Properties

Label 3895.ea
Modulus $3895$
Conductor $3895$
Order $40$
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3895, base_ring=CyclotomicField(40))
 
M = H._module
 
chi = DirichletCharacter(H, M([10,20,29]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(227,3895))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(3895\)
Conductor: \(3895\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(40\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{40})\)
Fixed field: Number field defined by a degree 40 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(7\) \(8\) \(9\) \(11\) \(12\) \(13\)
\(\chi_{3895}(227,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(i\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{29}{40}\right)\)
\(\chi_{3895}(322,\cdot)\) \(-1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(i\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{21}{40}\right)\)
\(\chi_{3895}(398,\cdot)\) \(-1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(-i\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{7}{40}\right)\)
\(\chi_{3895}(873,\cdot)\) \(-1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(-i\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{27}{40}\right)\)
\(\chi_{3895}(1633,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(-i\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{19}{40}\right)\)
\(\chi_{3895}(2203,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(-i\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{23}{40}\right)\)
\(\chi_{3895}(2488,\cdot)\) \(-1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(-i\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{11}{40}\right)\)
\(\chi_{3895}(2507,\cdot)\) \(-1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(i\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{1}{40}\right)\)
\(\chi_{3895}(2602,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(i\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{9}{40}\right)\)
\(\chi_{3895}(2678,\cdot)\) \(-1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(-i\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{31}{40}\right)\)
\(\chi_{3895}(2887,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(i\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{33}{40}\right)\)
\(\chi_{3895}(2963,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(-i\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{3}{40}\right)\)
\(\chi_{3895}(3172,\cdot)\) \(-1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(i\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{37}{40}\right)\)
\(\chi_{3895}(3533,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(-i\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{39}{40}\right)\)
\(\chi_{3895}(3552,\cdot)\) \(-1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(i\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{17}{40}\right)\)
\(\chi_{3895}(3837,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(i\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{13}{40}\right)\)