Number field 30.0.11277272245002111679540357002131401262707502951787.1

• Label: 30.0.112...787.1
• Degree: $30$
• Signature: $[0, 15]$
• Discriminant: $-1.128\times 10^{49}$
• Root discriminant: \(43.16\)
• Ramified primes: $3,7,11$
• Class number: $976$ (GRH)
• Class group: [2, 2, 2, 122] (GRH)
• Galois group: $C_{30}$ (as 30T1)

Normalized defining polynomial

x^30 - x^29 + 23*x^28 - 12*x^27 + 335*x^26 - 144*x^25 + 2773*x^24 - 863*x^23 + 16295*x^22 - 4775*x^21 + 62257*x^20 - 15750*x^19 + 170334*x^18 - 52802*x^17 + 293956*x^16 - 111720*x^15 + 369164*x^14 - 135917*x^13 + 276687*x^12 - 78965*x^11 + 139349*x^10 - 31906*x^9 + 42847*x^8 - 4541*x^7 + 8009*x^6 - 477*x^5 + 1036*x^4 + 2*x^3 + 63*x^2 - 6*x + 1

Invariants

Degree:		$30$
Signature:		$[0, 15]$
Discriminant:		\(-11277272245002111679540357002131401262707502951787\) \(\medspace = -\,3^{15}\cdot 7^{20}\cdot 11^{24}\)
Root discriminant:		\(43.16\)
Galois root discriminant:		$3^{1/2}7^{2/3}11^{4/5}\approx 43.15920823215784$
Ramified primes:		\(3\), \(7\), \(11\)
Discriminant root field:		\(\Q(\sqrt{-3}) \)
$\card{ \Gal(K/\Q) }$:		$30$
This field is Galois and abelian over $\Q$.
Conductor:		\(231=3\cdot 7\cdot 11\)
Dirichlet character group:		$\lbrace$$\chi_{231}(64,·)$, $\chi_{231}(1,·)$, $\chi_{231}(130,·)$, $\chi_{231}(67,·)$, $\chi_{231}(4,·)$, $\chi_{231}(86,·)$, $\chi_{231}(71,·)$, $\chi_{231}(137,·)$, $\chi_{231}(16,·)$, $\chi_{231}(148,·)$, $\chi_{231}(214,·)$, $\chi_{231}(23,·)$, $\chi_{231}(25,·)$, $\chi_{231}(218,·)$, $\chi_{231}(155,·)$, $\chi_{231}(92,·)$, $\chi_{231}(221,·)$, $\chi_{231}(158,·)$, $\chi_{231}(163,·)$, $\chi_{231}(100,·)$, $\chi_{231}(37,·)$, $\chi_{231}(169,·)$, $\chi_{231}(170,·)$, $\chi_{231}(113,·)$, $\chi_{231}(179,·)$, $\chi_{231}(53,·)$, $\chi_{231}(212,·)$, $\chi_{231}(58,·)$, $\chi_{231}(190,·)$, $\chi_{231}(191,·)$$\rbrace$
This is a CM field.
Reflex fields:		unavailable$^{16384}$

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

$1$, $a$, $a^{2}$, $a^{3}$, $a^{4}$, $a^{5}$, $a^{6}$, $a^{7}$, $a^{8}$, $a^{9}$, $a^{10}$, $a^{11}$, $a^{12}$, $a^{13}$, $a^{14}$, $a^{15}$, $a^{16}$, $a^{17}$, $a^{18}$, $a^{19}$, $a^{20}$, $a^{21}$, $a^{22}$, $a^{23}$, $a^{24}$, $\frac{1}{559}a^{25}+\frac{153}{559}a^{24}-\frac{72}{559}a^{23}+\frac{17}{559}a^{22}+\frac{277}{559}a^{21}+\frac{64}{559}a^{20}+\frac{9}{43}a^{19}+\frac{94}{559}a^{18}+\frac{98}{559}a^{17}+\frac{223}{559}a^{16}-\frac{48}{559}a^{15}-\frac{37}{559}a^{14}+\frac{152}{559}a^{13}+\frac{171}{559}a^{12}+\frac{62}{559}a^{11}+\frac{45}{559}a^{10}-\frac{232}{559}a^{9}-\frac{106}{559}a^{8}+\frac{268}{559}a^{7}+\frac{12}{43}a^{6}-\frac{89}{559}a^{5}+\frac{60}{559}a^{4}-\frac{266}{559}a^{3}+\frac{97}{559}a^{2}+\frac{80}{559}a+\frac{271}{559}$, $\frac{1}{559}a^{26}-\frac{3}{559}a^{24}-\frac{147}{559}a^{23}-\frac{88}{559}a^{22}+\frac{167}{559}a^{21}-\frac{4}{13}a^{20}+\frac{81}{559}a^{19}+\frac{250}{559}a^{18}-\frac{237}{559}a^{17}-\frac{68}{559}a^{16}+\frac{40}{559}a^{15}+\frac{223}{559}a^{14}-\frac{166}{559}a^{13}+\frac{4}{13}a^{12}+\frac{62}{559}a^{11}+\frac{150}{559}a^{10}+\frac{173}{559}a^{9}+\frac{275}{559}a^{8}-\frac{41}{559}a^{7}+\frac{80}{559}a^{6}+\frac{261}{559}a^{5}+\frac{57}{559}a^{4}-\frac{12}{559}a^{3}-\frac{227}{559}a^{2}-\frac{230}{559}a-\frac{97}{559}$, $\frac{1}{7453147}a^{27}+\frac{5318}{7453147}a^{26}+\frac{5442}{7453147}a^{25}+\frac{3213976}{7453147}a^{24}+\frac{57579}{573319}a^{23}+\frac{1217898}{7453147}a^{22}+\frac{138915}{573319}a^{21}-\frac{755077}{7453147}a^{20}-\frac{283589}{7453147}a^{19}+\frac{3647222}{7453147}a^{18}+\frac{464964}{7453147}a^{17}+\frac{1535190}{7453147}a^{16}+\frac{54439}{7453147}a^{15}-\frac{1991833}{7453147}a^{14}+\frac{1397306}{7453147}a^{13}-\frac{2988938}{7453147}a^{12}-\frac{45963}{111241}a^{11}-\frac{3357550}{7453147}a^{10}-\frac{110407}{7453147}a^{9}-\frac{1166291}{7453147}a^{8}+\frac{1135651}{7453147}a^{7}-\frac{749577}{7453147}a^{6}+\frac{2754858}{7453147}a^{5}+\frac{2622090}{7453147}a^{4}+\frac{1567677}{7453147}a^{3}+\frac{1439359}{7453147}a^{2}-\frac{3222641}{7453147}a+\frac{3132582}{7453147}$, $\frac{1}{101725029597347}a^{28}-\frac{3442475}{101725029597347}a^{27}-\frac{6492269699}{7825002276719}a^{26}+\frac{66857423989}{101725029597347}a^{25}+\frac{20225800327570}{101725029597347}a^{24}+\frac{48813119521087}{101725029597347}a^{23}-\frac{48123554680025}{101725029597347}a^{22}+\frac{20943291860421}{101725029597347}a^{21}+\frac{27562979945096}{101725029597347}a^{20}+\frac{40894153588173}{101725029597347}a^{19}-\frac{2068338725831}{101725029597347}a^{18}-\frac{26633229480333}{101725029597347}a^{17}-\frac{28345662164034}{101725029597347}a^{16}-\frac{45727029003182}{101725029597347}a^{15}+\frac{39852430332899}{101725029597347}a^{14}+\frac{3194433112281}{101725029597347}a^{13}-\frac{38075735517816}{101725029597347}a^{12}-\frac{906449876591}{101725029597347}a^{11}+\frac{800203541648}{7825002276719}a^{10}-\frac{3633669352494}{7825002276719}a^{9}-\frac{38258676150313}{101725029597347}a^{8}+\frac{6458408394895}{101725029597347}a^{7}-\frac{2266883133410}{101725029597347}a^{6}+\frac{44212067064012}{101725029597347}a^{5}-\frac{1698837855881}{7825002276719}a^{4}-\frac{7400841530825}{101725029597347}a^{3}-\frac{1534795111637}{101725029597347}a^{2}+\frac{28386429424084}{101725029597347}a-\frac{21101841351411}{101725029597347}$, $\frac{1}{30\!\cdots\!33}a^{29}+\frac{29\!\cdots\!06}{30\!\cdots\!33}a^{28}+\frac{35\!\cdots\!70}{23\!\cdots\!41}a^{27}-\frac{17\!\cdots\!59}{30\!\cdots\!33}a^{26}-\frac{83\!\cdots\!72}{23\!\cdots\!41}a^{25}+\frac{54\!\cdots\!43}{30\!\cdots\!33}a^{24}-\frac{28\!\cdots\!13}{30\!\cdots\!33}a^{23}-\frac{11\!\cdots\!36}{30\!\cdots\!33}a^{22}+\frac{13\!\cdots\!95}{30\!\cdots\!33}a^{21}-\frac{80\!\cdots\!73}{30\!\cdots\!33}a^{20}-\frac{65\!\cdots\!05}{30\!\cdots\!33}a^{19}+\frac{10\!\cdots\!39}{23\!\cdots\!41}a^{18}-\frac{79\!\cdots\!68}{30\!\cdots\!33}a^{17}+\frac{15\!\cdots\!32}{30\!\cdots\!33}a^{16}+\frac{87\!\cdots\!48}{30\!\cdots\!33}a^{15}-\frac{49\!\cdots\!55}{23\!\cdots\!41}a^{14}+\frac{78\!\cdots\!90}{30\!\cdots\!33}a^{13}+\frac{14\!\cdots\!54}{30\!\cdots\!33}a^{12}-\frac{48\!\cdots\!22}{30\!\cdots\!33}a^{11}+\frac{50\!\cdots\!20}{30\!\cdots\!33}a^{10}+\frac{26\!\cdots\!60}{30\!\cdots\!33}a^{9}+\frac{97\!\cdots\!47}{30\!\cdots\!33}a^{8}-\frac{91\!\cdots\!10}{30\!\cdots\!33}a^{7}+\frac{89\!\cdots\!97}{30\!\cdots\!33}a^{6}-\frac{80\!\cdots\!56}{30\!\cdots\!33}a^{5}+\frac{91\!\cdots\!36}{30\!\cdots\!33}a^{4}+\frac{39\!\cdots\!38}{30\!\cdots\!33}a^{3}-\frac{13\!\cdots\!60}{30\!\cdots\!33}a^{2}-\frac{35\!\cdots\!10}{30\!\cdots\!33}a-\frac{99\!\cdots\!19}{30\!\cdots\!33}$

Monogenic:		Not computed
Index:		$1$
Inessential primes:		None

Class group and class number

$C_{2}\times C_{2}\times C_{2}\times C_{122}$, which has order $976$ (assuming GRH)

Unit group

Rank:		$14$
Torsion generator:		\( -\frac{33818387380679807589465361410172326167}{226013889917515988574891368211254183533} a^{29} + \frac{31338667935399949868997219900410037083}{226013889917515988574891368211254183533} a^{28} - \frac{59533394026528196135127009037326757884}{17385683839808922198068566785481091041} a^{27} + \frac{26720697277131697071025705847393655581}{17385683839808922198068566785481091041} a^{26} - \frac{11267162530505485654312665849674405751741}{226013889917515988574891368211254183533} a^{25} + \frac{4022194077956355207850219157836948393930}{226013889917515988574891368211254183533} a^{24} - \frac{92953188386234510257152391692858763228843}{226013889917515988574891368211254183533} a^{23} + \frac{22104963375560112489949892735920235290783}{226013889917515988574891368211254183533} a^{22} - \frac{545080356364611035579293293564068809395600}{226013889917515988574891368211254183533} a^{21} + \frac{119856710703093578498163583079545405844510}{226013889917515988574891368211254183533} a^{20} - \frac{159315389114482945879813536122692152315726}{17385683839808922198068566785481091041} a^{19} + \frac{371505998836784739401662931229174563050057}{226013889917515988574891368211254183533} a^{18} - \frac{5636380533746118790557453282431658208023094}{226013889917515988574891368211254183533} a^{17} + \frac{1341202572841470363726285604899046711111310}{226013889917515988574891368211254183533} a^{16} - \frac{9580462806832944693507608665472531054975619}{226013889917515988574891368211254183533} a^{15} + \frac{2975338497658454058333296233214938733630477}{226013889917515988574891368211254183533} a^{14} - \frac{274902467923716523011393173737372315661302}{5256136974825953222671892283982655431} a^{13} + \frac{3528124328723702882659130579676347333166157}{226013889917515988574891368211254183533} a^{12} - \frac{8545078952599196519129045655575977701620936}{226013889917515988574891368211254183533} a^{11} + \frac{1804537778175184053576987723405631500682837}{226013889917515988574891368211254183533} a^{10} - \frac{4181221389403621251758861434697384536802496}{226013889917515988574891368211254183533} a^{9} + \frac{636454856620926484319260785746287491702239}{226013889917515988574891368211254183533} a^{8} - \frac{1210070166745826883897941813261487755642144}{226013889917515988574891368211254183533} a^{7} + \frac{8202236392955944036524565106868987880557}{226013889917515988574891368211254183533} a^{6} - \frac{216060402937800866443945700291944166376263}{226013889917515988574891368211254183533} a^{5} - \frac{8171735372298450139059825122527343449906}{226013889917515988574891368211254183533} a^{4} - \frac{26753434861254060031931004678000206681808}{226013889917515988574891368211254183533} a^{3} - \frac{3975069744616359074607077694949359502761}{226013889917515988574891368211254183533} a^{2} - \frac{1348278749125616613229589043671236379186}{226013889917515988574891368211254183533} a + \frac{1714530982849230131954290236414673446}{3373341640559940127983453256884390799} \)  (order $6$)
Fundamental units:		$\frac{49\!\cdots\!59}{23\!\cdots\!41}a^{29}-\frac{12\!\cdots\!65}{23\!\cdots\!41}a^{28}+\frac{12\!\cdots\!74}{23\!\cdots\!41}a^{27}-\frac{23\!\cdots\!25}{23\!\cdots\!41}a^{26}+\frac{18\!\cdots\!88}{23\!\cdots\!41}a^{25}-\frac{32\!\cdots\!39}{23\!\cdots\!41}a^{24}+\frac{15\!\cdots\!27}{23\!\cdots\!41}a^{23}-\frac{25\!\cdots\!99}{23\!\cdots\!41}a^{22}+\frac{93\!\cdots\!71}{23\!\cdots\!41}a^{21}-\frac{14\!\cdots\!78}{23\!\cdots\!41}a^{20}+\frac{38\!\cdots\!06}{23\!\cdots\!41}a^{19}-\frac{56\!\cdots\!14}{23\!\cdots\!41}a^{18}+\frac{11\!\cdots\!34}{23\!\cdots\!41}a^{17}-\frac{15\!\cdots\!32}{23\!\cdots\!41}a^{16}+\frac{22\!\cdots\!22}{23\!\cdots\!41}a^{15}-\frac{29\!\cdots\!71}{23\!\cdots\!41}a^{14}+\frac{33\!\cdots\!09}{23\!\cdots\!41}a^{13}-\frac{37\!\cdots\!06}{23\!\cdots\!41}a^{12}+\frac{73\!\cdots\!06}{55\!\cdots\!87}a^{11}-\frac{27\!\cdots\!52}{23\!\cdots\!41}a^{10}+\frac{17\!\cdots\!91}{23\!\cdots\!41}a^{9}-\frac{12\!\cdots\!18}{23\!\cdots\!41}a^{8}+\frac{65\!\cdots\!61}{23\!\cdots\!41}a^{7}-\frac{35\!\cdots\!19}{23\!\cdots\!41}a^{6}+\frac{11\!\cdots\!74}{23\!\cdots\!41}a^{5}-\frac{45\!\cdots\!87}{23\!\cdots\!41}a^{4}+\frac{97\!\cdots\!82}{23\!\cdots\!41}a^{3}-\frac{41\!\cdots\!85}{23\!\cdots\!41}a^{2}+\frac{45\!\cdots\!21}{23\!\cdots\!41}a-\frac{25\!\cdots\!27}{35\!\cdots\!23}$, $\frac{34\!\cdots\!98}{23\!\cdots\!41}a^{29}-\frac{11\!\cdots\!54}{23\!\cdots\!41}a^{28}+\frac{88\!\cdots\!83}{23\!\cdots\!41}a^{27}-\frac{22\!\cdots\!02}{23\!\cdots\!41}a^{26}+\frac{12\!\cdots\!40}{23\!\cdots\!41}a^{25}-\frac{30\!\cdots\!84}{23\!\cdots\!41}a^{24}+\frac{11\!\cdots\!44}{23\!\cdots\!41}a^{23}-\frac{24\!\cdots\!92}{23\!\cdots\!41}a^{22}+\frac{68\!\cdots\!45}{23\!\cdots\!41}a^{21}-\frac{14\!\cdots\!93}{23\!\cdots\!41}a^{20}+\frac{28\!\cdots\!88}{23\!\cdots\!41}a^{19}-\frac{53\!\cdots\!78}{23\!\cdots\!41}a^{18}+\frac{83\!\cdots\!88}{23\!\cdots\!41}a^{17}-\frac{15\!\cdots\!16}{23\!\cdots\!41}a^{16}+\frac{17\!\cdots\!13}{23\!\cdots\!41}a^{15}-\frac{27\!\cdots\!63}{23\!\cdots\!41}a^{14}+\frac{27\!\cdots\!40}{23\!\cdots\!41}a^{13}-\frac{34\!\cdots\!60}{23\!\cdots\!41}a^{12}+\frac{26\!\cdots\!45}{23\!\cdots\!41}a^{11}-\frac{25\!\cdots\!03}{23\!\cdots\!41}a^{10}+\frac{15\!\cdots\!40}{23\!\cdots\!41}a^{9}-\frac{12\!\cdots\!63}{23\!\cdots\!41}a^{8}+\frac{57\!\cdots\!00}{23\!\cdots\!41}a^{7}-\frac{33\!\cdots\!09}{23\!\cdots\!41}a^{6}+\frac{98\!\cdots\!49}{23\!\cdots\!41}a^{5}-\frac{42\!\cdots\!83}{23\!\cdots\!41}a^{4}+\frac{87\!\cdots\!69}{23\!\cdots\!41}a^{3}-\frac{37\!\cdots\!42}{23\!\cdots\!41}a^{2}+\frac{41\!\cdots\!39}{23\!\cdots\!41}a-\frac{37\!\cdots\!41}{35\!\cdots\!23}$, $\frac{11\!\cdots\!32}{23\!\cdots\!41}a^{29}-\frac{44\!\cdots\!54}{23\!\cdots\!41}a^{28}+\frac{30\!\cdots\!86}{23\!\cdots\!41}a^{27}-\frac{89\!\cdots\!04}{23\!\cdots\!41}a^{26}+\frac{43\!\cdots\!98}{23\!\cdots\!41}a^{25}-\frac{12\!\cdots\!60}{23\!\cdots\!41}a^{24}+\frac{38\!\cdots\!31}{23\!\cdots\!41}a^{23}-\frac{10\!\cdots\!26}{23\!\cdots\!41}a^{22}+\frac{23\!\cdots\!03}{23\!\cdots\!41}a^{21}-\frac{59\!\cdots\!74}{23\!\cdots\!41}a^{20}+\frac{10\!\cdots\!06}{23\!\cdots\!41}a^{19}-\frac{22\!\cdots\!27}{23\!\cdots\!41}a^{18}+\frac{29\!\cdots\!69}{23\!\cdots\!41}a^{17}-\frac{62\!\cdots\!42}{23\!\cdots\!41}a^{16}+\frac{64\!\cdots\!82}{23\!\cdots\!41}a^{15}-\frac{11\!\cdots\!27}{23\!\cdots\!41}a^{14}+\frac{10\!\cdots\!37}{23\!\cdots\!41}a^{13}-\frac{14\!\cdots\!72}{23\!\cdots\!41}a^{12}+\frac{10\!\cdots\!29}{23\!\cdots\!41}a^{11}-\frac{10\!\cdots\!56}{23\!\cdots\!41}a^{10}+\frac{59\!\cdots\!64}{23\!\cdots\!41}a^{9}-\frac{49\!\cdots\!87}{23\!\cdots\!41}a^{8}+\frac{22\!\cdots\!37}{23\!\cdots\!41}a^{7}-\frac{13\!\cdots\!33}{23\!\cdots\!41}a^{6}+\frac{39\!\cdots\!48}{23\!\cdots\!41}a^{5}-\frac{17\!\cdots\!41}{23\!\cdots\!41}a^{4}+\frac{35\!\cdots\!58}{23\!\cdots\!41}a^{3}-\frac{15\!\cdots\!18}{23\!\cdots\!41}a^{2}+\frac{16\!\cdots\!02}{23\!\cdots\!41}a-\frac{16\!\cdots\!95}{35\!\cdots\!23}$, $\frac{11\!\cdots\!32}{23\!\cdots\!41}a^{29}-\frac{44\!\cdots\!54}{23\!\cdots\!41}a^{28}+\frac{30\!\cdots\!86}{23\!\cdots\!41}a^{27}-\frac{89\!\cdots\!04}{23\!\cdots\!41}a^{26}+\frac{43\!\cdots\!98}{23\!\cdots\!41}a^{25}-\frac{12\!\cdots\!60}{23\!\cdots\!41}a^{24}+\frac{38\!\cdots\!31}{23\!\cdots\!41}a^{23}-\frac{10\!\cdots\!26}{23\!\cdots\!41}a^{22}+\frac{23\!\cdots\!03}{23\!\cdots\!41}a^{21}-\frac{59\!\cdots\!74}{23\!\cdots\!41}a^{20}+\frac{10\!\cdots\!06}{23\!\cdots\!41}a^{19}-\frac{22\!\cdots\!27}{23\!\cdots\!41}a^{18}+\frac{29\!\cdots\!69}{23\!\cdots\!41}a^{17}-\frac{62\!\cdots\!42}{23\!\cdots\!41}a^{16}+\frac{64\!\cdots\!82}{23\!\cdots\!41}a^{15}-\frac{11\!\cdots\!27}{23\!\cdots\!41}a^{14}+\frac{10\!\cdots\!37}{23\!\cdots\!41}a^{13}-\frac{14\!\cdots\!72}{23\!\cdots\!41}a^{12}+\frac{10\!\cdots\!29}{23\!\cdots\!41}a^{11}-\frac{10\!\cdots\!56}{23\!\cdots\!41}a^{10}+\frac{59\!\cdots\!64}{23\!\cdots\!41}a^{9}-\frac{49\!\cdots\!87}{23\!\cdots\!41}a^{8}+\frac{22\!\cdots\!37}{23\!\cdots\!41}a^{7}-\frac{13\!\cdots\!33}{23\!\cdots\!41}a^{6}+\frac{39\!\cdots\!48}{23\!\cdots\!41}a^{5}-\frac{17\!\cdots\!41}{23\!\cdots\!41}a^{4}+\frac{35\!\cdots\!58}{23\!\cdots\!41}a^{3}-\frac{15\!\cdots\!18}{23\!\cdots\!41}a^{2}+\frac{16\!\cdots\!02}{23\!\cdots\!41}a-\frac{52\!\cdots\!18}{35\!\cdots\!23}$, $\frac{26\!\cdots\!63}{23\!\cdots\!01}a^{29}-\frac{81\!\cdots\!36}{23\!\cdots\!01}a^{28}+\frac{51\!\cdots\!21}{17\!\cdots\!77}a^{27}-\frac{12\!\cdots\!60}{17\!\cdots\!77}a^{26}+\frac{97\!\cdots\!08}{23\!\cdots\!01}a^{25}-\frac{22\!\cdots\!24}{23\!\cdots\!01}a^{24}+\frac{84\!\cdots\!36}{23\!\cdots\!01}a^{23}-\frac{17\!\cdots\!14}{23\!\cdots\!01}a^{22}+\frac{51\!\cdots\!40}{23\!\cdots\!01}a^{21}-\frac{10\!\cdots\!55}{23\!\cdots\!01}a^{20}+\frac{16\!\cdots\!23}{17\!\cdots\!77}a^{19}-\frac{38\!\cdots\!58}{23\!\cdots\!01}a^{18}+\frac{61\!\cdots\!96}{23\!\cdots\!01}a^{17}-\frac{10\!\cdots\!18}{23\!\cdots\!01}a^{16}+\frac{12\!\cdots\!77}{23\!\cdots\!01}a^{15}-\frac{19\!\cdots\!82}{23\!\cdots\!01}a^{14}+\frac{19\!\cdots\!18}{23\!\cdots\!01}a^{13}-\frac{24\!\cdots\!12}{23\!\cdots\!01}a^{12}+\frac{18\!\cdots\!55}{23\!\cdots\!01}a^{11}-\frac{17\!\cdots\!91}{23\!\cdots\!01}a^{10}+\frac{10\!\cdots\!92}{23\!\cdots\!01}a^{9}-\frac{83\!\cdots\!21}{23\!\cdots\!01}a^{8}+\frac{40\!\cdots\!33}{23\!\cdots\!01}a^{7}-\frac{22\!\cdots\!91}{23\!\cdots\!01}a^{6}+\frac{68\!\cdots\!56}{23\!\cdots\!01}a^{5}-\frac{29\!\cdots\!67}{23\!\cdots\!01}a^{4}+\frac{67\!\cdots\!73}{23\!\cdots\!01}a^{3}-\frac{26\!\cdots\!04}{23\!\cdots\!01}a^{2}+\frac{28\!\cdots\!74}{23\!\cdots\!01}a-\frac{16\!\cdots\!32}{23\!\cdots\!01}$, $\frac{12\!\cdots\!02}{23\!\cdots\!41}a^{29}-\frac{16\!\cdots\!28}{23\!\cdots\!41}a^{28}+\frac{28\!\cdots\!23}{23\!\cdots\!41}a^{27}-\frac{23\!\cdots\!73}{23\!\cdots\!41}a^{26}+\frac{41\!\cdots\!13}{23\!\cdots\!41}a^{25}-\frac{30\!\cdots\!72}{23\!\cdots\!41}a^{24}+\frac{34\!\cdots\!40}{23\!\cdots\!41}a^{23}-\frac{20\!\cdots\!74}{23\!\cdots\!41}a^{22}+\frac{20\!\cdots\!20}{23\!\cdots\!41}a^{21}-\frac{11\!\cdots\!57}{23\!\cdots\!41}a^{20}+\frac{77\!\cdots\!80}{23\!\cdots\!41}a^{19}-\frac{41\!\cdots\!02}{23\!\cdots\!41}a^{18}+\frac{21\!\cdots\!14}{23\!\cdots\!41}a^{17}-\frac{12\!\cdots\!27}{23\!\cdots\!41}a^{16}+\frac{37\!\cdots\!48}{23\!\cdots\!41}a^{15}-\frac{23\!\cdots\!63}{23\!\cdots\!41}a^{14}+\frac{48\!\cdots\!39}{23\!\cdots\!41}a^{13}-\frac{28\!\cdots\!86}{23\!\cdots\!41}a^{12}+\frac{37\!\cdots\!82}{23\!\cdots\!41}a^{11}-\frac{17\!\cdots\!40}{23\!\cdots\!41}a^{10}+\frac{18\!\cdots\!53}{23\!\cdots\!41}a^{9}-\frac{70\!\cdots\!48}{23\!\cdots\!41}a^{8}+\frac{52\!\cdots\!93}{23\!\cdots\!41}a^{7}-\frac{11\!\cdots\!54}{23\!\cdots\!41}a^{6}+\frac{68\!\cdots\!59}{23\!\cdots\!41}a^{5}-\frac{74\!\cdots\!89}{23\!\cdots\!41}a^{4}+\frac{64\!\cdots\!17}{23\!\cdots\!41}a^{3}-\frac{23\!\cdots\!61}{23\!\cdots\!41}a^{2}-\frac{52\!\cdots\!38}{23\!\cdots\!41}a+\frac{75\!\cdots\!29}{23\!\cdots\!41}$, $\frac{59\!\cdots\!71}{30\!\cdots\!33}a^{29}-\frac{76\!\cdots\!93}{30\!\cdots\!33}a^{28}+\frac{13\!\cdots\!20}{30\!\cdots\!33}a^{27}-\frac{25\!\cdots\!57}{71\!\cdots\!31}a^{26}+\frac{20\!\cdots\!57}{30\!\cdots\!33}a^{25}-\frac{14\!\cdots\!54}{30\!\cdots\!33}a^{24}+\frac{16\!\cdots\!23}{30\!\cdots\!33}a^{23}-\frac{98\!\cdots\!49}{30\!\cdots\!33}a^{22}+\frac{98\!\cdots\!36}{30\!\cdots\!33}a^{21}-\frac{55\!\cdots\!44}{30\!\cdots\!33}a^{20}+\frac{28\!\cdots\!50}{23\!\cdots\!41}a^{19}-\frac{19\!\cdots\!79}{30\!\cdots\!33}a^{18}+\frac{10\!\cdots\!20}{30\!\cdots\!33}a^{17}-\frac{58\!\cdots\!85}{30\!\cdots\!33}a^{16}+\frac{18\!\cdots\!71}{30\!\cdots\!33}a^{15}-\frac{11\!\cdots\!15}{30\!\cdots\!33}a^{14}+\frac{23\!\cdots\!33}{30\!\cdots\!33}a^{13}-\frac{13\!\cdots\!05}{30\!\cdots\!33}a^{12}+\frac{17\!\cdots\!12}{30\!\cdots\!33}a^{11}-\frac{62\!\cdots\!86}{23\!\cdots\!41}a^{10}+\frac{85\!\cdots\!52}{30\!\cdots\!33}a^{9}-\frac{33\!\cdots\!05}{30\!\cdots\!33}a^{8}+\frac{57\!\cdots\!97}{71\!\cdots\!31}a^{7}-\frac{54\!\cdots\!15}{30\!\cdots\!33}a^{6}+\frac{31\!\cdots\!03}{30\!\cdots\!33}a^{5}-\frac{41\!\cdots\!03}{30\!\cdots\!33}a^{4}+\frac{29\!\cdots\!26}{30\!\cdots\!33}a^{3}-\frac{14\!\cdots\!23}{30\!\cdots\!33}a^{2}+\frac{68\!\cdots\!59}{30\!\cdots\!33}a+\frac{29\!\cdots\!45}{30\!\cdots\!33}$, $\frac{90\!\cdots\!23}{30\!\cdots\!33}a^{29}-\frac{14\!\cdots\!05}{30\!\cdots\!33}a^{28}+\frac{16\!\cdots\!69}{23\!\cdots\!41}a^{27}-\frac{18\!\cdots\!01}{23\!\cdots\!41}a^{26}+\frac{31\!\cdots\!76}{30\!\cdots\!33}a^{25}-\frac{32\!\cdots\!28}{30\!\cdots\!33}a^{24}+\frac{26\!\cdots\!87}{30\!\cdots\!33}a^{23}-\frac{24\!\cdots\!27}{30\!\cdots\!33}a^{22}+\frac{15\!\cdots\!22}{30\!\cdots\!33}a^{21}-\frac{14\!\cdots\!68}{30\!\cdots\!33}a^{20}+\frac{47\!\cdots\!62}{23\!\cdots\!41}a^{19}-\frac{51\!\cdots\!10}{30\!\cdots\!33}a^{18}+\frac{17\!\cdots\!30}{30\!\cdots\!33}a^{17}-\frac{15\!\cdots\!76}{30\!\cdots\!33}a^{16}+\frac{32\!\cdots\!51}{30\!\cdots\!33}a^{15}-\frac{28\!\cdots\!57}{30\!\cdots\!33}a^{14}+\frac{44\!\cdots\!53}{30\!\cdots\!33}a^{13}-\frac{36\!\cdots\!79}{30\!\cdots\!33}a^{12}+\frac{38\!\cdots\!96}{30\!\cdots\!33}a^{11}-\frac{26\!\cdots\!98}{30\!\cdots\!33}a^{10}+\frac{20\!\cdots\!23}{30\!\cdots\!33}a^{9}-\frac{12\!\cdots\!56}{30\!\cdots\!33}a^{8}+\frac{71\!\cdots\!05}{30\!\cdots\!33}a^{7}-\frac{32\!\cdots\!68}{30\!\cdots\!33}a^{6}+\frac{12\!\cdots\!00}{30\!\cdots\!33}a^{5}-\frac{10\!\cdots\!95}{71\!\cdots\!31}a^{4}+\frac{10\!\cdots\!79}{30\!\cdots\!33}a^{3}-\frac{40\!\cdots\!73}{30\!\cdots\!33}a^{2}+\frac{45\!\cdots\!31}{30\!\cdots\!33}a-\frac{63\!\cdots\!06}{46\!\cdots\!99}$, $\frac{14\!\cdots\!99}{30\!\cdots\!33}a^{29}-\frac{22\!\cdots\!24}{30\!\cdots\!33}a^{28}+\frac{33\!\cdots\!56}{30\!\cdots\!33}a^{27}-\frac{36\!\cdots\!65}{30\!\cdots\!33}a^{26}+\frac{49\!\cdots\!71}{30\!\cdots\!33}a^{25}-\frac{49\!\cdots\!40}{30\!\cdots\!33}a^{24}+\frac{41\!\cdots\!99}{30\!\cdots\!33}a^{23}-\frac{35\!\cdots\!43}{30\!\cdots\!33}a^{22}+\frac{24\!\cdots\!02}{30\!\cdots\!33}a^{21}-\frac{20\!\cdots\!14}{30\!\cdots\!33}a^{20}+\frac{92\!\cdots\!80}{30\!\cdots\!33}a^{19}-\frac{73\!\cdots\!67}{30\!\cdots\!33}a^{18}+\frac{25\!\cdots\!22}{30\!\cdots\!33}a^{17}-\frac{21\!\cdots\!49}{30\!\cdots\!33}a^{16}+\frac{35\!\cdots\!67}{23\!\cdots\!41}a^{15}-\frac{38\!\cdots\!55}{30\!\cdots\!33}a^{14}+\frac{59\!\cdots\!09}{30\!\cdots\!33}a^{13}-\frac{46\!\cdots\!01}{30\!\cdots\!33}a^{12}+\frac{36\!\cdots\!58}{23\!\cdots\!41}a^{11}-\frac{29\!\cdots\!68}{30\!\cdots\!33}a^{10}+\frac{22\!\cdots\!56}{30\!\cdots\!33}a^{9}-\frac{12\!\cdots\!37}{30\!\cdots\!33}a^{8}+\frac{64\!\cdots\!08}{30\!\cdots\!33}a^{7}-\frac{24\!\cdots\!71}{30\!\cdots\!33}a^{6}+\frac{62\!\cdots\!99}{30\!\cdots\!33}a^{5}-\frac{17\!\cdots\!19}{23\!\cdots\!41}a^{4}+\frac{33\!\cdots\!68}{30\!\cdots\!33}a^{3}-\frac{21\!\cdots\!61}{30\!\cdots\!33}a^{2}-\frac{53\!\cdots\!71}{30\!\cdots\!33}a-\frac{28\!\cdots\!57}{30\!\cdots\!33}$, $\frac{13\!\cdots\!25}{30\!\cdots\!33}a^{29}-\frac{16\!\cdots\!80}{30\!\cdots\!33}a^{28}+\frac{31\!\cdots\!45}{30\!\cdots\!33}a^{27}-\frac{22\!\cdots\!20}{30\!\cdots\!33}a^{26}+\frac{46\!\cdots\!10}{30\!\cdots\!33}a^{25}-\frac{28\!\cdots\!32}{30\!\cdots\!33}a^{24}+\frac{38\!\cdots\!83}{30\!\cdots\!33}a^{23}-\frac{19\!\cdots\!29}{30\!\cdots\!33}a^{22}+\frac{22\!\cdots\!12}{30\!\cdots\!33}a^{21}-\frac{10\!\cdots\!33}{30\!\cdots\!33}a^{20}+\frac{66\!\cdots\!90}{23\!\cdots\!41}a^{19}-\frac{37\!\cdots\!57}{30\!\cdots\!33}a^{18}+\frac{23\!\cdots\!72}{30\!\cdots\!33}a^{17}-\frac{11\!\cdots\!35}{30\!\cdots\!33}a^{16}+\frac{40\!\cdots\!73}{30\!\cdots\!33}a^{15}-\frac{22\!\cdots\!12}{30\!\cdots\!33}a^{14}+\frac{51\!\cdots\!13}{30\!\cdots\!33}a^{13}-\frac{26\!\cdots\!73}{30\!\cdots\!33}a^{12}+\frac{39\!\cdots\!06}{30\!\cdots\!33}a^{11}-\frac{15\!\cdots\!79}{30\!\cdots\!33}a^{10}+\frac{18\!\cdots\!09}{30\!\cdots\!33}a^{9}-\frac{63\!\cdots\!41}{30\!\cdots\!33}a^{8}+\frac{54\!\cdots\!09}{30\!\cdots\!33}a^{7}-\frac{93\!\cdots\!11}{30\!\cdots\!33}a^{6}+\frac{77\!\cdots\!58}{30\!\cdots\!33}a^{5}-\frac{59\!\cdots\!47}{30\!\cdots\!33}a^{4}+\frac{78\!\cdots\!31}{30\!\cdots\!33}a^{3}+\frac{18\!\cdots\!42}{30\!\cdots\!33}a^{2}+\frac{29\!\cdots\!38}{30\!\cdots\!33}a+\frac{16\!\cdots\!46}{30\!\cdots\!33}$, $\frac{41\!\cdots\!00}{30\!\cdots\!33}a^{29}-\frac{85\!\cdots\!07}{30\!\cdots\!33}a^{28}+\frac{93\!\cdots\!41}{30\!\cdots\!33}a^{27}+\frac{24\!\cdots\!03}{30\!\cdots\!33}a^{26}+\frac{13\!\cdots\!79}{30\!\cdots\!33}a^{25}+\frac{48\!\cdots\!62}{30\!\cdots\!33}a^{24}+\frac{89\!\cdots\!28}{23\!\cdots\!41}a^{23}+\frac{52\!\cdots\!40}{30\!\cdots\!33}a^{22}+\frac{69\!\cdots\!57}{30\!\cdots\!33}a^{21}+\frac{31\!\cdots\!29}{30\!\cdots\!33}a^{20}+\frac{26\!\cdots\!55}{30\!\cdots\!33}a^{19}+\frac{12\!\cdots\!38}{30\!\cdots\!33}a^{18}+\frac{75\!\cdots\!49}{30\!\cdots\!33}a^{17}+\frac{30\!\cdots\!15}{30\!\cdots\!33}a^{16}+\frac{13\!\cdots\!78}{30\!\cdots\!33}a^{15}+\frac{37\!\cdots\!74}{30\!\cdots\!33}a^{14}+\frac{12\!\cdots\!11}{23\!\cdots\!41}a^{13}+\frac{39\!\cdots\!56}{30\!\cdots\!33}a^{12}+\frac{12\!\cdots\!35}{30\!\cdots\!33}a^{11}+\frac{27\!\cdots\!20}{30\!\cdots\!33}a^{10}+\frac{66\!\cdots\!25}{30\!\cdots\!33}a^{9}+\frac{13\!\cdots\!14}{30\!\cdots\!33}a^{8}+\frac{22\!\cdots\!04}{30\!\cdots\!33}a^{7}+\frac{37\!\cdots\!94}{30\!\cdots\!33}a^{6}+\frac{50\!\cdots\!22}{30\!\cdots\!33}a^{5}+\frac{69\!\cdots\!85}{30\!\cdots\!33}a^{4}+\frac{44\!\cdots\!95}{23\!\cdots\!41}a^{3}+\frac{21\!\cdots\!33}{30\!\cdots\!33}a^{2}+\frac{26\!\cdots\!45}{30\!\cdots\!33}a-\frac{20\!\cdots\!14}{30\!\cdots\!33}$, $\frac{82\!\cdots\!56}{30\!\cdots\!33}a^{29}-\frac{56\!\cdots\!23}{30\!\cdots\!33}a^{28}+\frac{18\!\cdots\!89}{30\!\cdots\!33}a^{27}-\frac{39\!\cdots\!84}{30\!\cdots\!33}a^{26}+\frac{27\!\cdots\!30}{30\!\cdots\!33}a^{25}-\frac{33\!\cdots\!65}{30\!\cdots\!33}a^{24}+\frac{22\!\cdots\!92}{30\!\cdots\!33}a^{23}-\frac{18\!\cdots\!61}{30\!\cdots\!33}a^{22}+\frac{13\!\cdots\!73}{30\!\cdots\!33}a^{21}+\frac{60\!\cdots\!84}{30\!\cdots\!33}a^{20}+\frac{49\!\cdots\!79}{30\!\cdots\!33}a^{19}+\frac{17\!\cdots\!51}{30\!\cdots\!33}a^{18}+\frac{13\!\cdots\!48}{30\!\cdots\!33}a^{17}-\frac{47\!\cdots\!75}{30\!\cdots\!33}a^{16}+\frac{17\!\cdots\!00}{23\!\cdots\!41}a^{15}-\frac{30\!\cdots\!95}{30\!\cdots\!33}a^{14}+\frac{20\!\cdots\!28}{23\!\cdots\!41}a^{13}-\frac{40\!\cdots\!04}{30\!\cdots\!33}a^{12}+\frac{18\!\cdots\!23}{30\!\cdots\!33}a^{11}-\frac{20\!\cdots\!76}{30\!\cdots\!33}a^{10}+\frac{86\!\cdots\!48}{30\!\cdots\!33}a^{9}-\frac{84\!\cdots\!74}{30\!\cdots\!33}a^{8}+\frac{22\!\cdots\!92}{30\!\cdots\!33}a^{7}-\frac{11\!\cdots\!27}{30\!\cdots\!33}a^{6}+\frac{36\!\cdots\!64}{30\!\cdots\!33}a^{5}-\frac{33\!\cdots\!77}{30\!\cdots\!33}a^{4}+\frac{31\!\cdots\!46}{30\!\cdots\!33}a^{3}-\frac{59\!\cdots\!41}{30\!\cdots\!33}a^{2}+\frac{59\!\cdots\!97}{23\!\cdots\!41}a-\frac{66\!\cdots\!46}{30\!\cdots\!33}$, $\frac{48\!\cdots\!61}{30\!\cdots\!33}a^{29}-\frac{45\!\cdots\!88}{30\!\cdots\!33}a^{28}+\frac{85\!\cdots\!02}{23\!\cdots\!41}a^{27}-\frac{49\!\cdots\!81}{30\!\cdots\!33}a^{26}+\frac{16\!\cdots\!34}{30\!\cdots\!33}a^{25}-\frac{56\!\cdots\!04}{30\!\cdots\!33}a^{24}+\frac{13\!\cdots\!99}{30\!\cdots\!33}a^{23}-\frac{30\!\cdots\!36}{30\!\cdots\!33}a^{22}+\frac{76\!\cdots\!98}{30\!\cdots\!33}a^{21}-\frac{12\!\cdots\!71}{23\!\cdots\!41}a^{20}+\frac{28\!\cdots\!24}{30\!\cdots\!33}a^{19}-\frac{46\!\cdots\!70}{30\!\cdots\!33}a^{18}+\frac{76\!\cdots\!63}{30\!\cdots\!33}a^{17}-\frac{16\!\cdots\!50}{30\!\cdots\!33}a^{16}+\frac{12\!\cdots\!44}{30\!\cdots\!33}a^{15}-\frac{35\!\cdots\!76}{30\!\cdots\!33}a^{14}+\frac{14\!\cdots\!94}{30\!\cdots\!33}a^{13}-\frac{36\!\cdots\!56}{30\!\cdots\!33}a^{12}+\frac{95\!\cdots\!25}{30\!\cdots\!33}a^{11}-\frac{91\!\cdots\!10}{30\!\cdots\!33}a^{10}+\frac{19\!\cdots\!72}{15\!\cdots\!67}a^{9}+\frac{12\!\cdots\!60}{30\!\cdots\!33}a^{8}+\frac{73\!\cdots\!70}{30\!\cdots\!33}a^{7}+\frac{32\!\cdots\!46}{23\!\cdots\!41}a^{6}+\frac{21\!\cdots\!43}{30\!\cdots\!33}a^{5}+\frac{65\!\cdots\!26}{23\!\cdots\!41}a^{4}+\frac{29\!\cdots\!52}{30\!\cdots\!33}a^{3}+\frac{10\!\cdots\!65}{30\!\cdots\!33}a^{2}-\frac{11\!\cdots\!90}{30\!\cdots\!33}a+\frac{16\!\cdots\!44}{30\!\cdots\!33}$, $\frac{27\!\cdots\!55}{30\!\cdots\!33}a^{29}-\frac{82\!\cdots\!17}{71\!\cdots\!31}a^{28}+\frac{63\!\cdots\!10}{30\!\cdots\!33}a^{27}-\frac{51\!\cdots\!83}{30\!\cdots\!33}a^{26}+\frac{92\!\cdots\!67}{30\!\cdots\!33}a^{25}-\frac{66\!\cdots\!24}{30\!\cdots\!33}a^{24}+\frac{17\!\cdots\!13}{71\!\cdots\!31}a^{23}-\frac{45\!\cdots\!29}{30\!\cdots\!33}a^{22}+\frac{45\!\cdots\!84}{30\!\cdots\!33}a^{21}-\frac{19\!\cdots\!68}{23\!\cdots\!41}a^{20}+\frac{17\!\cdots\!07}{30\!\cdots\!33}a^{19}-\frac{21\!\cdots\!29}{71\!\cdots\!31}a^{18}+\frac{47\!\cdots\!62}{30\!\cdots\!33}a^{17}-\frac{27\!\cdots\!84}{30\!\cdots\!33}a^{16}+\frac{83\!\cdots\!37}{30\!\cdots\!33}a^{15}-\frac{39\!\cdots\!85}{23\!\cdots\!41}a^{14}+\frac{10\!\cdots\!44}{30\!\cdots\!33}a^{13}-\frac{61\!\cdots\!47}{30\!\cdots\!33}a^{12}+\frac{82\!\cdots\!80}{30\!\cdots\!33}a^{11}-\frac{37\!\cdots\!09}{30\!\cdots\!33}a^{10}+\frac{40\!\cdots\!04}{30\!\cdots\!33}a^{9}-\frac{15\!\cdots\!73}{30\!\cdots\!33}a^{8}+\frac{27\!\cdots\!34}{71\!\cdots\!31}a^{7}-\frac{24\!\cdots\!69}{30\!\cdots\!33}a^{6}+\frac{15\!\cdots\!15}{30\!\cdots\!33}a^{5}-\frac{15\!\cdots\!48}{30\!\cdots\!33}a^{4}+\frac{14\!\cdots\!14}{30\!\cdots\!33}a^{3}-\frac{27\!\cdots\!09}{23\!\cdots\!41}a^{2}+\frac{76\!\cdots\!11}{23\!\cdots\!41}a+\frac{20\!\cdots\!85}{30\!\cdots\!33}$ (assuming GRH)
Regulator:		\( 4697581952.048968 \) (assuming GRH)

Class number formula

\[ \begin{aligned}\lim_{s\to 1} (s-1)\zeta_K(s) =\mathstrut & \frac{2^{r_1}\cdot (2\pi)^{r_2}\cdot R\cdot h}{w\cdot\sqrt{|D|}}\cr \approx\mathstrut &\frac{2^{0}\cdot(2\pi)^{15}\cdot 4697581952.048968 \cdot 976}{6\cdot\sqrt{11277272245002111679540357002131401262707502951787}}\cr\approx \mathstrut & 0.213682484973285 \end{aligned}\] (assuming GRH)

Galois group

$C_{30}$ (as 30T1):

A cyclic group of order 30

The 30 conjugacy class representatives for $C_{30}$

Character table for $C_{30}$

Intermediate fields

\(\Q(\sqrt{-3}) \), \(\Q(\zeta_{7})^+\), \(\Q(\zeta_{11})^+\), 6.0.64827.1, 10.0.52089208083.1, 15.15.886528337182930278529.1

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	$30$	R	$30$	R	R	${\href{/padicField/13.5.0.1}{5} }^{6}$	$30$	$15^{2}$	${\href{/padicField/23.6.0.1}{6} }^{5}$	${\href{/padicField/29.10.0.1}{10} }^{3}$	$15^{2}$	$15^{2}$	${\href{/padicField/41.10.0.1}{10} }^{3}$	${\href{/padicField/43.1.0.1}{1} }^{30}$	$30$	$30$	$30$

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

Local algebras for ramified primes

$p$	Label	Polynomial	$e$	$f$	$c$	Galois group	Slope content
\(3\)		Deg $30$	$2$	$15$	$15$
\(7\)	7.15.10.1	$x^{15} + 35 x^{12} + 3 x^{11} + 12 x^{10} + 490 x^{9} - 315 x^{8} - 2517 x^{7} + 3454 x^{6} - 834 x^{5} + 26565 x^{4} + 12846 x^{3} + 13662 x^{2} - 19944 x + 16290$	$3$	$5$	$10$	$C_{15}$	$[\ ]_{3}^{5}$
	7.15.10.1	$x^{15} + 35 x^{12} + 3 x^{11} + 12 x^{10} + 490 x^{9} - 315 x^{8} - 2517 x^{7} + 3454 x^{6} - 834 x^{5} + 26565 x^{4} + 12846 x^{3} + 13662 x^{2} - 19944 x + 16290$	$3$	$5$	$10$	$C_{15}$	$[\ ]_{3}^{5}$
\(11\)		Deg $30$	$5$	$6$	$24$