Related objects

Show commands for: Pari/GP / SageMath
sage: H = DirichletGroup(68970)

sage: chi = H[1]

pari: [g,chi] = znchar(Mod(1,68970))

Basic properties

 Modulus: $$68970$$ Conductor: $$1$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$1$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: yes Primitive: no, induced from $$\chi_{1}(0,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

Related number fields

 Field of values: $$\Q$$

Values on generators

$$(22991,55177,21661,3631)$$ → $$(1,1,1,1)$$

First values

 $$-1$$ $$1$$ $$7$$ $$13$$ $$17$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
 value at e.g. 2