from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(35937, base_ring=CyclotomicField(3630))
M = H._module
chi = DirichletCharacter(H, M([1210,3426]))
chi.galois_orbit()
[g,chi] = znchar(Mod(37,35937))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(35937\) | |
| Conductor: | \(11979\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1815\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 11979.bs | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | $\Q(\zeta_{1815})$ |
| Fixed field: | Number field defined by a degree 1815 polynomial (not computed) |
First 31 of 880 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{35937}(37,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{503}{1815}\right)\) | \(e\left(\frac{1006}{1815}\right)\) | \(e\left(\frac{592}{1815}\right)\) | \(e\left(\frac{56}{1815}\right)\) | \(e\left(\frac{503}{605}\right)\) | \(e\left(\frac{73}{121}\right)\) | \(e\left(\frac{313}{1815}\right)\) | \(e\left(\frac{559}{1815}\right)\) | \(e\left(\frac{197}{1815}\right)\) | \(e\left(\frac{39}{605}\right)\) |
| \(\chi_{35937}(64,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{614}{1815}\right)\) | \(e\left(\frac{1228}{1815}\right)\) | \(e\left(\frac{1051}{1815}\right)\) | \(e\left(\frac{173}{1815}\right)\) | \(e\left(\frac{9}{605}\right)\) | \(e\left(\frac{111}{121}\right)\) | \(e\left(\frac{1129}{1815}\right)\) | \(e\left(\frac{787}{1815}\right)\) | \(e\left(\frac{641}{1815}\right)\) | \(e\left(\frac{477}{605}\right)\) |
| \(\chi_{35937}(91,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1427}{1815}\right)\) | \(e\left(\frac{1039}{1815}\right)\) | \(e\left(\frac{1813}{1815}\right)\) | \(e\left(\frac{1079}{1815}\right)\) | \(e\left(\frac{217}{605}\right)\) | \(e\left(\frac{95}{121}\right)\) | \(e\left(\frac{1072}{1815}\right)\) | \(e\left(\frac{691}{1815}\right)\) | \(e\left(\frac{263}{1815}\right)\) | \(e\left(\frac{6}{605}\right)\) |
| \(\chi_{35937}(181,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1291}{1815}\right)\) | \(e\left(\frac{767}{1815}\right)\) | \(e\left(\frac{989}{1815}\right)\) | \(e\left(\frac{952}{1815}\right)\) | \(e\left(\frac{81}{605}\right)\) | \(e\left(\frac{31}{121}\right)\) | \(e\left(\frac{1691}{1815}\right)\) | \(e\left(\frac{428}{1815}\right)\) | \(e\left(\frac{1534}{1815}\right)\) | \(e\left(\frac{58}{605}\right)\) |
| \(\chi_{35937}(235,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{973}{1815}\right)\) | \(e\left(\frac{131}{1815}\right)\) | \(e\left(\frac{557}{1815}\right)\) | \(e\left(\frac{1696}{1815}\right)\) | \(e\left(\frac{368}{605}\right)\) | \(e\left(\frac{102}{121}\right)\) | \(e\left(\frac{923}{1815}\right)\) | \(e\left(\frac{854}{1815}\right)\) | \(e\left(\frac{262}{1815}\right)\) | \(e\left(\frac{144}{605}\right)\) |
| \(\chi_{35937}(262,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{1815}\right)\) | \(e\left(\frac{8}{1815}\right)\) | \(e\left(\frac{131}{1815}\right)\) | \(e\left(\frac{1018}{1815}\right)\) | \(e\left(\frac{4}{605}\right)\) | \(e\left(\frac{9}{121}\right)\) | \(e\left(\frac{569}{1815}\right)\) | \(e\left(\frac{1022}{1815}\right)\) | \(e\left(\frac{16}{1815}\right)\) | \(e\left(\frac{212}{605}\right)\) |
| \(\chi_{35937}(280,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1721}{1815}\right)\) | \(e\left(\frac{1627}{1815}\right)\) | \(e\left(\frac{1459}{1815}\right)\) | \(e\left(\frac{1487}{1815}\right)\) | \(e\left(\frac{511}{605}\right)\) | \(e\left(\frac{91}{121}\right)\) | \(e\left(\frac{241}{1815}\right)\) | \(e\left(\frac{1393}{1815}\right)\) | \(e\left(\frac{1439}{1815}\right)\) | \(e\left(\frac{463}{605}\right)\) |
| \(\chi_{35937}(289,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1687}{1815}\right)\) | \(e\left(\frac{1559}{1815}\right)\) | \(e\left(\frac{1253}{1815}\right)\) | \(e\left(\frac{94}{1815}\right)\) | \(e\left(\frac{477}{605}\right)\) | \(e\left(\frac{75}{121}\right)\) | \(e\left(\frac{1757}{1815}\right)\) | \(e\left(\frac{1781}{1815}\right)\) | \(e\left(\frac{1303}{1815}\right)\) | \(e\left(\frac{476}{605}\right)\) |
| \(\chi_{35937}(334,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{878}{1815}\right)\) | \(e\left(\frac{1756}{1815}\right)\) | \(e\left(\frac{622}{1815}\right)\) | \(e\left(\frac{206}{1815}\right)\) | \(e\left(\frac{273}{605}\right)\) | \(e\left(\frac{100}{121}\right)\) | \(e\left(\frac{568}{1815}\right)\) | \(e\left(\frac{1084}{1815}\right)\) | \(e\left(\frac{1697}{1815}\right)\) | \(e\left(\frac{554}{605}\right)\) |
| \(\chi_{35937}(361,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{194}{1815}\right)\) | \(e\left(\frac{388}{1815}\right)\) | \(e\left(\frac{1}{1815}\right)\) | \(e\left(\frac{368}{1815}\right)\) | \(e\left(\frac{194}{605}\right)\) | \(e\left(\frac{13}{121}\right)\) | \(e\left(\frac{1279}{1815}\right)\) | \(e\left(\frac{562}{1815}\right)\) | \(e\left(\frac{776}{1815}\right)\) | \(e\left(\frac{602}{605}\right)\) |
| \(\chi_{35937}(388,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{827}{1815}\right)\) | \(e\left(\frac{1654}{1815}\right)\) | \(e\left(\frac{313}{1815}\right)\) | \(e\left(\frac{839}{1815}\right)\) | \(e\left(\frac{222}{605}\right)\) | \(e\left(\frac{76}{121}\right)\) | \(e\left(\frac{1027}{1815}\right)\) | \(e\left(\frac{1666}{1815}\right)\) | \(e\left(\frac{1493}{1815}\right)\) | \(e\left(\frac{271}{605}\right)\) |
| \(\chi_{35937}(478,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{271}{1815}\right)\) | \(e\left(\frac{542}{1815}\right)\) | \(e\left(\frac{254}{1815}\right)\) | \(e\left(\frac{907}{1815}\right)\) | \(e\left(\frac{271}{605}\right)\) | \(e\left(\frac{35}{121}\right)\) | \(e\left(\frac{1796}{1815}\right)\) | \(e\left(\frac{1178}{1815}\right)\) | \(e\left(\frac{1084}{1815}\right)\) | \(e\left(\frac{448}{605}\right)\) |
| \(\chi_{35937}(532,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{28}{1815}\right)\) | \(e\left(\frac{56}{1815}\right)\) | \(e\left(\frac{917}{1815}\right)\) | \(e\left(\frac{1681}{1815}\right)\) | \(e\left(\frac{28}{605}\right)\) | \(e\left(\frac{63}{121}\right)\) | \(e\left(\frac{353}{1815}\right)\) | \(e\left(\frac{1709}{1815}\right)\) | \(e\left(\frac{112}{1815}\right)\) | \(e\left(\frac{274}{605}\right)\) |
| \(\chi_{35937}(559,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1564}{1815}\right)\) | \(e\left(\frac{1313}{1815}\right)\) | \(e\left(\frac{401}{1815}\right)\) | \(e\left(\frac{553}{1815}\right)\) | \(e\left(\frac{354}{605}\right)\) | \(e\left(\frac{10}{121}\right)\) | \(e\left(\frac{1049}{1815}\right)\) | \(e\left(\frac{302}{1815}\right)\) | \(e\left(\frac{811}{1815}\right)\) | \(e\left(\frac{7}{605}\right)\) |
| \(\chi_{35937}(577,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{206}{1815}\right)\) | \(e\left(\frac{412}{1815}\right)\) | \(e\left(\frac{394}{1815}\right)\) | \(e\left(\frac{1607}{1815}\right)\) | \(e\left(\frac{206}{605}\right)\) | \(e\left(\frac{40}{121}\right)\) | \(e\left(\frac{1171}{1815}\right)\) | \(e\left(\frac{1813}{1815}\right)\) | \(e\left(\frac{824}{1815}\right)\) | \(e\left(\frac{28}{605}\right)\) |
| \(\chi_{35937}(586,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{757}{1815}\right)\) | \(e\left(\frac{1514}{1815}\right)\) | \(e\left(\frac{743}{1815}\right)\) | \(e\left(\frac{1174}{1815}\right)\) | \(e\left(\frac{152}{605}\right)\) | \(e\left(\frac{100}{121}\right)\) | \(e\left(\frac{1052}{1815}\right)\) | \(e\left(\frac{116}{1815}\right)\) | \(e\left(\frac{1213}{1815}\right)\) | \(e\left(\frac{191}{605}\right)\) |
| \(\chi_{35937}(631,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1088}{1815}\right)\) | \(e\left(\frac{361}{1815}\right)\) | \(e\left(\frac{1147}{1815}\right)\) | \(e\left(\frac{1016}{1815}\right)\) | \(e\left(\frac{483}{605}\right)\) | \(e\left(\frac{28}{121}\right)\) | \(e\left(\frac{493}{1815}\right)\) | \(e\left(\frac{289}{1815}\right)\) | \(e\left(\frac{722}{1815}\right)\) | \(e\left(\frac{189}{605}\right)\) |
| \(\chi_{35937}(658,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{929}{1815}\right)\) | \(e\left(\frac{43}{1815}\right)\) | \(e\left(\frac{931}{1815}\right)\) | \(e\left(\frac{1388}{1815}\right)\) | \(e\left(\frac{324}{605}\right)\) | \(e\left(\frac{3}{121}\right)\) | \(e\left(\frac{109}{1815}\right)\) | \(e\left(\frac{502}{1815}\right)\) | \(e\left(\frac{86}{1815}\right)\) | \(e\left(\frac{232}{605}\right)\) |
| \(\chi_{35937}(685,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1547}{1815}\right)\) | \(e\left(\frac{1279}{1815}\right)\) | \(e\left(\frac{298}{1815}\right)\) | \(e\left(\frac{764}{1815}\right)\) | \(e\left(\frac{337}{605}\right)\) | \(e\left(\frac{2}{121}\right)\) | \(e\left(\frac{1807}{1815}\right)\) | \(e\left(\frac{496}{1815}\right)\) | \(e\left(\frac{743}{1815}\right)\) | \(e\left(\frac{316}{605}\right)\) |
| \(\chi_{35937}(775,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1396}{1815}\right)\) | \(e\left(\frac{977}{1815}\right)\) | \(e\left(\frac{344}{1815}\right)\) | \(e\left(\frac{1357}{1815}\right)\) | \(e\left(\frac{186}{605}\right)\) | \(e\left(\frac{116}{121}\right)\) | \(e\left(\frac{746}{1815}\right)\) | \(e\left(\frac{938}{1815}\right)\) | \(e\left(\frac{139}{1815}\right)\) | \(e\left(\frac{178}{605}\right)\) |
| \(\chi_{35937}(829,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{733}{1815}\right)\) | \(e\left(\frac{1466}{1815}\right)\) | \(e\left(\frac{1772}{1815}\right)\) | \(e\left(\frac{511}{1815}\right)\) | \(e\left(\frac{128}{605}\right)\) | \(e\left(\frac{46}{121}\right)\) | \(e\left(\frac{1268}{1815}\right)\) | \(e\left(\frac{1244}{1815}\right)\) | \(e\left(\frac{1117}{1815}\right)\) | \(e\left(\frac{129}{605}\right)\) |
| \(\chi_{35937}(883,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1147}{1815}\right)\) | \(e\left(\frac{479}{1815}\right)\) | \(e\left(\frac{1718}{1815}\right)\) | \(e\left(\frac{604}{1815}\right)\) | \(e\left(\frac{542}{605}\right)\) | \(e\left(\frac{70}{121}\right)\) | \(e\left(\frac{1172}{1815}\right)\) | \(e\left(\frac{1751}{1815}\right)\) | \(e\left(\frac{958}{1815}\right)\) | \(e\left(\frac{291}{605}\right)\) |
| \(\chi_{35937}(955,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1004}{1815}\right)\) | \(e\left(\frac{193}{1815}\right)\) | \(e\left(\frac{211}{1815}\right)\) | \(e\left(\frac{1418}{1815}\right)\) | \(e\left(\frac{399}{605}\right)\) | \(e\left(\frac{81}{121}\right)\) | \(e\left(\frac{1249}{1815}\right)\) | \(e\left(\frac{607}{1815}\right)\) | \(e\left(\frac{386}{1815}\right)\) | \(e\left(\frac{577}{605}\right)\) |
| \(\chi_{35937}(982,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1772}{1815}\right)\) | \(e\left(\frac{1729}{1815}\right)\) | \(e\left(\frac{1768}{1815}\right)\) | \(e\left(\frac{854}{1815}\right)\) | \(e\left(\frac{562}{605}\right)\) | \(e\left(\frac{115}{121}\right)\) | \(e\left(\frac{1597}{1815}\right)\) | \(e\left(\frac{811}{1815}\right)\) | \(e\left(\frac{1643}{1815}\right)\) | \(e\left(\frac{141}{605}\right)\) |
| \(\chi_{35937}(1072,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1036}{1815}\right)\) | \(e\left(\frac{257}{1815}\right)\) | \(e\left(\frac{1259}{1815}\right)\) | \(e\left(\frac{487}{1815}\right)\) | \(e\left(\frac{431}{605}\right)\) | \(e\left(\frac{32}{121}\right)\) | \(e\left(\frac{356}{1815}\right)\) | \(e\left(\frac{1523}{1815}\right)\) | \(e\left(\frac{514}{1815}\right)\) | \(e\left(\frac{458}{605}\right)\) |
| \(\chi_{35937}(1126,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1273}{1815}\right)\) | \(e\left(\frac{731}{1815}\right)\) | \(e\left(\frac{1307}{1815}\right)\) | \(e\left(\frac{1}{1815}\right)\) | \(e\left(\frac{63}{605}\right)\) | \(e\left(\frac{51}{121}\right)\) | \(e\left(\frac{38}{1815}\right)\) | \(e\left(\frac{1274}{1815}\right)\) | \(e\left(\frac{1462}{1815}\right)\) | \(e\left(\frac{314}{605}\right)\) |
| \(\chi_{35937}(1153,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{889}{1815}\right)\) | \(e\left(\frac{1778}{1815}\right)\) | \(e\left(\frac{1436}{1815}\right)\) | \(e\left(\frac{283}{1815}\right)\) | \(e\left(\frac{284}{605}\right)\) | \(e\left(\frac{34}{121}\right)\) | \(e\left(\frac{1679}{1815}\right)\) | \(e\left(\frac{1172}{1815}\right)\) | \(e\left(\frac{1741}{1815}\right)\) | \(e\left(\frac{532}{605}\right)\) |
| \(\chi_{35937}(1171,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1796}{1815}\right)\) | \(e\left(\frac{1777}{1815}\right)\) | \(e\left(\frac{739}{1815}\right)\) | \(e\left(\frac{1517}{1815}\right)\) | \(e\left(\frac{586}{605}\right)\) | \(e\left(\frac{48}{121}\right)\) | \(e\left(\frac{1381}{1815}\right)\) | \(e\left(\frac{1498}{1815}\right)\) | \(e\left(\frac{1739}{1815}\right)\) | \(e\left(\frac{203}{605}\right)\) |
| \(\chi_{35937}(1180,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1042}{1815}\right)\) | \(e\left(\frac{269}{1815}\right)\) | \(e\left(\frac{548}{1815}\right)\) | \(e\left(\frac{199}{1815}\right)\) | \(e\left(\frac{437}{605}\right)\) | \(e\left(\frac{106}{121}\right)\) | \(e\left(\frac{302}{1815}\right)\) | \(e\left(\frac{1241}{1815}\right)\) | \(e\left(\frac{538}{1815}\right)\) | \(e\left(\frac{171}{605}\right)\) |
| \(\chi_{35937}(1225,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1013}{1815}\right)\) | \(e\left(\frac{211}{1815}\right)\) | \(e\left(\frac{52}{1815}\right)\) | \(e\left(\frac{986}{1815}\right)\) | \(e\left(\frac{408}{605}\right)\) | \(e\left(\frac{71}{121}\right)\) | \(e\left(\frac{1168}{1815}\right)\) | \(e\left(\frac{184}{1815}\right)\) | \(e\left(\frac{422}{1815}\right)\) | \(e\left(\frac{449}{605}\right)\) |
| \(\chi_{35937}(1252,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{419}{1815}\right)\) | \(e\left(\frac{838}{1815}\right)\) | \(e\left(\frac{1471}{1815}\right)\) | \(e\left(\frac{458}{1815}\right)\) | \(e\left(\frac{419}{605}\right)\) | \(e\left(\frac{5}{121}\right)\) | \(e\left(\frac{1069}{1815}\right)\) | \(e\left(\frac{877}{1815}\right)\) | \(e\left(\frac{1676}{1815}\right)\) | \(e\left(\frac{427}{605}\right)\) |