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Properties

Label 2475.dy
Modulus $2475$
Conductor $2475$
Order $30$
Real no
Primitive yes
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(30)) M = H._module chi = DirichletCharacter(H, M([25,6,9])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(41,2475)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(2475\)
Conductor: \(2475\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(30\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: yes
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: \(\Q(\zeta_{15})\)
Fixed field: Number field defined by a degree 30 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(7\) \(8\) \(13\) \(14\) \(16\) \(17\) \(19\) \(23\)
\(\chi_{2475}(41,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{30}\right)\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{2475}(446,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{19}{30}\right)\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{5}\right)\) \(-1\) \(e\left(\frac{23}{30}\right)\)
\(\chi_{2475}(866,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{23}{30}\right)\) \(1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{2475}(986,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{30}\right)\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{5}\right)\) \(-1\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{2475}(1256,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{30}\right)\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{5}\right)\) \(-1\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{2475}(1271,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{29}{30}\right)\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{5}\right)\) \(-1\) \(e\left(\frac{13}{30}\right)\)
\(\chi_{2475}(1811,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{17}{30}\right)\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{5}\right)\) \(-1\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{2475}(2081,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{30}\right)\) \(1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{5}\right)\) \(-1\) \(e\left(\frac{7}{30}\right)\)