Properties

Label 539.v
Modulus $539$
Conductor $539$
Order $35$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(539, base_ring=CyclotomicField(70))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([50,14]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(15,539))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(539\)
Conductor: \(539\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(35\)
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: $\Q(\zeta_{35})$
Fixed field: 35.35.73261800077965937220382205398471606200231960977600836588587975360331959691780081.1

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(8\) \(9\) \(10\) \(12\) \(13\)
\(\chi_{539}(15,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{3}{35}\right)\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{27}{35}\right)\)
\(\chi_{539}(36,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{32}{35}\right)\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{13}{35}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{8}{35}\right)\)
\(\chi_{539}(64,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{12}{35}\right)\) \(e\left(\frac{4}{35}\right)\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{6}{35}\right)\)
\(\chi_{539}(71,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{9}{35}\right)\)
\(\chi_{539}(92,\cdot)\) \(1\) \(1\) \(e\left(\frac{32}{35}\right)\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{29}{35}\right)\) \(e\left(\frac{33}{35}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{32}{35}\right)\)
\(\chi_{539}(113,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{35}\right)\) \(e\left(\frac{4}{35}\right)\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{32}{35}\right)\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{4}{35}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{13}{35}\right)\)
\(\chi_{539}(141,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{33}{35}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{33}{35}\right)\) \(e\left(\frac{31}{35}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{11}{35}\right)\)
\(\chi_{539}(169,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{4}{35}\right)\) \(e\left(\frac{13}{35}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{12}{35}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{2}{35}\right)\)
\(\chi_{539}(190,\cdot)\) \(1\) \(1\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{12}{35}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{3}{35}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{18}{35}\right)\)
\(\chi_{539}(218,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{13}{35}\right)\) \(e\left(\frac{32}{35}\right)\) \(e\left(\frac{34}{35}\right)\) \(e\left(\frac{29}{35}\right)\) \(e\left(\frac{13}{35}\right)\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{16}{35}\right)\)
\(\chi_{539}(225,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{3}{35}\right)\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{19}{35}\right)\)
\(\chi_{539}(267,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{34}{35}\right)\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{34}{35}\right)\) \(e\left(\frac{33}{35}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{23}{35}\right)\)
\(\chi_{539}(302,\cdot)\) \(1\) \(1\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{13}{35}\right)\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{4}{35}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{24}{35}\right)\)
\(\chi_{539}(323,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{35}\right)\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{13}{35}\right)\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{12}{35}\right)\)
\(\chi_{539}(372,\cdot)\) \(1\) \(1\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{29}{35}\right)\) \(e\left(\frac{34}{35}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{26}{35}\right)\)
\(\chi_{539}(379,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{35}\right)\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{31}{35}\right)\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{34}{35}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{29}{35}\right)\)
\(\chi_{539}(400,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{34}{35}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{33}{35}\right)\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{32}{35}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{17}{35}\right)\)
\(\chi_{539}(421,\cdot)\) \(1\) \(1\) \(e\left(\frac{33}{35}\right)\) \(e\left(\frac{29}{35}\right)\) \(e\left(\frac{31}{35}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{29}{35}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{33}{35}\right)\)
\(\chi_{539}(449,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{35}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{31}{35}\right)\)
\(\chi_{539}(456,\cdot)\) \(1\) \(1\) \(e\left(\frac{34}{35}\right)\) \(e\left(\frac{32}{35}\right)\) \(e\left(\frac{33}{35}\right)\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{31}{35}\right)\) \(e\left(\frac{32}{35}\right)\) \(e\left(\frac{29}{35}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{34}{35}\right)\)
\(\chi_{539}(477,\cdot)\) \(1\) \(1\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{31}{35}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{3}{35}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{31}{35}\right)\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{22}{35}\right)\)
\(\chi_{539}(498,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{35}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{12}{35}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{3}{35}\right)\)
\(\chi_{539}(526,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{3}{35}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{4}{35}\right)\) \(e\left(\frac{3}{35}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{35}\right)\)
\(\chi_{539}(533,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{35}\right)\) \(e\left(\frac{12}{35}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{12}{35}\right)\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{4}{35}\right)\)