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Properties

Label 7056.gz
Modulus $7056$
Conductor $441$
Order $42$
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(7056, base_ring=CyclotomicField(42)) M = H._module chi = DirichletCharacter(H, M([0,0,7,33])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(209,7056)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(7056\)
Conductor: \(441\)
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 441.bh
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: \(\Q(\zeta_{21})\)
Fixed field: Number field defined by a degree 42 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(11\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\) \(37\)
\(\chi_{7056}(209,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{1}{7}\right)\) \(-1\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{7056}(545,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{4}{7}\right)\) \(-1\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{7056}(1217,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{3}{7}\right)\) \(-1\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{7056}(1553,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{6}{7}\right)\) \(-1\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{7056}(2225,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{5}{7}\right)\) \(-1\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{7056}(2561,\cdot)\) \(1\) \(1\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{1}{7}\right)\) \(-1\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{7056}(3569,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{3}{7}\right)\) \(-1\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{7056}(4241,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{2}{7}\right)\) \(-1\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{7056}(4577,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{5}{7}\right)\) \(-1\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{7056}(5249,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{4}{7}\right)\) \(-1\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{7056}(6257,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{6}{7}\right)\) \(-1\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{7056}(6593,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{2}{7}\right)\) \(-1\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{7}\right)\)