Properties

Label 547.j
Modulus $547$
Conductor $547$
Order $39$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(547, base_ring=CyclotomicField(78))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([10]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(11,547))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(547\)
Conductor: \(547\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(39\)
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: $\Q(\zeta_{39})$
Fixed field: 39.39.110539730308983252644692019573737637228828219789892386533857010792412648335681998371651796263456819412889.1

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{547}(11,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{39}\right)\) \(1\) \(e\left(\frac{10}{39}\right)\) \(e\left(\frac{37}{39}\right)\) \(e\left(\frac{5}{39}\right)\) \(e\left(\frac{8}{39}\right)\) \(e\left(\frac{5}{13}\right)\) \(1\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{38}{39}\right)\)
\(\chi_{547}(21,\cdot)\) \(1\) \(1\) \(e\left(\frac{38}{39}\right)\) \(1\) \(e\left(\frac{37}{39}\right)\) \(e\left(\frac{16}{39}\right)\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{14}{39}\right)\) \(e\left(\frac{12}{13}\right)\) \(1\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{8}{39}\right)\)
\(\chi_{547}(47,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{39}\right)\) \(1\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{8}{39}\right)\) \(e\left(\frac{19}{39}\right)\) \(e\left(\frac{7}{39}\right)\) \(e\left(\frac{6}{13}\right)\) \(1\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{4}{39}\right)\)
\(\chi_{547}(54,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{39}\right)\) \(1\) \(e\left(\frac{28}{39}\right)\) \(e\left(\frac{10}{39}\right)\) \(e\left(\frac{14}{39}\right)\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{1}{13}\right)\) \(1\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{5}{39}\right)\)
\(\chi_{547}(96,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{39}\right)\) \(1\) \(e\left(\frac{23}{39}\right)\) \(e\left(\frac{11}{39}\right)\) \(e\left(\frac{31}{39}\right)\) \(e\left(\frac{34}{39}\right)\) \(e\left(\frac{5}{13}\right)\) \(1\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{25}{39}\right)\)
\(\chi_{547}(121,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{39}\right)\) \(1\) \(e\left(\frac{20}{39}\right)\) \(e\left(\frac{35}{39}\right)\) \(e\left(\frac{10}{39}\right)\) \(e\left(\frac{16}{39}\right)\) \(e\left(\frac{10}{13}\right)\) \(1\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{37}{39}\right)\)
\(\chi_{547}(129,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{39}\right)\) \(1\) \(e\left(\frac{4}{39}\right)\) \(e\left(\frac{7}{39}\right)\) \(e\left(\frac{2}{39}\right)\) \(e\left(\frac{11}{39}\right)\) \(e\left(\frac{2}{13}\right)\) \(1\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{23}{39}\right)\)
\(\chi_{547}(136,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{39}\right)\) \(1\) \(e\left(\frac{22}{39}\right)\) \(e\left(\frac{19}{39}\right)\) \(e\left(\frac{11}{39}\right)\) \(e\left(\frac{2}{39}\right)\) \(e\left(\frac{11}{13}\right)\) \(1\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{29}{39}\right)\)
\(\chi_{547}(181,\cdot)\) \(1\) \(1\) \(e\left(\frac{28}{39}\right)\) \(1\) \(e\left(\frac{17}{39}\right)\) \(e\left(\frac{20}{39}\right)\) \(e\left(\frac{28}{39}\right)\) \(e\left(\frac{37}{39}\right)\) \(e\left(\frac{2}{13}\right)\) \(1\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{10}{39}\right)\)
\(\chi_{547}(199,\cdot)\) \(1\) \(1\) \(e\left(\frac{34}{39}\right)\) \(1\) \(e\left(\frac{29}{39}\right)\) \(e\left(\frac{2}{39}\right)\) \(e\left(\frac{34}{39}\right)\) \(e\left(\frac{31}{39}\right)\) \(e\left(\frac{8}{13}\right)\) \(1\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{1}{39}\right)\)
\(\chi_{547}(217,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{39}\right)\) \(1\) \(e\left(\frac{19}{39}\right)\) \(e\left(\frac{4}{39}\right)\) \(e\left(\frac{29}{39}\right)\) \(e\left(\frac{23}{39}\right)\) \(e\left(\frac{3}{13}\right)\) \(1\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{2}{39}\right)\)
\(\chi_{547}(231,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{39}\right)\) \(1\) \(e\left(\frac{8}{39}\right)\) \(e\left(\frac{14}{39}\right)\) \(e\left(\frac{4}{39}\right)\) \(e\left(\frac{22}{39}\right)\) \(e\left(\frac{4}{13}\right)\) \(1\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{7}{39}\right)\)
\(\chi_{547}(233,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{39}\right)\) \(1\) \(e\left(\frac{11}{39}\right)\) \(e\left(\frac{29}{39}\right)\) \(e\left(\frac{25}{39}\right)\) \(e\left(\frac{1}{39}\right)\) \(e\left(\frac{12}{13}\right)\) \(1\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{34}{39}\right)\)
\(\chi_{547}(239,\cdot)\) \(1\) \(1\) \(e\left(\frac{32}{39}\right)\) \(1\) \(e\left(\frac{25}{39}\right)\) \(e\left(\frac{34}{39}\right)\) \(e\left(\frac{32}{39}\right)\) \(e\left(\frac{20}{39}\right)\) \(e\left(\frac{6}{13}\right)\) \(1\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{17}{39}\right)\)
\(\chi_{547}(296,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{39}\right)\) \(1\) \(e\left(\frac{31}{39}\right)\) \(e\left(\frac{25}{39}\right)\) \(e\left(\frac{35}{39}\right)\) \(e\left(\frac{17}{39}\right)\) \(e\left(\frac{9}{13}\right)\) \(1\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{32}{39}\right)\)
\(\chi_{547}(302,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{39}\right)\) \(1\) \(e\left(\frac{16}{39}\right)\) \(e\left(\frac{28}{39}\right)\) \(e\left(\frac{8}{39}\right)\) \(e\left(\frac{5}{39}\right)\) \(e\left(\frac{8}{13}\right)\) \(1\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{14}{39}\right)\)
\(\chi_{547}(325,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{39}\right)\) \(1\) \(e\left(\frac{14}{39}\right)\) \(e\left(\frac{5}{39}\right)\) \(e\left(\frac{7}{39}\right)\) \(e\left(\frac{19}{39}\right)\) \(e\left(\frac{7}{13}\right)\) \(1\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{22}{39}\right)\)
\(\chi_{547}(402,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{39}\right)\) \(1\) \(e\left(\frac{32}{39}\right)\) \(e\left(\frac{17}{39}\right)\) \(e\left(\frac{16}{39}\right)\) \(e\left(\frac{10}{39}\right)\) \(e\left(\frac{3}{13}\right)\) \(1\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{28}{39}\right)\)
\(\chi_{547}(419,\cdot)\) \(1\) \(1\) \(e\left(\frac{20}{39}\right)\) \(1\) \(e\left(\frac{1}{39}\right)\) \(e\left(\frac{31}{39}\right)\) \(e\left(\frac{20}{39}\right)\) \(e\left(\frac{32}{39}\right)\) \(e\left(\frac{7}{13}\right)\) \(1\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{35}{39}\right)\)
\(\chi_{547}(441,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{39}\right)\) \(1\) \(e\left(\frac{35}{39}\right)\) \(e\left(\frac{32}{39}\right)\) \(e\left(\frac{37}{39}\right)\) \(e\left(\frac{28}{39}\right)\) \(e\left(\frac{11}{13}\right)\) \(1\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{16}{39}\right)\)
\(\chi_{547}(445,\cdot)\) \(1\) \(1\) \(e\left(\frac{22}{39}\right)\) \(1\) \(e\left(\frac{5}{39}\right)\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{22}{39}\right)\) \(e\left(\frac{4}{39}\right)\) \(e\left(\frac{9}{13}\right)\) \(1\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{19}{39}\right)\)
\(\chi_{547}(464,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{39}\right)\) \(1\) \(e\left(\frac{7}{39}\right)\) \(e\left(\frac{22}{39}\right)\) \(e\left(\frac{23}{39}\right)\) \(e\left(\frac{29}{39}\right)\) \(e\left(\frac{10}{13}\right)\) \(1\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{11}{39}\right)\)
\(\chi_{547}(488,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{39}\right)\) \(1\) \(e\left(\frac{34}{39}\right)\) \(e\left(\frac{1}{39}\right)\) \(e\left(\frac{17}{39}\right)\) \(e\left(\frac{35}{39}\right)\) \(e\left(\frac{4}{13}\right)\) \(1\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{20}{39}\right)\)
\(\chi_{547}(521,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{39}\right)\) \(1\) \(e\left(\frac{2}{39}\right)\) \(e\left(\frac{23}{39}\right)\) \(e\left(\frac{1}{39}\right)\) \(e\left(\frac{25}{39}\right)\) \(e\left(\frac{1}{13}\right)\) \(1\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{31}{39}\right)\)