Properties

Label 1375.by
Modulus $1375$
Conductor $1375$
Order $50$
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1375, base_ring=CyclotomicField(50))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([9,15]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(19,1375))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1375\)
Conductor: \(1375\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(50\)
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: \(\Q(\zeta_{25})\)
Fixed field: Number field defined by a degree 50 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(7\) \(8\) \(9\) \(12\) \(13\) \(14\)
\(\chi_{1375}(19,\cdot)\) \(-1\) \(1\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{22}{25}\right)\)
\(\chi_{1375}(29,\cdot)\) \(-1\) \(1\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{23}{25}\right)\)
\(\chi_{1375}(189,\cdot)\) \(-1\) \(1\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{27}{50}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{24}{25}\right)\)
\(\chi_{1375}(259,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{6}{25}\right)\)
\(\chi_{1375}(294,\cdot)\) \(-1\) \(1\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{12}{25}\right)\)
\(\chi_{1375}(304,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{13}{25}\right)\)
\(\chi_{1375}(464,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{14}{25}\right)\)
\(\chi_{1375}(534,\cdot)\) \(-1\) \(1\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{21}{25}\right)\)
\(\chi_{1375}(569,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{2}{25}\right)\)
\(\chi_{1375}(579,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{3}{25}\right)\)
\(\chi_{1375}(739,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{4}{25}\right)\)
\(\chi_{1375}(809,\cdot)\) \(-1\) \(1\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{11}{25}\right)\)
\(\chi_{1375}(844,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{27}{50}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{17}{25}\right)\)
\(\chi_{1375}(854,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{27}{50}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{18}{25}\right)\)
\(\chi_{1375}(1014,\cdot)\) \(-1\) \(1\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{19}{25}\right)\)
\(\chi_{1375}(1084,\cdot)\) \(-1\) \(1\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{23}{50}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{1}{25}\right)\)
\(\chi_{1375}(1119,\cdot)\) \(-1\) \(1\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{23}{50}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{7}{25}\right)\)
\(\chi_{1375}(1129,\cdot)\) \(-1\) \(1\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{23}{50}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{8}{25}\right)\)
\(\chi_{1375}(1289,\cdot)\) \(-1\) \(1\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{9}{25}\right)\)
\(\chi_{1375}(1359,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{16}{25}\right)\)