↑

Properties

Label 1734.l
Modulus $1734$
Conductor $867$
Order $34$
Real no
Primitive no
Minimal yes
Parity odd

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1734, base_ring=CyclotomicField(34)) M = H._module chi = DirichletCharacter(H, M([17,9])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(101,1734)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1734\)
Conductor: \(867\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(34\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 867.m
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{17})\)
Fixed field: 34.0.12309522877752896848740501655027735029115386449381382152715887725819844838409975062613491.1

Characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(7\) \(11\) \(13\) \(19\) \(23\) \(25\) \(29\) \(31\) \(35\)
\(\chi_{1734}(101,\cdot)\) \(-1\) \(1\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{5}{34}\right)\)
\(\chi_{1734}(203,\cdot)\) \(-1\) \(1\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{27}{34}\right)\)
\(\chi_{1734}(305,\cdot)\) \(-1\) \(1\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{15}{34}\right)\)
\(\chi_{1734}(407,\cdot)\) \(-1\) \(1\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{3}{34}\right)\)
\(\chi_{1734}(509,\cdot)\) \(-1\) \(1\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{25}{34}\right)\)
\(\chi_{1734}(611,\cdot)\) \(-1\) \(1\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{13}{34}\right)\)
\(\chi_{1734}(713,\cdot)\) \(-1\) \(1\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{1}{34}\right)\)
\(\chi_{1734}(815,\cdot)\) \(-1\) \(1\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{23}{34}\right)\)
\(\chi_{1734}(917,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{11}{34}\right)\)
\(\chi_{1734}(1019,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{33}{34}\right)\)
\(\chi_{1734}(1121,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{21}{34}\right)\)
\(\chi_{1734}(1223,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{9}{34}\right)\)
\(\chi_{1734}(1325,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{31}{34}\right)\)
\(\chi_{1734}(1427,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{19}{34}\right)\)
\(\chi_{1734}(1529,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{7}{34}\right)\)
\(\chi_{1734}(1631,\cdot)\) \(-1\) \(1\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{29}{34}\right)\)