi\) | ||||
0.965656 | + | 0.259825i | \(0.0836650\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.0000 | + | 10.3923i | −0.631288 | + | 0.364474i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 40.0000 | − | 69.2820i | 1.40114 | − | 2.42684i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.50000 | + | 6.06218i | 0.122449 | + | 0.212089i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.00000 | − | 10.3923i | 0.209657 | − | 0.363137i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.0000 | + | 43.3013i | 0.872506 | + | 1.51122i | 0.859396 | + | 0.511311i | \(0.170840\pi\) |
0.0131101 | + | 0.999914i | \(0.495827\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.0000 | + | 24.2487i | −0.488009 | + | 0.845257i | −0.999905 | − | 0.0137907i | \(-0.995610\pi\) |
0.511896 | + | 0.859048i | \(0.328943\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 95.2628i | − | 3.31662i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.0000 | 0.973655 | 0.486828 | − | 0.873498i | \(-0.338154\pi\) | ||||
0.486828 | + | 0.873498i | \(0.338154\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.0000 | 0.486240 | 0.243120 | − | 0.969996i | \(-0.421829\pi\) | ||||
0.243120 | + | 0.969996i | \(0.421829\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.0000 | + | 12.1244i | 0.728482 | + | 0.420589i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.50000 | + | 7.79423i | −0.155916 | + | 0.270054i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32.0000 | + | 55.4256i | 1.10741 | + | 1.91808i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −18.0000 | − | 10.3923i | −0.622171 | − | 0.359211i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.00000 | + | 3.46410i | 0.0690477 | + | 0.119594i | 0.898482 | − | 0.439010i | \(-0.144671\pi\) |
−0.829435 | + | 0.558604i | \(0.811337\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.5000 | − | 21.6506i | 0.431034 | − | 0.746574i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 27.0000 | + | 15.5885i | 0.929929 | + | 0.536895i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −36.0000 | −1.23844 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −28.0000 | −0.962091 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 48.4974i | − | 1.66443i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24.0000 | + | 41.5692i | −0.822709 | + | 1.42497i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.0000 | − | 25.9808i | −0.513590 | − | 0.889564i | −0.999876 | − | 0.0157644i | \(-0.994982\pi\) |
0.486286 | − | 0.873800i | \(-0.338351\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.00000 | + | 10.3923i | 0.205196 | + | 0.355409i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.00000 | + | 8.66025i | 0.170797 | + | 0.295829i | 0.938699 | − | 0.344739i | \(-0.112033\pi\) |
−0.767902 | + | 0.640567i | \(0.778699\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.50000 | + | 4.33013i | −0.0852989 | + | 0.147742i | −0.905519 | − | 0.424307i | \(-0.860518\pi\) |
0.820220 | + | 0.572049i | \(0.193851\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.00000 | + | 1.73205i | −0.102240 | + | 0.0590281i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28.0000 | −0.953131 | −0.476566 | − | 0.879139i | \(-0.658119\pi\) | ||||
−0.476566 | + | 0.879139i | \(0.658119\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 72.0000 | 2.44807 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.0000 | + | 6.92820i | −0.407541 | + | 0.235294i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.0000 | − | 34.6410i | 0.678454 | − | 1.17512i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.0000 | − | 22.5167i | −0.440488 | − | 0.762948i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 33.0000 | 1.11688 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 24.0000 | + | 41.5692i | 0.811348 | + | 1.40530i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.0000 | + | 34.6410i | −0.675352 | + | 1.16974i | 0.301014 | + | 0.953620i | \(0.402675\pi\) |
−0.976366 | + | 0.216124i | \(0.930658\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 51.9615i | 1.75262i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.0000 | 1.01073 | 0.505363 | − | 0.862907i | \(-0.331359\pi\) | ||||
0.505363 | + | 0.862907i | \(0.331359\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.0000 | −0.437485 | −0.218742 | − | 0.975783i | \(-0.570195\pi\) | ||||
−0.218742 | + | 0.975783i | \(0.570195\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −30.0000 | − | 17.3205i | −1.00844 | − | 0.582223i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.0000 | + | 31.1769i | −0.604381 | + | 1.04682i | 0.387768 | + | 0.921757i | \(0.373246\pi\) |
−0.992149 | + | 0.125061i | \(0.960087\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.00000 | + | 3.46410i | 0.0670778 | + | 0.116182i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 22.5000 | − | 38.9711i | 0.753778 | − | 1.30558i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.00000 | − | 1.73205i | −0.0334637 | − | 0.0579609i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.0000 | + | 41.5692i | −0.802232 | + | 1.38951i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18.0000 | − | 10.3923i | −0.601003 | − | 0.346989i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.00000 | 0.266815 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0000 | 0.399778 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24.2487i | 0.806947i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.00000 | + | 6.92820i | −0.132964 | + | 0.230301i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.50000 | − | 6.06218i | −0.116216 | − | 0.201291i | 0.802049 | − | 0.597258i | \(-0.203743\pi\) |
−0.918265 | + | 0.395966i | \(0.870410\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −36.0000 | −1.19404 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0000 | + | 20.7846i | 0.397578 | + | 0.688625i | 0.993426 | − | 0.114472i | \(-0.0365176\pi\) |
−0.595849 | + | 0.803097i | \(0.703184\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30.0000 | − | 51.9615i | 0.992855 | − | 1.71968i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −32.0000 | −1.05673 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 54.0000 | 1.78130 | 0.890648 | − | 0.454694i | \(-0.150251\pi\) | ||||
0.890648 | + | 0.454694i | \(0.150251\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.5000 | + | 7.79423i | −0.444840 | + | 0.256829i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.00000 | − | 13.8564i | 0.263323 | − | 0.456089i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 44.0000 | + | 76.2102i | 1.44671 | + | 2.50578i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.00000 | + | 15.5885i | 0.295599 | + | 0.511992i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.00000 | + | 5.19615i | 0.0984268 | + | 0.170480i | 0.911034 | − | 0.412332i | \(-0.135286\pi\) |
−0.812607 | + | 0.582812i | \(0.801952\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.50000 | − | 2.59808i | 0.0491605 | − | 0.0851485i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 31.1769i | 1.02069i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 60.0000 | 1.96221 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −58.0000 | −1.89478 | −0.947389 | − | 0.320085i | \(-0.896288\pi\) | ||||
−0.947389 | + | 0.320085i | \(0.896288\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.5000 | − | 11.2583i | −0.636358 | − | 0.367402i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.0000 | − | 24.2487i | 0.456387 | − | 0.790485i | −0.542380 | − | 0.840133i | \(-0.682477\pi\) |
0.998767 | + | 0.0496480i | \(0.0158099\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.00000 | + | 5.19615i | 0.0976934 | + | 0.169210i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 41.5692i | 1.35225i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.5000 | + | 23.3827i | 0.438691 | + | 0.759835i | 0.997589 | − | 0.0694014i | \(-0.0221089\pi\) |
−0.558898 | + | 0.829237i | \(0.688776\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.00000 | − | 5.19615i | 0.0973841 | − | 0.168674i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −27.0000 | − | 15.5885i | −0.875535 | − | 0.505490i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39.0000 | −1.26333 | −0.631667 | − | 0.775240i | \(-0.717629\pi\) | ||||
−0.631667 | + | 0.775240i | \(0.717629\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.0000 | −0.776622 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17.3205i | 0.559893i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.00000 | + | 5.19615i | −0.0968751 | + | 0.167793i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.50000 | − | 12.9904i | 0.241684 | − | 0.418609i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.00000 | + | 10.3923i | 0.193147 | + | 0.334540i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.0000 | − | 36.3731i | 0.675314 | − | 1.16968i | −0.301062 | − | 0.953604i | \(-0.597341\pi\) |
0.976377 | − | 0.216075i | \(-0.0693254\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.50000 | + | 2.59808i | −0.144561 | + | 0.0834622i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.0000 | −0.641831 | −0.320915 | − | 0.947108i | \(-0.603990\pi\) | ||||
−0.320915 | + | 0.947108i | \(0.603990\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.0000 | 0.833522 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −33.0000 | + | 19.0526i | −1.05685 | + | 0.610170i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.50000 | − | 9.52628i | 0.175961 | − | 0.304773i | −0.764533 | − | 0.644585i | \(-0.777030\pi\) |
0.940493 | + | 0.339812i | \(0.110364\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.0000 | − | 43.3013i | −0.799003 | − | 1.38391i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.0000 | − | 20.7846i | 0.383131 | − | 0.663602i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.0000 | − | 31.1769i | −0.574111 | − | 0.994389i | −0.996138 | − | 0.0878058i | \(-0.972015\pi\) |
0.422027 | − | 0.906583i | \(-0.361319\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.00000 | + | 13.8564i | −0.254901 | + | 0.441502i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 6.92820i | − | 0.220527i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 42.0000 | 1.33552 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0000 | −0.508257 | −0.254128 | − | 0.967170i | \(-0.581789\pi\) | ||||
−0.254128 | + | 0.967170i | \(0.581789\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.00000 | + | 3.46410i | 0.190404 | + | 0.109930i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.00000 | + | 6.92820i | −0.126809 | + | 0.219639i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.0000 | − | 51.9615i | −0.950110 | − | 1.64564i | −0.745182 | − | 0.666861i | \(-0.767638\pi\) |
−0.204927 | − | 0.978777i | \(-0.565696\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 41.5692i | 1.31519i |
(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 | 288.2.i.b.193.1 | yes | 2 | |
3.2 | odd | 2 | 864.2.i.b.577.1 | 2 | |||
4.3 | odd | 2 | 288.2.i.a.193.1 | yes | 2 | ||
8.3 | odd | 2 | 576.2.i.h.193.1 | 2 | |||
8.5 | even | 2 | 576.2.i.b.193.1 | 2 | |||
9.2 | odd | 6 | 864.2.i.b.289.1 | 2 | |||
9.4 | even | 3 | 2592.2.a.g.1.1 | 1 | |||
9.5 | odd | 6 | 2592.2.a.a.1.1 | 1 | |||
9.7 | even | 3 | inner | 288.2.i.b.97.1 | yes | 2 | |
12.11 | even | 2 | 864.2.i.a.577.1 | 2 | |||
24.5 | odd | 2 | 1728.2.i.b.577.1 | 2 | |||
24.11 | even | 2 | 1728.2.i.a.577.1 | 2 | |||
36.7 | odd | 6 | 288.2.i.a.97.1 | ✓ | 2 | ||
36.11 | even | 6 | 864.2.i.a.289.1 | 2 | |||
36.23 | even | 6 | 2592.2.a.b.1.1 | 1 | |||
36.31 | odd | 6 | 2592.2.a.h.1.1 | 1 | |||
72.5 | odd | 6 | 5184.2.a.be.1.1 | 1 | |||
72.11 | even | 6 | 1728.2.i.a.1153.1 | 2 | |||
72.13 | even | 6 | 5184.2.a.a.1.1 | 1 | |||
72.29 | odd | 6 | 1728.2.i.b.1153.1 | 2 | |||
72.43 | odd | 6 | 576.2.i.h.385.1 | 2 | |||
72.59 | even | 6 | 5184.2.a.bf.1.1 | 1 | |||
72.61 | even | 6 | 576.2.i.b.385.1 | 2 | |||
72.67 | odd | 6 | 5184.2.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.i.a.97.1 | ✓ | 2 | 36.7 | odd | 6 | ||
288.2.i.a.193.1 | yes | 2 | 4.3 | odd | 2 | ||
288.2.i.b.97.1 | yes | 2 | 9.7 | even | 3 | inner | |
288.2.i.b.193.1 | yes | 2 | 1.1 | even | 1 | trivial | |
576.2.i.b.193.1 | 2 | 8.5 | even | 2 | |||
576.2.i.b.385.1 | 2 | 72.61 | even | 6 | |||
576.2.i.h.193.1 | 2 | 8.3 | odd | 2 | |||
576.2.i.h.385.1 | 2 | 72.43 | odd | 6 | |||
864.2.i.a.289.1 | 2 | 36.11 | even | 6 | |||
864.2.i.a.577.1 | 2 | 12.11 | even | 2 | |||
864.2.i.b.289.1 | 2 | 9.2 | odd | 6 | |||
864.2.i.b.577.1 | 2 | 3.2 | odd | 2 | |||
1728.2.i.a.577.1 | 2 | 24.11 | even | 2 | |||
1728.2.i.a.1153.1 | 2 | 72.11 | even | 6 | |||
1728.2.i.b.577.1 | 2 | 24.5 | odd | 2 | |||
1728.2.i.b.1153.1 | 2 | 72.29 | odd | 6 | |||
2592.2.a.a.1.1 | 1 | 9.5 | odd | 6 | |||
2592.2.a.b.1.1 | 1 | 36.23 | even | 6 | |||
2592.2.a.g.1.1 | 1 | 9.4 | even | 3 | |||
2592.2.a.h.1.1 | 1 | 36.31 | odd | 6 | |||
5184.2.a.a.1.1 | 1 | 72.13 | even | 6 | |||
5184.2.a.b.1.1 | 1 | 72.67 | odd | 6 | |||
5184.2.a.be.1.1 | 1 | 72.5 | odd | 6 | |||
5184.2.a.bf.1.1 | 1 | 72.59 | even | 6 |