Properties

Label 2243.h
Modulus 22432243
Conductor 22432243
Order 22422242
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2243, base_ring=CyclotomicField(2242))
 
M = H._module
 
chi = DirichletCharacter(H, M([1]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(2,2243))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 22432243
Conductor: 22432243
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 22422242
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ1121)\Q(\zeta_{1121})
Fixed field: Number field defined by a degree 2242 polynomial (not computed)

First 31 of 1044 characters in Galois orbit

Character 1-1 11 22 33 44 55 66 77 88 99 1010 1111
χ2243(2,)\chi_{2243}(2,\cdot) 1-1 11 e(12242)e\left(\frac{1}{2242}\right) e(731121)e\left(\frac{73}{1121}\right) e(11121)e\left(\frac{1}{1121}\right) e(13632242)e\left(\frac{1363}{2242}\right) e(1472242)e\left(\frac{147}{2242}\right) e(10701121)e\left(\frac{1070}{1121}\right) e(32242)e\left(\frac{3}{2242}\right) e(1461121)e\left(\frac{146}{1121}\right) e(6821121)e\left(\frac{682}{1121}\right) e(10141121)e\left(\frac{1014}{1121}\right)
χ2243(5,)\chi_{2243}(5,\cdot) 1-1 11 e(13632242)e\left(\frac{1363}{2242}\right) e(8511121)e\left(\frac{851}{1121}\right) e(2421121)e\left(\frac{242}{1121}\right) e(13932242)e\left(\frac{1393}{2242}\right) e(8232242)e\left(\frac{823}{2242}\right) e(11101121)e\left(\frac{1110}{1121}\right) e(18472242)e\left(\frac{1847}{2242}\right) e(5811121)e\left(\frac{581}{1121}\right) e(2571121)e\left(\frac{257}{1121}\right) e(10101121)e\left(\frac{1010}{1121}\right)
χ2243(6,)\chi_{2243}(6,\cdot) 1-1 11 e(1472242)e\left(\frac{147}{2242}\right) e(6421121)e\left(\frac{642}{1121}\right) e(1471121)e\left(\frac{147}{1121}\right) e(8232242)e\left(\frac{823}{2242}\right) e(14312242)e\left(\frac{1431}{2242}\right) e(3501121)e\left(\frac{350}{1121}\right) e(4412242)e\left(\frac{441}{2242}\right) e(1631121)e\left(\frac{163}{1121}\right) e(4851121)e\left(\frac{485}{1121}\right) e(10861121)e\left(\frac{1086}{1121}\right)
χ2243(8,)\chi_{2243}(8,\cdot) 1-1 11 e(32242)e\left(\frac{3}{2242}\right) e(2191121)e\left(\frac{219}{1121}\right) e(31121)e\left(\frac{3}{1121}\right) e(18472242)e\left(\frac{1847}{2242}\right) e(4412242)e\left(\frac{441}{2242}\right) e(9681121)e\left(\frac{968}{1121}\right) e(92242)e\left(\frac{9}{2242}\right) e(4381121)e\left(\frac{438}{1121}\right) e(9251121)e\left(\frac{925}{1121}\right) e(8001121)e\left(\frac{800}{1121}\right)
χ2243(13,)\chi_{2243}(13,\cdot) 1-1 11 e(18652242)e\left(\frac{1865}{2242}\right) e(5041121)e\left(\frac{504}{1121}\right) e(7441121)e\left(\frac{744}{1121}\right) e(18092242)e\left(\frac{1809}{2242}\right) e(6312242)e\left(\frac{631}{2242}\right) e(1701121)e\left(\frac{170}{1121}\right) e(11112242)e\left(\frac{1111}{2242}\right) e(10081121)e\left(\frac{1008}{1121}\right) e(7161121)e\left(\frac{716}{1121}\right) e(11041121)e\left(\frac{1104}{1121}\right)
χ2243(14,)\chi_{2243}(14,\cdot) 1-1 11 e(21412242)e\left(\frac{2141}{2242}\right) e(4741121)e\left(\frac{474}{1121}\right) e(10201121)e\left(\frac{1020}{1121}\right) e(13412242)e\left(\frac{1341}{2242}\right) e(8472242)e\left(\frac{847}{2242}\right) e(6671121)e\left(\frac{667}{1121}\right) e(19392242)e\left(\frac{1939}{2242}\right) e(9481121)e\left(\frac{948}{1121}\right) e(6201121)e\left(\frac{620}{1121}\right) e(7181121)e\left(\frac{718}{1121}\right)
χ2243(15,)\chi_{2243}(15,\cdot) 1-1 11 e(15092242)e\left(\frac{1509}{2242}\right) e(2991121)e\left(\frac{299}{1121}\right) e(3881121)e\left(\frac{388}{1121}\right) e(8532242)e\left(\frac{853}{2242}\right) e(21072242)e\left(\frac{2107}{2242}\right) e(3901121)e\left(\frac{390}{1121}\right) e(432242)e\left(\frac{43}{2242}\right) e(5981121)e\left(\frac{598}{1121}\right) e(601121)e\left(\frac{60}{1121}\right) e(10821121)e\left(\frac{1082}{1121}\right)
χ2243(18,)\chi_{2243}(18,\cdot) 1-1 11 e(2932242)e\left(\frac{293}{2242}\right) e(901121)e\left(\frac{90}{1121}\right) e(2931121)e\left(\frac{293}{1121}\right) e(2832242)e\left(\frac{283}{2242}\right) e(4732242)e\left(\frac{473}{2242}\right) e(7511121)e\left(\frac{751}{1121}\right) e(8792242)e\left(\frac{879}{2242}\right) e(1801121)e\left(\frac{180}{1121}\right) e(2881121)e\left(\frac{288}{1121}\right) e(371121)e\left(\frac{37}{1121}\right)
χ2243(19,)\chi_{2243}(19,\cdot) 1-1 11 e(3292242)e\left(\frac{329}{2242}\right) e(4761121)e\left(\frac{476}{1121}\right) e(3291121)e\left(\frac{329}{1121}\right) e(272242)e\left(\frac{27}{2242}\right) e(12812242)e\left(\frac{1281}{2242}\right) e(361121)e\left(\frac{36}{1121}\right) e(9872242)e\left(\frac{987}{2242}\right) e(9521121)e\left(\frac{952}{1121}\right) e(1781121)e\left(\frac{178}{1121}\right) e(6691121)e\left(\frac{669}{1121}\right)
χ2243(20,)\chi_{2243}(20,\cdot) 1-1 11 e(13652242)e\left(\frac{1365}{2242}\right) e(9971121)e\left(\frac{997}{1121}\right) e(2441121)e\left(\frac{244}{1121}\right) e(18772242)e\left(\frac{1877}{2242}\right) e(11172242)e\left(\frac{1117}{2242}\right) e(10081121)e\left(\frac{1008}{1121}\right) e(18532242)e\left(\frac{1853}{2242}\right) e(8731121)e\left(\frac{873}{1121}\right) e(5001121)e\left(\frac{500}{1121}\right) e(7961121)e\left(\frac{796}{1121}\right)
χ2243(22,)\chi_{2243}(22,\cdot) 1-1 11 e(20292242)e\left(\frac{2029}{2242}\right) e(1451121)e\left(\frac{145}{1121}\right) e(9081121)e\left(\frac{908}{1121}\right) e(11412242)e\left(\frac{1141}{2242}\right) e(772242)e\left(\frac{77}{2242}\right) e(7741121)e\left(\frac{774}{1121}\right) e(16032242)e\left(\frac{1603}{2242}\right) e(2901121)e\left(\frac{290}{1121}\right) e(4641121)e\left(\frac{464}{1121}\right) e(3711121)e\left(\frac{371}{1121}\right)
χ2243(23,)\chi_{2243}(23,\cdot) 1-1 11 e(22312242)e\left(\frac{2231}{2242}\right) e(3181121)e\left(\frac{318}{1121}\right) e(11101121)e\left(\frac{1110}{1121}\right) e(7012242)e\left(\frac{701}{2242}\right) e(6252242)e\left(\frac{625}{2242}\right) e(5611121)e\left(\frac{561}{1121}\right) e(22092242)e\left(\frac{2209}{2242}\right) e(6361121)e\left(\frac{636}{1121}\right) e(3451121)e\left(\frac{345}{1121}\right) e(561121)e\left(\frac{56}{1121}\right)
χ2243(24,)\chi_{2243}(24,\cdot) 1-1 11 e(1492242)e\left(\frac{149}{2242}\right) e(7881121)e\left(\frac{788}{1121}\right) e(1491121)e\left(\frac{149}{1121}\right) e(13072242)e\left(\frac{1307}{2242}\right) e(17252242)e\left(\frac{1725}{2242}\right) e(2481121)e\left(\frac{248}{1121}\right) e(4472242)e\left(\frac{447}{2242}\right) e(4551121)e\left(\frac{455}{1121}\right) e(7281121)e\left(\frac{728}{1121}\right) e(8721121)e\left(\frac{872}{1121}\right)
χ2243(29,)\chi_{2243}(29,\cdot) 1-1 11 e(5592242)e\left(\frac{559}{2242}\right) e(4511121)e\left(\frac{451}{1121}\right) e(5591121)e\left(\frac{559}{1121}\right) e(18792242)e\left(\frac{1879}{2242}\right) e(14612242)e\left(\frac{1461}{2242}\right) e(6371121)e\left(\frac{637}{1121}\right) e(16772242)e\left(\frac{1677}{2242}\right) e(9021121)e\left(\frac{902}{1121}\right) e(981121)e\left(\frac{98}{1121}\right) e(7211121)e\left(\frac{721}{1121}\right)
χ2243(32,)\chi_{2243}(32,\cdot) 1-1 11 e(52242)e\left(\frac{5}{2242}\right) e(3651121)e\left(\frac{365}{1121}\right) e(51121)e\left(\frac{5}{1121}\right) e(892242)e\left(\frac{89}{2242}\right) e(7352242)e\left(\frac{735}{2242}\right) e(8661121)e\left(\frac{866}{1121}\right) e(152242)e\left(\frac{15}{2242}\right) e(7301121)e\left(\frac{730}{1121}\right) e(471121)e\left(\frac{47}{1121}\right) e(5861121)e\left(\frac{586}{1121}\right)
χ2243(34,)\chi_{2243}(34,\cdot) 1-1 11 e(672242)e\left(\frac{67}{2242}\right) e(4071121)e\left(\frac{407}{1121}\right) e(671121)e\left(\frac{67}{1121}\right) e(16412242)e\left(\frac{1641}{2242}\right) e(8812242)e\left(\frac{881}{2242}\right) e(10671121)e\left(\frac{1067}{1121}\right) e(2012242)e\left(\frac{201}{2242}\right) e(8141121)e\left(\frac{814}{1121}\right) e(8541121)e\left(\frac{854}{1121}\right) e(6781121)e\left(\frac{678}{1121}\right)
χ2243(35,)\chi_{2243}(35,\cdot) 1-1 11 e(12612242)e\left(\frac{1261}{2242}\right) e(1311121)e\left(\frac{131}{1121}\right) e(1401121)e\left(\frac{140}{1121}\right) e(13712242)e\left(\frac{1371}{2242}\right) e(15232242)e\left(\frac{1523}{2242}\right) e(7071121)e\left(\frac{707}{1121}\right) e(15412242)e\left(\frac{1541}{2242}\right) e(2621121)e\left(\frac{262}{1121}\right) e(1951121)e\left(\frac{195}{1121}\right) e(7141121)e\left(\frac{714}{1121}\right)
χ2243(37,)\chi_{2243}(37,\cdot) 1-1 11 e(18412242)e\left(\frac{1841}{2242}\right) e(9941121)e\left(\frac{994}{1121}\right) e(7201121)e\left(\frac{720}{1121}\right) e(4852242)e\left(\frac{485}{2242}\right) e(15872242)e\left(\frac{1587}{2242}\right) e(2731121)e\left(\frac{273}{1121}\right) e(10392242)e\left(\frac{1039}{2242}\right) e(8671121)e\left(\frac{867}{1121}\right) e(421121)e\left(\frac{42}{1121}\right) e(3091121)e\left(\frac{309}{1121}\right)
χ2243(39,)\chi_{2243}(39,\cdot) 1-1 11 e(20112242)e\left(\frac{2011}{2242}\right) e(10731121)e\left(\frac{1073}{1121}\right) e(8901121)e\left(\frac{890}{1121}\right) e(12692242)e\left(\frac{1269}{2242}\right) e(19152242)e\left(\frac{1915}{2242}\right) e(5711121)e\left(\frac{571}{1121}\right) e(15492242)e\left(\frac{1549}{2242}\right) e(10251121)e\left(\frac{1025}{1121}\right) e(5191121)e\left(\frac{519}{1121}\right) e(551121)e\left(\frac{55}{1121}\right)
χ2243(41,)\chi_{2243}(41,\cdot) 1-1 11 e(12412242)e\left(\frac{1241}{2242}\right) e(9131121)e\left(\frac{913}{1121}\right) e(1201121)e\left(\frac{120}{1121}\right) e(10152242)e\left(\frac{1015}{2242}\right) e(8252242)e\left(\frac{825}{2242}\right) e(6061121)e\left(\frac{606}{1121}\right) e(14812242)e\left(\frac{1481}{2242}\right) e(7051121)e\left(\frac{705}{1121}\right) e(71121)e\left(\frac{7}{1121}\right) e(6121121)e\left(\frac{612}{1121}\right)
χ2243(42,)\chi_{2243}(42,\cdot) 1-1 11 e(452242)e\left(\frac{45}{2242}\right) e(10431121)e\left(\frac{1043}{1121}\right) e(451121)e\left(\frac{45}{1121}\right) e(8012242)e\left(\frac{801}{2242}\right) e(21312242)e\left(\frac{2131}{2242}\right) e(10681121)e\left(\frac{1068}{1121}\right) e(1352242)e\left(\frac{135}{2242}\right) e(9651121)e\left(\frac{965}{1121}\right) e(4231121)e\left(\frac{423}{1121}\right) e(7901121)e\left(\frac{790}{1121}\right)
χ2243(45,)\chi_{2243}(45,\cdot) 1-1 11 e(16552242)e\left(\frac{1655}{2242}\right) e(8681121)e\left(\frac{868}{1121}\right) e(5341121)e\left(\frac{534}{1121}\right) e(3132242)e\left(\frac{313}{2242}\right) e(11492242)e\left(\frac{1149}{2242}\right) e(7911121)e\left(\frac{791}{1121}\right) e(4812242)e\left(\frac{481}{2242}\right) e(6151121)e\left(\frac{615}{1121}\right) e(9841121)e\left(\frac{984}{1121}\right) e(331121)e\left(\frac{33}{1121}\right)
χ2243(47,)\chi_{2243}(47,\cdot) 1-1 11 e(17152242)e\left(\frac{1715}{2242}\right) e(7641121)e\left(\frac{764}{1121}\right) e(5941121)e\left(\frac{594}{1121}\right) e(13812242)e\left(\frac{1381}{2242}\right) e(10012242)e\left(\frac{1001}{2242}\right) e(10941121)e\left(\frac{1094}{1121}\right) e(6612242)e\left(\frac{661}{2242}\right) e(4071121)e\left(\frac{407}{1121}\right) e(4271121)e\left(\frac{427}{1121}\right) e(3391121)e\left(\frac{339}{1121}\right)
χ2243(50,)\chi_{2243}(50,\cdot) 1-1 11 e(4852242)e\left(\frac{485}{2242}\right) e(6541121)e\left(\frac{654}{1121}\right) e(4851121)e\left(\frac{485}{1121}\right) e(19072242)e\left(\frac{1907}{2242}\right) e(17932242)e\left(\frac{1793}{2242}\right) e(10481121)e\left(\frac{1048}{1121}\right) e(14552242)e\left(\frac{1455}{2242}\right) e(1871121)e\left(\frac{187}{1121}\right) e(751121)e\left(\frac{75}{1121}\right) e(7921121)e\left(\frac{792}{1121}\right)
χ2243(52,)\chi_{2243}(52,\cdot) 1-1 11 e(18672242)e\left(\frac{1867}{2242}\right) e(6501121)e\left(\frac{650}{1121}\right) e(7461121)e\left(\frac{746}{1121}\right) e(512242)e\left(\frac{51}{2242}\right) e(9252242)e\left(\frac{925}{2242}\right) e(681121)e\left(\frac{68}{1121}\right) e(11172242)e\left(\frac{1117}{2242}\right) e(1791121)e\left(\frac{179}{1121}\right) e(9591121)e\left(\frac{959}{1121}\right) e(8901121)e\left(\frac{890}{1121}\right)
χ2243(54,)\chi_{2243}(54,\cdot) 1-1 11 e(4392242)e\left(\frac{439}{2242}\right) e(6591121)e\left(\frac{659}{1121}\right) e(4391121)e\left(\frac{439}{1121}\right) e(19852242)e\left(\frac{1985}{2242}\right) e(17572242)e\left(\frac{1757}{2242}\right) e(311121)e\left(\frac{31}{1121}\right) e(13172242)e\left(\frac{1317}{2242}\right) e(1971121)e\left(\frac{197}{1121}\right) e(911121)e\left(\frac{91}{1121}\right) e(1091121)e\left(\frac{109}{1121}\right)
χ2243(55,)\chi_{2243}(55,\cdot) 1-1 11 e(11492242)e\left(\frac{1149}{2242}\right) e(9231121)e\left(\frac{923}{1121}\right) e(281121)e\left(\frac{28}{1121}\right) e(11712242)e\left(\frac{1171}{2242}\right) e(7532242)e\left(\frac{753}{2242}\right) e(8141121)e\left(\frac{814}{1121}\right) e(12052242)e\left(\frac{1205}{2242}\right) e(7251121)e\left(\frac{725}{1121}\right) e(391121)e\left(\frac{39}{1121}\right) e(3671121)e\left(\frac{367}{1121}\right)
χ2243(56,)\chi_{2243}(56,\cdot) 1-1 11 e(21432242)e\left(\frac{2143}{2242}\right) e(6201121)e\left(\frac{620}{1121}\right) e(10221121)e\left(\frac{1022}{1121}\right) e(18252242)e\left(\frac{1825}{2242}\right) e(11412242)e\left(\frac{1141}{2242}\right) e(5651121)e\left(\frac{565}{1121}\right) e(19452242)e\left(\frac{1945}{2242}\right) e(1191121)e\left(\frac{119}{1121}\right) e(8631121)e\left(\frac{863}{1121}\right) e(5041121)e\left(\frac{504}{1121}\right)
χ2243(59,)\chi_{2243}(59,\cdot) 1-1 11 e(7912242)e\left(\frac{791}{2242}\right) e(5721121)e\left(\frac{572}{1121}\right) e(7911121)e\left(\frac{791}{1121}\right) e(19732242)e\left(\frac{1973}{2242}\right) e(19352242)e\left(\frac{1935}{2242}\right) e(151121)e\left(\frac{15}{1121}\right) e(1312242)e\left(\frac{131}{2242}\right) e(231121)e\left(\frac{23}{1121}\right) e(2611121)e\left(\frac{261}{1121}\right) e(5591121)e\left(\frac{559}{1121}\right)
χ2243(60,)\chi_{2243}(60,\cdot) 1-1 11 e(15112242)e\left(\frac{1511}{2242}\right) e(4451121)e\left(\frac{445}{1121}\right) e(3901121)e\left(\frac{390}{1121}\right) e(13372242)e\left(\frac{1337}{2242}\right) e(1592242)e\left(\frac{159}{2242}\right) e(2881121)e\left(\frac{288}{1121}\right) e(492242)e\left(\frac{49}{2242}\right) e(8901121)e\left(\frac{890}{1121}\right) e(3031121)e\left(\frac{303}{1121}\right) e(8681121)e\left(\frac{868}{1121}\right)
χ2243(62,)\chi_{2243}(62,\cdot) 1-1 11 e(6132242)e\left(\frac{613}{2242}\right) e(10301121)e\left(\frac{1030}{1121}\right) e(6131121)e\left(\frac{613}{1121}\right) e(14952242)e\left(\frac{1495}{2242}\right) e(4312242)e\left(\frac{431}{2242}\right) e(1251121)e\left(\frac{125}{1121}\right) e(18392242)e\left(\frac{1839}{2242}\right) e(9391121)e\left(\frac{939}{1121}\right) e(10541121)e\left(\frac{1054}{1121}\right) e(5481121)e\left(\frac{548}{1121}\right)