Properties

Label 265.o
Modulus $265$
Conductor $265$
Order $52$
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(265, base_ring=CyclotomicField(52))
 
M = H._module
 
chi = DirichletCharacter(H, M([39,17]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(3,265))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(265\)
Conductor: \(265\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(52\)
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: $\Q(\zeta_{52})$
Fixed field: Number field defined by a degree 52 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(7\) \(8\) \(9\) \(11\) \(12\) \(13\)
\(\chi_{265}(3,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{17}{52}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{5}{52}\right)\)
\(\chi_{265}(12,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{19}{52}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{27}{52}\right)\)
\(\chi_{265}(22,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{7}{52}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{51}{52}\right)\)
\(\chi_{265}(27,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{51}{52}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{15}{52}\right)\)
\(\chi_{265}(48,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{21}{52}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{49}{52}\right)\)
\(\chi_{265}(67,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{15}{52}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{35}{52}\right)\)
\(\chi_{265}(73,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{49}{52}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{45}{52}\right)\)
\(\chi_{265}(87,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{11}{52}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{43}{52}\right)\)
\(\chi_{265}(88,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{9}{52}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{21}{52}\right)\)
\(\chi_{265}(98,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{29}{52}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{33}{52}\right)\)
\(\chi_{265}(108,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{1}{52}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{37}{52}\right)\)
\(\chi_{265}(127,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{31}{52}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{3}{52}\right)\)
\(\chi_{265}(138,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{5}{52}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{29}{52}\right)\)
\(\chi_{265}(157,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{27}{52}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{11}{52}\right)\)
\(\chi_{265}(167,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{3}{52}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{7}{52}\right)\)
\(\chi_{265}(177,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{35}{52}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{47}{52}\right)\)
\(\chi_{265}(178,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{37}{52}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{17}{52}\right)\)
\(\chi_{265}(192,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{23}{52}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{19}{52}\right)\)
\(\chi_{265}(198,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{41}{52}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{9}{52}\right)\)
\(\chi_{265}(217,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{47}{52}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{23}{52}\right)\)
\(\chi_{265}(238,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{25}{52}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{41}{52}\right)\)
\(\chi_{265}(243,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{33}{52}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{25}{52}\right)\)
\(\chi_{265}(253,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{45}{52}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{1}{52}\right)\)
\(\chi_{265}(262,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{43}{52}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{31}{52}\right)\)