from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, base_ring=CyclotomicField(420))
M = H._module
chi = DirichletCharacter(H, M([0,220,231]))
chi.galois_orbit()
[g,chi] = znchar(Mod(46,6027))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(6027\) | |
| Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(420\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 2009.cj | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | $\Q(\zeta_{420})$ |
| Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
First 31 of 96 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{6027}(46,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{193}{210}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{61}{210}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{22}{105}\right)\) | \(e\left(\frac{253}{420}\right)\) | \(e\left(\frac{47}{140}\right)\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{103}{420}\right)\) | \(e\left(\frac{17}{60}\right)\) |
| \(\chi_{6027}(121,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{210}\right)\) | \(e\left(\frac{89}{105}\right)\) | \(e\left(\frac{113}{210}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{101}{105}\right)\) | \(e\left(\frac{269}{420}\right)\) | \(e\left(\frac{71}{140}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{239}{420}\right)\) | \(e\left(\frac{1}{60}\right)\) |
| \(\chi_{6027}(172,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{127}{210}\right)\) | \(e\left(\frac{22}{105}\right)\) | \(e\left(\frac{199}{210}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{58}{105}\right)\) | \(e\left(\frac{37}{420}\right)\) | \(e\left(\frac{3}{140}\right)\) | \(e\left(\frac{44}{105}\right)\) | \(e\left(\frac{367}{420}\right)\) | \(e\left(\frac{53}{60}\right)\) |
| \(\chi_{6027}(184,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{191}{210}\right)\) | \(e\left(\frac{86}{105}\right)\) | \(e\left(\frac{167}{210}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{74}{105}\right)\) | \(e\left(\frac{11}{420}\right)\) | \(e\left(\frac{69}{140}\right)\) | \(e\left(\frac{67}{105}\right)\) | \(e\left(\frac{41}{420}\right)\) | \(e\left(\frac{19}{60}\right)\) |
| \(\chi_{6027}(289,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{179}{210}\right)\) | \(e\left(\frac{74}{105}\right)\) | \(e\left(\frac{173}{210}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{239}{420}\right)\) | \(e\left(\frac{61}{140}\right)\) | \(e\left(\frac{43}{105}\right)\) | \(e\left(\frac{89}{420}\right)\) | \(e\left(\frac{31}{60}\right)\) |
| \(\chi_{6027}(415,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{173}{210}\right)\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{71}{210}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{353}{420}\right)\) | \(e\left(\frac{127}{140}\right)\) | \(e\left(\frac{31}{105}\right)\) | \(e\left(\frac{323}{420}\right)\) | \(e\left(\frac{37}{60}\right)\) |
| \(\chi_{6027}(487,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{193}{210}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{61}{210}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{22}{105}\right)\) | \(e\left(\frac{43}{420}\right)\) | \(e\left(\frac{117}{140}\right)\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{313}{420}\right)\) | \(e\left(\frac{47}{60}\right)\) |
| \(\chi_{6027}(541,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{167}{210}\right)\) | \(e\left(\frac{62}{105}\right)\) | \(e\left(\frac{179}{210}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{257}{420}\right)\) | \(e\left(\frac{123}{140}\right)\) | \(e\left(\frac{19}{105}\right)\) | \(e\left(\frac{347}{420}\right)\) | \(e\left(\frac{13}{60}\right)\) |
| \(\chi_{6027}(613,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{169}{210}\right)\) | \(e\left(\frac{64}{105}\right)\) | \(e\left(\frac{73}{210}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{16}{105}\right)\) | \(e\left(\frac{289}{420}\right)\) | \(e\left(\frac{31}{140}\right)\) | \(e\left(\frac{23}{105}\right)\) | \(e\left(\frac{199}{420}\right)\) | \(e\left(\frac{41}{60}\right)\) |
| \(\chi_{6027}(676,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{210}\right)\) | \(e\left(\frac{31}{105}\right)\) | \(e\left(\frac{37}{210}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{391}{420}\right)\) | \(e\left(\frac{9}{140}\right)\) | \(e\left(\frac{62}{105}\right)\) | \(e\left(\frac{121}{420}\right)\) | \(e\left(\frac{59}{60}\right)\) |
| \(\chi_{6027}(718,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{121}{210}\right)\) | \(e\left(\frac{16}{105}\right)\) | \(e\left(\frac{97}{210}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{4}{105}\right)\) | \(e\left(\frac{361}{420}\right)\) | \(e\left(\frac{139}{140}\right)\) | \(e\left(\frac{32}{105}\right)\) | \(e\left(\frac{391}{420}\right)\) | \(e\left(\frac{29}{60}\right)\) |
| \(\chi_{6027}(730,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{137}{210}\right)\) | \(e\left(\frac{32}{105}\right)\) | \(e\left(\frac{89}{210}\right)\) | \(e\left(\frac{67}{70}\right)\) | \(e\left(\frac{8}{105}\right)\) | \(e\left(\frac{407}{420}\right)\) | \(e\left(\frac{33}{140}\right)\) | \(e\left(\frac{64}{105}\right)\) | \(e\left(\frac{257}{420}\right)\) | \(e\left(\frac{43}{60}\right)\) |
| \(\chi_{6027}(781,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{109}{210}\right)\) | \(e\left(\frac{4}{105}\right)\) | \(e\left(\frac{103}{210}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{1}{105}\right)\) | \(e\left(\frac{379}{420}\right)\) | \(e\left(\frac{61}{140}\right)\) | \(e\left(\frac{8}{105}\right)\) | \(e\left(\frac{229}{420}\right)\) | \(e\left(\frac{11}{60}\right)\) |
| \(\chi_{6027}(856,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{173}{210}\right)\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{71}{210}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{143}{420}\right)\) | \(e\left(\frac{57}{140}\right)\) | \(e\left(\frac{31}{105}\right)\) | \(e\left(\frac{113}{420}\right)\) | \(e\left(\frac{7}{60}\right)\) |
| \(\chi_{6027}(907,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{210}\right)\) | \(e\left(\frac{43}{105}\right)\) | \(e\left(\frac{31}{210}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{37}{105}\right)\) | \(e\left(\frac{373}{420}\right)\) | \(e\left(\frac{87}{140}\right)\) | \(e\left(\frac{86}{105}\right)\) | \(e\left(\frac{283}{420}\right)\) | \(e\left(\frac{17}{60}\right)\) |
| \(\chi_{6027}(982,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{209}{210}\right)\) | \(e\left(\frac{104}{105}\right)\) | \(e\left(\frac{53}{210}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{26}{105}\right)\) | \(e\left(\frac{89}{420}\right)\) | \(e\left(\frac{11}{140}\right)\) | \(e\left(\frac{103}{105}\right)\) | \(e\left(\frac{179}{420}\right)\) | \(e\left(\frac{1}{60}\right)\) |
| \(\chi_{6027}(1033,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{187}{210}\right)\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{169}{210}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{157}{420}\right)\) | \(e\left(\frac{43}{140}\right)\) | \(e\left(\frac{59}{105}\right)\) | \(e\left(\frac{127}{420}\right)\) | \(e\left(\frac{53}{60}\right)\) |
| \(\chi_{6027}(1045,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{101}{210}\right)\) | \(e\left(\frac{101}{105}\right)\) | \(e\left(\frac{107}{210}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{104}{105}\right)\) | \(e\left(\frac{251}{420}\right)\) | \(e\left(\frac{9}{140}\right)\) | \(e\left(\frac{97}{105}\right)\) | \(e\left(\frac{401}{420}\right)\) | \(e\left(\frac{19}{60}\right)\) |
| \(\chi_{6027}(1087,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{71}{210}\right)\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{17}{210}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{44}{105}\right)\) | \(e\left(\frac{401}{420}\right)\) | \(e\left(\frac{59}{140}\right)\) | \(e\left(\frac{37}{105}\right)\) | \(e\left(\frac{311}{420}\right)\) | \(e\left(\frac{49}{60}\right)\) |
| \(\chi_{6027}(1150,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{210}\right)\) | \(e\left(\frac{89}{105}\right)\) | \(e\left(\frac{113}{210}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{101}{105}\right)\) | \(e\left(\frac{59}{420}\right)\) | \(e\left(\frac{1}{140}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{29}{420}\right)\) | \(e\left(\frac{31}{60}\right)\) |
| \(\chi_{6027}(1222,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{67}{210}\right)\) | \(e\left(\frac{67}{105}\right)\) | \(e\left(\frac{19}{210}\right)\) | \(e\left(\frac{67}{70}\right)\) | \(e\left(\frac{43}{105}\right)\) | \(e\left(\frac{127}{420}\right)\) | \(e\left(\frac{33}{140}\right)\) | \(e\left(\frac{29}{105}\right)\) | \(e\left(\frac{397}{420}\right)\) | \(e\left(\frac{23}{60}\right)\) |
| \(\chi_{6027}(1276,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{83}{210}\right)\) | \(e\left(\frac{83}{105}\right)\) | \(e\left(\frac{11}{210}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{173}{420}\right)\) | \(e\left(\frac{67}{140}\right)\) | \(e\left(\frac{61}{105}\right)\) | \(e\left(\frac{263}{420}\right)\) | \(e\left(\frac{37}{60}\right)\) |
| \(\chi_{6027}(1348,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{210}\right)\) | \(e\left(\frac{43}{105}\right)\) | \(e\left(\frac{31}{210}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{37}{105}\right)\) | \(e\left(\frac{163}{420}\right)\) | \(e\left(\frac{17}{140}\right)\) | \(e\left(\frac{86}{105}\right)\) | \(e\left(\frac{73}{420}\right)\) | \(e\left(\frac{47}{60}\right)\) |
| \(\chi_{6027}(1474,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{210}\right)\) | \(e\left(\frac{19}{105}\right)\) | \(e\left(\frac{43}{210}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{31}{105}\right)\) | \(e\left(\frac{409}{420}\right)\) | \(e\left(\frac{71}{140}\right)\) | \(e\left(\frac{38}{105}\right)\) | \(e\left(\frac{379}{420}\right)\) | \(e\left(\frac{41}{60}\right)\) |
| \(\chi_{6027}(1579,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{181}{210}\right)\) | \(e\left(\frac{76}{105}\right)\) | \(e\left(\frac{67}{210}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{19}{105}\right)\) | \(e\left(\frac{61}{420}\right)\) | \(e\left(\frac{39}{140}\right)\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{151}{420}\right)\) | \(e\left(\frac{29}{60}\right)\) |
| \(\chi_{6027}(1591,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{210}\right)\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{29}{210}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{38}{105}\right)\) | \(e\left(\frac{227}{420}\right)\) | \(e\left(\frac{113}{140}\right)\) | \(e\left(\frac{94}{105}\right)\) | \(e\left(\frac{197}{420}\right)\) | \(e\left(\frac{43}{60}\right)\) |
| \(\chi_{6027}(1642,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{169}{210}\right)\) | \(e\left(\frac{64}{105}\right)\) | \(e\left(\frac{73}{210}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{16}{105}\right)\) | \(e\left(\frac{79}{420}\right)\) | \(e\left(\frac{101}{140}\right)\) | \(e\left(\frac{23}{105}\right)\) | \(e\left(\frac{409}{420}\right)\) | \(e\left(\frac{11}{60}\right)\) |
| \(\chi_{6027}(1717,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{83}{210}\right)\) | \(e\left(\frac{83}{105}\right)\) | \(e\left(\frac{11}{210}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{383}{420}\right)\) | \(e\left(\frac{137}{140}\right)\) | \(e\left(\frac{61}{105}\right)\) | \(e\left(\frac{53}{420}\right)\) | \(e\left(\frac{7}{60}\right)\) |
| \(\chi_{6027}(1768,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{103}{210}\right)\) | \(e\left(\frac{103}{105}\right)\) | \(e\left(\frac{1}{210}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{52}{105}\right)\) | \(e\left(\frac{73}{420}\right)\) | \(e\left(\frac{127}{140}\right)\) | \(e\left(\frac{101}{105}\right)\) | \(e\left(\frac{43}{420}\right)\) | \(e\left(\frac{17}{60}\right)\) |
| \(\chi_{6027}(1894,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{210}\right)\) | \(e\left(\frac{37}{105}\right)\) | \(e\left(\frac{139}{210}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{277}{420}\right)\) | \(e\left(\frac{83}{140}\right)\) | \(e\left(\frac{74}{105}\right)\) | \(e\left(\frac{307}{420}\right)\) | \(e\left(\frac{53}{60}\right)\) |
| \(\chi_{6027}(1906,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{210}\right)\) | \(e\left(\frac{11}{105}\right)\) | \(e\left(\frac{47}{210}\right)\) | \(e\left(\frac{11}{70}\right)\) | \(e\left(\frac{29}{105}\right)\) | \(e\left(\frac{71}{420}\right)\) | \(e\left(\frac{89}{140}\right)\) | \(e\left(\frac{22}{105}\right)\) | \(e\left(\frac{341}{420}\right)\) | \(e\left(\frac{19}{60}\right)\) |