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Properties

Label 8664.cd
Modulus $8664$
Conductor $8664$
Order $38$
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8664, base_ring=CyclotomicField(38)) M = H._module chi = DirichletCharacter(H, M([19,19,19,2])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(419,8664)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(8664\)
Conductor: \(8664\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(38\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: yes
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{19})\)
Fixed field: Number field defined by a degree 38 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(7\) \(11\) \(13\) \(17\) \(23\) \(25\) \(29\) \(31\) \(35\)
\(\chi_{8664}(419,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{23}{38}\right)\)
\(\chi_{8664}(875,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{17}{38}\right)\)
\(\chi_{8664}(1331,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{11}{38}\right)\)
\(\chi_{8664}(1787,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{5}{38}\right)\)
\(\chi_{8664}(2243,\cdot)\) \(1\) \(1\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{37}{38}\right)\)
\(\chi_{8664}(2699,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{31}{38}\right)\)
\(\chi_{8664}(3155,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{37}{38}\right)\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{25}{38}\right)\)
\(\chi_{8664}(4067,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{13}{38}\right)\)
\(\chi_{8664}(4523,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{7}{38}\right)\)
\(\chi_{8664}(4979,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{37}{38}\right)\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{37}{38}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{9}{38}\right)\) \(e\left(\frac{1}{38}\right)\)
\(\chi_{8664}(5435,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{33}{38}\right)\)
\(\chi_{8664}(5891,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{9}{38}\right)\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{27}{38}\right)\)
\(\chi_{8664}(6347,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{37}{38}\right)\) \(e\left(\frac{21}{38}\right)\)
\(\chi_{8664}(6803,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{15}{38}\right)\)
\(\chi_{8664}(7259,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{9}{38}\right)\)
\(\chi_{8664}(7715,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{9}{38}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{3}{38}\right)\)
\(\chi_{8664}(8171,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{37}{38}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{35}{38}\right)\)
\(\chi_{8664}(8627,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{9}{38}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{9}{38}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{29}{38}\right)\)