↑

Properties

Label 676.m
Modulus $676$
Conductor $169$
Order $13$
Real no
Primitive no
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(676, base_ring=CyclotomicField(26)) M = H._module chi = DirichletCharacter(H, M([0,20])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(53,676)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(676\)
Conductor: \(169\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(13\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 169.g
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: \(\Q(\zeta_{13})\)
Fixed field: 13.13.542800770374370512771595361.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(15\) \(17\) \(19\) \(21\) \(23\)
\(\chi_{676}(53,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(1\) \(e\left(\frac{9}{13}\right)\) \(1\)
\(\chi_{676}(105,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{8}{13}\right)\) \(1\) \(e\left(\frac{5}{13}\right)\) \(1\)
\(\chi_{676}(157,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{12}{13}\right)\) \(1\) \(e\left(\frac{1}{13}\right)\) \(1\)
\(\chi_{676}(209,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{3}{13}\right)\) \(1\) \(e\left(\frac{10}{13}\right)\) \(1\)
\(\chi_{676}(261,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(1\) \(e\left(\frac{6}{13}\right)\) \(1\)
\(\chi_{676}(313,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{11}{13}\right)\) \(1\) \(e\left(\frac{2}{13}\right)\) \(1\)
\(\chi_{676}(365,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{2}{13}\right)\) \(1\) \(e\left(\frac{11}{13}\right)\) \(1\)
\(\chi_{676}(417,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{6}{13}\right)\) \(1\) \(e\left(\frac{7}{13}\right)\) \(1\)
\(\chi_{676}(469,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(1\) \(e\left(\frac{3}{13}\right)\) \(1\)
\(\chi_{676}(521,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(1\) \(e\left(\frac{12}{13}\right)\) \(1\)
\(\chi_{676}(573,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{5}{13}\right)\) \(1\) \(e\left(\frac{8}{13}\right)\) \(1\)
\(\chi_{676}(625,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{9}{13}\right)\) \(1\) \(e\left(\frac{4}{13}\right)\) \(1\)