from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(35937, base_ring=CyclotomicField(1210))
M = H._module
chi = DirichletCharacter(H, M([0,559]))
chi.galois_orbit()
[g,chi] = znchar(Mod(28,35937))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(35937\) | |
| Conductor: | \(1331\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 1331.l | 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: | $\Q(\zeta_{605})$ |
| Fixed field: | Number field defined by a degree 1210 polynomial (not computed) |
First 20 of 440 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{35937}(28,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{559}{1210}\right)\) | \(e\left(\frac{559}{605}\right)\) | \(e\left(\frac{3}{605}\right)\) | \(e\left(\frac{393}{1210}\right)\) | \(e\left(\frac{467}{1210}\right)\) | \(e\left(\frac{113}{242}\right)\) | \(e\left(\frac{1019}{1210}\right)\) | \(e\left(\frac{476}{605}\right)\) | \(e\left(\frac{513}{605}\right)\) | \(e\left(\frac{551}{1210}\right)\) |
| \(\chi_{35937}(217,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{313}{1210}\right)\) | \(e\left(\frac{313}{605}\right)\) | \(e\left(\frac{361}{605}\right)\) | \(e\left(\frac{101}{1210}\right)\) | \(e\left(\frac{939}{1210}\right)\) | \(e\left(\frac{207}{242}\right)\) | \(e\left(\frac{813}{1210}\right)\) | \(e\left(\frac{207}{605}\right)\) | \(e\left(\frac{21}{605}\right)\) | \(e\left(\frac{157}{1210}\right)\) |
| \(\chi_{35937}(244,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{991}{1210}\right)\) | \(e\left(\frac{386}{605}\right)\) | \(e\left(\frac{422}{605}\right)\) | \(e\left(\frac{227}{1210}\right)\) | \(e\left(\frac{553}{1210}\right)\) | \(e\left(\frac{125}{242}\right)\) | \(e\left(\frac{761}{1210}\right)\) | \(e\left(\frac{4}{605}\right)\) | \(e\left(\frac{167}{605}\right)\) | \(e\left(\frac{269}{1210}\right)\) |
| \(\chi_{35937}(271,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{457}{1210}\right)\) | \(e\left(\frac{457}{605}\right)\) | \(e\left(\frac{299}{605}\right)\) | \(e\left(\frac{449}{1210}\right)\) | \(e\left(\frac{161}{1210}\right)\) | \(e\left(\frac{211}{242}\right)\) | \(e\left(\frac{727}{1210}\right)\) | \(e\left(\frac{453}{605}\right)\) | \(e\left(\frac{309}{605}\right)\) | \(e\left(\frac{63}{1210}\right)\) |
| \(\chi_{35937}(325,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{359}{1210}\right)\) | \(e\left(\frac{359}{605}\right)\) | \(e\left(\frac{358}{605}\right)\) | \(e\left(\frac{313}{1210}\right)\) | \(e\left(\frac{1077}{1210}\right)\) | \(e\left(\frac{215}{242}\right)\) | \(e\left(\frac{399}{1210}\right)\) | \(e\left(\frac{336}{605}\right)\) | \(e\left(\frac{113}{605}\right)\) | \(e\left(\frac{211}{1210}\right)\) |
| \(\chi_{35937}(514,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{713}{1210}\right)\) | \(e\left(\frac{108}{605}\right)\) | \(e\left(\frac{256}{605}\right)\) | \(e\left(\frac{261}{1210}\right)\) | \(e\left(\frac{929}{1210}\right)\) | \(e\left(\frac{3}{242}\right)\) | \(e\left(\frac{843}{1210}\right)\) | \(e\left(\frac{487}{605}\right)\) | \(e\left(\frac{216}{605}\right)\) | \(e\left(\frac{837}{1210}\right)\) |
| \(\chi_{35937}(541,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{61}{1210}\right)\) | \(e\left(\frac{61}{605}\right)\) | \(e\left(\frac{167}{605}\right)\) | \(e\left(\frac{97}{1210}\right)\) | \(e\left(\frac{183}{1210}\right)\) | \(e\left(\frac{79}{242}\right)\) | \(e\left(\frac{661}{1210}\right)\) | \(e\left(\frac{79}{605}\right)\) | \(e\left(\frac{122}{605}\right)\) | \(e\left(\frac{19}{1210}\right)\) |
| \(\chi_{35937}(568,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{207}{1210}\right)\) | \(e\left(\frac{207}{605}\right)\) | \(e\left(\frac{289}{605}\right)\) | \(e\left(\frac{349}{1210}\right)\) | \(e\left(\frac{621}{1210}\right)\) | \(e\left(\frac{157}{242}\right)\) | \(e\left(\frac{557}{1210}\right)\) | \(e\left(\frac{278}{605}\right)\) | \(e\left(\frac{414}{605}\right)\) | \(e\left(\frac{243}{1210}\right)\) |
| \(\chi_{35937}(622,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{379}{1210}\right)\) | \(e\left(\frac{379}{605}\right)\) | \(e\left(\frac{383}{605}\right)\) | \(e\left(\frac{563}{1210}\right)\) | \(e\left(\frac{1137}{1210}\right)\) | \(e\left(\frac{229}{242}\right)\) | \(e\left(\frac{219}{1210}\right)\) | \(e\left(\frac{471}{605}\right)\) | \(e\left(\frac{153}{605}\right)\) | \(e\left(\frac{971}{1210}\right)\) |
| \(\chi_{35937}(811,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{783}{1210}\right)\) | \(e\left(\frac{178}{605}\right)\) | \(e\left(\frac{41}{605}\right)\) | \(e\left(\frac{531}{1210}\right)\) | \(e\left(\frac{1139}{1210}\right)\) | \(e\left(\frac{173}{242}\right)\) | \(e\left(\frac{213}{1210}\right)\) | \(e\left(\frac{52}{605}\right)\) | \(e\left(\frac{356}{605}\right)\) | \(e\left(\frac{1077}{1210}\right)\) |
| \(\chi_{35937}(865,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1057}{1210}\right)\) | \(e\left(\frac{452}{605}\right)\) | \(e\left(\frac{444}{605}\right)\) | \(e\left(\frac{689}{1210}\right)\) | \(e\left(\frac{751}{1210}\right)\) | \(e\left(\frac{147}{242}\right)\) | \(e\left(\frac{167}{1210}\right)\) | \(e\left(\frac{268}{605}\right)\) | \(e\left(\frac{299}{605}\right)\) | \(e\left(\frac{1083}{1210}\right)\) |
| \(\chi_{35937}(919,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{619}{1210}\right)\) | \(e\left(\frac{14}{605}\right)\) | \(e\left(\frac{78}{605}\right)\) | \(e\left(\frac{1143}{1210}\right)\) | \(e\left(\frac{647}{1210}\right)\) | \(e\left(\frac{155}{242}\right)\) | \(e\left(\frac{479}{1210}\right)\) | \(e\left(\frac{276}{605}\right)\) | \(e\left(\frac{28}{605}\right)\) | \(e\left(\frac{411}{1210}\right)\) |
| \(\chi_{35937}(1108,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{523}{1210}\right)\) | \(e\left(\frac{523}{605}\right)\) | \(e\left(\frac{321}{605}\right)\) | \(e\left(\frac{911}{1210}\right)\) | \(e\left(\frac{359}{1210}\right)\) | \(e\left(\frac{233}{242}\right)\) | \(e\left(\frac{133}{1210}\right)\) | \(e\left(\frac{112}{605}\right)\) | \(e\left(\frac{441}{605}\right)\) | \(e\left(\frac{877}{1210}\right)\) |
| \(\chi_{35937}(1135,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{511}{1210}\right)\) | \(e\left(\frac{511}{605}\right)\) | \(e\left(\frac{427}{605}\right)\) | \(e\left(\frac{277}{1210}\right)\) | \(e\left(\frac{323}{1210}\right)\) | \(e\left(\frac{31}{242}\right)\) | \(e\left(\frac{241}{1210}\right)\) | \(e\left(\frac{394}{605}\right)\) | \(e\left(\frac{417}{605}\right)\) | \(e\left(\frac{179}{1210}\right)\) |
| \(\chi_{35937}(1162,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{587}{1210}\right)\) | \(e\left(\frac{587}{605}\right)\) | \(e\left(\frac{159}{605}\right)\) | \(e\left(\frac{259}{1210}\right)\) | \(e\left(\frac{551}{1210}\right)\) | \(e\left(\frac{181}{242}\right)\) | \(e\left(\frac{767}{1210}\right)\) | \(e\left(\frac{423}{605}\right)\) | \(e\left(\frac{569}{605}\right)\) | \(e\left(\frac{163}{1210}\right)\) |
| \(\chi_{35937}(1216,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1079}{1210}\right)\) | \(e\left(\frac{474}{605}\right)\) | \(e\left(\frac{48}{605}\right)\) | \(e\left(\frac{843}{1210}\right)\) | \(e\left(\frac{817}{1210}\right)\) | \(e\left(\frac{235}{242}\right)\) | \(e\left(\frac{1179}{1210}\right)\) | \(e\left(\frac{356}{605}\right)\) | \(e\left(\frac{343}{605}\right)\) | \(e\left(\frac{951}{1210}\right)\) |
| \(\chi_{35937}(1405,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1143}{1210}\right)\) | \(e\left(\frac{538}{605}\right)\) | \(e\left(\frac{491}{605}\right)\) | \(e\left(\frac{191}{1210}\right)\) | \(e\left(\frac{1009}{1210}\right)\) | \(e\left(\frac{183}{242}\right)\) | \(e\left(\frac{603}{1210}\right)\) | \(e\left(\frac{62}{605}\right)\) | \(e\left(\frac{471}{605}\right)\) | \(e\left(\frac{237}{1210}\right)\) |
| \(\chi_{35937}(1432,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{681}{1210}\right)\) | \(e\left(\frac{76}{605}\right)\) | \(e\left(\frac{337}{605}\right)\) | \(e\left(\frac{587}{1210}\right)\) | \(e\left(\frac{833}{1210}\right)\) | \(e\left(\frac{29}{242}\right)\) | \(e\left(\frac{1131}{1210}\right)\) | \(e\left(\frac{29}{605}\right)\) | \(e\left(\frac{152}{605}\right)\) | \(e\left(\frac{589}{1210}\right)\) |
| \(\chi_{35937}(1459,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{7}{1210}\right)\) | \(e\left(\frac{7}{605}\right)\) | \(e\left(\frac{39}{605}\right)\) | \(e\left(\frac{269}{1210}\right)\) | \(e\left(\frac{21}{1210}\right)\) | \(e\left(\frac{17}{242}\right)\) | \(e\left(\frac{1147}{1210}\right)\) | \(e\left(\frac{138}{605}\right)\) | \(e\left(\frac{14}{605}\right)\) | \(e\left(\frac{1113}{1210}\right)\) |
| \(\chi_{35937}(1513,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{549}{1210}\right)\) | \(e\left(\frac{549}{605}\right)\) | \(e\left(\frac{293}{605}\right)\) | \(e\left(\frac{873}{1210}\right)\) | \(e\left(\frac{437}{1210}\right)\) | \(e\left(\frac{227}{242}\right)\) | \(e\left(\frac{1109}{1210}\right)\) | \(e\left(\frac{106}{605}\right)\) | \(e\left(\frac{493}{605}\right)\) | \(e\left(\frac{171}{1210}\right)\) |