Properties

Label 3381.bu
Modulus $3381$
Conductor $161$
Order $66$
Real no
Primitive no
Minimal no
Parity odd

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(3381, base_ring=CyclotomicField(66))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,11,18]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(31,3381))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(3381\)
Conductor: \(161\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(66\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 161.n
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{33})\)
Fixed field: Number field defined by a degree 66 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(5\) \(8\) \(10\) \(11\) \(13\) \(16\) \(17\) \(19\)
\(\chi_{3381}(31,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{61}{66}\right)\)
\(\chi_{3381}(325,\cdot)\) \(-1\) \(1\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{49}{66}\right)\)
\(\chi_{3381}(472,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{31}{66}\right)\)
\(\chi_{3381}(607,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{65}{66}\right)\)
\(\chi_{3381}(754,\cdot)\) \(-1\) \(1\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{23}{66}\right)\)
\(\chi_{3381}(901,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{59}{66}\right)\)
\(\chi_{3381}(913,\cdot)\) \(-1\) \(1\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{19}{66}\right)\)
\(\chi_{3381}(1048,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{47}{66}\right)\)
\(\chi_{3381}(1060,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{13}{66}\right)\)
\(\chi_{3381}(1342,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{17}{66}\right)\)
\(\chi_{3381}(1501,\cdot)\) \(-1\) \(1\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{7}{66}\right)\)
\(\chi_{3381}(1636,\cdot)\) \(-1\) \(1\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{5}{66}\right)\)
\(\chi_{3381}(1783,\cdot)\) \(-1\) \(1\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{53}{66}\right)\)
\(\chi_{3381}(2224,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{41}{66}\right)\)
\(\chi_{3381}(2371,\cdot)\) \(-1\) \(1\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{35}{66}\right)\)
\(\chi_{3381}(2677,\cdot)\) \(-1\) \(1\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{43}{66}\right)\)
\(\chi_{3381}(2812,\cdot)\) \(-1\) \(1\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{29}{66}\right)\)
\(\chi_{3381}(2824,\cdot)\) \(-1\) \(1\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{1}{66}\right)\)
\(\chi_{3381}(2971,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{37}{66}\right)\)
\(\chi_{3381}(3118,\cdot)\) \(-1\) \(1\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{25}{66}\right)\)