# Properties

 Label 1225.34 Modulus $1225$ Conductor $1225$ Order $70$ Real no Primitive yes Minimal yes Parity odd

# Related objects

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

sage: H = DirichletGroup(1225)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([49,15]))

pari: [g,chi] = znchar(Mod(34,1225))

## Basic properties

 Modulus: $$1225$$ Conductor: $$1225$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$70$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 1225.bk

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

$$(1177,101)$$ → $$(e\left(\frac{7}{10}\right),e\left(\frac{3}{14}\right))$$

## Values

 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$6$$ $$8$$ $$9$$ $$11$$ $$12$$ $$13$$ $$16$$ $$-1$$ $$1$$ $$e\left(\frac{19}{70}\right)$$ $$e\left(\frac{4}{35}\right)$$ $$e\left(\frac{19}{35}\right)$$ $$e\left(\frac{27}{70}\right)$$ $$e\left(\frac{57}{70}\right)$$ $$e\left(\frac{8}{35}\right)$$ $$e\left(\frac{27}{35}\right)$$ $$e\left(\frac{23}{35}\right)$$ $$e\left(\frac{13}{35}\right)$$ $$e\left(\frac{3}{35}\right)$$
 value at e.g. 2

## Related number fields

 Field of values: $\Q(\zeta_{35})$ Fixed field: Number field defined by a degree 70 polynomial