# Properties

 Label 6025.57 Modulus $6025$ Conductor $1205$ Order $80$ Real no Primitive no Minimal yes Parity even

# Learn more about

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

sage: H = DirichletGroup(6025)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([20,9]))

pari: [g,chi] = znchar(Mod(57,6025))

## Basic properties

 Modulus: $$6025$$ Conductor: $$1205$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$80$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{1205}(57,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 6025.hb

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

$$(2652,2176)$$ → $$(i,e\left(\frac{9}{80}\right))$$

## Values

 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$6$$ $$7$$ $$8$$ $$9$$ $$11$$ $$12$$ $$13$$ $$1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$i$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{29}{80}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{3}{80}\right)$$
 value at e.g. 2

## Related number fields

 Field of values: $\Q(\zeta_{80})$ Fixed field: Number field defined by a degree 80 polynomial