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Properties

Label 2475.da
Modulus $2475$
Conductor $825$
Order $20$
Real no
Primitive no
Minimal yes
Parity even

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2475, base_ring=CyclotomicField(20)) M = H._module chi = DirichletCharacter(H, M([10,11,4])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(323,2475)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(2475\)
Conductor: \(825\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(20\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 825.ci
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: \(\Q(\zeta_{20})\)
Fixed field: Number field defined by a degree 20 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(7\) \(8\) \(13\) \(14\) \(16\) \(17\) \(19\) \(23\)
\(\chi_{2475}(323,\cdot)\) \(1\) \(1\) \(i\) \(-1\) \(e\left(\frac{3}{20}\right)\) \(-i\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(1\) \(e\left(\frac{9}{20}\right)\) \(-1\) \(e\left(\frac{11}{20}\right)\)
\(\chi_{2475}(1142,\cdot)\) \(1\) \(1\) \(-i\) \(-1\) \(e\left(\frac{9}{20}\right)\) \(i\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(e\left(\frac{7}{20}\right)\) \(-1\) \(e\left(\frac{13}{20}\right)\)
\(\chi_{2475}(1763,\cdot)\) \(1\) \(1\) \(i\) \(-1\) \(e\left(\frac{7}{20}\right)\) \(-i\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(e\left(\frac{1}{20}\right)\) \(-1\) \(e\left(\frac{19}{20}\right)\)
\(\chi_{2475}(1853,\cdot)\) \(1\) \(1\) \(i\) \(-1\) \(e\left(\frac{11}{20}\right)\) \(-i\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(1\) \(e\left(\frac{13}{20}\right)\) \(-1\) \(e\left(\frac{7}{20}\right)\)
\(\chi_{2475}(1862,\cdot)\) \(1\) \(1\) \(-i\) \(-1\) \(e\left(\frac{17}{20}\right)\) \(i\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(e\left(\frac{11}{20}\right)\) \(-1\) \(e\left(\frac{9}{20}\right)\)
\(\chi_{2475}(2033,\cdot)\) \(1\) \(1\) \(i\) \(-1\) \(e\left(\frac{19}{20}\right)\) \(-i\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(e\left(\frac{17}{20}\right)\) \(-1\) \(e\left(\frac{3}{20}\right)\)
\(\chi_{2475}(2402,\cdot)\) \(1\) \(1\) \(-i\) \(-1\) \(e\left(\frac{13}{20}\right)\) \(i\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(1\) \(e\left(\frac{19}{20}\right)\) \(-1\) \(e\left(\frac{1}{20}\right)\)
\(\chi_{2475}(2447,\cdot)\) \(1\) \(1\) \(-i\) \(-1\) \(e\left(\frac{1}{20}\right)\) \(i\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(1\) \(e\left(\frac{3}{20}\right)\) \(-1\) \(e\left(\frac{17}{20}\right)\)