Properties

Label 507.s
Modulus $507$
Conductor $507$
Order $52$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(507, base_ring=CyclotomicField(52))
 
M = H._module
 
chi = DirichletCharacter(H, M([26,3]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(5,507))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(507\)
Conductor: \(507\)
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 \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(11\) \(14\) \(16\) \(17\)
\(\chi_{507}(5,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{52}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{1}{52}\right)\) \(e\left(\frac{9}{52}\right)\) \(e\left(\frac{35}{52}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{23}{52}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{12}{13}\right)\)
\(\chi_{507}(8,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{52}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{35}{52}\right)\) \(e\left(\frac{3}{52}\right)\) \(e\left(\frac{29}{52}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{25}{52}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{4}{13}\right)\)
\(\chi_{507}(44,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{52}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{29}{52}\right)\) \(e\left(\frac{1}{52}\right)\) \(e\left(\frac{27}{52}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{43}{52}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{10}{13}\right)\)
\(\chi_{507}(47,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{52}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{7}{52}\right)\) \(e\left(\frac{11}{52}\right)\) \(e\left(\frac{37}{52}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{5}{52}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{6}{13}\right)\)
\(\chi_{507}(83,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{52}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{5}{52}\right)\) \(e\left(\frac{45}{52}\right)\) \(e\left(\frac{19}{52}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{11}{52}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{8}{13}\right)\)
\(\chi_{507}(86,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{52}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{31}{52}\right)\) \(e\left(\frac{19}{52}\right)\) \(e\left(\frac{45}{52}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{37}{52}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{8}{13}\right)\)
\(\chi_{507}(122,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{52}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{33}{52}\right)\) \(e\left(\frac{37}{52}\right)\) \(e\left(\frac{11}{52}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{31}{52}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{6}{13}\right)\)
\(\chi_{507}(125,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{52}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{3}{52}\right)\) \(e\left(\frac{27}{52}\right)\) \(e\left(\frac{1}{52}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{17}{52}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{10}{13}\right)\)
\(\chi_{507}(161,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{52}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{9}{52}\right)\) \(e\left(\frac{29}{52}\right)\) \(e\left(\frac{3}{52}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{51}{52}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{4}{13}\right)\)
\(\chi_{507}(164,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{52}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{27}{52}\right)\) \(e\left(\frac{35}{52}\right)\) \(e\left(\frac{9}{52}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{49}{52}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{12}{13}\right)\)
\(\chi_{507}(200,\cdot)\) \(1\) \(1\) \(e\left(\frac{33}{52}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{37}{52}\right)\) \(e\left(\frac{21}{52}\right)\) \(e\left(\frac{47}{52}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{19}{52}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{2}{13}\right)\)
\(\chi_{507}(203,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{52}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{51}{52}\right)\) \(e\left(\frac{43}{52}\right)\) \(e\left(\frac{17}{52}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{29}{52}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{1}{13}\right)\)
\(\chi_{507}(242,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{52}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{23}{52}\right)\) \(e\left(\frac{51}{52}\right)\) \(e\left(\frac{25}{52}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{9}{52}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{3}{13}\right)\)
\(\chi_{507}(278,\cdot)\) \(1\) \(1\) \(e\left(\frac{45}{52}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{41}{52}\right)\) \(e\left(\frac{5}{52}\right)\) \(e\left(\frac{31}{52}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{7}{52}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{11}{13}\right)\)
\(\chi_{507}(281,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{52}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{47}{52}\right)\) \(e\left(\frac{7}{52}\right)\) \(e\left(\frac{33}{52}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{41}{52}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{5}{13}\right)\)
\(\chi_{507}(317,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{52}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{17}{52}\right)\) \(e\left(\frac{49}{52}\right)\) \(e\left(\frac{23}{52}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{27}{52}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{9}{13}\right)\)
\(\chi_{507}(320,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{52}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{19}{52}\right)\) \(e\left(\frac{15}{52}\right)\) \(e\left(\frac{41}{52}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{21}{52}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{7}{13}\right)\)
\(\chi_{507}(356,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{52}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{45}{52}\right)\) \(e\left(\frac{41}{52}\right)\) \(e\left(\frac{15}{52}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{47}{52}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{7}{13}\right)\)
\(\chi_{507}(359,\cdot)\) \(1\) \(1\) \(e\left(\frac{51}{52}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{43}{52}\right)\) \(e\left(\frac{23}{52}\right)\) \(e\left(\frac{49}{52}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{1}{52}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{9}{13}\right)\)
\(\chi_{507}(395,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{52}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{21}{52}\right)\) \(e\left(\frac{33}{52}\right)\) \(e\left(\frac{7}{52}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{15}{52}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{5}{13}\right)\)
\(\chi_{507}(398,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{52}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{15}{52}\right)\) \(e\left(\frac{31}{52}\right)\) \(e\left(\frac{5}{52}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{33}{52}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{11}{13}\right)\)
\(\chi_{507}(434,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{52}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{49}{52}\right)\) \(e\left(\frac{25}{52}\right)\) \(e\left(\frac{51}{52}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{35}{52}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{3}{13}\right)\)
\(\chi_{507}(473,\cdot)\) \(1\) \(1\) \(e\left(\frac{49}{52}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{25}{52}\right)\) \(e\left(\frac{17}{52}\right)\) \(e\left(\frac{43}{52}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{3}{52}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{1}{13}\right)\)
\(\chi_{507}(476,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{52}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{11}{52}\right)\) \(e\left(\frac{47}{52}\right)\) \(e\left(\frac{21}{52}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{45}{52}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{2}{13}\right)\)