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Properties

Label 980.br
Modulus $980$
Conductor $245$
Order $42$
Real no
Primitive no
Minimal yes
Parity odd

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(42)) M = H._module chi = DirichletCharacter(H, M([0,21,23])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(89,980)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(980\)
Conductor: \(245\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(42\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 245.u
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: \(\Q(\zeta_{21})\)
Fixed field: 42.0.56353276529596271503862578540802938668269419115433656434196014026165008544921875.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(9\) \(11\) \(13\) \(17\) \(19\) \(23\) \(27\) \(29\) \(31\)
\(\chi_{980}(89,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{980}(229,\cdot)\) \(-1\) \(1\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{980}(269,\cdot)\) \(-1\) \(1\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{980}(369,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{980}(409,\cdot)\) \(-1\) \(1\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{980}(549,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{980}(649,\cdot)\) \(-1\) \(1\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{980}(689,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{980}(789,\cdot)\) \(-1\) \(1\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{980}(829,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{980}(929,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{980}(969,\cdot)\) \(-1\) \(1\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{6}\right)\)