Properties

Label 405.q
Modulus $405$
Conductor $81$
Order $27$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(405, base_ring=CyclotomicField(54))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([4,0]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(16,405))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(405\)
Conductor: \(81\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(27\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 81.g
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: \(\Q(\zeta_{27})\)
Fixed field: \(\Q(\zeta_{81})^+\)

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(7\) \(8\) \(11\) \(13\) \(14\) \(16\) \(17\) \(19\)
\(\chi_{405}(16,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{27}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{7}{27}\right)\) \(e\left(\frac{8}{27}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{405}(31,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{8}{27}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{405}(61,\cdot)\) \(1\) \(1\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{405}(76,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{405}(106,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{27}\right)\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{405}(121,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{7}{27}\right)\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{405}(151,\cdot)\) \(1\) \(1\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{405}(166,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{2}{27}\right)\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{8}{27}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{405}(196,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{7}{27}\right)\) \(e\left(\frac{2}{27}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{405}(211,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{2}{27}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{405}(241,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{8}{27}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{2}{27}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{405}(256,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{8}{27}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{405}(286,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{8}{27}\right)\) \(e\left(\frac{7}{27}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{405}(301,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{7}{27}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{405}(331,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{27}\right)\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{405}(346,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{27}\right)\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{2}{27}\right)\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{405}(376,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{405}(391,\cdot)\) \(1\) \(1\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{7}{27}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{9}\right)\)