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Properties

Label 28.0.22737730143...3249.1
Degree $28$
Signature $[0, 14]$
Discriminant $3^{14}\cdot 11^{14}\cdot 29^{24}$
Root discriminant $102.98$
Ramified primes $3, 11, 29$
Class number $2752$ (GRH)
Class group $[4, 4, 172]$ (GRH)
Galois group $C_2\times C_{14}$ (as 28T2)

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Show commands for: Magma / SageMath / Pari/GP

magma: R<x> := PolynomialRing(Rationals()); K<a> := NumberField(R![16939803409, -8862898688, -9487528803, 4993294824, 2642888941, -1338303622, -1302809622, 663677457, 391036360, -226684219, -27922208, 25878608, 8898705, -6050900, -2715569, 1635850, -606436, 350432, 49006, -77733, 20866, -5204, 772, 291, 37, -52, 19, -5, 1]);
 
sage: x = polygen(QQ); K.<a> = NumberField(x^28 - 5*x^27 + 19*x^26 - 52*x^25 + 37*x^24 + 291*x^23 + 772*x^22 - 5204*x^21 + 20866*x^20 - 77733*x^19 + 49006*x^18 + 350432*x^17 - 606436*x^16 + 1635850*x^15 - 2715569*x^14 - 6050900*x^13 + 8898705*x^12 + 25878608*x^11 - 27922208*x^10 - 226684219*x^9 + 391036360*x^8 + 663677457*x^7 - 1302809622*x^6 - 1338303622*x^5 + 2642888941*x^4 + 4993294824*x^3 - 9487528803*x^2 - 8862898688*x + 16939803409)
 
gp: K = bnfinit(x^28 - 5*x^27 + 19*x^26 - 52*x^25 + 37*x^24 + 291*x^23 + 772*x^22 - 5204*x^21 + 20866*x^20 - 77733*x^19 + 49006*x^18 + 350432*x^17 - 606436*x^16 + 1635850*x^15 - 2715569*x^14 - 6050900*x^13 + 8898705*x^12 + 25878608*x^11 - 27922208*x^10 - 226684219*x^9 + 391036360*x^8 + 663677457*x^7 - 1302809622*x^6 - 1338303622*x^5 + 2642888941*x^4 + 4993294824*x^3 - 9487528803*x^2 - 8862898688*x + 16939803409, 1)
 

Normalized defining polynomial

\( x^{28} - 5 x^{27} + 19 x^{26} - 52 x^{25} + 37 x^{24} + 291 x^{23} + 772 x^{22} - 5204 x^{21} + 20866 x^{20} - 77733 x^{19} + 49006 x^{18} + 350432 x^{17} - 606436 x^{16} + 1635850 x^{15} - 2715569 x^{14} - 6050900 x^{13} + 8898705 x^{12} + 25878608 x^{11} - 27922208 x^{10} - 226684219 x^{9} + 391036360 x^{8} + 663677457 x^{7} - 1302809622 x^{6} - 1338303622 x^{5} + 2642888941 x^{4} + 4993294824 x^{3} - 9487528803 x^{2} - 8862898688 x + 16939803409 \)

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

Invariants

Degree:  $28$
magma: Degree(K);
 
sage: K.degree()
 
gp: poldegree(K.pol)
 
Signature:  $[0, 14]$
magma: Signature(K);
 
sage: K.signature()
 
gp: K.sign
 
Discriminant:  \(227377301430762366815308745905009164830324961107925753249=3^{14}\cdot 11^{14}\cdot 29^{24}\)
magma: Discriminant(Integers(K));
 
sage: K.disc()
 
gp: K.disc
 
Root discriminant:  $102.98$
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:  $3, 11, 29$
magma: PrimeDivisors(Discriminant(Integers(K)));
 
sage: K.disc().support()
 
gp: factor(abs(K.disc))[,1]~
 
This field is Galois and abelian over $\Q$.
Conductor:  \(957=3\cdot 11\cdot 29\)
Dirichlet character group:    $\lbrace$$\chi_{957}(320,·)$, $\chi_{957}(1,·)$, $\chi_{957}(835,·)$, $\chi_{957}(197,·)$, $\chi_{957}(518,·)$, $\chi_{957}(65,·)$, $\chi_{957}(716,·)$, $\chi_{957}(397,·)$, $\chi_{957}(848,·)$, $\chi_{957}(529,·)$, $\chi_{957}(661,·)$, $\chi_{957}(23,·)$, $\chi_{957}(857,·)$, $\chi_{957}(538,·)$, $\chi_{957}(923,·)$, $\chi_{957}(604,·)$, $\chi_{957}(199,·)$, $\chi_{957}(683,·)$, $\chi_{957}(364,·)$, $\chi_{957}(749,·)$, $\chi_{957}(430,·)$, $\chi_{957}(175,·)$, $\chi_{957}(692,·)$, $\chi_{957}(373,·)$, $\chi_{957}(494,·)$, $\chi_{957}(890,·)$, $\chi_{957}(571,·)$, $\chi_{957}(703,·)$$\rbrace$
This is a CM field.

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

$1$, $a$, $a^{2}$, $a^{3}$, $a^{4}$, $a^{5}$, $a^{6}$, $a^{7}$, $a^{8}$, $a^{9}$, $a^{10}$, $a^{11}$, $a^{12}$, $a^{13}$, $a^{14}$, $a^{15}$, $a^{16}$, $a^{17}$, $a^{18}$, $a^{19}$, $a^{20}$, $\frac{1}{29} a^{21} + \frac{1}{29} a^{18} - \frac{12}{29} a^{15} - \frac{7}{29} a^{12} - \frac{1}{29} a^{9} + \frac{14}{29} a^{6} - \frac{9}{29} a^{3} + \frac{1}{29}$, $\frac{1}{29} a^{22} + \frac{1}{29} a^{19} - \frac{12}{29} a^{16} - \frac{7}{29} a^{13} - \frac{1}{29} a^{10} + \frac{14}{29} a^{7} - \frac{9}{29} a^{4} + \frac{1}{29} a$, $\frac{1}{493} a^{23} - \frac{3}{493} a^{22} - \frac{2}{493} a^{21} + \frac{175}{493} a^{20} + \frac{229}{493} a^{19} + \frac{201}{493} a^{18} + \frac{104}{493} a^{17} + \frac{7}{493} a^{16} + \frac{111}{493} a^{15} - \frac{123}{493} a^{14} + \frac{108}{493} a^{13} - \frac{44}{493} a^{12} - \frac{146}{493} a^{11} + \frac{32}{493} a^{10} - \frac{5}{29} a^{9} + \frac{43}{493} a^{8} - \frac{13}{493} a^{7} - \frac{144}{493} a^{6} - \frac{9}{493} a^{5} + \frac{201}{493} a^{4} - \frac{185}{493} a^{3} - \frac{202}{493} a^{2} - \frac{3}{493} a + \frac{201}{493}$, $\frac{1}{493} a^{24} + \frac{6}{493} a^{22} - \frac{1}{493} a^{21} - \frac{8}{17} a^{20} - \frac{81}{493} a^{19} + \frac{44}{493} a^{18} - \frac{6}{17} a^{17} - \frac{72}{493} a^{16} - \frac{215}{493} a^{15} + \frac{8}{17} a^{14} + \frac{161}{493} a^{13} - \frac{74}{493} a^{12} + \frac{3}{17} a^{11} - \frac{6}{493} a^{10} - \frac{42}{493} a^{9} + \frac{4}{17} a^{8} + \frac{55}{493} a^{7} + \frac{137}{493} a^{6} + \frac{6}{17} a^{5} - \frac{228}{493} a^{4} - \frac{213}{493} a^{3} - \frac{4}{17} a^{2} + \frac{209}{493} a - \frac{60}{493}$, $\frac{1}{163183} a^{25} + \frac{30}{163183} a^{24} - \frac{159}{163183} a^{23} + \frac{1439}{163183} a^{22} + \frac{71}{9599} a^{21} + \frac{63177}{163183} a^{20} + \frac{4062}{9599} a^{19} - \frac{76729}{163183} a^{18} + \frac{63330}{163183} a^{17} - \frac{50671}{163183} a^{16} + \frac{34270}{163183} a^{15} - \frac{26321}{163183} a^{14} - \frac{13982}{163183} a^{13} - \frac{25524}{163183} a^{12} - \frac{47749}{163183} a^{11} + \frac{75571}{163183} a^{10} - \frac{70589}{163183} a^{9} - \frac{15392}{163183} a^{8} + \frac{78732}{163183} a^{7} - \frac{2845}{163183} a^{6} + \frac{1251}{9599} a^{5} + \frac{72203}{163183} a^{4} + \frac{56166}{163183} a^{3} - \frac{18255}{163183} a^{2} + \frac{33106}{163183} a - \frac{60941}{163183}$, $\frac{1}{12309974925790837601828265901679} a^{26} - \frac{6249368920279340563148451}{12309974925790837601828265901679} a^{25} + \frac{2953575244484278935042127187}{12309974925790837601828265901679} a^{24} + \frac{6499278361551051322445461405}{12309974925790837601828265901679} a^{23} + \frac{158056674326246388347560111094}{12309974925790837601828265901679} a^{22} - \frac{175604973049780808581622589942}{12309974925790837601828265901679} a^{21} + \frac{1543764115702216055814560279492}{12309974925790837601828265901679} a^{20} + \frac{5527642642088219751804818497178}{12309974925790837601828265901679} a^{19} - \frac{4778391666713335160976955515607}{12309974925790837601828265901679} a^{18} - \frac{5770208635215686839721451271061}{12309974925790837601828265901679} a^{17} - \frac{2407302621754725463113388363496}{12309974925790837601828265901679} a^{16} + \frac{4816056770464444328097499819672}{12309974925790837601828265901679} a^{15} + \frac{4513460376800503945338623988168}{12309974925790837601828265901679} a^{14} + \frac{1984370216358829348084822650628}{12309974925790837601828265901679} a^{13} + \frac{15290784025573076000889947894}{12309974925790837601828265901679} a^{12} - \frac{3544019436436272585303869923854}{12309974925790837601828265901679} a^{11} + \frac{222960535023888150547355287283}{12309974925790837601828265901679} a^{10} + \frac{3739400503765060080140616495884}{12309974925790837601828265901679} a^{9} + \frac{430514816149940502166170143514}{12309974925790837601828265901679} a^{8} - \frac{186747812378502933335292015921}{724116172105343388342839170687} a^{7} - \frac{5712639981896357282474059661017}{12309974925790837601828265901679} a^{6} - \frac{3361986626145358906226827430564}{12309974925790837601828265901679} a^{5} - \frac{65490961303638681554856967419}{208643642810014196641157049181} a^{4} - \frac{1089914421074094352384380603899}{12309974925790837601828265901679} a^{3} - \frac{5259325456856149485328787357061}{12309974925790837601828265901679} a^{2} - \frac{5120658641124584666693417167772}{12309974925790837601828265901679} a + \frac{34607168800621948399983991047}{78407483603763296826931629947}$, $\frac{1}{279179361357530920802976438360208687980137631505674982433023694924798700572149365871972717746293} a^{27} - \frac{5496607480232658579243256501408883584471509168851136515360193}{1778212492723126884095391327135087184586863894940604983649832451750310194727066024662246609849} a^{26} - \frac{719706824228376762711861427048878618927762937397558501662510655491551203119920100425801629}{279179361357530920802976438360208687980137631505674982433023694924798700572149365871972717746293} a^{25} - \frac{8805698216040267594900422853658573174059012555314655935271151320711038707360963000217428222}{16422315373972407106057437550600511057655154794451469554883746760282276504244080345410159867429} a^{24} + \frac{174306101176405956517758885027665381485982290135356414431611545299600156832908116772742689022}{279179361357530920802976438360208687980137631505674982433023694924798700572149365871972717746293} a^{23} + \frac{1920903817776333296948578019419030400615827110979402679219269953089101786499135260253504374295}{279179361357530920802976438360208687980137631505674982433023694924798700572149365871972717746293} a^{22} + \frac{458471281776454253926102611121434385702865957316999415911362592738443277672641160562427230593}{279179361357530920802976438360208687980137631505674982433023694924798700572149365871972717746293} a^{21} - \frac{1696058960793011814958571292153058218861258590087462619465039307972211746387095809843783648428}{9626874529570031751826773736558920275177159707092240773552541204303403468005150547309404060217} a^{20} + \frac{79188201618695885310756301475635248314348007584338333581669423463781361492376786887572241650196}{279179361357530920802976438360208687980137631505674982433023694924798700572149365871972717746293} a^{19} + \frac{18597471423025360899020841418334618866563795042720759950867090648782576429689339884909887830448}{279179361357530920802976438360208687980137631505674982433023694924798700572149365871972717746293} a^{18} - \frac{117403648573137206573832477333079721372600289365229651965896492962300115810381928424675244195416}{279179361357530920802976438360208687980137631505674982433023694924798700572149365871972717746293} a^{17} + \frac{20259406455220066116057577712989893780695637605331246345324426586376265751702364198936144988366}{279179361357530920802976438360208687980137631505674982433023694924798700572149365871972717746293} a^{16} + \frac{15920345548806219045408672466741754385118935612638431838260816880047400623458525206197348993681}{279179361357530920802976438360208687980137631505674982433023694924798700572149365871972717746293} a^{15} + \frac{111159564979537166574607653360404407094793742445206961810279625915316121491094806833998500361356}{279179361357530920802976438360208687980137631505674982433023694924798700572149365871972717746293} a^{14} + \frac{21418377804274202903091902643734784796542303910466402055895079440655620303854953671534436668455}{279179361357530920802976438360208687980137631505674982433023694924798700572149365871972717746293} a^{13} + \frac{2093417514523206873380096682514762792173681946732982851326003482203151391894342390275067604543}{16422315373972407106057437550600511057655154794451469554883746760282276504244080345410159867429} a^{12} + \frac{62726577048946237151708351604136180164677810600026111420855961140338477205246281809590730373439}{279179361357530920802976438360208687980137631505674982433023694924798700572149365871972717746293} a^{11} + \frac{15632616128918904449704910830803565876322813625145594022207247030662044567965431828056736746578}{279179361357530920802976438360208687980137631505674982433023694924798700572149365871972717746293} a^{10} - \frac{19252932284048117778530822633923588361180315703895720409177274223377115520451058285379493644283}{279179361357530920802976438360208687980137631505674982433023694924798700572149365871972717746293} a^{9} + \frac{109228348039346607993113562230615181914808355418180310256752432730768134223003528507207352913952}{279179361357530920802976438360208687980137631505674982433023694924798700572149365871972717746293} a^{8} + \frac{100958704498491763244539320653292864265866399516360535323375110631530141536928031834430540449445}{279179361357530920802976438360208687980137631505674982433023694924798700572149365871972717746293} a^{7} + \frac{26727049869015398091956100890492772216790863976658133188734575551156791514251486220123851528145}{279179361357530920802976438360208687980137631505674982433023694924798700572149365871972717746293} a^{6} + \frac{19499955722669710186105079231008174147881443917551983746085908016535251688655249527863085268285}{279179361357530920802976438360208687980137631505674982433023694924798700572149365871972717746293} a^{5} + \frac{115824731619375533012134772700065226747129751032676518866832269562813677023592505201571281254300}{279179361357530920802976438360208687980137631505674982433023694924798700572149365871972717746293} a^{4} + \frac{96216702358828729919161234343704491371173100443579581025292413184766078551931026483926077109792}{279179361357530920802976438360208687980137631505674982433023694924798700572149365871972717746293} a^{3} + \frac{127814426691590014630661839691601738911984664711917245720184413615697179925687114363832362686660}{279179361357530920802976438360208687980137631505674982433023694924798700572149365871972717746293} a^{2} + \frac{12408587846279464108667175600551814994395949058991060770443948910279654616500948340351310002433}{279179361357530920802976438360208687980137631505674982433023694924798700572149365871972717746293} a + \frac{109970487072823879977892346198639622461855256503567556739083939562156866126561217798529385}{2145009038266739305302040201610479112891271284608691174487132028649348847680417400075086381}$

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

Class group and class number

$C_{4}\times C_{4}\times C_{172}$, which has order $2752$ (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:  $13$
magma: UnitRank(K);
 
sage: UK.rank()
 
gp: K.fu
 
Torsion generator:  \( -\frac{584120095343790085707759237454095575988859031236228004687432890}{581032876334005560019546181090062639572167446050959011412179881086890177} a^{27} + \frac{5297812147698894456329718101348259246613536235620100371721544171}{581032876334005560019546181090062639572167446050959011412179881086890177} a^{26} - \frac{25393270222061762188747996020322846408950822416444300155373258561}{581032876334005560019546181090062639572167446050959011412179881086890177} a^{25} + \frac{95724416501739248338103739559444710666891049514553008383868727765}{581032876334005560019546181090062639572167446050959011412179881086890177} a^{24} - \frac{241017880383014458718467207836075996579402859796568710340588073902}{581032876334005560019546181090062639572167446050959011412179881086890177} a^{23} + \frac{273210723006642777785937178980330715465354365892887329270520346240}{581032876334005560019546181090062639572167446050959011412179881086890177} a^{22} - \frac{627802466119777201510883936509226661946940638824700093973762888032}{581032876334005560019546181090062639572167446050959011412179881086890177} a^{21} + \frac{5785263531528662995296374194743322410622091672424689582561925152413}{581032876334005560019546181090062639572167446050959011412179881086890177} a^{20} - \frac{27206907943831901812448124492078405073935685158565447451262621627949}{581032876334005560019546181090062639572167446050959011412179881086890177} a^{19} + \frac{6882105300460315481845190284183770940804868423078656100406245013798}{34178404490235621177620363593533096445421614473585824200716463593346481} a^{18} - \frac{316362413637561037497046078242440920316697442030909791528025796068756}{581032876334005560019546181090062639572167446050959011412179881086890177} a^{17} + \frac{350710621328998237094752288572556192392375702472632491752947847280555}{581032876334005560019546181090062639572167446050959011412179881086890177} a^{16} + \frac{52928517737619105299086131368263188735695730531914147040783232463715}{581032876334005560019546181090062639572167446050959011412179881086890177} a^{15} - \frac{1214891340136017932733513965298160131961665009695780615107501529328922}{581032876334005560019546181090062639572167446050959011412179881086890177} a^{14} + \frac{5678514306461165489677629537869904369047054077787401273017851011634412}{581032876334005560019546181090062639572167446050959011412179881086890177} a^{13} - \frac{7645515200663118888691724110138796238033007336699515556572853612308418}{581032876334005560019546181090062639572167446050959011412179881086890177} a^{12} + \frac{1070382960724290705588558486761121320073613887158661787565200324542711}{581032876334005560019546181090062639572167446050959011412179881086890177} a^{11} - \frac{19459076427037388701840925371310780567788625881660477243709151983538001}{581032876334005560019546181090062639572167446050959011412179881086890177} a^{10} + \frac{82365795161566120466330058047746631978804105357402299605516126672657869}{581032876334005560019546181090062639572167446050959011412179881086890177} a^{9} - \frac{12679999254611076859101263154641283242272341187597758516271459316115460}{581032876334005560019546181090062639572167446050959011412179881086890177} a^{8} - \frac{471446937713722047985199355093825420640722202279599795582121136125962552}{581032876334005560019546181090062639572167446050959011412179881086890177} a^{7} + \frac{562297780328205287478353816843790987255910198928456248028205646341102352}{581032876334005560019546181090062639572167446050959011412179881086890177} a^{6} + \frac{623107350155483073265328956938223913592429118240663779888714001267694147}{581032876334005560019546181090062639572167446050959011412179881086890177} a^{5} - \frac{545665582285528042520345091397239721012989222023036328704896680740008614}{581032876334005560019546181090062639572167446050959011412179881086890177} a^{4} - \frac{2444212082073878767666117095375524013598484981073333913432061861265276998}{581032876334005560019546181090062639572167446050959011412179881086890177} a^{3} + \frac{2093041310911391360916378642767049798851974399934101317945819557089930511}{581032876334005560019546181090062639572167446050959011412179881086890177} a^{2} + \frac{8496866870975971045052989622990980412753047449473402384329338708280948363}{581032876334005560019546181090062639572167446050959011412179881086890177} a - \frac{90474222073124948902974672958678817011023745781392875268685795300981}{4464229609259913793915977204444481798899506319877060163132466259609} \) (order $6$)
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:  \( 26171553169497.523 \) (assuming GRH)
magma: Regulator(K);
 
sage: K.regulator()
 
gp: K.reg
 

Galois group

$C_2\times C_{14}$ (as 28T2):

magma: GaloisGroup(K);
 
sage: K.galois_group(type='pari')
 
gp: polgalois(K.pol)
 
An abelian group of order 28
The 28 conjugacy class representatives for $C_2\times C_{14}$
Character table for $C_2\times C_{14}$ is not computed

Intermediate fields

\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{33}) \), \(\Q(\sqrt{-3}, \sqrt{-11})\), 7.7.594823321.1, 14.0.6894849182652903337173011.1, 14.0.773792930870360792667.1, 14.14.15079035162461899598397375057.1

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 ${\href{/LocalNumberField/2.14.0.1}{14} }^{2}$ R ${\href{/LocalNumberField/5.14.0.1}{14} }^{2}$ ${\href{/LocalNumberField/7.14.0.1}{14} }^{2}$ R ${\href{/LocalNumberField/13.14.0.1}{14} }^{2}$ ${\href{/LocalNumberField/17.2.0.1}{2} }^{14}$ ${\href{/LocalNumberField/19.14.0.1}{14} }^{2}$ ${\href{/LocalNumberField/23.14.0.1}{14} }^{2}$ R ${\href{/LocalNumberField/31.7.0.1}{7} }^{4}$ ${\href{/LocalNumberField/37.7.0.1}{7} }^{4}$ ${\href{/LocalNumberField/41.2.0.1}{2} }^{14}$ ${\href{/LocalNumberField/43.14.0.1}{14} }^{2}$ ${\href{/LocalNumberField/47.14.0.1}{14} }^{2}$ ${\href{/LocalNumberField/53.14.0.1}{14} }^{2}$ ${\href{/LocalNumberField/59.2.0.1}{2} }^{14}$

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
$3$3.14.7.2$x^{14} + 243 x^{4} - 729 x^{2} + 2187$$2$$7$$7$$C_{14}$$[\ ]_{2}^{7}$
3.14.7.2$x^{14} + 243 x^{4} - 729 x^{2} + 2187$$2$$7$$7$$C_{14}$$[\ ]_{2}^{7}$
11Data not computed
$29$29.14.12.1$x^{14} + 2407 x^{7} + 1839267$$7$$2$$12$$C_{14}$$[\ ]_{7}^{2}$
29.14.12.1$x^{14} + 2407 x^{7} + 1839267$$7$$2$$12$$C_{14}$$[\ ]_{7}^{2}$