Properties

Label 1444.o
Modulus $1444$
Conductor $361$
Order $38$
Real no
Primitive no
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1444, base_ring=CyclotomicField(38))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,5]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(37,1444))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1444\)
Conductor: \(361\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(38\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 361.h
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: \(\Q(\zeta_{19})\)
Fixed field: 38.0.2233638411813024816853081773648251688534529753590642239923912316757382599022775822751448518259.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(13\) \(15\) \(17\) \(21\) \(23\)
\(\chi_{1444}(37,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{4}{19}\right)\)
\(\chi_{1444}(113,\cdot)\) \(-1\) \(1\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{12}{19}\right)\)
\(\chi_{1444}(189,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{1}{19}\right)\)
\(\chi_{1444}(265,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{9}{19}\right)\)
\(\chi_{1444}(341,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{9}{38}\right)\) \(e\left(\frac{17}{19}\right)\)
\(\chi_{1444}(417,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{37}{38}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{6}{19}\right)\)
\(\chi_{1444}(493,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{14}{19}\right)\)
\(\chi_{1444}(569,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{9}{38}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{3}{19}\right)\)
\(\chi_{1444}(645,\cdot)\) \(-1\) \(1\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{11}{19}\right)\)
\(\chi_{1444}(797,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{8}{19}\right)\)
\(\chi_{1444}(873,\cdot)\) \(-1\) \(1\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{16}{19}\right)\)
\(\chi_{1444}(949,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{38}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{9}{38}\right)\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{5}{19}\right)\)
\(\chi_{1444}(1025,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{13}{19}\right)\)
\(\chi_{1444}(1101,\cdot)\) \(-1\) \(1\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{2}{19}\right)\)
\(\chi_{1444}(1177,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{38}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{37}{38}\right)\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{10}{19}\right)\)
\(\chi_{1444}(1253,\cdot)\) \(-1\) \(1\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{18}{19}\right)\)
\(\chi_{1444}(1329,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{7}{19}\right)\)
\(\chi_{1444}(1405,\cdot)\) \(-1\) \(1\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{37}{38}\right)\) \(e\left(\frac{15}{19}\right)\)