Properties

Label 175.t
Modulus $175$
Conductor $175$
Order $30$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(175, base_ring=CyclotomicField(30))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([3,20]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(4,175))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(175\)
Conductor: \(175\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(30\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{15})\)
Fixed field: 30.30.35434884492252294752034913472016341984272003173828125.1

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(8\) \(9\) \(11\) \(12\) \(13\) \(16\)
\(\chi_{175}(4,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{175}(9,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{15}\right)\)
\(\chi_{175}(39,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{8}{15}\right)\)
\(\chi_{175}(44,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{175}(79,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{15}\right)\)
\(\chi_{175}(109,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{15}\right)\)
\(\chi_{175}(114,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{175}(144,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{14}{15}\right)\)