Properties

Label 1600.cg
Modulus $1600$
Conductor $800$
Order $40$
Real no
Primitive no
Minimal no
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1600, base_ring=CyclotomicField(40))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,15,28]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(9,1600))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1600\)
Conductor: \(800\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(40\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 800.by
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{40})\)
Fixed field: 40.40.15474250491067253436239052800000000000000000000000000000000000000000000000000000000000000000000.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(7\) \(9\) \(11\) \(13\) \(17\) \(19\) \(21\) \(23\) \(27\)
\(\chi_{1600}(9,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{40}\right)\) \(i\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{40}\right)\)
\(\chi_{1600}(89,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{40}\right)\) \(-i\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{17}{40}\right)\)
\(\chi_{1600}(169,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{40}\right)\) \(i\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{31}{40}\right)\)
\(\chi_{1600}(329,\cdot)\) \(1\) \(1\) \(e\left(\frac{33}{40}\right)\) \(i\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{19}{40}\right)\)
\(\chi_{1600}(409,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{40}\right)\) \(-i\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{33}{40}\right)\)
\(\chi_{1600}(489,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{40}\right)\) \(i\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{40}\right)\)
\(\chi_{1600}(569,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{40}\right)\) \(-i\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{21}{40}\right)\)
\(\chi_{1600}(729,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{40}\right)\) \(-i\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{9}{40}\right)\)
\(\chi_{1600}(809,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{40}\right)\) \(i\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{23}{40}\right)\)
\(\chi_{1600}(889,\cdot)\) \(1\) \(1\) \(e\left(\frac{39}{40}\right)\) \(-i\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{37}{40}\right)\)
\(\chi_{1600}(969,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{40}\right)\) \(i\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{11}{40}\right)\)
\(\chi_{1600}(1129,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{40}\right)\) \(i\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{39}{40}\right)\)
\(\chi_{1600}(1209,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{40}\right)\) \(-i\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{13}{40}\right)\)
\(\chi_{1600}(1289,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{40}\right)\) \(i\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{27}{40}\right)\)
\(\chi_{1600}(1369,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{40}\right)\) \(-i\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{40}\right)\)
\(\chi_{1600}(1529,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{40}\right)\) \(-i\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{29}{40}\right)\)