# Properties

 Label 2601.1939 Modulus $2601$ Conductor $2601$ Order $51$ 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(2601, base_ring=CyclotomicField(102))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([34,48]))

pari: [g,chi] = znchar(Mod(1939,2601))

## Basic properties

 Modulus: $$2601$$ Conductor: $$2601$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$51$$ 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 2601.y

sage: chi.galois_orbit()

pari: order = charorder(g,chi)

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

## Related number fields

 Field of values: $\Q(\zeta_{51})$ Fixed field: Number field defined by a degree 51 polynomial

## Values on generators

$$(290,2026)$$ → $$(e\left(\frac{1}{3}\right),e\left(\frac{8}{17}\right))$$

## Values

 $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$7$$ $$8$$ $$10$$ $$11$$ $$13$$ $$14$$ $$16$$ $$1$$ $$1$$ $$e\left(\frac{38}{51}\right)$$ $$e\left(\frac{25}{51}\right)$$ $$e\left(\frac{22}{51}\right)$$ $$e\left(\frac{14}{51}\right)$$ $$e\left(\frac{4}{17}\right)$$ $$e\left(\frac{3}{17}\right)$$ $$e\left(\frac{8}{51}\right)$$ $$e\left(\frac{46}{51}\right)$$ $$e\left(\frac{1}{51}\right)$$ $$e\left(\frac{50}{51}\right)$$
 value at e.g. 2