Properties

Label 1380.bo
Modulus $1380$
Conductor $345$
Order $44$
Real no
Primitive no
Minimal yes
Parity odd

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1380, base_ring=CyclotomicField(44))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,22,11,14]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(17,1380))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1380\)
Conductor: \(345\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 345.u
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: \(\Q(\zeta_{44})\)
Fixed field: 44.0.5691763675094128540646263027975260328820026154733783913534198355344240553677082061767578125.1

Characters in Galois orbit

Character \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(19\) \(29\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{1380}(17,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{15}{44}\right)\)
\(\chi_{1380}(53,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{25}{44}\right)\)
\(\chi_{1380}(113,\cdot)\) \(-1\) \(1\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{9}{44}\right)\)
\(\chi_{1380}(293,\cdot)\) \(-1\) \(1\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{37}{44}\right)\)
\(\chi_{1380}(497,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{23}{44}\right)\)
\(\chi_{1380}(557,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{43}{44}\right)\)
\(\chi_{1380}(617,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{7}{44}\right)\)
\(\chi_{1380}(677,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{19}{44}\right)\)
\(\chi_{1380}(773,\cdot)\) \(-1\) \(1\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{1}{44}\right)\)
\(\chi_{1380}(797,\cdot)\) \(-1\) \(1\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{27}{44}\right)\)
\(\chi_{1380}(833,\cdot)\) \(-1\) \(1\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{21}{44}\right)\)
\(\chi_{1380}(893,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{29}{44}\right)\)
\(\chi_{1380}(917,\cdot)\) \(-1\) \(1\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{39}{44}\right)\)
\(\chi_{1380}(953,\cdot)\) \(-1\) \(1\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{41}{44}\right)\)
\(\chi_{1380}(977,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{35}{44}\right)\)
\(\chi_{1380}(1073,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{5}{44}\right)\)
\(\chi_{1380}(1157,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{3}{44}\right)\)
\(\chi_{1380}(1193,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{17}{44}\right)\)
\(\chi_{1380}(1217,\cdot)\) \(-1\) \(1\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{31}{44}\right)\)
\(\chi_{1380}(1253,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{13}{44}\right)\)