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Properties

Label 8712.dq
Modulus $8712$
Conductor $4356$
Order $66$
Real no
Primitive no
Minimal no
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8712, base_ring=CyclotomicField(66)) M = H._module chi = DirichletCharacter(H, M([33,0,22,27])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(175,8712)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(8712\)
Conductor: \(4356\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(66\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 4356.bw
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
Copy content sage:chi.is_odd()
 
Copy content 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 \(-1\) \(1\) \(5\) \(7\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\) \(35\)
\(\chi_{8712}(175,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{8712}(439,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{8712}(1231,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{8712}(1759,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{8712}(2023,\cdot)\) \(1\) \(1\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{8712}(2551,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{8712}(2815,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{8712}(3343,\cdot)\) \(1\) \(1\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{8712}(3607,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{8712}(4135,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{8712}(4399,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{8712}(4927,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{8712}(5191,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{8712}(5719,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{8712}(5983,\cdot)\) \(1\) \(1\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{8712}(6511,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{8712}(7303,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{8712}(7567,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{8712}(8095,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{8712}(8359,\cdot)\) \(1\) \(1\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{8}{11}\right)\)