Properties

Label 2415.de
Modulus $2415$
Conductor $2415$
Order $66$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(2415, base_ring=CyclotomicField(66))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([33,33,11,42]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(59,2415))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(2415\)
Conductor: \(2415\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(66\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
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: \(\Q(\zeta_{33})\)
Fixed field: Number field defined by a degree 66 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(8\) \(11\) \(13\) \(16\) \(17\) \(19\) \(22\) \(26\)
\(\chi_{2415}(59,\cdot)\) \(1\) \(1\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{25}{66}\right)\) \(-1\) \(e\left(\frac{17}{33}\right)\)
\(\chi_{2415}(164,\cdot)\) \(1\) \(1\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{49}{66}\right)\) \(-1\) \(e\left(\frac{32}{33}\right)\)
\(\chi_{2415}(269,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{19}{66}\right)\) \(-1\) \(e\left(\frac{5}{33}\right)\)
\(\chi_{2415}(374,\cdot)\) \(1\) \(1\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{7}{66}\right)\) \(-1\) \(e\left(\frac{14}{33}\right)\)
\(\chi_{2415}(404,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{47}{66}\right)\) \(-1\) \(e\left(\frac{28}{33}\right)\)
\(\chi_{2415}(509,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{5}{66}\right)\) \(-1\) \(e\left(\frac{10}{33}\right)\)
\(\chi_{2415}(584,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{43}{66}\right)\) \(-1\) \(e\left(\frac{20}{33}\right)\)
\(\chi_{2415}(614,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{41}{66}\right)\) \(-1\) \(e\left(\frac{16}{33}\right)\)
\(\chi_{2415}(719,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{29}{66}\right)\) \(-1\) \(e\left(\frac{25}{33}\right)\)
\(\chi_{2415}(794,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{31}{66}\right)\) \(-1\) \(e\left(\frac{29}{33}\right)\)
\(\chi_{2415}(899,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{13}{66}\right)\) \(-1\) \(e\left(\frac{26}{33}\right)\)
\(\chi_{2415}(929,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{65}{66}\right)\) \(-1\) \(e\left(\frac{31}{33}\right)\)
\(\chi_{2415}(1139,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{53}{66}\right)\) \(-1\) \(e\left(\frac{7}{33}\right)\)
\(\chi_{2415}(1214,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{1}{66}\right)\) \(-1\) \(e\left(\frac{2}{33}\right)\)
\(\chi_{2415}(1244,\cdot)\) \(1\) \(1\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{35}{66}\right)\) \(-1\) \(e\left(\frac{4}{33}\right)\)
\(\chi_{2415}(1319,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{61}{66}\right)\) \(-1\) \(e\left(\frac{23}{33}\right)\)
\(\chi_{2415}(1559,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{23}{66}\right)\) \(-1\) \(e\left(\frac{13}{33}\right)\)
\(\chi_{2415}(1664,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{17}{66}\right)\) \(-1\) \(e\left(\frac{1}{33}\right)\)
\(\chi_{2415}(1844,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{37}{66}\right)\) \(-1\) \(e\left(\frac{8}{33}\right)\)
\(\chi_{2415}(2189,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{59}{66}\right)\) \(-1\) \(e\left(\frac{19}{33}\right)\)