# Properties

 Label 9900.8759 Modulus $9900$ Conductor $9900$ Order $30$ Real no Primitive yes Minimal yes Parity even

# Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter

sage: H = DirichletGroup(9900)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([15,5,21,24]))

pari: [g,chi] = znchar(Mod(8759,9900))

## Basic properties

 Modulus: $$9900$$ Conductor: $$9900$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$30$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 9900.jq

sage: chi.galois_orbit()

pari: order = charorder(g,chi)

pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

## Values on generators

$$(4951,5501,2377,4501)$$ → $$(-1,e\left(\frac{1}{6}\right),e\left(\frac{7}{10}\right),e\left(\frac{4}{5}\right))$$

## Values

 $$-1$$ $$1$$ $$7$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$ $$1$$ $$1$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$-1$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{2}{3}\right)$$
 value at e.g. 2

## Related number fields

 Field of values: $$\Q(\zeta_{15})$$ Fixed field: Number field defined by a degree 30 polynomial