from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(85600, base_ring=CyclotomicField(2120))
M = H._module
chi = DirichletCharacter(H, M([0,1855,2014,280]))
chi.galois_orbit()
[g,chi] = znchar(Mod(13,85600))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(85600\) | |
| Conductor: | \(85600\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2120\) | 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: | $\Q(\zeta_{2120})$ |
| Fixed field: | Number field defined by a degree 2120 polynomial (not computed) |
First 23 of 832 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{85600}(13,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1103}{2120}\right)\) | \(e\left(\frac{19}{106}\right)\) | \(e\left(\frac{43}{1060}\right)\) | \(e\left(\frac{1019}{2120}\right)\) | \(e\left(\frac{51}{2120}\right)\) | \(e\left(\frac{721}{1060}\right)\) | \(e\left(\frac{1117}{2120}\right)\) | \(e\left(\frac{1483}{2120}\right)\) | \(e\left(\frac{471}{530}\right)\) | \(e\left(\frac{1189}{2120}\right)\) |
| \(\chi_{85600}(37,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1313}{2120}\right)\) | \(e\left(\frac{97}{106}\right)\) | \(e\left(\frac{253}{1060}\right)\) | \(e\left(\frac{1509}{2120}\right)\) | \(e\left(\frac{941}{2120}\right)\) | \(e\left(\frac{791}{1060}\right)\) | \(e\left(\frac{1987}{2120}\right)\) | \(e\left(\frac{1133}{2120}\right)\) | \(e\left(\frac{491}{530}\right)\) | \(e\left(\frac{1819}{2120}\right)\) |
| \(\chi_{85600}(117,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{261}{2120}\right)\) | \(e\left(\frac{103}{106}\right)\) | \(e\left(\frac{261}{1060}\right)\) | \(e\left(\frac{1033}{2120}\right)\) | \(e\left(\frac{137}{2120}\right)\) | \(e\left(\frac{87}{1060}\right)\) | \(e\left(\frac{839}{2120}\right)\) | \(e\left(\frac{201}{2120}\right)\) | \(e\left(\frac{517}{530}\right)\) | \(e\left(\frac{783}{2120}\right)\) |
| \(\chi_{85600}(197,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1009}{2120}\right)\) | \(e\left(\frac{81}{106}\right)\) | \(e\left(\frac{1009}{1060}\right)\) | \(e\left(\frac{517}{2120}\right)\) | \(e\left(\frac{1813}{2120}\right)\) | \(e\left(\frac{1043}{1060}\right)\) | \(e\left(\frac{1091}{2120}\right)\) | \(e\left(\frac{509}{2120}\right)\) | \(e\left(\frac{33}{530}\right)\) | \(e\left(\frac{907}{2120}\right)\) |
| \(\chi_{85600}(253,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{99}{2120}\right)\) | \(e\left(\frac{61}{106}\right)\) | \(e\left(\frac{99}{1060}\right)\) | \(e\left(\frac{1927}{2120}\right)\) | \(e\left(\frac{783}{2120}\right)\) | \(e\left(\frac{33}{1060}\right)\) | \(e\left(\frac{1561}{2120}\right)\) | \(e\left(\frac{1319}{2120}\right)\) | \(e\left(\frac{123}{530}\right)\) | \(e\left(\frac{297}{2120}\right)\) |
| \(\chi_{85600}(333,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{471}{2120}\right)\) | \(e\left(\frac{75}{106}\right)\) | \(e\left(\frac{471}{1060}\right)\) | \(e\left(\frac{1523}{2120}\right)\) | \(e\left(\frac{1027}{2120}\right)\) | \(e\left(\frac{157}{1060}\right)\) | \(e\left(\frac{1709}{2120}\right)\) | \(e\left(\frac{1971}{2120}\right)\) | \(e\left(\frac{7}{530}\right)\) | \(e\left(\frac{1413}{2120}\right)\) |
| \(\chi_{85600}(413,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{83}{2120}\right)\) | \(e\left(\frac{49}{106}\right)\) | \(e\left(\frac{83}{1060}\right)\) | \(e\left(\frac{759}{2120}\right)\) | \(e\left(\frac{271}{2120}\right)\) | \(e\left(\frac{381}{1060}\right)\) | \(e\left(\frac{1737}{2120}\right)\) | \(e\left(\frac{1063}{2120}\right)\) | \(e\left(\frac{71}{530}\right)\) | \(e\left(\frac{249}{2120}\right)\) |
| \(\chi_{85600}(437,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1013}{2120}\right)\) | \(e\left(\frac{31}{106}\right)\) | \(e\left(\frac{1013}{1060}\right)\) | \(e\left(\frac{809}{2120}\right)\) | \(e\left(\frac{881}{2120}\right)\) | \(e\left(\frac{691}{1060}\right)\) | \(e\left(\frac{1047}{2120}\right)\) | \(e\left(\frac{1633}{2120}\right)\) | \(e\left(\frac{311}{530}\right)\) | \(e\left(\frac{919}{2120}\right)\) |
| \(\chi_{85600}(517,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{81}{2120}\right)\) | \(e\left(\frac{21}{106}\right)\) | \(e\left(\frac{81}{1060}\right)\) | \(e\left(\frac{613}{2120}\right)\) | \(e\left(\frac{1797}{2120}\right)\) | \(e\left(\frac{27}{1060}\right)\) | \(e\left(\frac{699}{2120}\right)\) | \(e\left(\frac{501}{2120}\right)\) | \(e\left(\frac{197}{530}\right)\) | \(e\left(\frac{243}{2120}\right)\) |
| \(\chi_{85600}(597,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{669}{2120}\right)\) | \(e\left(\frac{91}{106}\right)\) | \(e\left(\frac{669}{1060}\right)\) | \(e\left(\frac{1137}{2120}\right)\) | \(e\left(\frac{473}{2120}\right)\) | \(e\left(\frac{223}{1060}\right)\) | \(e\left(\frac{591}{2120}\right)\) | \(e\left(\frac{369}{2120}\right)\) | \(e\left(\frac{253}{530}\right)\) | \(e\left(\frac{2007}{2120}\right)\) |
| \(\chi_{85600}(653,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1279}{2120}\right)\) | \(e\left(\frac{45}{106}\right)\) | \(e\left(\frac{219}{1060}\right)\) | \(e\left(\frac{1147}{2120}\right)\) | \(e\left(\frac{1443}{2120}\right)\) | \(e\left(\frac{73}{1060}\right)\) | \(e\left(\frac{1301}{2120}\right)\) | \(e\left(\frac{59}{2120}\right)\) | \(e\left(\frac{513}{530}\right)\) | \(e\left(\frac{1717}{2120}\right)\) |
| \(\chi_{85600}(677,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{337}{2120}\right)\) | \(e\left(\frac{1}{106}\right)\) | \(e\left(\frac{337}{1060}\right)\) | \(e\left(\frac{221}{2120}\right)\) | \(e\left(\frac{1509}{2120}\right)\) | \(e\left(\frac{819}{1060}\right)\) | \(e\left(\frac{3}{2120}\right)\) | \(e\left(\frac{357}{2120}\right)\) | \(e\left(\frac{499}{530}\right)\) | \(e\left(\frac{1011}{2120}\right)\) |
| \(\chi_{85600}(813,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{503}{2120}\right)\) | \(e\left(\frac{99}{106}\right)\) | \(e\left(\frac{503}{1060}\right)\) | \(e\left(\frac{1739}{2120}\right)\) | \(e\left(\frac{2051}{2120}\right)\) | \(e\left(\frac{521}{1060}\right)\) | \(e\left(\frac{1357}{2120}\right)\) | \(e\left(\frac{363}{2120}\right)\) | \(e\left(\frac{111}{530}\right)\) | \(e\left(\frac{1509}{2120}\right)\) |
| \(\chi_{85600}(917,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{61}{2120}\right)\) | \(e\left(\frac{59}{106}\right)\) | \(e\left(\frac{61}{1060}\right)\) | \(e\left(\frac{1273}{2120}\right)\) | \(e\left(\frac{97}{2120}\right)\) | \(e\left(\frac{727}{1060}\right)\) | \(e\left(\frac{919}{2120}\right)\) | \(e\left(\frac{1241}{2120}\right)\) | \(e\left(\frac{397}{530}\right)\) | \(e\left(\frac{183}{2120}\right)\) |
| \(\chi_{85600}(973,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{367}{2120}\right)\) | \(e\left(\frac{103}{106}\right)\) | \(e\left(\frac{367}{1060}\right)\) | \(e\left(\frac{291}{2120}\right)\) | \(e\left(\frac{1939}{2120}\right)\) | \(e\left(\frac{829}{1060}\right)\) | \(e\left(\frac{733}{2120}\right)\) | \(e\left(\frac{307}{2120}\right)\) | \(e\left(\frac{199}{530}\right)\) | \(e\left(\frac{1101}{2120}\right)\) |
| \(\chi_{85600}(997,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{289}{2120}\right)\) | \(e\left(\frac{71}{106}\right)\) | \(e\left(\frac{289}{1060}\right)\) | \(e\left(\frac{957}{2120}\right)\) | \(e\left(\frac{2093}{2120}\right)\) | \(e\left(\frac{803}{1060}\right)\) | \(e\left(\frac{531}{2120}\right)\) | \(e\left(\frac{1709}{2120}\right)\) | \(e\left(\frac{343}{530}\right)\) | \(e\left(\frac{867}{2120}\right)\) |
| \(\chi_{85600}(1053,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1539}{2120}\right)\) | \(e\left(\frac{81}{106}\right)\) | \(e\left(\frac{479}{1060}\right)\) | \(e\left(\frac{1047}{2120}\right)\) | \(e\left(\frac{223}{2120}\right)\) | \(e\left(\frac{513}{1060}\right)\) | \(e\left(\frac{561}{2120}\right)\) | \(e\left(\frac{1039}{2120}\right)\) | \(e\left(\frac{33}{530}\right)\) | \(e\left(\frac{377}{2120}\right)\) |
| \(\chi_{85600}(1213,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1163}{2120}\right)\) | \(e\left(\frac{11}{106}\right)\) | \(e\left(\frac{103}{1060}\right)\) | \(e\left(\frac{1159}{2120}\right)\) | \(e\left(\frac{911}{2120}\right)\) | \(e\left(\frac{741}{1060}\right)\) | \(e\left(\frac{457}{2120}\right)\) | \(e\left(\frac{1383}{2120}\right)\) | \(e\left(\frac{401}{530}\right)\) | \(e\left(\frac{1369}{2120}\right)\) |
| \(\chi_{85600}(1317,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1441}{2120}\right)\) | \(e\left(\frac{87}{106}\right)\) | \(e\left(\frac{381}{1060}\right)\) | \(e\left(\frac{253}{2120}\right)\) | \(e\left(\frac{797}{2120}\right)\) | \(e\left(\frac{127}{1060}\right)\) | \(e\left(\frac{579}{2120}\right)\) | \(e\left(\frac{1061}{2120}\right)\) | \(e\left(\frac{377}{530}\right)\) | \(e\left(\frac{83}{2120}\right)\) |
| \(\chi_{85600}(1373,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{187}{2120}\right)\) | \(e\left(\frac{21}{106}\right)\) | \(e\left(\frac{187}{1060}\right)\) | \(e\left(\frac{1991}{2120}\right)\) | \(e\left(\frac{1479}{2120}\right)\) | \(e\left(\frac{769}{1060}\right)\) | \(e\left(\frac{593}{2120}\right)\) | \(e\left(\frac{607}{2120}\right)\) | \(e\left(\frac{409}{530}\right)\) | \(e\left(\frac{561}{2120}\right)\) |
| \(\chi_{85600}(1453,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1199}{2120}\right)\) | \(e\left(\frac{91}{106}\right)\) | \(e\left(\frac{139}{1060}\right)\) | \(e\left(\frac{1667}{2120}\right)\) | \(e\left(\frac{1003}{2120}\right)\) | \(e\left(\frac{753}{1060}\right)\) | \(e\left(\frac{61}{2120}\right)\) | \(e\left(\frac{899}{2120}\right)\) | \(e\left(\frac{253}{530}\right)\) | \(e\left(\frac{1477}{2120}\right)\) |
| \(\chi_{85600}(1477,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{737}{2120}\right)\) | \(e\left(\frac{89}{106}\right)\) | \(e\left(\frac{737}{1060}\right)\) | \(e\left(\frac{1861}{2120}\right)\) | \(e\left(\frac{1589}{2120}\right)\) | \(e\left(\frac{599}{1060}\right)\) | \(e\left(\frac{1963}{2120}\right)\) | \(e\left(\frac{397}{2120}\right)\) | \(e\left(\frac{209}{530}\right)\) | \(e\left(\frac{91}{2120}\right)\) |
| \(\chi_{85600}(1533,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1291}{2120}\right)\) | \(e\left(\frac{1}{106}\right)\) | \(e\left(\frac{231}{1060}\right)\) | \(e\left(\frac{2023}{2120}\right)\) | \(e\left(\frac{767}{2120}\right)\) | \(e\left(\frac{77}{1060}\right)\) | \(e\left(\frac{1169}{2120}\right)\) | \(e\left(\frac{1311}{2120}\right)\) | \(e\left(\frac{287}{530}\right)\) | \(e\left(\frac{1753}{2120}\right)\) |