↑

Properties

Label 644.z
Modulus $644$
Conductor $644$
Order $66$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(644, base_ring=CyclotomicField(66)) M = H._module chi = DirichletCharacter(H, M([33,44,27])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(11,644)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(644\)
Conductor: \(644\)
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: yes
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
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 \(-1\) \(1\) \(3\) \(5\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(25\) \(27\)
\(\chi_{644}(11,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{644}(51,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{644}(67,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{19}{22}\right)\)
\(\chi_{644}(79,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{644}(107,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{644}(135,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{644}(191,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{21}{22}\right)\)
\(\chi_{644}(235,\cdot)\) \(1\) \(1\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{644}(247,\cdot)\) \(1\) \(1\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{644}(263,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{644}(291,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{644}(319,\cdot)\) \(1\) \(1\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{644}(359,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{7}{22}\right)\)
\(\chi_{644}(375,\cdot)\) \(1\) \(1\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{21}{22}\right)\)
\(\chi_{644}(387,\cdot)\) \(1\) \(1\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{644}(431,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{644}(471,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{644}(527,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{19}{22}\right)\)
\(\chi_{644}(543,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{7}{22}\right)\)
\(\chi_{644}(571,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{5}{22}\right)\)