Properties

Label 967.h
Modulus $967$
Conductor $967$
Order $23$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(967, base_ring=CyclotomicField(46))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([2]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(69,967))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(967\)
Conductor: \(967\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(23\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
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: \(\Q(\zeta_{23})\)
Fixed field: 23.23.477949960252640343082669666642744217085836889062320413931701625489.1

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{967}(69,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{14}{23}\right)\)
\(\chi_{967}(72,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{3}{23}\right)\)
\(\chi_{967}(133,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{17}{23}\right)\)
\(\chi_{967}(157,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{4}{23}\right)\)
\(\chi_{967}(187,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{2}{23}\right)\)
\(\chi_{967}(196,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{18}{23}\right)\)
\(\chi_{967}(283,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{11}{23}\right)\)
\(\chi_{967}(332,\cdot)\) \(1\) \(1\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{16}{23}\right)\)
\(\chi_{967}(349,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{6}{23}\right)\)
\(\chi_{967}(474,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{8}{23}\right)\)
\(\chi_{967}(574,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{21}{23}\right)\)
\(\chi_{967}(641,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{10}{23}\right)\)
\(\chi_{967}(667,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{7}{23}\right)\)
\(\chi_{967}(696,\cdot)\) \(1\) \(1\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{19}{23}\right)\)
\(\chi_{967}(703,\cdot)\) \(1\) \(1\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{13}{23}\right)\)
\(\chi_{967}(714,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{1}{23}\right)\)
\(\chi_{967}(795,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{22}{23}\right)\)
\(\chi_{967}(873,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{20}{23}\right)\)
\(\chi_{967}(893,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{5}{23}\right)\)
\(\chi_{967}(916,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{15}{23}\right)\)
\(\chi_{967}(926,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{12}{23}\right)\)
\(\chi_{967}(953,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{9}{23}\right)\)