↑

Properties

Label 1740.ce
Modulus $1740$
Conductor $580$
Order $28$
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(1740, base_ring=CyclotomicField(28)) M = H._module chi = DirichletCharacter(H, M([14,0,14,9])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(19,1740)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1740\)
Conductor: \(580\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(28\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 580.be
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: \(\Q(\zeta_{28})\)
Fixed field: 28.28.5002255640118107399365159746748272082794905600000000000000.1

Characters in Galois orbit

Character \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{1740}(19,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{2}{7}\right)\) \(i\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{13}{28}\right)\) \(i\) \(e\left(\frac{5}{28}\right)\)
\(\chi_{1740}(79,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(i\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{9}{28}\right)\) \(i\) \(e\left(\frac{25}{28}\right)\)
\(\chi_{1740}(259,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{1}{7}\right)\) \(-i\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{3}{28}\right)\) \(-i\) \(e\left(\frac{27}{28}\right)\)
\(\chi_{1740}(379,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{1}{7}\right)\) \(i\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{17}{28}\right)\) \(i\) \(e\left(\frac{13}{28}\right)\)
\(\chi_{1740}(559,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(-i\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{23}{28}\right)\) \(-i\) \(e\left(\frac{11}{28}\right)\)
\(\chi_{1740}(619,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{2}{7}\right)\) \(-i\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{27}{28}\right)\) \(-i\) \(e\left(\frac{19}{28}\right)\)
\(\chi_{1740}(739,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(i\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{25}{28}\right)\) \(i\) \(e\left(\frac{1}{28}\right)\)
\(\chi_{1740}(859,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(-i\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{19}{28}\right)\) \(-i\) \(e\left(\frac{3}{28}\right)\)
\(\chi_{1740}(1099,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(-i\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{15}{28}\right)\) \(-i\) \(e\left(\frac{23}{28}\right)\)
\(\chi_{1740}(1279,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(i\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{1}{28}\right)\) \(i\) \(e\left(\frac{9}{28}\right)\)
\(\chi_{1740}(1519,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(i\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{5}{28}\right)\) \(i\) \(e\left(\frac{17}{28}\right)\)
\(\chi_{1740}(1639,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(-i\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{11}{28}\right)\) \(-i\) \(e\left(\frac{15}{28}\right)\)