Properties

Label 336.2.bc.f.257.6
Level $336$
Weight $2$
Character 336.257
Analytic conductor $2.683$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [336,2,Mod(17,336)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(336, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("336.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 336.bc (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: \(2.68297350792\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 6 x^{15} + 19 x^{14} - 42 x^{13} + 65 x^{12} - 48 x^{11} - 94 x^{10} + 444 x^{9} - 962 x^{8} + 1332 x^{7} - 846 x^{6} - 1296 x^{5} + 5265 x^{4} - 10206 x^{3} + 13851 x^{2} + \cdots + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 168)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 257.6
Root \(1.22961 + 1.21986i\) of defining polynomial
Character \(\chi\) \(=\) 336.257
Dual form 336.2.bc.f.17.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.21986 - 1.22961i) q^{3} +(-1.40397 + 2.43175i) q^{5} +(2.08606 + 1.62738i) q^{7} +(-0.0238727 - 2.99991i) q^{9} +O(q^{10})\) \(q+(1.21986 - 1.22961i) q^{3} +(-1.40397 + 2.43175i) q^{5} +(2.08606 + 1.62738i) q^{7} +(-0.0238727 - 2.99991i) q^{9} +(4.74645 - 2.74036i) q^{11} +1.35669i q^{13} +(1.27745 + 4.69274i) q^{15} +(2.88753 + 5.00135i) q^{17} +(-1.71973 - 0.992889i) q^{19} +(4.54574 - 0.579855i) q^{21} +(-2.09928 - 1.21202i) q^{23} +(-1.44228 - 2.49811i) q^{25} +(-3.71783 - 3.63012i) q^{27} -7.05668i q^{29} +(3.07596 - 1.77591i) q^{31} +(2.42044 - 9.17913i) q^{33} +(-6.88616 + 2.78798i) q^{35} +(-2.14377 + 3.71312i) q^{37} +(1.66820 + 1.65498i) q^{39} -1.81976 q^{41} -11.2288 q^{43} +(7.32855 + 4.15374i) q^{45} +(0.201213 - 0.348512i) q^{47} +(1.70327 + 6.78961i) q^{49} +(9.67209 + 2.55043i) q^{51} +(-5.28097 + 3.04897i) q^{53} +15.3896i q^{55} +(-3.31870 + 0.903412i) q^{57} +(-1.28234 - 2.22108i) q^{59} +(-4.75817 - 2.74713i) q^{61} +(4.83218 - 6.29682i) q^{63} +(-3.29914 - 1.90476i) q^{65} +(-3.45238 - 5.97970i) q^{67} +(-4.05114 + 1.10279i) q^{69} +2.08251i q^{71} +(-0.295696 + 0.170720i) q^{73} +(-4.83108 - 1.27390i) q^{75} +(14.3610 + 2.00772i) q^{77} +(-1.19139 + 2.06355i) q^{79} +(-8.99886 + 0.143232i) q^{81} +11.8717 q^{83} -16.2161 q^{85} +(-8.67696 - 8.60818i) q^{87} +(-0.576571 + 0.998650i) q^{89} +(-2.20785 + 2.83014i) q^{91} +(1.56858 - 5.94859i) q^{93} +(4.82892 - 2.78798i) q^{95} +16.0187i q^{97} +(-8.33413 - 14.1735i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{7} + 2 q^{9} - 8 q^{15} + 6 q^{19} + 14 q^{21} - 18 q^{25} + 48 q^{31} - 12 q^{33} - 2 q^{37} + 22 q^{39} - 20 q^{43} - 42 q^{45} - 28 q^{49} - 6 q^{51} - 8 q^{57} + 36 q^{61} + 32 q^{63} - 14 q^{67} + 30 q^{73} - 54 q^{75} - 28 q^{79} + 30 q^{81} + 16 q^{85} - 78 q^{87} - 66 q^{91} + 16 q^{93} - 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.21986 1.22961i 0.704288 0.709915i
\(4\) 0 0
\(5\) −1.40397 + 2.43175i −0.627876 + 1.08751i 0.360101 + 0.932913i \(0.382742\pi\)
−0.987977 + 0.154600i \(0.950591\pi\)
\(6\) 0 0
\(7\) 2.08606 + 1.62738i 0.788456 + 0.615092i
\(8\) 0 0
\(9\) −0.0238727 2.99991i −0.00795756 0.999968i
\(10\) 0 0
\(11\) 4.74645 2.74036i 1.43111 0.826250i 0.433902 0.900960i \(-0.357136\pi\)
0.997205 + 0.0747101i \(0.0238032\pi\)
\(12\) 0 0
\(13\) 1.35669i 0.376279i 0.982142 + 0.188139i \(0.0602457\pi\)
−0.982142 + 0.188139i \(0.939754\pi\)
\(14\) 0 0
\(15\) 1.27745 + 4.69274i 0.329836 + 1.21166i
\(16\) 0 0
\(17\) 2.88753 + 5.00135i 0.700329 + 1.21301i 0.968351 + 0.249593i \(0.0802967\pi\)
−0.268022 + 0.963413i \(0.586370\pi\)
\(18\) 0 0
\(19\) −1.71973 0.992889i −0.394534 0.227784i 0.289589 0.957151i \(-0.406481\pi\)
−0.684123 + 0.729367i \(0.739815\pi\)
\(20\) 0 0
\(21\) 4.54574 0.579855i 0.991962 0.126535i
\(22\) 0 0
\(23\) −2.09928 1.21202i −0.437730 0.252723i 0.264904 0.964275i \(-0.414660\pi\)
−0.702634 + 0.711551i \(0.747993\pi\)
\(24\) 0 0
\(25\) −1.44228 2.49811i −0.288457 0.499622i
\(26\) 0 0
\(27\) −3.71783 3.63012i −0.715497 0.698616i
\(28\) 0 0
\(29\) 7.05668i 1.31039i −0.755458 0.655197i \(-0.772586\pi\)
0.755458 0.655197i \(-0.227414\pi\)
\(30\) 0 0
\(31\) 3.07596 1.77591i 0.552459 0.318962i −0.197654 0.980272i \(-0.563332\pi\)
0.750113 + 0.661309i \(0.229999\pi\)
\(32\) 0 0
\(33\) 2.42044 9.17913i 0.421344 1.59788i
\(34\) 0 0
\(35\) −6.88616 + 2.78798i −1.16397 + 0.471255i
\(36\) 0 0
\(37\) −2.14377 + 3.71312i −0.352434 + 0.610434i −0.986675 0.162701i \(-0.947979\pi\)
0.634241 + 0.773135i \(0.281313\pi\)
\(38\) 0 0
\(39\) 1.66820 + 1.65498i 0.267126 + 0.265009i
\(40\) 0 0
\(41\) −1.81976 −0.284199 −0.142100 0.989852i \(-0.545385\pi\)
−0.142100 + 0.989852i \(0.545385\pi\)
\(42\) 0 0
\(43\) −11.2288 −1.71238 −0.856188 0.516665i \(-0.827173\pi\)
−0.856188 + 0.516665i \(0.827173\pi\)
\(44\) 0 0
\(45\) 7.32855 + 4.15374i 1.09248 + 0.619202i
\(46\) 0 0
\(47\) 0.201213 0.348512i 0.0293500 0.0508356i −0.850977 0.525202i \(-0.823990\pi\)
0.880327 + 0.474367i \(0.157323\pi\)
\(48\) 0 0
\(49\) 1.70327 + 6.78961i 0.243325 + 0.969945i
\(50\) 0 0
\(51\) 9.67209 + 2.55043i 1.35436 + 0.357131i
\(52\) 0 0
\(53\) −5.28097 + 3.04897i −0.725397 + 0.418808i −0.816736 0.577012i \(-0.804219\pi\)
0.0913389 + 0.995820i \(0.470885\pi\)
\(54\) 0 0
\(55\) 15.3896i 2.07513i
\(56\) 0 0
\(57\) −3.31870 + 0.903412i −0.439573 + 0.119660i
\(58\) 0 0
\(59\) −1.28234 2.22108i −0.166947 0.289161i 0.770398 0.637563i \(-0.220058\pi\)
−0.937345 + 0.348403i \(0.886724\pi\)
\(60\) 0 0
\(61\) −4.75817 2.74713i −0.609222 0.351734i 0.163439 0.986553i \(-0.447741\pi\)
−0.772661 + 0.634819i \(0.781075\pi\)
\(62\) 0 0
\(63\) 4.83218 6.29682i 0.608798 0.793325i
\(64\) 0 0
\(65\) −3.29914 1.90476i −0.409208 0.236257i
\(66\) 0 0
\(67\) −3.45238 5.97970i −0.421775 0.730536i 0.574338 0.818618i \(-0.305260\pi\)
−0.996113 + 0.0880819i \(0.971926\pi\)
\(68\) 0 0
\(69\) −4.05114 + 1.10279i −0.487700 + 0.132761i
\(70\) 0 0
\(71\) 2.08251i 0.247148i 0.992335 + 0.123574i \(0.0394357\pi\)
−0.992335 + 0.123574i \(0.960564\pi\)
\(72\) 0 0
\(73\) −0.295696 + 0.170720i −0.0346086 + 0.0199813i −0.517204 0.855862i \(-0.673027\pi\)
0.482596 + 0.875843i \(0.339694\pi\)
\(74\) 0 0
\(75\) −4.83108 1.27390i −0.557846 0.147098i
\(76\) 0 0
\(77\) 14.3610 + 2.00772i 1.63658 + 0.228800i
\(78\) 0 0
\(79\) −1.19139 + 2.06355i −0.134042 + 0.232168i −0.925231 0.379404i \(-0.876129\pi\)
0.791189 + 0.611572i \(0.209462\pi\)
\(80\) 0 0
\(81\) −8.99886 + 0.143232i −0.999873 + 0.0159146i
\(82\) 0 0
\(83\) 11.8717 1.30309 0.651543 0.758611i \(-0.274122\pi\)
0.651543 + 0.758611i \(0.274122\pi\)
\(84\) 0 0
\(85\) −16.2161 −1.75888
\(86\) 0 0
\(87\) −8.67696 8.60818i −0.930267 0.922894i
\(88\) 0 0
\(89\) −0.576571 + 0.998650i −0.0611164 + 0.105857i −0.894965 0.446137i \(-0.852799\pi\)
0.833848 + 0.551994i \(0.186133\pi\)
\(90\) 0 0
\(91\) −2.20785 + 2.83014i −0.231446 + 0.296679i
\(92\) 0 0
\(93\) 1.56858 5.94859i 0.162654 0.616840i
\(94\) 0 0
\(95\) 4.82892 2.78798i 0.495437 0.286041i
\(96\) 0 0
\(97\) 16.0187i 1.62645i 0.581950 + 0.813225i \(0.302290\pi\)
−0.581950 + 0.813225i \(0.697710\pi\)
\(98\) 0 0
\(99\) −8.33413 14.1735i −0.837612 1.42449i
\(100\) 0 0
\(101\) −7.33982 12.7129i −0.730339 1.26498i −0.956738 0.290950i \(-0.906029\pi\)
0.226399 0.974035i \(-0.427305\pi\)
\(102\) 0 0
\(103\) −4.06960 2.34958i −0.400989 0.231511i 0.285922 0.958253i \(-0.407700\pi\)
−0.686911 + 0.726742i \(0.741034\pi\)
\(104\) 0 0
\(105\) −4.97204 + 11.8682i −0.485221 + 1.15822i
\(106\) 0 0
\(107\) −7.14150 4.12315i −0.690395 0.398600i 0.113365 0.993553i \(-0.463837\pi\)
−0.803760 + 0.594954i \(0.797170\pi\)
\(108\) 0 0
\(109\) −4.41113 7.64030i −0.422509 0.731808i 0.573675 0.819083i \(-0.305517\pi\)
−0.996184 + 0.0872755i \(0.972184\pi\)
\(110\) 0 0
\(111\) 1.95058 + 7.16550i 0.185141 + 0.680119i
\(112\) 0 0
\(113\) 4.00000i 0.376288i −0.982141 0.188144i \(-0.939753\pi\)
0.982141 0.188144i \(-0.0602472\pi\)
\(114\) 0 0
\(115\) 5.89467 3.40329i 0.549680 0.317358i
\(116\) 0 0
\(117\) 4.06995 0.0323879i 0.376267 0.00299426i
\(118\) 0 0
\(119\) −2.11554 + 15.1322i −0.193931 + 1.38717i
\(120\) 0 0
\(121\) 9.51916 16.4877i 0.865378 1.49888i
\(122\) 0 0
\(123\) −2.21986 + 2.23760i −0.200158 + 0.201757i
\(124\) 0 0
\(125\) −5.94002 −0.531291
\(126\) 0 0
\(127\) 6.93769 0.615620 0.307810 0.951448i \(-0.400404\pi\)
0.307810 + 0.951448i \(0.400404\pi\)
\(128\) 0 0
\(129\) −13.6976 + 13.8070i −1.20601 + 1.21564i
\(130\) 0 0
\(131\) −0.118734 + 0.205654i −0.0103739 + 0.0179680i −0.871166 0.490989i \(-0.836635\pi\)
0.860792 + 0.508957i \(0.169969\pi\)
\(132\) 0 0
\(133\) −1.97166 4.86988i −0.170964 0.422273i
\(134\) 0 0
\(135\) 14.0473 3.94426i 1.20900 0.339468i
\(136\) 0 0
\(137\) 9.58873 5.53606i 0.819221 0.472977i −0.0309270 0.999522i \(-0.509846\pi\)
0.850148 + 0.526544i \(0.176513\pi\)
\(138\) 0 0
\(139\) 1.02466i 0.0869108i 0.999055 + 0.0434554i \(0.0138366\pi\)
−0.999055 + 0.0434554i \(0.986163\pi\)
\(140\) 0 0
\(141\) −0.183080 0.672550i −0.0154181 0.0566389i
\(142\) 0 0
\(143\) 3.71783 + 6.43947i 0.310900 + 0.538495i
\(144\) 0 0
\(145\) 17.1601 + 9.90740i 1.42507 + 0.822765i
\(146\) 0 0
\(147\) 10.4263 + 6.18804i 0.859949 + 0.510381i
\(148\) 0 0
\(149\) 19.0549 + 11.0013i 1.56104 + 0.901266i 0.997152 + 0.0754127i \(0.0240274\pi\)
0.563886 + 0.825853i \(0.309306\pi\)
\(150\) 0 0
\(151\) −3.63368 6.29371i −0.295704 0.512175i 0.679444 0.733727i \(-0.262221\pi\)
−0.975149 + 0.221552i \(0.928888\pi\)
\(152\) 0 0
\(153\) 14.9346 8.78171i 1.20739 0.709959i
\(154\) 0 0
\(155\) 9.97331i 0.801075i
\(156\) 0 0
\(157\) 19.6994 11.3735i 1.57219 0.907702i 0.576285 0.817249i \(-0.304502\pi\)
0.995901 0.0904525i \(-0.0288313\pi\)
\(158\) 0 0
\(159\) −2.69302 + 10.2128i −0.213570 + 0.809931i
\(160\) 0 0
\(161\) −2.40680 5.94467i −0.189683 0.468505i
\(162\) 0 0
\(163\) 9.06678 15.7041i 0.710165 1.23004i −0.254630 0.967039i \(-0.581954\pi\)
0.964795 0.263003i \(-0.0847130\pi\)
\(164\) 0 0
\(165\) 18.9232 + 18.7732i 1.47317 + 1.46149i
\(166\) 0 0
\(167\) −24.0942 −1.86447 −0.932233 0.361858i \(-0.882143\pi\)
−0.932233 + 0.361858i \(0.882143\pi\)
\(168\) 0 0
\(169\) 11.1594 0.858414
\(170\) 0 0
\(171\) −2.93752 + 5.18274i −0.224638 + 0.396334i
\(172\) 0 0
\(173\) −5.18802 + 8.98592i −0.394438 + 0.683187i −0.993029 0.117868i \(-0.962394\pi\)
0.598591 + 0.801055i \(0.295727\pi\)
\(174\) 0 0
\(175\) 1.05668 7.55835i 0.0798778 0.571357i
\(176\) 0 0
\(177\) −4.29535 1.13264i −0.322858 0.0851342i
\(178\) 0 0
\(179\) −11.5922 + 6.69274i −0.866439 + 0.500239i −0.866163 0.499761i \(-0.833421\pi\)
−0.000276030 1.00000i \(0.500088\pi\)
\(180\) 0 0
\(181\) 18.4339i 1.37018i 0.728457 + 0.685092i \(0.240238\pi\)
−0.728457 + 0.685092i \(0.759762\pi\)
\(182\) 0 0
\(183\) −9.18221 + 2.49957i −0.678769 + 0.184773i
\(184\) 0 0
\(185\) −6.01960 10.4263i −0.442570 0.766554i
\(186\) 0 0
\(187\) 27.4110 + 15.8258i 2.00449 + 1.15729i
\(188\) 0 0
\(189\) −1.84803 13.6230i −0.134424 0.990924i
\(190\) 0 0
\(191\) 3.59492 + 2.07553i 0.260119 + 0.150180i 0.624389 0.781114i \(-0.285348\pi\)
−0.364270 + 0.931293i \(0.618681\pi\)
\(192\) 0 0
\(193\) −9.75462 16.8955i −0.702153 1.21616i −0.967709 0.252069i \(-0.918889\pi\)
0.265556 0.964095i \(-0.414444\pi\)
\(194\) 0 0
\(195\) −6.36661 + 1.73311i −0.455922 + 0.124110i
\(196\) 0 0
\(197\) 3.80952i 0.271417i 0.990749 + 0.135709i \(0.0433311\pi\)
−0.990749 + 0.135709i \(0.956669\pi\)
\(198\) 0 0
\(199\) 5.30327 3.06185i 0.375939 0.217049i −0.300111 0.953904i \(-0.597024\pi\)
0.676050 + 0.736856i \(0.263690\pi\)
\(200\) 0 0
\(201\) −11.5641 3.04933i −0.815670 0.215083i
\(202\) 0 0
\(203\) 11.4839 14.7206i 0.806012 1.03319i
\(204\) 0 0
\(205\) 2.55490 4.42522i 0.178442 0.309071i
\(206\) 0 0
\(207\) −3.58583 + 6.32657i −0.249232 + 0.439727i
\(208\) 0 0
\(209\) −10.8835 −0.752827
\(210\) 0 0
\(211\) −2.93058 −0.201750 −0.100875 0.994899i \(-0.532164\pi\)
−0.100875 + 0.994899i \(0.532164\pi\)
\(212\) 0 0
\(213\) 2.56067 + 2.54037i 0.175454 + 0.174063i
\(214\) 0 0
\(215\) 15.7649 27.3057i 1.07516 1.86223i
\(216\) 0 0
\(217\) 9.30671 + 1.30111i 0.631780 + 0.0883252i
\(218\) 0 0
\(219\) −0.150789 + 0.571845i −0.0101894 + 0.0386417i
\(220\) 0 0
\(221\) −6.78530 + 3.91749i −0.456428 + 0.263519i
\(222\) 0 0
\(223\) 4.61145i 0.308806i −0.988008 0.154403i \(-0.950655\pi\)
0.988008 0.154403i \(-0.0493454\pi\)
\(224\) 0 0
\(225\) −7.45966 + 4.38635i −0.497311 + 0.292424i
\(226\) 0 0
\(227\) 8.62344 + 14.9362i 0.572358 + 0.991353i 0.996323 + 0.0856745i \(0.0273045\pi\)
−0.423965 + 0.905678i \(0.639362\pi\)
\(228\) 0 0
\(229\) −11.5705 6.68024i −0.764601 0.441443i 0.0663443 0.997797i \(-0.478866\pi\)
−0.830945 + 0.556354i \(0.812200\pi\)
\(230\) 0 0
\(231\) 19.9871 15.2092i 1.31505 1.00069i
\(232\) 0 0
\(233\) 15.5908 + 9.00135i 1.02139 + 0.589698i 0.914505 0.404574i \(-0.132580\pi\)
0.106882 + 0.994272i \(0.465913\pi\)
\(234\) 0 0
\(235\) 0.564996 + 0.978602i 0.0368563 + 0.0638370i
\(236\) 0 0
\(237\) 1.08403 + 3.98220i 0.0704151 + 0.258671i
\(238\) 0 0
\(239\) 23.6499i 1.52979i −0.644158 0.764893i \(-0.722792\pi\)
0.644158 0.764893i \(-0.277208\pi\)
\(240\) 0 0
\(241\) 3.53574 2.04136i 0.227757 0.131496i −0.381780 0.924253i \(-0.624689\pi\)
0.609537 + 0.792758i \(0.291355\pi\)
\(242\) 0 0
\(243\) −10.8013 + 11.2398i −0.692901 + 0.721033i
\(244\) 0 0
\(245\) −18.9020 5.39050i −1.20761 0.344386i
\(246\) 0 0
\(247\) 1.34705 2.33315i 0.0857105 0.148455i
\(248\) 0 0
\(249\) 14.4818 14.5975i 0.917748 0.925080i
\(250\) 0 0
\(251\) 5.78085 0.364884 0.182442 0.983217i \(-0.441600\pi\)
0.182442 + 0.983217i \(0.441600\pi\)
\(252\) 0 0
\(253\) −13.2855 −0.835251
\(254\) 0 0
\(255\) −19.7814 + 19.9394i −1.23876 + 1.24865i
\(256\) 0 0
\(257\) −10.4824 + 18.1560i −0.653871 + 1.13254i 0.328304 + 0.944572i \(0.393523\pi\)
−0.982175 + 0.187966i \(0.939810\pi\)
\(258\) 0 0
\(259\) −10.5147 + 4.25706i −0.653351 + 0.264521i
\(260\) 0 0
\(261\) −21.1694 + 0.168462i −1.31035 + 0.0104275i
\(262\) 0 0
\(263\) 4.32937 2.49957i 0.266961 0.154130i −0.360545 0.932742i \(-0.617409\pi\)
0.627506 + 0.778612i \(0.284076\pi\)
\(264\) 0 0
\(265\) 17.1227i 1.05184i
\(266\) 0 0
\(267\) 0.524611 + 1.92717i 0.0321057 + 0.117941i
\(268\) 0 0
\(269\) 7.67602 + 13.2953i 0.468015 + 0.810626i 0.999332 0.0365470i \(-0.0116359\pi\)
−0.531317 + 0.847173i \(0.678303\pi\)
\(270\) 0 0
\(271\) −14.4761 8.35779i −0.879362 0.507700i −0.00891391 0.999960i \(-0.502837\pi\)
−0.870448 + 0.492260i \(0.836171\pi\)
\(272\) 0 0
\(273\) 0.786685 + 6.16718i 0.0476124 + 0.373254i
\(274\) 0 0
\(275\) −13.6914 7.90476i −0.825625 0.476675i
\(276\) 0 0
\(277\) 11.2571 + 19.4979i 0.676376 + 1.17152i 0.976065 + 0.217481i \(0.0697839\pi\)
−0.299689 + 0.954037i \(0.596883\pi\)
\(278\) 0 0
\(279\) −5.40098 9.18520i −0.323348 0.549903i
\(280\) 0 0
\(281\) 18.1134i 1.08055i 0.841488 + 0.540276i \(0.181680\pi\)
−0.841488 + 0.540276i \(0.818320\pi\)
\(282\) 0 0
\(283\) 5.00728 2.89095i 0.297652 0.171849i −0.343736 0.939066i \(-0.611692\pi\)
0.641388 + 0.767217i \(0.278359\pi\)
\(284\) 0 0
\(285\) 2.46250 9.33864i 0.145866 0.553173i
\(286\) 0 0
\(287\) −3.79613 2.96145i −0.224079 0.174809i
\(288\) 0 0
\(289\) −8.17567 + 14.1607i −0.480921 + 0.832980i
\(290\) 0 0
\(291\) 19.6967 + 19.5406i 1.15464 + 1.14549i
\(292\) 0 0
\(293\) 9.38786 0.548445 0.274222 0.961666i \(-0.411580\pi\)
0.274222 + 0.961666i \(0.411580\pi\)
\(294\) 0 0
\(295\) 7.20151 0.419288
\(296\) 0 0
\(297\) −27.5943 7.04195i −1.60118 0.408616i
\(298\) 0 0
\(299\) 1.64434 2.84808i 0.0950945 0.164709i
\(300\) 0 0
\(301\) −23.4239 18.2735i −1.35013 1.05327i
\(302\) 0 0
\(303\) −24.5855 6.48293i −1.41240 0.372435i
\(304\) 0 0
\(305\) 13.3607 7.71380i 0.765031 0.441691i
\(306\) 0 0
\(307\) 19.7599i 1.12776i 0.825857 + 0.563880i \(0.190692\pi\)
−0.825857 + 0.563880i \(0.809308\pi\)
\(308\) 0 0
\(309\) −7.85341 + 2.13784i −0.446765 + 0.121618i
\(310\) 0 0
\(311\) 10.1911 + 17.6515i 0.577884 + 1.00092i 0.995722 + 0.0924025i \(0.0294546\pi\)
−0.417838 + 0.908522i \(0.637212\pi\)
\(312\) 0 0
\(313\) 6.19972 + 3.57941i 0.350429 + 0.202320i 0.664874 0.746955i \(-0.268485\pi\)
−0.314445 + 0.949276i \(0.601818\pi\)
\(314\) 0 0
\(315\) 8.52807 + 20.5913i 0.480502 + 1.16019i
\(316\) 0 0
\(317\) −9.81412 5.66618i −0.551216 0.318245i 0.198396 0.980122i \(-0.436427\pi\)
−0.749612 + 0.661877i \(0.769760\pi\)
\(318\) 0 0
\(319\) −19.3379 33.4942i −1.08271 1.87531i
\(320\) 0 0
\(321\) −13.7815 + 3.75158i −0.769208 + 0.209393i
\(322\) 0 0
\(323\) 11.4680i 0.638096i
\(324\) 0 0
\(325\) 3.38917 1.95674i 0.187997 0.108540i
\(326\) 0 0
\(327\) −14.7755 3.89615i −0.817089 0.215458i
\(328\) 0 0
\(329\) 0.986903 0.399565i 0.0544097 0.0220287i
\(330\) 0 0
\(331\) −9.41383 + 16.3052i −0.517431 + 0.896216i 0.482364 + 0.875971i \(0.339778\pi\)
−0.999795 + 0.0202456i \(0.993555\pi\)
\(332\) 0 0
\(333\) 11.1902 + 6.34247i 0.613219 + 0.347565i
\(334\) 0 0
\(335\) 19.3882 1.05929
\(336\) 0 0
\(337\) 28.9739 1.57831 0.789156 0.614193i \(-0.210518\pi\)
0.789156 + 0.614193i \(0.210518\pi\)
\(338\) 0 0
\(339\) −4.91843 4.87945i −0.267133 0.265015i
\(340\) 0 0
\(341\) 9.73325 16.8585i 0.527085 0.912939i
\(342\) 0 0
\(343\) −7.49615 + 16.9354i −0.404754 + 0.914426i
\(344\) 0 0
\(345\) 3.00597 11.3997i 0.161836 0.613738i
\(346\) 0 0
\(347\) −15.6525 + 9.03697i −0.840270 + 0.485130i −0.857356 0.514724i \(-0.827894\pi\)
0.0170860 + 0.999854i \(0.494561\pi\)
\(348\) 0 0
\(349\) 12.8624i 0.688510i −0.938876 0.344255i \(-0.888132\pi\)
0.938876 0.344255i \(-0.111868\pi\)
\(350\) 0 0
\(351\) 4.92495 5.04395i 0.262875 0.269226i
\(352\) 0 0
\(353\) −13.6386 23.6227i −0.725909 1.25731i −0.958599 0.284760i \(-0.908086\pi\)
0.232690 0.972551i \(-0.425247\pi\)
\(354\) 0 0
\(355\) −5.06415 2.92379i −0.268777 0.155178i
\(356\) 0 0
\(357\) 16.0260 + 21.0605i 0.848187 + 1.11464i
\(358\) 0 0
\(359\) −0.773273 0.446450i −0.0408118 0.0235627i 0.479455 0.877566i \(-0.340834\pi\)
−0.520267 + 0.854004i \(0.674168\pi\)
\(360\) 0 0
\(361\) −7.52834 13.0395i −0.396229 0.686288i
\(362\) 0 0
\(363\) −8.66131 31.8175i −0.454601 1.66999i
\(364\) 0 0
\(365\) 0.958746i 0.0501831i
\(366\) 0 0
\(367\) 9.57418 5.52765i 0.499768 0.288541i −0.228850 0.973462i \(-0.573496\pi\)
0.728618 + 0.684921i \(0.240163\pi\)
\(368\) 0 0
\(369\) 0.0434426 + 5.45912i 0.00226153 + 0.284190i
\(370\) 0 0
\(371\) −15.9782 2.23382i −0.829549 0.115974i
\(372\) 0 0
\(373\) −11.5503 + 20.0057i −0.598053 + 1.03586i 0.395055 + 0.918657i \(0.370725\pi\)
−0.993108 + 0.117201i \(0.962608\pi\)
\(374\) 0 0
\(375\) −7.24600 + 7.30390i −0.374182 + 0.377172i
\(376\) 0 0
\(377\) 9.57375 0.493073
\(378\) 0 0
\(379\) 23.3938 1.20166 0.600830 0.799377i \(-0.294837\pi\)
0.600830 + 0.799377i \(0.294837\pi\)
\(380\) 0 0
\(381\) 8.46302 8.53063i 0.433574 0.437038i
\(382\) 0 0
\(383\) −11.5139 + 19.9426i −0.588331 + 1.01902i 0.406120 + 0.913820i \(0.366881\pi\)
−0.994451 + 0.105200i \(0.966452\pi\)
\(384\) 0 0
\(385\) −25.0447 + 32.1036i −1.27640 + 1.63615i
\(386\) 0 0
\(387\) 0.268062 + 33.6853i 0.0136263 + 1.71232i
\(388\) 0 0
\(389\) 5.45545 3.14970i 0.276602 0.159696i −0.355282 0.934759i \(-0.615615\pi\)
0.631884 + 0.775063i \(0.282282\pi\)
\(390\) 0 0
\(391\) 13.9990i 0.707958i
\(392\) 0 0
\(393\) 0.108034 + 0.396866i 0.00544960 + 0.0200192i
\(394\) 0 0
\(395\) −3.34537 5.79435i −0.168324 0.291545i
\(396\) 0 0
\(397\) 6.27940 + 3.62541i 0.315154 + 0.181954i 0.649230 0.760592i \(-0.275091\pi\)
−0.334077 + 0.942546i \(0.608424\pi\)
\(398\) 0 0
\(399\) −8.39320 3.51622i −0.420186 0.176031i
\(400\) 0 0
\(401\) 11.8188 + 6.82360i 0.590204 + 0.340755i 0.765178 0.643819i \(-0.222651\pi\)
−0.174974 + 0.984573i \(0.555984\pi\)
\(402\) 0 0
\(403\) 2.40936 + 4.17314i 0.120019 + 0.207879i
\(404\) 0 0
\(405\) 12.2859 22.0841i 0.610489 1.09737i
\(406\) 0 0
\(407\) 23.4989i 1.16479i
\(408\) 0 0
\(409\) −11.9303 + 6.88797i −0.589916 + 0.340588i −0.765064 0.643954i \(-0.777293\pi\)
0.175148 + 0.984542i \(0.443959\pi\)
\(410\) 0 0
\(411\) 4.88975 18.5436i 0.241194 0.914689i
\(412\) 0 0
\(413\) 0.939504 6.72017i 0.0462300 0.330678i
\(414\) 0 0
\(415\) −16.6675 + 28.8690i −0.818177 + 1.41712i
\(416\) 0 0
\(417\) 1.25993 + 1.24995i 0.0616992 + 0.0612102i
\(418\) 0 0
\(419\) 6.94914 0.339488 0.169744 0.985488i \(-0.445706\pi\)
0.169744 + 0.985488i \(0.445706\pi\)
\(420\) 0 0
\(421\) −0.349861 −0.0170512 −0.00852560 0.999964i \(-0.502714\pi\)
−0.00852560 + 0.999964i \(0.502714\pi\)
\(422\) 0 0
\(423\) −1.05031 0.595301i −0.0510676 0.0289445i
\(424\) 0 0
\(425\) 8.32928 14.4267i 0.404029 0.699800i
\(426\) 0 0
\(427\) −5.45520 13.4740i −0.263995 0.652054i
\(428\) 0 0
\(429\) 12.4533 + 3.28379i 0.601249 + 0.158543i
\(430\) 0 0
\(431\) −17.4513 + 10.0755i −0.840601 + 0.485321i −0.857468 0.514537i \(-0.827964\pi\)
0.0168676 + 0.999858i \(0.494631\pi\)
\(432\) 0 0
\(433\) 1.42453i 0.0684585i 0.999414 + 0.0342292i \(0.0108976\pi\)
−0.999414 + 0.0342292i \(0.989102\pi\)
\(434\) 0 0
\(435\) 33.1152 9.01456i 1.58775 0.432215i
\(436\) 0 0
\(437\) 2.40680 + 4.16870i 0.115133 + 0.199416i
\(438\) 0 0
\(439\) −1.76541 1.01926i −0.0842583 0.0486465i 0.457279 0.889323i \(-0.348824\pi\)
−0.541537 + 0.840677i \(0.682157\pi\)
\(440\) 0 0
\(441\) 20.3275 5.27174i 0.967978 0.251035i
\(442\) 0 0
\(443\) 11.1751 + 6.45195i 0.530945 + 0.306541i 0.741401 0.671062i \(-0.234162\pi\)
−0.210456 + 0.977603i \(0.567495\pi\)
\(444\) 0 0
\(445\) −1.61898 2.80416i −0.0767471 0.132930i
\(446\) 0 0
\(447\) 36.7717 10.0099i 1.73924 0.473453i
\(448\) 0 0
\(449\) 2.49432i 0.117714i 0.998266 + 0.0588572i \(0.0187457\pi\)
−0.998266 + 0.0588572i \(0.981254\pi\)
\(450\) 0 0
\(451\) −8.63741 + 4.98681i −0.406720 + 0.234820i
\(452\) 0 0
\(453\) −12.1714 3.20946i −0.571862 0.150794i
\(454\) 0 0
\(455\) −3.78243 9.34240i −0.177323 0.437978i
\(456\) 0 0
\(457\) −7.30952 + 12.6605i −0.341925 + 0.592232i −0.984790 0.173748i \(-0.944412\pi\)
0.642865 + 0.765979i \(0.277746\pi\)
\(458\) 0 0
\(459\) 7.42014 29.0762i 0.346342 1.35716i
\(460\) 0 0
\(461\) 2.83467 0.132024 0.0660120 0.997819i \(-0.478972\pi\)
0.0660120 + 0.997819i \(0.478972\pi\)
\(462\) 0 0
\(463\) −14.1594 −0.658042 −0.329021 0.944323i \(-0.606719\pi\)
−0.329021 + 0.944323i \(0.606719\pi\)
\(464\) 0 0
\(465\) 12.2633 + 12.1661i 0.568695 + 0.564188i
\(466\) 0 0
\(467\) 4.98809 8.63963i 0.230821 0.399794i −0.727229 0.686395i \(-0.759192\pi\)
0.958050 + 0.286601i \(0.0925254\pi\)
\(468\) 0 0
\(469\) 2.52937 18.0923i 0.116796 0.835426i
\(470\) 0 0
\(471\) 10.0457 38.0966i 0.462880 1.75540i
\(472\) 0 0
\(473\) −53.2969 + 30.7710i −2.45059 + 1.41485i
\(474\) 0 0
\(475\) 5.72811i 0.262824i
\(476\) 0 0
\(477\) 9.27269 + 15.7696i 0.424567 + 0.722041i
\(478\) 0 0
\(479\) −21.7575 37.6850i −0.994124 1.72187i −0.590805 0.806815i \(-0.701190\pi\)
−0.403320 0.915059i \(-0.632144\pi\)
\(480\) 0 0
\(481\) −5.03757 2.90844i −0.229693 0.132614i
\(482\) 0 0
\(483\) −10.2456 4.29225i −0.466190 0.195304i
\(484\) 0 0
\(485\) −38.9535 22.4898i −1.76879 1.02121i
\(486\) 0 0
\(487\) 18.5796 + 32.1808i 0.841921 + 1.45825i 0.888269 + 0.459324i \(0.151908\pi\)
−0.0463476 + 0.998925i \(0.514758\pi\)
\(488\) 0 0
\(489\) −8.24970 30.3055i −0.373064 1.37046i
\(490\) 0 0
\(491\) 22.1831i 1.00111i 0.865704 + 0.500556i \(0.166871\pi\)
−0.865704 + 0.500556i \(0.833129\pi\)
\(492\) 0 0
\(493\) 35.2929 20.3764i 1.58951 0.917707i
\(494\) 0 0
\(495\) 46.1673 0.367391i 2.07507 0.0165130i
\(496\) 0 0
\(497\) −3.38903 + 4.34423i −0.152019 + 0.194865i
\(498\) 0 0
\(499\) 8.33695 14.4400i 0.373213 0.646424i −0.616845 0.787085i \(-0.711589\pi\)
0.990058 + 0.140661i \(0.0449227\pi\)
\(500\) 0 0
\(501\) −29.3916 + 29.6265i −1.31312 + 1.32361i
\(502\) 0 0
\(503\) 8.55884 0.381620 0.190810 0.981627i \(-0.438889\pi\)
0.190810 + 0.981627i \(0.438889\pi\)
\(504\) 0 0
\(505\) 41.2196 1.83425
\(506\) 0 0
\(507\) 13.6129 13.7217i 0.604571 0.609401i
\(508\) 0 0
\(509\) 14.1072 24.4345i 0.625292 1.08304i −0.363192 0.931714i \(-0.618313\pi\)
0.988484 0.151324i \(-0.0483536\pi\)
\(510\) 0 0
\(511\) −0.894665 0.125077i −0.0395777 0.00553310i
\(512\) 0 0
\(513\) 2.78938 + 9.93423i 0.123154 + 0.438607i
\(514\) 0 0
\(515\) 11.4272 6.59750i 0.503543 0.290721i
\(516\) 0 0
\(517\) 2.20559i 0.0970017i
\(518\) 0 0
\(519\) 4.72049 + 17.3408i 0.207206 + 0.761177i
\(520\) 0 0
\(521\) 9.00041 + 15.5892i 0.394315 + 0.682974i 0.993014 0.118001i \(-0.0376485\pi\)
−0.598698 + 0.800975i \(0.704315\pi\)
\(522\) 0 0
\(523\) 11.9049 + 6.87332i 0.520567 + 0.300549i 0.737167 0.675711i \(-0.236163\pi\)
−0.216600 + 0.976260i \(0.569497\pi\)
\(524\) 0 0
\(525\) −8.00479 10.5194i −0.349358 0.459106i
\(526\) 0 0
\(527\) 17.7639 + 10.2560i 0.773806 + 0.446757i
\(528\) 0 0
\(529\) −8.56202 14.8299i −0.372262 0.644776i
\(530\) 0 0
\(531\) −6.63243 + 3.89993i −0.287823 + 0.169243i
\(532\) 0 0
\(533\) 2.46886i 0.106938i
\(534\) 0 0
\(535\) 20.0530 11.5776i 0.866965 0.500542i
\(536\) 0 0
\(537\) −5.91140 + 22.4180i −0.255096 + 0.967410i
\(538\) 0 0
\(539\) 26.6905 + 27.5589i 1.14964 + 1.18705i
\(540\) 0 0
\(541\) −19.6272 + 33.9953i −0.843839 + 1.46157i 0.0427866 + 0.999084i \(0.486376\pi\)
−0.886626 + 0.462488i \(0.846957\pi\)
\(542\) 0 0
\(543\) 22.6665 + 22.4869i 0.972714 + 0.965004i
\(544\) 0 0
\(545\) 24.7724 1.06113
\(546\) 0 0
\(547\) 12.4980 0.534375 0.267188 0.963645i \(-0.413906\pi\)
0.267188 + 0.963645i \(0.413906\pi\)
\(548\) 0 0
\(549\) −8.12755 + 14.3396i −0.346875 + 0.612001i
\(550\) 0 0
\(551\) −7.00651 + 12.1356i −0.298487 + 0.516995i
\(552\) 0 0
\(553\) −5.84350 + 2.36584i −0.248491 + 0.100606i
\(554\) 0 0
\(555\) −20.1633 5.31684i −0.855884 0.225687i
\(556\) 0 0
\(557\) 15.4816 8.93830i 0.655976 0.378728i −0.134766 0.990877i \(-0.543028\pi\)
0.790742 + 0.612150i \(0.209695\pi\)
\(558\) 0 0
\(559\) 15.2340i 0.644331i
\(560\) 0 0
\(561\) 52.8971 14.3996i 2.23332 0.607950i
\(562\) 0 0
\(563\) 1.36644 + 2.36674i 0.0575885 + 0.0997462i 0.893382 0.449297i \(-0.148326\pi\)
−0.835794 + 0.549043i \(0.814992\pi\)
\(564\) 0 0
\(565\) 9.72702 + 5.61589i 0.409219 + 0.236262i
\(566\) 0 0
\(567\) −19.0052 14.3458i −0.798145 0.602466i
\(568\) 0 0
\(569\) −1.72971 0.998650i −0.0725133 0.0418656i 0.463305 0.886199i \(-0.346663\pi\)
−0.535818 + 0.844333i \(0.679997\pi\)
\(570\) 0 0
\(571\) −1.00728 1.74466i −0.0421534 0.0730118i 0.844179 0.536061i \(-0.180088\pi\)
−0.886332 + 0.463050i \(0.846755\pi\)
\(572\) 0 0
\(573\) 6.93739 1.88848i 0.289814 0.0788926i
\(574\) 0 0
\(575\) 6.99231i 0.291599i
\(576\) 0 0
\(577\) −22.0199 + 12.7132i −0.916701 + 0.529258i −0.882581 0.470160i \(-0.844196\pi\)
−0.0341199 + 0.999418i \(0.510863\pi\)
\(578\) 0 0
\(579\) −32.6741 8.61582i −1.35789 0.358061i
\(580\) 0 0
\(581\) 24.7650 + 19.3197i 1.02743 + 0.801518i
\(582\) 0 0
\(583\) −16.7106 + 28.9435i −0.692080 + 1.19872i
\(584\) 0 0
\(585\) −5.63534 + 9.94259i −0.232993 + 0.411075i
\(586\) 0 0
\(587\) −34.4645 −1.42250 −0.711251 0.702939i \(-0.751871\pi\)
−0.711251 + 0.702939i \(0.751871\pi\)
\(588\) 0 0
\(589\) −7.05312 −0.290619
\(590\) 0 0
\(591\) 4.68422 + 4.64709i 0.192683 + 0.191156i
\(592\) 0 0
\(593\) −3.62199 + 6.27347i −0.148737 + 0.257620i −0.930761 0.365628i \(-0.880854\pi\)
0.782024 + 0.623249i \(0.214188\pi\)
\(594\) 0 0
\(595\) −33.8277 26.3897i −1.38680 1.08187i
\(596\) 0 0
\(597\) 2.70439 10.2560i 0.110683 0.419749i
\(598\) 0 0
\(599\) 32.5464 18.7907i 1.32981 0.767766i 0.344540 0.938772i \(-0.388035\pi\)
0.985270 + 0.171005i \(0.0547015\pi\)
\(600\) 0 0
\(601\) 3.78103i 0.154232i −0.997022 0.0771158i \(-0.975429\pi\)
0.997022 0.0771158i \(-0.0245711\pi\)
\(602\) 0 0
\(603\) −17.8561 + 10.4996i −0.727157 + 0.427575i
\(604\) 0 0
\(605\) 26.7293 + 46.2965i 1.08670 + 1.88222i
\(606\) 0 0
\(607\) 24.0353 + 13.8768i 0.975565 + 0.563242i 0.900928 0.433968i \(-0.142887\pi\)
0.0746364 + 0.997211i \(0.476220\pi\)
\(608\) 0 0
\(609\) −4.09185 32.0779i −0.165810 1.29986i
\(610\) 0 0
\(611\) 0.472823 + 0.272985i 0.0191284 + 0.0110438i
\(612\) 0 0
\(613\) 15.3570 + 26.5991i 0.620264 + 1.07433i 0.989436 + 0.144968i \(0.0463080\pi\)
−0.369172 + 0.929361i \(0.620359\pi\)
\(614\) 0 0
\(615\) −2.32466 8.53968i −0.0937392 0.344353i
\(616\) 0 0
\(617\) 44.3075i 1.78375i −0.452279 0.891877i \(-0.649389\pi\)
0.452279 0.891877i \(-0.350611\pi\)
\(618\) 0 0
\(619\) −27.4026 + 15.8209i −1.10140 + 0.635895i −0.936589 0.350430i \(-0.886035\pi\)
−0.164813 + 0.986325i \(0.552702\pi\)
\(620\) 0 0
\(621\) 3.40499 + 12.1267i 0.136638 + 0.486628i
\(622\) 0 0
\(623\) −2.82794 + 1.14494i −0.113299 + 0.0458711i
\(624\) 0 0
\(625\) 15.5511 26.9352i 0.622042 1.07741i
\(626\) 0 0
\(627\) −13.2764 + 13.3824i −0.530207 + 0.534443i
\(628\) 0 0
\(629\) −24.7608 −0.987279
\(630\) 0 0
\(631\) 20.7528 0.826157 0.413079 0.910695i \(-0.364453\pi\)
0.413079 + 0.910695i \(0.364453\pi\)
\(632\) 0 0
\(633\) −3.57491 + 3.60347i −0.142090 + 0.143225i
\(634\) 0 0
\(635\) −9.74033 + 16.8707i −0.386533 + 0.669495i
\(636\) 0 0
\(637\) −9.21142 + 2.31082i −0.364970 + 0.0915580i
\(638\) 0 0
\(639\) 6.24732 0.0497150i 0.247140 0.00196670i
\(640\) 0 0
\(641\) 33.0033 19.0545i 1.30355 0.752606i 0.322541 0.946556i \(-0.395463\pi\)
0.981012 + 0.193949i \(0.0621298\pi\)
\(642\) 0 0
\(643\) 29.5791i 1.16648i −0.812298 0.583242i \(-0.801784\pi\)
0.812298 0.583242i \(-0.198216\pi\)
\(644\) 0 0
\(645\) −14.3442 52.6939i −0.564804 2.07482i
\(646\) 0 0
\(647\) −10.5935 18.3485i −0.416474 0.721354i 0.579108 0.815251i \(-0.303401\pi\)
−0.995582 + 0.0938966i \(0.970068\pi\)
\(648\) 0 0
\(649\) −12.1731 7.02817i −0.477838 0.275880i
\(650\) 0 0
\(651\) 12.9528 9.85643i 0.507659 0.386304i
\(652\) 0 0
\(653\) −23.0548 13.3107i −0.902204 0.520888i −0.0242893 0.999705i \(-0.507732\pi\)
−0.877915 + 0.478817i \(0.841066\pi\)
\(654\) 0 0
\(655\) −0.333399 0.577465i −0.0130270 0.0225634i
\(656\) 0 0
\(657\) 0.519203 + 0.882984i 0.0202560 + 0.0344485i
\(658\) 0 0
\(659\) 16.3864i 0.638322i 0.947701 + 0.319161i \(0.103401\pi\)
−0.947701 + 0.319161i \(0.896599\pi\)
\(660\) 0 0
\(661\) −16.0227 + 9.25072i −0.623211 + 0.359811i −0.778118 0.628118i \(-0.783826\pi\)
0.154907 + 0.987929i \(0.450492\pi\)
\(662\) 0 0
\(663\) −3.46014 + 13.1221i −0.134381 + 0.509618i
\(664\) 0 0
\(665\) 14.6105 + 2.04260i 0.566572 + 0.0792088i
\(666\) 0 0
\(667\) −8.55284 + 14.8139i −0.331167 + 0.573598i
\(668\) 0 0
\(669\) −5.67028 5.62534i −0.219226 0.217488i
\(670\) 0 0
\(671\) −30.1125 −1.16248
\(672\) 0 0
\(673\) −45.4357 −1.75142 −0.875708 0.482841i \(-0.839605\pi\)
−0.875708 + 0.482841i \(0.839605\pi\)
\(674\) 0 0
\(675\) −3.70626 + 14.5232i −0.142654 + 0.558998i
\(676\) 0 0
\(677\) −15.8566 + 27.4644i −0.609419 + 1.05554i 0.381917 + 0.924196i \(0.375264\pi\)
−0.991336 + 0.131348i \(0.958069\pi\)
\(678\) 0 0
\(679\) −26.0684 + 33.4159i −1.00042 + 1.28238i
\(680\) 0 0
\(681\) 28.8851 + 7.61670i 1.10688 + 0.291872i
\(682\) 0 0
\(683\) 31.0917 17.9508i 1.18969 0.686868i 0.231454 0.972846i \(-0.425652\pi\)
0.958236 + 0.285978i \(0.0923183\pi\)
\(684\) 0 0
\(685\) 31.0899i 1.18788i
\(686\) 0 0
\(687\) −22.3285 + 6.07823i −0.851886 + 0.231899i
\(688\) 0 0
\(689\) −4.13651 7.16465i −0.157589 0.272952i
\(690\) 0 0
\(691\) −22.2415 12.8411i −0.846106 0.488499i 0.0132293 0.999912i \(-0.495789\pi\)
−0.859335 + 0.511413i \(0.829122\pi\)
\(692\) 0 0
\(693\) 5.68012 43.1295i 0.215770 1.63835i
\(694\) 0 0
\(695\) −2.49173 1.43860i −0.0945167 0.0545692i
\(696\) 0 0
\(697\) −5.25462 9.10127i −0.199033 0.344735i
\(698\) 0 0
\(699\) 30.0868 8.19016i 1.13799 0.309780i
\(700\) 0 0
\(701\) 1.29881i 0.0490553i 0.999699 + 0.0245276i \(0.00780818\pi\)
−0.999699 + 0.0245276i \(0.992192\pi\)
\(702\) 0 0
\(703\) 7.37344 4.25706i 0.278095 0.160558i
\(704\) 0 0
\(705\) 1.89252 + 0.499036i 0.0712762 + 0.0187948i
\(706\) 0 0
\(707\) 5.37749 38.4646i 0.202241 1.44661i
\(708\) 0 0
\(709\) 13.8609 24.0077i 0.520556 0.901629i −0.479158 0.877728i \(-0.659058\pi\)
0.999714 0.0239010i \(-0.00760863\pi\)
\(710\) 0 0
\(711\) 6.21890 + 3.52480i 0.233227 + 0.132190i
\(712\) 0 0
\(713\) −8.60973 −0.322437
\(714\) 0 0
\(715\) −20.8789 −0.780828
\(716\) 0 0
\(717\) −29.0801 28.8496i −1.08602 1.07741i
\(718\) 0 0
\(719\) −20.9122 + 36.2210i −0.779893 + 1.35081i 0.152109 + 0.988364i \(0.451393\pi\)
−0.932003 + 0.362451i \(0.881940\pi\)
\(720\) 0 0
\(721\) −4.66575 11.5241i −0.173762 0.429181i
\(722\) 0 0
\(723\) 1.80304 6.83775i 0.0670558 0.254299i
\(724\) 0 0
\(725\) −17.6284 + 10.1777i −0.654701 + 0.377992i
\(726\) 0 0
\(727\) 2.19295i 0.0813319i 0.999173 + 0.0406660i \(0.0129479\pi\)
−0.999173 + 0.0406660i \(0.987052\pi\)
\(728\) 0 0
\(729\) 0.644508 + 26.9923i 0.0238707 + 0.999715i
\(730\) 0 0
\(731\) −32.4235 56.1592i −1.19923 2.07712i
\(732\) 0 0
\(733\) 18.0850 + 10.4414i 0.667986 + 0.385662i 0.795313 0.606199i \(-0.207307\pi\)
−0.127327 + 0.991861i \(0.540640\pi\)
\(734\) 0 0
\(735\) −29.6861 + 16.6664i −1.09499 + 0.614750i
\(736\) 0 0
\(737\) −32.7731 18.9215i −1.20721 0.696984i
\(738\) 0 0
\(739\) −6.65032 11.5187i −0.244636 0.423722i 0.717393 0.696668i \(-0.245335\pi\)
−0.962029 + 0.272947i \(0.912002\pi\)
\(740\) 0 0
\(741\) −1.22565 4.50246i −0.0450255 0.165402i
\(742\) 0 0
\(743\) 24.8226i 0.910653i −0.890324 0.455327i \(-0.849522\pi\)
0.890324 0.455327i \(-0.150478\pi\)
\(744\) 0 0
\(745\) −53.5051 + 30.8912i −1.96028 + 1.13177i
\(746\) 0 0
\(747\) −0.283409 35.6139i −0.0103694 1.30305i
\(748\) 0 0
\(749\) −8.18765 20.2230i −0.299170 0.738934i
\(750\) 0 0
\(751\) −5.98635 + 10.3687i −0.218445 + 0.378358i −0.954333 0.298746i \(-0.903432\pi\)
0.735888 + 0.677104i \(0.236765\pi\)
\(752\) 0 0
\(753\) 7.05184 7.10818i 0.256983 0.259037i
\(754\) 0 0
\(755\) 20.4063 0.742663
\(756\) 0 0
\(757\) 29.8095 1.08345 0.541723 0.840557i \(-0.317772\pi\)
0.541723 + 0.840557i \(0.317772\pi\)
\(758\) 0 0
\(759\) −16.2065 + 16.3359i −0.588257 + 0.592957i
\(760\) 0 0
\(761\) 16.7439 29.0013i 0.606967 1.05130i −0.384770 0.923012i \(-0.625719\pi\)
0.991737 0.128286i \(-0.0409474\pi\)
\(762\) 0 0
\(763\) 3.23180 23.1167i 0.116999 0.836880i
\(764\) 0 0
\(765\) 0.387121 + 48.6467i 0.0139964 + 1.75882i
\(766\) 0 0
\(767\) 3.01333 1.73975i 0.108805 0.0628186i
\(768\) 0 0
\(769\) 19.6491i 0.708566i −0.935138 0.354283i \(-0.884725\pi\)
0.935138 0.354283i \(-0.115275\pi\)
\(770\) 0 0
\(771\) 9.53770 + 35.0370i 0.343492 + 1.26183i
\(772\) 0 0
\(773\) 6.51659 + 11.2871i 0.234385 + 0.405968i 0.959094 0.283088i \(-0.0913589\pi\)
−0.724708 + 0.689056i \(0.758026\pi\)
\(774\) 0 0
\(775\) −8.87282 5.12273i −0.318721 0.184014i
\(776\) 0 0
\(777\) −7.59197 + 18.1220i −0.272360 + 0.650122i
\(778\) 0 0
\(779\) 3.12951 + 1.80682i 0.112126 + 0.0647362i
\(780\) 0 0
\(781\) 5.70682 + 9.88451i 0.204206 + 0.353695i
\(782\) 0 0
\(783\) −25.6166 + 26.2355i −0.915462 + 0.937582i
\(784\) 0 0
\(785\) 63.8722i 2.27970i
\(786\) 0 0
\(787\) −21.1053 + 12.1852i −0.752324 + 0.434354i −0.826533 0.562888i \(-0.809690\pi\)
0.0742091 + 0.997243i \(0.476357\pi\)
\(788\) 0 0
\(789\) 2.20775 8.37256i 0.0785981 0.298071i
\(790\) 0 0
\(791\) 6.50952 8.34423i 0.231452 0.296687i
\(792\) 0 0
\(793\) 3.72702 6.45538i 0.132350 0.229237i
\(794\) 0 0
\(795\) −21.0542 20.8873i −0.746715 0.740797i
\(796\) 0 0
\(797\) −3.14465 −0.111389 −0.0556947 0.998448i \(-0.517737\pi\)
−0.0556947 + 0.998448i \(0.517737\pi\)
\(798\) 0 0
\(799\) 2.32404 0.0822186
\(800\) 0 0
\(801\) 3.00962 + 1.70582i 0.106340 + 0.0602721i
\(802\) 0 0
\(803\) −0.935670 + 1.62063i −0.0330191 + 0.0571907i
\(804\) 0 0
\(805\) 17.8350 + 2.49340i 0.628603 + 0.0878810i
\(806\) 0 0
\(807\) 25.7117 + 6.77989i 0.905093 + 0.238663i
\(808\) 0 0
\(809\) −5.76799 + 3.33015i −0.202792 + 0.117082i −0.597957 0.801528i \(-0.704021\pi\)
0.395165 + 0.918610i \(0.370687\pi\)
\(810\) 0 0
\(811\) 48.8504i 1.71537i 0.514176 + 0.857685i \(0.328098\pi\)
−0.514176 + 0.857685i \(0.671902\pi\)
\(812\) 0 0
\(813\) −27.9357 + 7.60460i −0.979747 + 0.266705i
\(814\) 0 0
\(815\) 25.4590 + 44.0964i 0.891791 + 1.54463i
\(816\) 0 0
\(817\) 19.3106 + 11.1490i 0.675591 + 0.390053i
\(818\) 0 0
\(819\) 8.54286 + 6.55579i 0.298512 + 0.229078i
\(820\) 0 0
\(821\) 35.0636 + 20.2440i 1.22373 + 0.706520i 0.965711 0.259621i \(-0.0835975\pi\)
0.258017 + 0.966140i \(0.416931\pi\)
\(822\) 0 0
\(823\) 17.2956 + 29.9568i 0.602886 + 1.04423i 0.992382 + 0.123201i \(0.0393160\pi\)
−0.389496 + 0.921028i \(0.627351\pi\)
\(824\) 0 0
\(825\) −26.4214 + 7.19240i −0.919876 + 0.250407i
\(826\) 0 0
\(827\) 29.3071i 1.01911i −0.860438 0.509555i \(-0.829810\pi\)
0.860438 0.509555i \(-0.170190\pi\)
\(828\) 0 0
\(829\) 12.7957 7.38763i 0.444414 0.256583i −0.261054 0.965324i \(-0.584070\pi\)
0.705468 + 0.708741i \(0.250737\pi\)
\(830\) 0 0
\(831\) 37.7070 + 9.94293i 1.30804 + 0.344916i
\(832\) 0 0
\(833\) −29.0390 + 28.1239i −1.00614 + 0.974435i
\(834\) 0 0
\(835\) 33.8277 58.5912i 1.17065 2.02763i
\(836\) 0 0
\(837\) −17.8826 4.56358i −0.618115 0.157740i
\(838\) 0 0
\(839\) 32.0373 1.10605 0.553026 0.833164i \(-0.313473\pi\)
0.553026 + 0.833164i \(0.313473\pi\)
\(840\) 0 0
\(841\) −20.7968 −0.717131
\(842\) 0 0
\(843\) 22.2723 + 22.0958i 0.767100 + 0.761020i
\(844\) 0 0
\(845\) −15.6675 + 27.1369i −0.538978 + 0.933537i
\(846\) 0 0
\(847\) 46.6892 18.9029i 1.60426 0.649513i
\(848\) 0 0
\(849\) 2.55345 9.68356i 0.0876342 0.332339i
\(850\) 0 0
\(851\) 9.00076 5.19659i 0.308542 0.178137i
\(852\) 0 0
\(853\) 33.1110i 1.13370i −0.823821 0.566850i \(-0.808162\pi\)
0.823821 0.566850i \(-0.191838\pi\)
\(854\) 0 0
\(855\) −8.47896 14.4198i −0.289974 0.493145i
\(856\) 0 0
\(857\) 9.00041 + 15.5892i 0.307448 + 0.532516i 0.977803 0.209524i \(-0.0671916\pi\)
−0.670355 + 0.742040i \(0.733858\pi\)
\(858\) 0 0
\(859\) 23.1107 + 13.3430i 0.788528 + 0.455257i 0.839444 0.543446i \(-0.182881\pi\)
−0.0509160 + 0.998703i \(0.516214\pi\)
\(860\) 0 0
\(861\) −8.27217 + 1.05520i −0.281915 + 0.0359611i
\(862\) 0 0
\(863\) 8.69289 + 5.01884i 0.295909 + 0.170843i 0.640604 0.767872i \(-0.278684\pi\)
−0.344694 + 0.938715i \(0.612017\pi\)
\(864\) 0 0
\(865\) −14.5677 25.2320i −0.495317 0.857913i
\(866\) 0 0
\(867\) 7.43889 + 27.3269i 0.252638 + 0.928071i
\(868\) 0 0
\(869\) 13.0594i 0.443009i
\(870\) 0 0
\(871\) 8.11262 4.68382i 0.274885 0.158705i
\(872\) 0 0
\(873\) 48.0545 0.382409i 1.62640 0.0129426i
\(874\) 0 0
\(875\) −12.3912 9.66666i −0.418900 0.326793i
\(876\) 0 0
\(877\) 7.38102 12.7843i 0.249239 0.431695i −0.714076 0.700069i \(-0.753153\pi\)
0.963315 + 0.268373i \(0.0864861\pi\)
\(878\) 0 0
\(879\) 11.4519 11.5434i 0.386263 0.389349i
\(880\) 0 0
\(881\) −4.42345 −0.149030 −0.0745148 0.997220i \(-0.523741\pi\)
−0.0745148 + 0.997220i \(0.523741\pi\)
\(882\) 0 0
\(883\) 10.5403 0.354711 0.177355 0.984147i \(-0.443246\pi\)
0.177355 + 0.984147i \(0.443246\pi\)
\(884\) 0 0
\(885\) 8.78485 8.85503i 0.295299 0.297659i
\(886\) 0 0
\(887\) 4.92026 8.52213i 0.165206 0.286145i −0.771522 0.636202i \(-0.780504\pi\)
0.936728 + 0.350057i \(0.113838\pi\)
\(888\) 0 0
\(889\) 14.4724 + 11.2902i 0.485389 + 0.378663i
\(890\) 0 0
\(891\) −42.3201 + 25.3400i −1.41778 + 0.848921i
\(892\) 0 0
\(893\) −0.692067 + 0.399565i −0.0231591 + 0.0133709i
\(894\) 0 0
\(895\) 37.5857i 1.25635i
\(896\) 0 0
\(897\) −1.49615 5.49615i −0.0499551 0.183511i
\(898\) 0 0
\(899\) −12.5320 21.7061i −0.417966 0.723939i
\(900\) 0 0
\(901\) −30.4979 17.6080i −1.01603 0.586607i
\(902\) 0 0
\(903\) −51.0432 + 6.51108i −1.69861 + 0.216675i
\(904\) 0 0
\(905\) −44.8268 25.8808i −1.49009 0.860306i
\(906\) 0 0
\(907\) −4.10609 7.11195i −0.136340 0.236148i 0.789768 0.613405i \(-0.210201\pi\)
−0.926109 + 0.377257i \(0.876867\pi\)
\(908\) 0 0
\(909\) −37.9624 + 22.3222i −1.25913 + 0.740382i
\(910\) 0 0
\(911\) 44.6131i 1.47810i −0.673652 0.739049i \(-0.735275\pi\)
0.673652 0.739049i \(-0.264725\pi\)
\(912\) 0 0
\(913\) 56.3483 32.5327i 1.86486 1.07668i
\(914\) 0 0
\(915\) 6.81326 25.8382i 0.225239 0.854185i
\(916\) 0 0
\(917\) −0.582363 + 0.235780i −0.0192313 + 0.00778614i
\(918\) 0 0
\(919\) 15.3222 26.5388i 0.505431 0.875433i −0.494549 0.869150i \(-0.664667\pi\)
0.999980 0.00628290i \(-0.00199992\pi\)
\(920\) 0 0
\(921\) 24.2970 + 24.1044i 0.800613 + 0.794267i
\(922\) 0 0
\(923\) −2.82532 −0.0929966
\(924\) 0 0
\(925\) 12.3677 0.406648
\(926\) 0 0
\(927\) −6.95137 + 12.2645i −0.228313 + 0.402819i
\(928\) 0 0
\(929\) 10.7198 18.5673i 0.351706 0.609173i −0.634842 0.772642i \(-0.718935\pi\)
0.986548 + 0.163469i \(0.0522683\pi\)
\(930\) 0 0
\(931\) 3.81216 13.3675i 0.124938 0.438102i
\(932\) 0 0
\(933\) 34.1361 + 9.00133i 1.11757 + 0.294690i
\(934\) 0 0
\(935\) −76.9687 + 44.4379i −2.51714 + 1.45327i
\(936\) 0 0
\(937\) 25.1409i 0.821319i 0.911789 + 0.410659i \(0.134701\pi\)
−0.911789 + 0.410659i \(0.865299\pi\)
\(938\) 0 0
\(939\) 11.9641 3.25684i 0.390433 0.106283i
\(940\) 0 0
\(941\) −26.0598 45.1369i −0.849525 1.47142i −0.881633 0.471936i \(-0.843555\pi\)
0.0321082 0.999484i \(-0.489778\pi\)
\(942\) 0 0
\(943\) 3.82019 + 2.20559i 0.124403 + 0.0718238i
\(944\) 0 0
\(945\) 35.7222 + 14.6323i 1.16204 + 0.475989i
\(946\) 0 0
\(947\) 35.8943 + 20.7236i 1.16641 + 0.673427i 0.952832 0.303500i \(-0.0981551\pi\)
0.213578 + 0.976926i \(0.431488\pi\)
\(948\) 0 0
\(949\) −0.231615 0.401169i −0.00751853 0.0130225i
\(950\) 0 0
\(951\) −18.9391 + 5.15556i −0.614141 + 0.167180i
\(952\) 0 0
\(953\) 29.7579i 0.963952i −0.876184 0.481976i \(-0.839919\pi\)
0.876184 0.481976i \(-0.160081\pi\)
\(954\) 0 0
\(955\) −10.0943 + 5.82797i −0.326645 + 0.188589i
\(956\) 0 0
\(957\) −64.7742 17.0803i −2.09385 0.552127i
\(958\) 0 0
\(959\) 29.0119 + 4.05597i 0.936844 + 0.130974i
\(960\) 0 0
\(961\) −9.19231 + 15.9215i −0.296526 + 0.513598i
\(962\) 0 0
\(963\) −12.1986 + 21.5222i −0.393093 + 0.693545i
\(964\) 0 0
\(965\) 54.7809 1.76346
\(966\) 0 0
\(967\) 16.6814 0.536436 0.268218 0.963358i \(-0.413565\pi\)
0.268218 + 0.963358i \(0.413565\pi\)
\(968\) 0 0
\(969\) −14.1011 13.9894i −0.452994 0.449403i
\(970\) 0 0
\(971\) −25.6466 + 44.4211i −0.823037 + 1.42554i 0.0803734 + 0.996765i \(0.474389\pi\)
−0.903410 + 0.428777i \(0.858945\pi\)
\(972\) 0 0
\(973\) −1.66752 + 2.13751i −0.0534581 + 0.0685253i
\(974\) 0 0
\(975\) 1.72830 6.55430i 0.0553498 0.209906i
\(976\) 0 0
\(977\) 16.6912 9.63669i 0.534000 0.308305i −0.208644 0.977992i \(-0.566905\pi\)
0.742644 + 0.669687i \(0.233572\pi\)
\(978\) 0 0
\(979\) 6.32005i 0.201990i
\(980\) 0 0
\(981\) −22.8149 + 13.4154i −0.728422 + 0.428319i
\(982\) 0 0
\(983\) −1.85925 3.22031i −0.0593008 0.102712i 0.834851 0.550476i \(-0.185554\pi\)
−0.894152 + 0.447764i \(0.852220\pi\)
\(984\) 0 0
\(985\) −9.26382 5.34847i −0.295170 0.170416i
\(986\) 0 0
\(987\) 0.712577 1.70092i 0.0226816 0.0541408i
\(988\) 0 0
\(989\) 23.5724 + 13.6095i 0.749558 + 0.432758i
\(990\) 0 0
\(991\) −25.4914 44.1525i −0.809762 1.40255i −0.913029 0.407896i \(-0.866263\pi\)
0.103266 0.994654i \(-0.467071\pi\)
\(992\) 0 0
\(993\) 8.56547 + 31.4654i 0.271817 + 0.998526i
\(994\) 0 0
\(995\) 17.1950i 0.545118i
\(996\) 0 0
\(997\) 45.6801 26.3734i 1.44670 0.835254i 0.448419 0.893823i \(-0.351987\pi\)
0.998283 + 0.0585692i \(0.0186538\pi\)
\(998\) 0 0
\(999\) 21.4493 6.02261i 0.678624 0.190547i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 336.2.bc.f.257.6 16
3.2 odd 2 inner 336.2.bc.f.257.8 16
4.3 odd 2 168.2.u.a.89.3 yes 16
7.2 even 3 2352.2.k.i.881.10 16
7.3 odd 6 inner 336.2.bc.f.17.8 16
7.5 odd 6 2352.2.k.i.881.7 16
12.11 even 2 168.2.u.a.89.1 yes 16
21.2 odd 6 2352.2.k.i.881.8 16
21.5 even 6 2352.2.k.i.881.9 16
21.17 even 6 inner 336.2.bc.f.17.6 16
28.3 even 6 168.2.u.a.17.1 16
28.11 odd 6 1176.2.u.b.521.8 16
28.19 even 6 1176.2.k.a.881.10 16
28.23 odd 6 1176.2.k.a.881.7 16
28.27 even 2 1176.2.u.b.1097.6 16
84.11 even 6 1176.2.u.b.521.6 16
84.23 even 6 1176.2.k.a.881.9 16
84.47 odd 6 1176.2.k.a.881.8 16
84.59 odd 6 168.2.u.a.17.3 yes 16
84.83 odd 2 1176.2.u.b.1097.8 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
168.2.u.a.17.1 16 28.3 even 6
168.2.u.a.17.3 yes 16 84.59 odd 6
168.2.u.a.89.1 yes 16 12.11 even 2
168.2.u.a.89.3 yes 16 4.3 odd 2
336.2.bc.f.17.6 16 21.17 even 6 inner
336.2.bc.f.17.8 16 7.3 odd 6 inner
336.2.bc.f.257.6 16 1.1 even 1 trivial
336.2.bc.f.257.8 16 3.2 odd 2 inner
1176.2.k.a.881.7 16 28.23 odd 6
1176.2.k.a.881.8 16 84.47 odd 6
1176.2.k.a.881.9 16 84.23 even 6
1176.2.k.a.881.10 16 28.19 even 6
1176.2.u.b.521.6 16 84.11 even 6
1176.2.u.b.521.8 16 28.11 odd 6
1176.2.u.b.1097.6 16 28.27 even 2
1176.2.u.b.1097.8 16 84.83 odd 2
2352.2.k.i.881.7 16 7.5 odd 6
2352.2.k.i.881.8 16 21.2 odd 6
2352.2.k.i.881.9 16 21.5 even 6
2352.2.k.i.881.10 16 7.2 even 3