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Properties

Label 9900.id
Modulus $9900$
Conductor $2475$
Order $30$
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(9900, base_ring=CyclotomicField(30)) M = H._module chi = DirichletCharacter(H, M([0,25,6,9])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(41,9900)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(9900\)
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: no, induced from 2475.dy
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 \(-1\) \(1\) \(7\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{9900}(41,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{9900}(2081,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(-1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{9900}(2921,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(-1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{9900}(3341,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{9900}(3461,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(-1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{9900}(6221,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(-1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{9900}(6761,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(-1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{9900}(8681,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(-1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{5}{6}\right)\)