from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4235, base_ring=CyclotomicField(330))
M = H._module
chi = DirichletCharacter(H, M([0,275,306]))
chi.galois_orbit()
[g,chi] = znchar(Mod(26,4235))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(4235\) | |
Conductor: | \(847\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from 847.bd | 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: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
First 31 of 80 characters in Galois orbit
Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(12\) | \(13\) | \(16\) | \(17\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{4235}(26,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{98}{165}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{31}{165}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{17}{110}\right)\) | \(e\left(\frac{62}{165}\right)\) | \(e\left(\frac{89}{330}\right)\) |
\(\chi_{4235}(31,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{19}{165}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{38}{165}\right)\) | \(e\left(\frac{9}{110}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{76}{165}\right)\) | \(e\left(\frac{157}{330}\right)\) |
\(\chi_{4235}(136,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{133}{165}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{101}{165}\right)\) | \(e\left(\frac{63}{110}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{27}{110}\right)\) | \(e\left(\frac{37}{165}\right)\) | \(e\left(\frac{109}{330}\right)\) |
\(\chi_{4235}(201,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{62}{165}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{124}{165}\right)\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{13}{110}\right)\) | \(e\left(\frac{83}{165}\right)\) | \(e\left(\frac{191}{330}\right)\) |
\(\chi_{4235}(236,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{161}{165}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{157}{165}\right)\) | \(e\left(\frac{1}{110}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{149}{165}\right)\) | \(e\left(\frac{323}{330}\right)\) |
\(\chi_{4235}(306,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{119}{165}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{73}{165}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{9}{55}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{5}{66}\right)\) | \(e\left(\frac{1}{110}\right)\) | \(e\left(\frac{146}{165}\right)\) | \(e\left(\frac{167}{330}\right)\) |
\(\chi_{4235}(311,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{127}{165}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{89}{165}\right)\) | \(e\left(\frac{37}{110}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{7}{66}\right)\) | \(e\left(\frac{63}{110}\right)\) | \(e\left(\frac{13}{165}\right)\) | \(e\left(\frac{181}{330}\right)\) |
\(\chi_{4235}(346,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{46}{165}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{92}{165}\right)\) | \(e\left(\frac{71}{110}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{61}{66}\right)\) | \(e\left(\frac{109}{110}\right)\) | \(e\left(\frac{19}{165}\right)\) | \(e\left(\frac{163}{330}\right)\) |
\(\chi_{4235}(411,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{83}{165}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{1}{165}\right)\) | \(e\left(\frac{103}{110}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{2}{165}\right)\) | \(e\left(\frac{269}{330}\right)\) |
\(\chi_{4235}(416,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{49}{165}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{98}{165}\right)\) | \(e\left(\frac{29}{110}\right)\) | \(e\left(\frac{49}{55}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{37}{66}\right)\) | \(e\left(\frac{91}{110}\right)\) | \(e\left(\frac{31}{165}\right)\) | \(e\left(\frac{127}{330}\right)\) |
\(\chi_{4235}(521,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{118}{165}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{71}{165}\right)\) | \(e\left(\frac{53}{110}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{7}{110}\right)\) | \(e\left(\frac{142}{165}\right)\) | \(e\left(\frac{289}{330}\right)\) |
\(\chi_{4235}(586,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{152}{165}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{139}{165}\right)\) | \(e\left(\frac{17}{110}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{5}{66}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{113}{165}\right)\) | \(e\left(\frac{101}{330}\right)\) |
\(\chi_{4235}(621,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{116}{165}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{67}{165}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{19}{110}\right)\) | \(e\left(\frac{134}{165}\right)\) | \(e\left(\frac{203}{330}\right)\) |
\(\chi_{4235}(691,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{149}{165}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{133}{165}\right)\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{41}{110}\right)\) | \(e\left(\frac{101}{165}\right)\) | \(e\left(\frac{137}{330}\right)\) |
\(\chi_{4235}(696,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{52}{165}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{104}{165}\right)\) | \(e\left(\frac{97}{110}\right)\) | \(e\left(\frac{52}{55}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{43}{165}\right)\) | \(e\left(\frac{91}{330}\right)\) |
\(\chi_{4235}(731,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{165}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{2}{165}\right)\) | \(e\left(\frac{41}{110}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{49}{110}\right)\) | \(e\left(\frac{4}{165}\right)\) | \(e\left(\frac{43}{330}\right)\) |
\(\chi_{4235}(796,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{68}{165}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{136}{165}\right)\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{87}{110}\right)\) | \(e\left(\frac{107}{165}\right)\) | \(e\left(\frac{119}{330}\right)\) |
\(\chi_{4235}(801,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{79}{165}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{158}{165}\right)\) | \(e\left(\frac{49}{110}\right)\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{61}{66}\right)\) | \(e\left(\frac{21}{110}\right)\) | \(e\left(\frac{151}{165}\right)\) | \(e\left(\frac{97}{330}\right)\) |
\(\chi_{4235}(906,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{103}{165}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{41}{165}\right)\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{1}{66}\right)\) | \(e\left(\frac{97}{110}\right)\) | \(e\left(\frac{82}{165}\right)\) | \(e\left(\frac{139}{330}\right)\) |
\(\chi_{4235}(1006,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{71}{165}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{142}{165}\right)\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{119}{165}\right)\) | \(e\left(\frac{83}{330}\right)\) |
\(\chi_{4235}(1076,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{14}{165}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{28}{165}\right)\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{53}{66}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{56}{165}\right)\) | \(e\left(\frac{107}{330}\right)\) |
\(\chi_{4235}(1081,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{142}{165}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{119}{165}\right)\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{73}{165}\right)\) | \(e\left(\frac{1}{330}\right)\) |
\(\chi_{4235}(1181,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{53}{165}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{106}{165}\right)\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{5}{66}\right)\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{47}{165}\right)\) | \(e\left(\frac{299}{330}\right)\) |
\(\chi_{4235}(1186,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{109}{165}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{53}{165}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{106}{165}\right)\) | \(e\left(\frac{67}{330}\right)\) |
\(\chi_{4235}(1356,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{165}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{4}{165}\right)\) | \(e\left(\frac{27}{110}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{8}{165}\right)\) | \(e\left(\frac{251}{330}\right)\) |
\(\chi_{4235}(1391,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{26}{165}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{52}{165}\right)\) | \(e\left(\frac{21}{110}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{23}{66}\right)\) | \(e\left(\frac{9}{110}\right)\) | \(e\left(\frac{104}{165}\right)\) | \(e\left(\frac{293}{330}\right)\) |
\(\chi_{4235}(1466,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{67}{165}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{134}{165}\right)\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{103}{165}\right)\) | \(e\left(\frac{241}{330}\right)\) |
\(\chi_{4235}(1501,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{76}{165}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{152}{165}\right)\) | \(e\left(\frac{91}{110}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{139}{165}\right)\) | \(e\left(\frac{133}{330}\right)\) |
\(\chi_{4235}(1566,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{38}{165}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{76}{165}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{38}{55}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{152}{165}\right)\) | \(e\left(\frac{149}{330}\right)\) |
\(\chi_{4235}(1571,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{139}{165}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{113}{165}\right)\) | \(e\left(\frac{89}{110}\right)\) | \(e\left(\frac{29}{55}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{61}{165}\right)\) | \(e\left(\frac{37}{330}\right)\) |
\(\chi_{4235}(1676,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{73}{165}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{146}{165}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{57}{110}\right)\) | \(e\left(\frac{127}{165}\right)\) | \(e\left(\frac{169}{330}\right)\) |