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Properties

Label 8624.dn
Modulus $8624$
Conductor $784$
Order $28$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8624, base_ring=CyclotomicField(28)) M = H._module chi = DirichletCharacter(H, M([0,7,20,0])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(309,8624)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(8624\)
Conductor: \(784\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(28\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 784.bh
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{28})\)
Fixed field: Number field defined by a degree 28 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(9\) \(13\) \(15\) \(17\) \(19\) \(23\) \(25\) \(27\)
\(\chi_{8624}(309,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(-i\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{11}{28}\right)\)
\(\chi_{8624}(925,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(i\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{28}\right)\)
\(\chi_{8624}(1541,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(-i\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{27}{28}\right)\)
\(\chi_{8624}(2773,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(-i\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{15}{28}\right)\)
\(\chi_{8624}(3389,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(i\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{9}{28}\right)\)
\(\chi_{8624}(4005,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(-i\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{3}{28}\right)\)
\(\chi_{8624}(4621,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(i\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{25}{28}\right)\)
\(\chi_{8624}(5237,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(-i\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{19}{28}\right)\)
\(\chi_{8624}(5853,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(i\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{13}{28}\right)\)
\(\chi_{8624}(7085,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(i\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{28}\right)\)
\(\chi_{8624}(7701,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(-i\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{23}{28}\right)\)
\(\chi_{8624}(8317,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(i\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{17}{28}\right)\)