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Properties

Label 6525.cz
Modulus $6525$
Conductor $435$
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(6525, base_ring=CyclotomicField(28)) M = H._module chi = DirichletCharacter(H, M([14,7,24])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(107,6525)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(6525\)
Conductor: \(435\)
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 435.bj
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 \(-1\) \(1\) \(2\) \(4\) \(7\) \(8\) \(11\) \(13\) \(14\) \(16\) \(17\) \(19\)
\(\chi_{6525}(107,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(-i\) \(e\left(\frac{3}{14}\right)\)
\(\chi_{6525}(368,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(i\) \(e\left(\frac{3}{14}\right)\)
\(\chi_{6525}(1457,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(-i\) \(e\left(\frac{5}{14}\right)\)
\(\chi_{6525}(1718,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(i\) \(e\left(\frac{5}{14}\right)\)
\(\chi_{6525}(2807,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(-i\) \(e\left(\frac{13}{14}\right)\)
\(\chi_{6525}(3032,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(-i\) \(e\left(\frac{11}{14}\right)\)
\(\chi_{6525}(3068,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(i\) \(e\left(\frac{13}{14}\right)\)
\(\chi_{6525}(3293,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(i\) \(e\left(\frac{11}{14}\right)\)
\(\chi_{6525}(3707,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(-i\) \(e\left(\frac{1}{14}\right)\)
\(\chi_{6525}(3968,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(i\) \(e\left(\frac{1}{14}\right)\)
\(\chi_{6525}(4607,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(-i\) \(e\left(\frac{9}{14}\right)\)
\(\chi_{6525}(4868,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(i\) \(e\left(\frac{9}{14}\right)\)