Number field 44.44.637355869329332251201071317246647563330929205499488362752542693433916506945636309928088212472341047144500892270592.1

• Label: 44.44.637...592.1
• Degree: $44$
• Signature: $[44, 0]$
• Discriminant: $6.374\times 10^{113}$
• Root discriminant: \(385.89\)
• Ramified primes: $2,11,23$
• Class number: not computed
• Class group: not computed
• Galois group: $C_{44}$ (as 44T1)

Normalized defining polynomial

x^44 - 4*x^43 - 518*x^42 + 2000*x^41 + 123695*x^40 - 459748*x^39 - 18087686*x^38 + 64526368*x^37 + 1814718170*x^36 - 6193598864*x^35 - 132652778312*x^34 + 431592034416*x^33 + 7322641999369*x^32 - 22620901951108*x^31 - 312213864021222*x^30 + 911625919935664*x^29 + 10428557133688448*x^28 - 28632966062679464*x^27 - 275153226057488700*x^26 + 706138883506843248*x^25 + 5755458135761929268*x^24 - 13708810607046879776*x^23 - 95402397945332529568*x^22 + 209124175237528510660*x^21 + 1247774847261692294200*x^20 - 2491218736839344027580*x^19 - 12768555115287243960480*x^18 + 22921502637491324570520*x^17 + 100892818549479033335683*x^16 - 160189450592105018388264*x^15 - 604073477669952541913906*x^14 + 830168648776296532696712*x^13 + 2669691653231711217287495*x^12 - 3084641614773903378251660*x^11 - 8402909238349260115510110*x^10 + 7838442656464813878762480*x^9 + 17939980086056148516506513*x^8 - 12740874854008502250569040*x^7 - 24307959814290565973589250*x^6 + 12024186839228160225449764*x^5 + 19062897072891746307946582*x^4 - 5669046506562441271268732*x^3 - 7530340857502322841857016*x^2 + 983032042850730761279048*x + 1119566782360897493140321

Invariants

Degree:		$44$
Signature:		$[44, 0]$
Discriminant:		637355869329332251201071317246647563330929205499488362752542693433916506945636309928088212472341047144500892270592
Root discriminant:		\(385.89\)
Galois root discriminant:		$2^{11/4}11^{1/2}23^{10/11}\approx 385.8897358154046$
Ramified primes:		\(2\), \(11\), \(23\)
Discriminant root field:		\(\Q(\sqrt{2}) \)
$\card{ \Gal(K/\Q) }$:		$44$
This field is Galois and abelian over $\Q$.
Conductor:		\(4048=2^{4}\cdot 11\cdot 23\)
Dirichlet character group:		$\lbrace$$\chi_{4048}(1,·)$, $\chi_{4048}(131,·)$, $\chi_{4048}(1409,·)$, $\chi_{4048}(265,·)$, $\chi_{4048}(1803,·)$, $\chi_{4048}(3475,·)$, $\chi_{4048}(2201,·)$, $\chi_{4048}(923,·)$, $\chi_{4048}(2465,·)$, $\chi_{4048}(4003,·)$, $\chi_{4048}(3739,·)$, $\chi_{4048}(2993,·)$, $\chi_{4048}(1451,·)$, $\chi_{4048}(307,·)$, $\chi_{4048}(177,·)$, $\chi_{4048}(3123,·)$, $\chi_{4048}(1715,·)$, $\chi_{4048}(969,·)$, $\chi_{4048}(441,·)$, $\chi_{4048}(3387,·)$, $\chi_{4048}(2947,·)$, $\chi_{4048}(3521,·)$, $\chi_{4048}(2243,·)$, $\chi_{4048}(353,·)$, $\chi_{4048}(3785,·)$, $\chi_{4048}(1099,·)$, $\chi_{4048}(1363,·)$, $\chi_{4048}(1849,·)$, $\chi_{4048}(1497,·)$, $\chi_{4048}(219,·)$, $\chi_{4048}(395,·)$, $\chi_{4048}(3873,·)$, $\chi_{4048}(2377,·)$, $\chi_{4048}(1761,·)$, $\chi_{4048}(1979,·)$, $\chi_{4048}(3169,·)$, $\chi_{4048}(3433,·)$, $\chi_{4048}(2155,·)$, $\chi_{4048}(2289,·)$, $\chi_{4048}(3827,·)$, $\chi_{4048}(2025,·)$, $\chi_{4048}(2331,·)$, $\chi_{4048}(1145,·)$, $\chi_{4048}(2419,·)$$\rbrace$
This is not a CM field.

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

$1$, $a$, $a^{2}$, $a^{3}$, $a^{4}$, $a^{5}$, $a^{6}$, $a^{7}$, $a^{8}$, $a^{9}$, $a^{10}$, $a^{11}$, $a^{12}$, $a^{13}$, $a^{14}$, $a^{15}$, $a^{16}$, $a^{17}$, $a^{18}$, $a^{19}$, $a^{20}$, $a^{21}$, $\frac{1}{11}a^{22}-\frac{2}{11}a^{21}+\frac{3}{11}a^{20}+\frac{5}{11}a^{19}-\frac{2}{11}a^{16}+\frac{4}{11}a^{15}-\frac{2}{11}a^{14}+\frac{4}{11}a^{13}+\frac{2}{11}a^{10}-\frac{4}{11}a^{9}-\frac{3}{11}a^{8}-\frac{5}{11}a^{7}-\frac{1}{11}a^{6}+\frac{2}{11}a^{5}-\frac{4}{11}a^{4}-\frac{3}{11}a^{3}-\frac{5}{11}a^{2}-\frac{1}{11}a+\frac{1}{11}$, $\frac{1}{11}a^{23}-\frac{1}{11}a^{21}-\frac{1}{11}a^{19}-\frac{2}{11}a^{17}-\frac{5}{11}a^{15}-\frac{3}{11}a^{13}+\frac{2}{11}a^{11}-\frac{1}{11}a+\frac{2}{11}$, $\frac{1}{11}a^{24}-\frac{2}{11}a^{21}+\frac{2}{11}a^{20}+\frac{5}{11}a^{19}-\frac{2}{11}a^{18}+\frac{4}{11}a^{16}+\frac{4}{11}a^{15}-\frac{5}{11}a^{14}+\frac{4}{11}a^{13}+\frac{2}{11}a^{12}+\frac{2}{11}a^{10}-\frac{4}{11}a^{9}-\frac{3}{11}a^{8}-\frac{5}{11}a^{7}-\frac{1}{11}a^{6}+\frac{2}{11}a^{5}-\frac{4}{11}a^{4}-\frac{3}{11}a^{3}+\frac{5}{11}a^{2}+\frac{1}{11}a+\frac{1}{11}$, $\frac{1}{11}a^{25}-\frac{2}{11}a^{21}-\frac{3}{11}a^{19}+\frac{4}{11}a^{17}+\frac{3}{11}a^{15}-\frac{1}{11}a^{13}+\frac{2}{11}a^{11}-\frac{1}{11}a^{3}+\frac{2}{11}a^{2}-\frac{1}{11}a+\frac{2}{11}$, $\frac{1}{11}a^{26}-\frac{4}{11}a^{21}+\frac{3}{11}a^{20}-\frac{1}{11}a^{19}+\frac{4}{11}a^{18}-\frac{1}{11}a^{16}-\frac{3}{11}a^{15}-\frac{5}{11}a^{14}-\frac{3}{11}a^{13}+\frac{2}{11}a^{12}+\frac{4}{11}a^{10}+\frac{3}{11}a^{9}+\frac{5}{11}a^{8}+\frac{1}{11}a^{7}-\frac{2}{11}a^{6}+\frac{4}{11}a^{5}+\frac{2}{11}a^{4}-\frac{4}{11}a^{3}+\frac{2}{11}$, $\frac{1}{11}a^{27}-\frac{5}{11}a^{21}+\frac{2}{11}a^{19}-\frac{1}{11}a^{17}-\frac{4}{11}a^{13}+\frac{4}{11}a^{11}-\frac{1}{11}a^{5}+\frac{2}{11}a^{4}-\frac{1}{11}a^{3}+\frac{2}{11}a^{2}-\frac{2}{11}a+\frac{4}{11}$, $\frac{1}{11}a^{28}+\frac{1}{11}a^{21}-\frac{5}{11}a^{20}+\frac{3}{11}a^{19}-\frac{1}{11}a^{18}+\frac{1}{11}a^{16}-\frac{2}{11}a^{15}-\frac{3}{11}a^{14}-\frac{2}{11}a^{13}+\frac{4}{11}a^{12}-\frac{1}{11}a^{10}+\frac{2}{11}a^{9}-\frac{4}{11}a^{8}-\frac{3}{11}a^{7}+\frac{5}{11}a^{6}+\frac{1}{11}a^{5}+\frac{1}{11}a^{4}-\frac{2}{11}a^{3}-\frac{5}{11}a^{2}-\frac{1}{11}a+\frac{5}{11}$, $\frac{1}{11}a^{29}-\frac{3}{11}a^{21}+\frac{5}{11}a^{19}+\frac{1}{11}a^{17}+\frac{4}{11}a^{15}-\frac{1}{11}a^{11}-\frac{1}{11}a^{7}+\frac{2}{11}a^{6}-\frac{1}{11}a^{5}+\frac{2}{11}a^{4}-\frac{2}{11}a^{3}+\frac{4}{11}a^{2}-\frac{5}{11}a-\frac{1}{11}$, $\frac{1}{11}a^{30}+\frac{5}{11}a^{21}+\frac{3}{11}a^{20}+\frac{4}{11}a^{19}+\frac{1}{11}a^{18}-\frac{2}{11}a^{16}+\frac{1}{11}a^{15}+\frac{5}{11}a^{14}+\frac{1}{11}a^{13}-\frac{1}{11}a^{12}-\frac{5}{11}a^{10}-\frac{1}{11}a^{9}+\frac{1}{11}a^{8}-\frac{2}{11}a^{7}-\frac{4}{11}a^{6}-\frac{3}{11}a^{5}-\frac{3}{11}a^{4}-\frac{5}{11}a^{3}+\frac{2}{11}a^{2}-\frac{4}{11}a+\frac{3}{11}$, $\frac{1}{11}a^{31}+\frac{2}{11}a^{21}-\frac{2}{11}a^{19}-\frac{2}{11}a^{17}-\frac{4}{11}a^{15}+\frac{1}{11}a^{13}-\frac{5}{11}a^{11}-\frac{1}{11}a^{9}+\frac{2}{11}a^{8}-\frac{1}{11}a^{7}+\frac{2}{11}a^{6}-\frac{2}{11}a^{5}+\frac{4}{11}a^{4}-\frac{5}{11}a^{3}-\frac{1}{11}a^{2}-\frac{3}{11}a-\frac{5}{11}$, $\frac{1}{11}a^{32}+\frac{4}{11}a^{21}+\frac{3}{11}a^{20}+\frac{1}{11}a^{19}-\frac{2}{11}a^{18}+\frac{3}{11}a^{15}+\frac{5}{11}a^{14}+\frac{3}{11}a^{13}-\frac{5}{11}a^{12}-\frac{5}{11}a^{10}-\frac{1}{11}a^{9}+\frac{5}{11}a^{8}+\frac{1}{11}a^{7}+\frac{3}{11}a^{4}+\frac{5}{11}a^{3}-\frac{4}{11}a^{2}-\frac{3}{11}a-\frac{2}{11}$, $\frac{1}{11}a^{33}+\frac{1}{11}a^{13}-\frac{5}{11}a^{11}+\frac{2}{11}a^{10}-\frac{1}{11}a^{9}+\frac{2}{11}a^{8}-\frac{2}{11}a^{7}+\frac{4}{11}a^{6}-\frac{5}{11}a^{5}-\frac{1}{11}a^{4}-\frac{3}{11}a^{3}-\frac{5}{11}a^{2}+\frac{2}{11}a-\frac{4}{11}$, $\frac{1}{11}a^{34}+\frac{1}{11}a^{14}-\frac{5}{11}a^{12}+\frac{2}{11}a^{11}-\frac{1}{11}a^{10}+\frac{2}{11}a^{9}-\frac{2}{11}a^{8}+\frac{4}{11}a^{7}-\frac{5}{11}a^{6}-\frac{1}{11}a^{5}-\frac{3}{11}a^{4}-\frac{5}{11}a^{3}+\frac{2}{11}a^{2}-\frac{4}{11}a$, $\frac{1}{11}a^{35}+\frac{1}{11}a^{15}-\frac{5}{11}a^{13}+\frac{2}{11}a^{12}-\frac{1}{11}a^{11}+\frac{2}{11}a^{10}-\frac{2}{11}a^{9}+\frac{4}{11}a^{8}-\frac{5}{11}a^{7}-\frac{1}{11}a^{6}-\frac{3}{11}a^{5}-\frac{5}{11}a^{4}+\frac{2}{11}a^{3}-\frac{4}{11}a^{2}$, $\frac{1}{11}a^{36}+\frac{1}{11}a^{16}-\frac{5}{11}a^{14}+\frac{2}{11}a^{13}-\frac{1}{11}a^{12}+\frac{2}{11}a^{11}-\frac{2}{11}a^{10}+\frac{4}{11}a^{9}-\frac{5}{11}a^{8}-\frac{1}{11}a^{7}-\frac{3}{11}a^{6}-\frac{5}{11}a^{5}+\frac{2}{11}a^{4}-\frac{4}{11}a^{3}$, $\frac{1}{11}a^{37}+\frac{1}{11}a^{17}-\frac{5}{11}a^{15}+\frac{2}{11}a^{14}-\frac{1}{11}a^{13}+\frac{2}{11}a^{12}-\frac{2}{11}a^{11}+\frac{4}{11}a^{10}-\frac{5}{11}a^{9}-\frac{1}{11}a^{8}-\frac{3}{11}a^{7}-\frac{5}{11}a^{6}+\frac{2}{11}a^{5}-\frac{4}{11}a^{4}$, $\frac{1}{11}a^{38}+\frac{1}{11}a^{18}-\frac{5}{11}a^{16}+\frac{2}{11}a^{15}-\frac{1}{11}a^{14}+\frac{2}{11}a^{13}-\frac{2}{11}a^{12}+\frac{4}{11}a^{11}-\frac{5}{11}a^{10}-\frac{1}{11}a^{9}-\frac{3}{11}a^{8}-\frac{5}{11}a^{7}+\frac{2}{11}a^{6}-\frac{4}{11}a^{5}$, $\frac{1}{11}a^{39}+\frac{1}{11}a^{19}-\frac{5}{11}a^{17}+\frac{2}{11}a^{16}-\frac{1}{11}a^{15}+\frac{2}{11}a^{14}-\frac{2}{11}a^{13}+\frac{4}{11}a^{12}-\frac{5}{11}a^{11}-\frac{1}{11}a^{10}-\frac{3}{11}a^{9}-\frac{5}{11}a^{8}+\frac{2}{11}a^{7}-\frac{4}{11}a^{6}$, $\frac{1}{11}a^{40}+\frac{1}{11}a^{20}-\frac{5}{11}a^{18}+\frac{2}{11}a^{17}-\frac{1}{11}a^{16}+\frac{2}{11}a^{15}-\frac{2}{11}a^{14}+\frac{4}{11}a^{13}-\frac{5}{11}a^{12}-\frac{1}{11}a^{11}-\frac{3}{11}a^{10}-\frac{5}{11}a^{9}+\frac{2}{11}a^{8}-\frac{4}{11}a^{7}$, $\frac{1}{11}a^{41}+\frac{1}{11}a^{21}-\frac{5}{11}a^{19}+\frac{2}{11}a^{18}-\frac{1}{11}a^{17}+\frac{2}{11}a^{16}-\frac{2}{11}a^{15}+\frac{4}{11}a^{14}-\frac{5}{11}a^{13}-\frac{1}{11}a^{12}-\frac{3}{11}a^{11}-\frac{5}{11}a^{10}+\frac{2}{11}a^{9}-\frac{4}{11}a^{8}$, $\frac{1}{62\!\cdots\!93}a^{42}+\frac{34\!\cdots\!94}{62\!\cdots\!93}a^{41}-\frac{24\!\cdots\!97}{62\!\cdots\!93}a^{40}-\frac{69\!\cdots\!55}{62\!\cdots\!93}a^{39}-\frac{28\!\cdots\!02}{62\!\cdots\!93}a^{38}+\frac{15\!\cdots\!04}{56\!\cdots\!63}a^{37}-\frac{13\!\cdots\!08}{62\!\cdots\!93}a^{36}+\frac{15\!\cdots\!49}{62\!\cdots\!93}a^{35}-\frac{19\!\cdots\!72}{62\!\cdots\!93}a^{34}+\frac{27\!\cdots\!29}{62\!\cdots\!93}a^{33}-\frac{18\!\cdots\!47}{62\!\cdots\!93}a^{32}+\frac{24\!\cdots\!80}{62\!\cdots\!93}a^{31}-\frac{24\!\cdots\!78}{62\!\cdots\!93}a^{30}+\frac{23\!\cdots\!39}{56\!\cdots\!63}a^{29}+\frac{22\!\cdots\!10}{62\!\cdots\!93}a^{28}-\frac{12\!\cdots\!12}{62\!\cdots\!93}a^{27}-\frac{20\!\cdots\!41}{62\!\cdots\!93}a^{26}-\frac{18\!\cdots\!14}{62\!\cdots\!93}a^{25}-\frac{21\!\cdots\!12}{62\!\cdots\!93}a^{24}+\frac{32\!\cdots\!50}{62\!\cdots\!93}a^{23}+\frac{10\!\cdots\!95}{62\!\cdots\!93}a^{22}-\frac{19\!\cdots\!75}{62\!\cdots\!93}a^{21}-\frac{12\!\cdots\!93}{62\!\cdots\!93}a^{20}+\frac{78\!\cdots\!67}{62\!\cdots\!93}a^{19}+\frac{26\!\cdots\!61}{62\!\cdots\!93}a^{18}-\frac{19\!\cdots\!10}{62\!\cdots\!93}a^{17}+\frac{29\!\cdots\!43}{62\!\cdots\!93}a^{16}+\frac{28\!\cdots\!37}{62\!\cdots\!93}a^{15}+\frac{16\!\cdots\!99}{62\!\cdots\!93}a^{14}-\frac{11\!\cdots\!17}{62\!\cdots\!93}a^{13}+\frac{23\!\cdots\!08}{62\!\cdots\!93}a^{12}-\frac{23\!\cdots\!16}{56\!\cdots\!63}a^{11}-\frac{10\!\cdots\!03}{62\!\cdots\!93}a^{10}-\frac{16\!\cdots\!46}{62\!\cdots\!93}a^{9}-\frac{30\!\cdots\!39}{62\!\cdots\!93}a^{8}-\frac{29\!\cdots\!84}{62\!\cdots\!93}a^{7}-\frac{18\!\cdots\!95}{62\!\cdots\!93}a^{6}+\frac{21\!\cdots\!48}{62\!\cdots\!93}a^{5}-\frac{14\!\cdots\!84}{62\!\cdots\!93}a^{4}-\frac{76\!\cdots\!17}{62\!\cdots\!93}a^{3}+\frac{20\!\cdots\!02}{62\!\cdots\!93}a^{2}+\frac{10\!\cdots\!22}{62\!\cdots\!93}a+\frac{15\!\cdots\!30}{62\!\cdots\!93}$, $\frac{1}{43\!\cdots\!17}a^{43}-\frac{50\!\cdots\!63}{43\!\cdots\!17}a^{42}-\frac{19\!\cdots\!69}{43\!\cdots\!17}a^{41}+\frac{13\!\cdots\!50}{43\!\cdots\!17}a^{40}-\frac{10\!\cdots\!21}{39\!\cdots\!47}a^{39}-\frac{10\!\cdots\!15}{43\!\cdots\!17}a^{38}+\frac{18\!\cdots\!33}{43\!\cdots\!17}a^{37}+\frac{98\!\cdots\!75}{43\!\cdots\!17}a^{36}+\frac{22\!\cdots\!02}{43\!\cdots\!17}a^{35}+\frac{11\!\cdots\!71}{43\!\cdots\!17}a^{34}-\frac{10\!\cdots\!97}{39\!\cdots\!47}a^{33}+\frac{14\!\cdots\!91}{39\!\cdots\!47}a^{32}+\frac{64\!\cdots\!18}{43\!\cdots\!17}a^{31}+\frac{13\!\cdots\!76}{43\!\cdots\!17}a^{30}+\frac{13\!\cdots\!03}{43\!\cdots\!17}a^{29}-\frac{97\!\cdots\!04}{43\!\cdots\!17}a^{28}+\frac{59\!\cdots\!48}{43\!\cdots\!17}a^{27}-\frac{52\!\cdots\!51}{43\!\cdots\!17}a^{26}+\frac{13\!\cdots\!44}{39\!\cdots\!47}a^{25}+\frac{15\!\cdots\!73}{43\!\cdots\!17}a^{24}-\frac{61\!\cdots\!19}{43\!\cdots\!17}a^{23}-\frac{15\!\cdots\!84}{39\!\cdots\!47}a^{22}-\frac{14\!\cdots\!43}{43\!\cdots\!17}a^{21}+\frac{98\!\cdots\!94}{43\!\cdots\!17}a^{20}+\frac{16\!\cdots\!80}{43\!\cdots\!17}a^{19}+\frac{66\!\cdots\!39}{43\!\cdots\!17}a^{18}+\frac{18\!\cdots\!74}{43\!\cdots\!17}a^{17}-\frac{17\!\cdots\!11}{43\!\cdots\!17}a^{16}+\frac{10\!\cdots\!09}{43\!\cdots\!17}a^{15}-\frac{86\!\cdots\!11}{43\!\cdots\!17}a^{14}+\frac{67\!\cdots\!22}{43\!\cdots\!17}a^{13}+\frac{49\!\cdots\!68}{43\!\cdots\!17}a^{12}+\frac{19\!\cdots\!14}{43\!\cdots\!17}a^{11}+\frac{15\!\cdots\!45}{43\!\cdots\!17}a^{10}+\frac{11\!\cdots\!59}{43\!\cdots\!17}a^{9}-\frac{27\!\cdots\!43}{43\!\cdots\!17}a^{8}+\frac{75\!\cdots\!01}{39\!\cdots\!47}a^{7}-\frac{11\!\cdots\!25}{43\!\cdots\!17}a^{6}-\frac{76\!\cdots\!01}{43\!\cdots\!17}a^{5}+\frac{96\!\cdots\!32}{43\!\cdots\!17}a^{4}+\frac{85\!\cdots\!21}{43\!\cdots\!17}a^{3}+\frac{22\!\cdots\!04}{43\!\cdots\!17}a^{2}-\frac{17\!\cdots\!75}{43\!\cdots\!17}a-\frac{13\!\cdots\!47}{43\!\cdots\!17}$

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

Class group and class number

not computed

Unit group

Rank:		$43$
Torsion generator:		\( -1 \)  (order $2$)
Fundamental units:		not computed
Regulator:		not computed

Class number formula

\[ \begin{aligned}\lim_{s\to 1} (s-1)\zeta_K(s) =\mathstrut & \frac{2^{r_1}\cdot (2\pi)^{r_2}\cdot R\cdot h}{w\cdot\sqrt{|D|}}\cr $ not computed \end{aligned}\]

Galois group

$C_{44}$ (as 44T1):

A cyclic group of order 44

The 44 conjugacy class representatives for $C_{44}$

Character table for $C_{44}$ is not computed

Intermediate fields

\(\Q(\sqrt{2}) \), 4.4.247808.1, \(\Q(\zeta_{23})^+\), 22.22.14741666340843480753092741810452692992.1

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	R	$44$	$44$	$22^{2}$	R	$44$	$22^{2}$	$44$	R	$44$	$22^{2}$	$44$	${\href{/padicField/41.11.0.1}{11} }^{4}$	$44$	${\href{/padicField/47.2.0.1}{2} }^{22}$	$44$	$44$

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
\(2\)		Deg $44$	$4$	$11$	$121$
\(11\)		Deg $44$	$2$	$22$	$22$
\(23\)	23.11.10.10	$x^{11} + 23$	$11$	$1$	$10$	$C_{11}$	$[\ ]_{11}$
	23.11.10.10	$x^{11} + 23$	$11$	$1$	$10$	$C_{11}$	$[\ ]_{11}$
	23.11.10.10	$x^{11} + 23$	$11$	$1$	$10$	$C_{11}$	$[\ ]_{11}$
	23.11.10.10	$x^{11} + 23$	$11$	$1$	$10$	$C_{11}$	$[\ ]_{11}$