# Properties

 Label 6001.30 Modulus $6001$ Conductor $6001$ Order $176$ Real no Primitive yes Minimal yes Parity even

# Related objects

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

sage: H = DirichletGroup(6001)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([44,61]))

pari: [g,chi] = znchar(Mod(30,6001))

## Basic properties

 Modulus: $$6001$$ Conductor: $$6001$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$176$$ 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 6001.dx

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

$$(2825,3180)$$ → $$(i,e\left(\frac{61}{176}\right))$$

## Values

 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$ $$1$$ $$1$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{105}{176}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{61}{176}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{17}{88}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{6}{11}\right)$$
 value at e.g. 2

## Related number fields

 Field of values: $\Q(\zeta_{176})$ Fixed field: Number field defined by a degree 176 polynomial