Properties

Label 103.f
Modulus $103$
Conductor $103$
Order $34$
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(103, base_ring=CyclotomicField(34))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([13]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(3,103))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(103\)
Conductor: \(103\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(34\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{17})\)
Fixed field: 34.0.2652335238355663972863781109929452800183143879582476922663961790823.1

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{103}(3,\cdot)\) \(-1\) \(1\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{11}{34}\right)\)
\(\chi_{103}(10,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{31}{34}\right)\)
\(\chi_{103}(22,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{27}{34}\right)\)
\(\chi_{103}(24,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{9}{34}\right)\)
\(\chi_{103}(27,\cdot)\) \(-1\) \(1\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{33}{34}\right)\)
\(\chi_{103}(31,\cdot)\) \(-1\) \(1\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{3}{34}\right)\)
\(\chi_{103}(37,\cdot)\) \(-1\) \(1\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{21}{34}\right)\)
\(\chi_{103}(39,\cdot)\) \(-1\) \(1\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{13}{34}\right)\)
\(\chi_{103}(42,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{1}{34}\right)\)
\(\chi_{103}(69,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{23}{34}\right)\)
\(\chi_{103}(73,\cdot)\) \(-1\) \(1\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{25}{34}\right)\)
\(\chi_{103}(80,\cdot)\) \(-1\) \(1\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{29}{34}\right)\)
\(\chi_{103}(89,\cdot)\) \(-1\) \(1\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{7}{34}\right)\)
\(\chi_{103}(90,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{19}{34}\right)\)
\(\chi_{103}(94,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{5}{34}\right)\)
\(\chi_{103}(95,\cdot)\) \(-1\) \(1\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{15}{34}\right)\)