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Properties

Label 8464.u
Modulus $8464$
Conductor $529$
Order $23$
Real no
Primitive no
Minimal no
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8464, base_ring=CyclotomicField(46)) M = H._module chi = DirichletCharacter(H, M([0,0,22])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(369,8464)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(8464\)
Conductor: \(529\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(23\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 529.e
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{23})\)
Fixed field: Number field defined by a degree 23 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(21\)
\(\chi_{8464}(369,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{8}{23}\right)\)
\(\chi_{8464}(737,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{16}{23}\right)\)
\(\chi_{8464}(1105,\cdot)\) \(1\) \(1\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{1}{23}\right)\)
\(\chi_{8464}(1473,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{9}{23}\right)\)
\(\chi_{8464}(1841,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{17}{23}\right)\)
\(\chi_{8464}(2209,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{2}{23}\right)\)
\(\chi_{8464}(2577,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{10}{23}\right)\)
\(\chi_{8464}(2945,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{18}{23}\right)\)
\(\chi_{8464}(3313,\cdot)\) \(1\) \(1\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{3}{23}\right)\)
\(\chi_{8464}(3681,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{11}{23}\right)\)
\(\chi_{8464}(4049,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{19}{23}\right)\)
\(\chi_{8464}(4417,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{4}{23}\right)\)
\(\chi_{8464}(4785,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{12}{23}\right)\)
\(\chi_{8464}(5153,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{20}{23}\right)\)
\(\chi_{8464}(5521,\cdot)\) \(1\) \(1\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{5}{23}\right)\)
\(\chi_{8464}(5889,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{13}{23}\right)\)
\(\chi_{8464}(6257,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{21}{23}\right)\)
\(\chi_{8464}(6625,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{6}{23}\right)\)
\(\chi_{8464}(6993,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{14}{23}\right)\)
\(\chi_{8464}(7361,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{22}{23}\right)\)
\(\chi_{8464}(7729,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{7}{23}\right)\)
\(\chi_{8464}(8097,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{15}{23}\right)\)