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Properties

Label 42237.kx
Modulus $42237$
Conductor $4693$
Order $38$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(42237, base_ring=CyclotomicField(38)) M = H._module chi = DirichletCharacter(H, M([0,19,34])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(2053,42237)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(42237\)
Conductor: \(4693\)
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: no, induced from 4693.by
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 \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(11\) \(14\) \(16\) \(17\)
\(\chi_{42237}(2053,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{4}{19}\right)\)
\(\chi_{42237}(4276,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{2}{19}\right)\)
\(\chi_{42237}(8722,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{17}{19}\right)\)
\(\chi_{42237}(10945,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{9}{38}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{15}{19}\right)\)
\(\chi_{42237}(13168,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{37}{38}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{13}{19}\right)\)
\(\chi_{42237}(15391,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{37}{38}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{11}{19}\right)\)
\(\chi_{42237}(17614,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{37}{38}\right)\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{9}{19}\right)\)
\(\chi_{42237}(19837,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{7}{19}\right)\)
\(\chi_{42237}(22060,\cdot)\) \(1\) \(1\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{37}{38}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{5}{19}\right)\)
\(\chi_{42237}(24283,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{3}{19}\right)\)
\(\chi_{42237}(26506,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{38}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{1}{19}\right)\)
\(\chi_{42237}(28729,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{18}{19}\right)\)
\(\chi_{42237}(30952,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{9}{38}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{16}{19}\right)\)
\(\chi_{42237}(33175,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{9}{38}\right)\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{14}{19}\right)\)
\(\chi_{42237}(35398,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{9}{38}\right)\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{12}{19}\right)\)
\(\chi_{42237}(37621,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{38}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{10}{19}\right)\)
\(\chi_{42237}(39844,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{8}{19}\right)\)
\(\chi_{42237}(42067,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{6}{19}\right)\)