Properties

Label 8470.cq
Modulus $8470$
Conductor $4235$
Order $66$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(8470, base_ring=CyclotomicField(66))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([33,44,18]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(529,8470))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(8470\)
Conductor: \(4235\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(66\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 4235.cn
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 \(-1\) \(1\) \(3\) \(9\) \(13\) \(17\) \(19\) \(23\) \(27\) \(29\) \(31\) \(37\)
\(\chi_{8470}(529,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{61}{66}\right)\) \(-1\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{19}{66}\right)\)
\(\chi_{8470}(639,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{65}{66}\right)\) \(-1\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{17}{66}\right)\)
\(\chi_{8470}(1299,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{1}{66}\right)\) \(-1\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{49}{66}\right)\)
\(\chi_{8470}(1409,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{5}{66}\right)\) \(-1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{47}{66}\right)\)
\(\chi_{8470}(2069,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{7}{66}\right)\) \(-1\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{13}{66}\right)\)
\(\chi_{8470}(2839,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{13}{66}\right)\) \(-1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{43}{66}\right)\)
\(\chi_{8470}(2949,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{17}{66}\right)\) \(-1\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{41}{66}\right)\)
\(\chi_{8470}(3609,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{19}{66}\right)\) \(-1\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{7}{66}\right)\)
\(\chi_{8470}(3719,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{23}{66}\right)\) \(-1\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{5}{66}\right)\)
\(\chi_{8470}(4379,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{25}{66}\right)\) \(-1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{37}{66}\right)\)
\(\chi_{8470}(4489,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{29}{66}\right)\) \(-1\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{35}{66}\right)\)
\(\chi_{8470}(5149,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{31}{66}\right)\) \(-1\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{1}{66}\right)\)
\(\chi_{8470}(5259,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{35}{66}\right)\) \(-1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{65}{66}\right)\)
\(\chi_{8470}(5919,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{37}{66}\right)\) \(-1\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{31}{66}\right)\)
\(\chi_{8470}(6029,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{41}{66}\right)\) \(-1\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{29}{66}\right)\)
\(\chi_{8470}(6689,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{43}{66}\right)\) \(-1\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{61}{66}\right)\)
\(\chi_{8470}(6799,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{47}{66}\right)\) \(-1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{59}{66}\right)\)
\(\chi_{8470}(7459,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{49}{66}\right)\) \(-1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{25}{66}\right)\)
\(\chi_{8470}(7569,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{53}{66}\right)\) \(-1\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{23}{66}\right)\)
\(\chi_{8470}(8339,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{59}{66}\right)\) \(-1\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{53}{66}\right)\)