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Properties

Label 27.27.5659106580...6209.5
Degree $27$
Signature $[27, 0]$
Discriminant $3^{66}\cdot 7^{18}\cdot 13^{18}$
Root discriminant $296.70$
Ramified primes $3, 7, 13$
Class number $3$ (GRH)
Class group $[3]$ (GRH)
Galois group $C_3\times C_9$ (as 27T2)

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Show commands for: Magma / SageMath / Pari/GP

magma: R<x> := PolynomialRing(Rationals()); K<a> := NumberField(R![3142740871297, 1878327723222, -15143291321652, -5674509280383, 24929372870136, 5926406371776, -19863323081169, -2901631249080, 8983662014547, 703772052814, -2499184727280, -65737507815, 446404796160, -6034174794, -52402519296, 2275361346, 4084767207, -267170931, -211132411, 17169588, 7112223, -659574, -149400, 15075, 1770, -189, -9, 1]);
 
sage: x = polygen(QQ); K.<a> = NumberField(x^27 - 9*x^26 - 189*x^25 + 1770*x^24 + 15075*x^23 - 149400*x^22 - 659574*x^21 + 7112223*x^20 + 17169588*x^19 - 211132411*x^18 - 267170931*x^17 + 4084767207*x^16 + 2275361346*x^15 - 52402519296*x^14 - 6034174794*x^13 + 446404796160*x^12 - 65737507815*x^11 - 2499184727280*x^10 + 703772052814*x^9 + 8983662014547*x^8 - 2901631249080*x^7 - 19863323081169*x^6 + 5926406371776*x^5 + 24929372870136*x^4 - 5674509280383*x^3 - 15143291321652*x^2 + 1878327723222*x + 3142740871297)
 
gp: K = bnfinit(x^27 - 9*x^26 - 189*x^25 + 1770*x^24 + 15075*x^23 - 149400*x^22 - 659574*x^21 + 7112223*x^20 + 17169588*x^19 - 211132411*x^18 - 267170931*x^17 + 4084767207*x^16 + 2275361346*x^15 - 52402519296*x^14 - 6034174794*x^13 + 446404796160*x^12 - 65737507815*x^11 - 2499184727280*x^10 + 703772052814*x^9 + 8983662014547*x^8 - 2901631249080*x^7 - 19863323081169*x^6 + 5926406371776*x^5 + 24929372870136*x^4 - 5674509280383*x^3 - 15143291321652*x^2 + 1878327723222*x + 3142740871297, 1)
 

Normalized defining polynomial

\( x^{27} - 9 x^{26} - 189 x^{25} + 1770 x^{24} + 15075 x^{23} - 149400 x^{22} - 659574 x^{21} + 7112223 x^{20} + 17169588 x^{19} - 211132411 x^{18} - 267170931 x^{17} + 4084767207 x^{16} + 2275361346 x^{15} - 52402519296 x^{14} - 6034174794 x^{13} + 446404796160 x^{12} - 65737507815 x^{11} - 2499184727280 x^{10} + 703772052814 x^{9} + 8983662014547 x^{8} - 2901631249080 x^{7} - 19863323081169 x^{6} + 5926406371776 x^{5} + 24929372870136 x^{4} - 5674509280383 x^{3} - 15143291321652 x^{2} + 1878327723222 x + 3142740871297 \)

magma: DefiningPolynomial(K);
 
sage: K.defining_polynomial()
 
gp: K.pol
 

Invariants

Degree:  $27$
magma: Degree(K);
 
sage: K.degree()
 
gp: poldegree(K.pol)
 
Signature:  $[27, 0]$
magma: Signature(K);
 
sage: K.signature()
 
gp: K.sign
 
Discriminant:  \(5659106580522258442740055894009895600932750567734671570320232266209=3^{66}\cdot 7^{18}\cdot 13^{18}\)
magma: Discriminant(Integers(K));
 
sage: K.disc()
 
gp: K.disc
 
Root discriminant:  $296.70$
magma: Abs(Discriminant(Integers(K)))^(1/Degree(K));
 
sage: (K.disc().abs())^(1./K.degree())
 
gp: abs(K.disc)^(1/poldegree(K.pol))
 
Ramified primes:  $3, 7, 13$
magma: PrimeDivisors(Discriminant(Integers(K)));
 
sage: K.disc().support()
 
gp: factor(abs(K.disc))[,1]~
 
This field is Galois and abelian over $\Q$.
Conductor:  \(2457=3^{3}\cdot 7\cdot 13\)
Dirichlet character group:    $\lbrace$$\chi_{2457}(1600,·)$, $\chi_{2457}(1,·)$, $\chi_{2457}(1348,·)$, $\chi_{2457}(625,·)$, $\chi_{2457}(1537,·)$, $\chi_{2457}(781,·)$, $\chi_{2457}(718,·)$, $\chi_{2457}(529,·)$, $\chi_{2457}(2263,·)$, $\chi_{2457}(2200,·)$, $\chi_{2457}(2011,·)$, $\chi_{2457}(2206,·)$, $\chi_{2457}(2395,·)$, $\chi_{2457}(1444,·)$, $\chi_{2457}(1381,·)$, $\chi_{2457}(1639,·)$, $\chi_{2457}(1576,·)$, $\chi_{2457}(1387,·)$, $\chi_{2457}(1192,·)$, $\chi_{2457}(562,·)$, $\chi_{2457}(2419,·)$, $\chi_{2457}(2356,·)$, $\chi_{2457}(757,·)$, $\chi_{2457}(2167,·)$, $\chi_{2457}(568,·)$, $\chi_{2457}(820,·)$, $\chi_{2457}(373,·)$$\rbrace$
This is not a CM field.

Integral basis (with respect to field generator \(a\))

$1$, $a$, $a^{2}$, $a^{3}$, $a^{4}$, $a^{5}$, $a^{6}$, $a^{7}$, $a^{8}$, $\frac{1}{7} a^{9} - \frac{3}{7} a^{8} - \frac{2}{7} a^{7} - \frac{1}{7} a^{6} + \frac{1}{7} a^{4} - \frac{1}{7} a^{3} - \frac{2}{7} a^{2} + \frac{2}{7} a - \frac{1}{7}$, $\frac{1}{7} a^{10} + \frac{3}{7} a^{8} - \frac{3}{7} a^{6} + \frac{1}{7} a^{5} + \frac{2}{7} a^{4} + \frac{2}{7} a^{3} + \frac{3}{7} a^{2} - \frac{2}{7} a - \frac{3}{7}$, $\frac{1}{7} a^{11} + \frac{2}{7} a^{8} + \frac{3}{7} a^{7} - \frac{3}{7} a^{6} + \frac{2}{7} a^{5} - \frac{1}{7} a^{4} - \frac{1}{7} a^{3} - \frac{3}{7} a^{2} - \frac{2}{7} a + \frac{3}{7}$, $\frac{1}{7} a^{12} + \frac{2}{7} a^{8} + \frac{1}{7} a^{7} - \frac{3}{7} a^{6} - \frac{1}{7} a^{5} - \frac{3}{7} a^{4} - \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{1}{7} a + \frac{2}{7}$, $\frac{1}{7} a^{13} + \frac{1}{7} a^{7} + \frac{1}{7} a^{6} - \frac{3}{7} a^{5} - \frac{3}{7} a^{4} - \frac{3}{7} a^{3} + \frac{3}{7} a^{2} - \frac{2}{7} a + \frac{2}{7}$, $\frac{1}{7} a^{14} + \frac{1}{7} a^{8} + \frac{1}{7} a^{7} - \frac{3}{7} a^{6} - \frac{3}{7} a^{5} - \frac{3}{7} a^{4} + \frac{3}{7} a^{3} - \frac{2}{7} a^{2} + \frac{2}{7} a$, $\frac{1}{133} a^{15} + \frac{3}{133} a^{13} - \frac{4}{133} a^{12} + \frac{1}{19} a^{11} - \frac{8}{133} a^{10} - \frac{6}{133} a^{9} + \frac{39}{133} a^{8} + \frac{66}{133} a^{7} - \frac{34}{133} a^{6} - \frac{44}{133} a^{5} - \frac{17}{133} a^{4} - \frac{16}{133} a^{3} + \frac{9}{19} a^{2} + \frac{5}{19} a - \frac{48}{133}$, $\frac{1}{133} a^{16} + \frac{3}{133} a^{14} - \frac{4}{133} a^{13} + \frac{1}{19} a^{12} - \frac{8}{133} a^{11} - \frac{6}{133} a^{10} + \frac{1}{133} a^{9} + \frac{47}{133} a^{8} + \frac{6}{19} a^{7} - \frac{6}{133} a^{6} - \frac{17}{133} a^{5} - \frac{54}{133} a^{4} - \frac{32}{133} a^{3} - \frac{22}{133} a^{2} + \frac{9}{133} a + \frac{2}{7}$, $\frac{1}{133} a^{17} - \frac{4}{133} a^{14} - \frac{2}{133} a^{13} + \frac{4}{133} a^{12} - \frac{8}{133} a^{11} + \frac{6}{133} a^{10} + \frac{8}{133} a^{9} - \frac{8}{19} a^{8} - \frac{33}{133} a^{7} + \frac{9}{133} a^{6} - \frac{36}{133} a^{5} + \frac{2}{7} a^{4} + \frac{26}{133} a^{3} - \frac{47}{133} a^{2} - \frac{48}{133} a + \frac{7}{19}$, $\frac{1}{931} a^{18} + \frac{1}{931} a^{17} - \frac{2}{931} a^{16} + \frac{3}{931} a^{15} + \frac{45}{931} a^{14} - \frac{64}{931} a^{13} + \frac{1}{19} a^{12} - \frac{51}{931} a^{11} + \frac{46}{931} a^{10} + \frac{3}{931} a^{9} + \frac{185}{931} a^{8} + \frac{278}{931} a^{7} - \frac{386}{931} a^{6} - \frac{139}{931} a^{5} + \frac{243}{931} a^{4} - \frac{69}{931} a^{3} - \frac{104}{931} a^{2} + \frac{23}{49} a + \frac{169}{931}$, $\frac{1}{931} a^{19} - \frac{3}{931} a^{17} - \frac{2}{931} a^{16} + \frac{3}{931} a^{14} + \frac{15}{931} a^{13} + \frac{1}{49} a^{12} - \frac{8}{931} a^{11} - \frac{64}{931} a^{10} + \frac{4}{133} a^{9} + \frac{387}{931} a^{8} + \frac{393}{931} a^{7} - \frac{278}{931} a^{6} - \frac{45}{931} a^{5} - \frac{18}{931} a^{4} - \frac{29}{133} a^{3} - \frac{222}{931} a^{2} + \frac{61}{931} a - \frac{148}{931}$, $\frac{1}{931} a^{20} + \frac{1}{931} a^{17} + \frac{1}{931} a^{16} - \frac{2}{931} a^{15} + \frac{2}{49} a^{14} + \frac{23}{931} a^{13} - \frac{22}{931} a^{12} + \frac{4}{133} a^{11} - \frac{30}{931} a^{10} - \frac{45}{931} a^{9} - \frac{200}{931} a^{8} + \frac{192}{931} a^{7} - \frac{104}{931} a^{6} + \frac{461}{931} a^{5} + \frac{253}{931} a^{4} + \frac{103}{931} a^{3} + \frac{176}{931} a^{2} - \frac{195}{931} a + \frac{248}{931}$, $\frac{1}{931} a^{21} - \frac{22}{931} a^{14} - \frac{9}{133} a^{13} - \frac{2}{133} a^{12} + \frac{6}{133} a^{11} + \frac{8}{133} a^{10} + \frac{1}{133} a^{9} + \frac{53}{133} a^{8} - \frac{165}{931} a^{7} + \frac{25}{133} a^{6} - \frac{47}{133} a^{5} + \frac{46}{133} a^{4} + \frac{58}{133} a^{3} - \frac{5}{133} a^{2} + \frac{45}{133} a - \frac{351}{931}$, $\frac{1}{931} a^{22} - \frac{1}{931} a^{15} - \frac{9}{133} a^{14} + \frac{1}{19} a^{13} - \frac{6}{133} a^{12} - \frac{9}{133} a^{11} - \frac{4}{133} a^{10} - \frac{3}{133} a^{9} + \frac{388}{931} a^{8} + \frac{52}{133} a^{7} - \frac{54}{133} a^{6} - \frac{10}{133} a^{5} + \frac{45}{133} a^{4} + \frac{61}{133} a^{3} - \frac{51}{133} a^{2} + \frac{118}{931} a - \frac{11}{133}$, $\frac{1}{931} a^{23} - \frac{1}{931} a^{16} + \frac{1}{19} a^{14} + \frac{2}{133} a^{13} - \frac{1}{19} a^{12} + \frac{2}{133} a^{11} + \frac{1}{133} a^{10} + \frac{10}{931} a^{9} + \frac{61}{133} a^{8} - \frac{11}{133} a^{7} + \frac{26}{133} a^{6} + \frac{29}{133} a^{5} + \frac{60}{133} a^{4} + \frac{33}{133} a^{3} - \frac{435}{931} a^{2} + \frac{5}{133}$, $\frac{1}{931} a^{24} - \frac{1}{931} a^{17} + \frac{2}{133} a^{14} - \frac{9}{133} a^{13} - \frac{8}{133} a^{12} + \frac{9}{133} a^{11} + \frac{3}{931} a^{10} + \frac{8}{133} a^{9} + \frac{1}{133} a^{8} + \frac{39}{133} a^{7} - \frac{37}{133} a^{6} + \frac{1}{19} a^{5} - \frac{3}{7} a^{4} - \frac{316}{931} a^{3} + \frac{53}{133} a^{2} - \frac{31}{133} a - \frac{9}{19}$, $\frac{1}{931} a^{25} + \frac{1}{931} a^{17} - \frac{2}{931} a^{16} + \frac{3}{931} a^{15} - \frac{18}{931} a^{14} - \frac{29}{931} a^{13} + \frac{5}{133} a^{12} - \frac{13}{931} a^{11} - \frac{52}{931} a^{10} - \frac{39}{931} a^{9} + \frac{444}{931} a^{8} - \frac{240}{931} a^{7} + \frac{272}{931} a^{6} - \frac{188}{931} a^{5} + \frac{298}{931} a^{4} - \frac{272}{931} a^{3} - \frac{139}{931} a^{2} + \frac{16}{49} a + \frac{309}{931}$, $\frac{1}{772413987138487006047191002772144337504772136920104340930363470704490025576829603284559170064536429681247089921339763669911} a^{26} + \frac{267153361054162047941611268074241597560827181578204268803595594722512202059127782306383917179795984968144021726753658246}{772413987138487006047191002772144337504772136920104340930363470704490025576829603284559170064536429681247089921339763669911} a^{25} - \frac{39008885301746528431140875383845038680730385788139148285917941026294994671321653596938132842379725914059582693513047482}{110344855305498143721027286110306333929253162417157762990051924386355717939547086183508452866362347097321012845905680524273} a^{24} - \frac{381924715125359650970548791549522990082075691916966548341593352073749408039956213887646920869122467397424389402738687545}{772413987138487006047191002772144337504772136920104340930363470704490025576829603284559170064536429681247089921339763669911} a^{23} + \frac{333737352267138366322583062869988146038360567297227984247371386965825155562436695676044100172982286941161062048609231675}{772413987138487006047191002772144337504772136920104340930363470704490025576829603284559170064536429681247089921339763669911} a^{22} - \frac{105723031855023805251858028937142227405619710135321696515752962576686980753823275675848565497800982417255133763838943153}{772413987138487006047191002772144337504772136920104340930363470704490025576829603284559170064536429681247089921339763669911} a^{21} - \frac{18514734404486347681623369979818286828124585374239955336085822207743259252212500654366645389768297092731314909411328836}{40653367744130895055115315935376017763409059837900228470019130037078422398780505436029430003396654193749846837965250719469} a^{20} + \frac{410227085467607575459335687251317428024644805648236588273403689803575173853330648602017854440974169836121352943613463535}{772413987138487006047191002772144337504772136920104340930363470704490025576829603284559170064536429681247089921339763669911} a^{19} + \frac{116737410808141547518409668673591022534680013004306180897090569404568029589093857110003888065149168939932665994301215725}{772413987138487006047191002772144337504772136920104340930363470704490025576829603284559170064536429681247089921339763669911} a^{18} - \frac{1483740730754242214135636848476946453371626103511708355173940364339620209550841931272974124090587135970740643867918556194}{772413987138487006047191002772144337504772136920104340930363470704490025576829603284559170064536429681247089921339763669911} a^{17} - \frac{1924311197442800366246384525500082644728731214127437263125895309013866072011915485151160802595111951217192272637650804582}{772413987138487006047191002772144337504772136920104340930363470704490025576829603284559170064536429681247089921339763669911} a^{16} - \frac{1665732181107150025215912332194369051626068542244159027048601917588718441613396145588972885057203441335551535900586191081}{772413987138487006047191002772144337504772136920104340930363470704490025576829603284559170064536429681247089921339763669911} a^{15} + \frac{2555258855456908450735906615658521210015223707626432561865976423493270532581684459227046298519012412722174624340336260647}{772413987138487006047191002772144337504772136920104340930363470704490025576829603284559170064536429681247089921339763669911} a^{14} + \frac{26218447760522353289205915700558417897660113744195831965824995463257834672436603523487464241884957743851385197458733800048}{772413987138487006047191002772144337504772136920104340930363470704490025576829603284559170064536429681247089921339763669911} a^{13} + \frac{37763713172703091348081455419082373727646681430435268392977792519192428310620231171850485825280640122311208290402199028618}{772413987138487006047191002772144337504772136920104340930363470704490025576829603284559170064536429681247089921339763669911} a^{12} - \frac{44587282550731014827970374801429851389325845092666935307997399426178119742708642291705880049448620086185486235036718280855}{772413987138487006047191002772144337504772136920104340930363470704490025576829603284559170064536429681247089921339763669911} a^{11} + \frac{3526083470514138271604361265119887856840998834569574337675259534649203451000475574217359000574271459193941136877332339892}{110344855305498143721027286110306333929253162417157762990051924386355717939547086183508452866362347097321012845905680524273} a^{10} + \frac{7389216634832395295743000490379039979096138741657961409451301520886548100125718153868254399839300578304926532759023649009}{110344855305498143721027286110306333929253162417157762990051924386355717939547086183508452866362347097321012845905680524273} a^{9} - \frac{210036167960791727757253434318805554448156209379079432685974564412619484753689645674347843274544842702959352686696543098982}{772413987138487006047191002772144337504772136920104340930363470704490025576829603284559170064536429681247089921339763669911} a^{8} - \frac{24070183461609265145013492068058978304022224417826415498560738175274400860705093339074235061500749743142348074586888166658}{772413987138487006047191002772144337504772136920104340930363470704490025576829603284559170064536429681247089921339763669911} a^{7} + \frac{204370262053900103947257021614799708321489315027950050563701231281534104137888170184205933846020735266374133555316095331648}{772413987138487006047191002772144337504772136920104340930363470704490025576829603284559170064536429681247089921339763669911} a^{6} + \frac{307818880529348276676283646315967410669250570805426563798275462198471792658195509216514959744092966695884224454344127354583}{772413987138487006047191002772144337504772136920104340930363470704490025576829603284559170064536429681247089921339763669911} a^{5} + \frac{145696382996795778793249379220111968066888850465898847197294191391107949932055725476001671859831758122926804399561256577608}{772413987138487006047191002772144337504772136920104340930363470704490025576829603284559170064536429681247089921339763669911} a^{4} + \frac{234969935870177365588949106469372976066318751184037022548924421077557235735092517671241537836303916391496579638808960328514}{772413987138487006047191002772144337504772136920104340930363470704490025576829603284559170064536429681247089921339763669911} a^{3} + \frac{345444858135347709580921906390659846072644496675907315197508484032806992401934043510747087655323179259465740570172556903013}{772413987138487006047191002772144337504772136920104340930363470704490025576829603284559170064536429681247089921339763669911} a^{2} + \frac{103288213346334227599913143807866689956320814053859167272865475998448143247974618046385601680346043332557597893051966033842}{772413987138487006047191002772144337504772136920104340930363470704490025576829603284559170064536429681247089921339763669911} a - \frac{296196047439674212787178242062472631119320667625951995915900730149478514541797003508433220275422687753153395891741662757074}{772413987138487006047191002772144337504772136920104340930363470704490025576829603284559170064536429681247089921339763669911}$

magma: IntegralBasis(K);
 
sage: K.integral_basis()
 
gp: K.zk
 

Class group and class number

$C_{3}$, which has order $3$ (assuming GRH)

magma: ClassGroup(K);
 
sage: K.class_group().invariants()
 
gp: K.clgp
 

Unit group

magma: UK, f := UnitGroup(K);
 
sage: UK = K.unit_group()
 
Rank:  $26$
magma: UnitRank(K);
 
sage: UK.rank()
 
gp: K.fu
 
Torsion generator:  \( -1 \) (order $2$)
magma: K!f(TU.1) where TU,f is TorsionUnitGroup(K);
 
sage: UK.torsion_generator()
 
gp: K.tu[2]
 
Fundamental units:  Units are too long to display, but can be downloaded with other data for this field from 'Stored data to gp' link to the right (assuming GRH)
magma: [K!f(g): g in Generators(UK)];
 
sage: UK.fundamental_units()
 
gp: K.fu
 
Regulator:  \( 1289110163972655300000000 \) (assuming GRH)
magma: Regulator(K);
 
sage: K.regulator()
 
gp: K.reg
 

Galois group

$C_3\times C_9$ (as 27T2):

magma: GaloisGroup(K);
 
sage: K.galois_group(type='pari')
 
gp: polgalois(K.pol)
 
An abelian group of order 27
The 27 conjugacy class representatives for $C_3\times C_9$
Character table for $C_3\times C_9$ is not computed

Intermediate fields

3.3.13689.2, \(\Q(\zeta_{9})^+\), 3.3.13689.1, 3.3.169.1, 9.9.2565164201769.1, 9.9.3691950281939241.2, 9.9.17820338848416865911969.1, 9.9.17820338848416865911969.4

Fields in the database are given up to isomorphism. Isomorphic intermediate fields are shown with their multiplicities.

Frobenius cycle types

$p$ 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59
Cycle type ${\href{/LocalNumberField/2.9.0.1}{9} }^{3}$ R ${\href{/LocalNumberField/5.9.0.1}{9} }^{3}$ R ${\href{/LocalNumberField/11.9.0.1}{9} }^{3}$ R ${\href{/LocalNumberField/17.3.0.1}{3} }^{9}$ ${\href{/LocalNumberField/19.3.0.1}{3} }^{9}$ ${\href{/LocalNumberField/23.9.0.1}{9} }^{3}$ ${\href{/LocalNumberField/29.9.0.1}{9} }^{3}$ ${\href{/LocalNumberField/31.9.0.1}{9} }^{3}$ ${\href{/LocalNumberField/37.3.0.1}{3} }^{9}$ ${\href{/LocalNumberField/41.9.0.1}{9} }^{3}$ ${\href{/LocalNumberField/43.9.0.1}{9} }^{3}$ ${\href{/LocalNumberField/47.9.0.1}{9} }^{3}$ ${\href{/LocalNumberField/53.3.0.1}{3} }^{9}$ ${\href{/LocalNumberField/59.9.0.1}{9} }^{3}$

In the table, R denotes a ramified prime. Cycle lengths which are repeated in a cycle type are indicated by exponents.

magma: p := 7; // to obtain a list of $[e_i,f_i]$ for the factorization of the ideal $p\mathcal{O}_K$:
 
magma: idealfactors := Factorization(p*Integers(K)); // get the data
 
magma: [<primefactor[2], Valuation(Norm(primefactor[1]), p)> : primefactor in idealfactors];
 
sage: p = 7; # to obtain a list of $[e_i,f_i]$ for the factorization of the ideal $p\mathcal{O}_K$:
 
sage: [(e, pr.norm().valuation(p)) for pr,e in K.factor(p)]
 
gp: p = 7; \\ to obtain a list of $[e_i,f_i]$ for the factorization of the ideal $p\mathcal{O}_K$:
 
gp: idealfactors = idealprimedec(K, p); \\ get the data
 
gp: vector(length(idealfactors), j, [idealfactors[j][3], idealfactors[j][4]])
 

Local algebras for ramified primes

$p$LabelPolynomial $e$ $f$ $c$ Galois group Slope content
3Data not computed
$7$7.9.6.3$x^{9} - 14 x^{6} + 49 x^{3} - 1372$$3$$3$$6$$C_9$$[\ ]_{3}^{3}$
7.9.6.3$x^{9} - 14 x^{6} + 49 x^{3} - 1372$$3$$3$$6$$C_9$$[\ ]_{3}^{3}$
7.9.6.3$x^{9} - 14 x^{6} + 49 x^{3} - 1372$$3$$3$$6$$C_9$$[\ ]_{3}^{3}$
13Data not computed