# Properties

 Label 6025.1399 Modulus $6025$ Conductor $1205$ Order $40$ Real no Primitive no Minimal no Parity even

# Related objects

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([20,39]))

pari: [g,chi] = znchar(Mod(1399,6025))

## Basic properties

 Modulus: $$6025$$ Conductor: $$1205$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$40$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{1205}(194,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 6025.et

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

$$(2652,2176)$$ → $$(-1,e\left(\frac{39}{40}\right))$$

## Values

 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$6$$ $$7$$ $$8$$ $$9$$ $$11$$ $$12$$ $$13$$ $$1$$ $$1$$ $$-i$$ $$e\left(\frac{19}{20}\right)$$ $$-1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$i$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{13}{40}\right)$$
 value at e.g. 2

## Related number fields

 Field of values: $$\Q(\zeta_{40})$$ Fixed field: Number field defined by a degree 40 polynomial