# Properties

 Label 273.bu Modulus $273$ Conductor $91$ Order $12$ Real no Primitive no Minimal yes Parity odd

# Related objects

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

M = H._module

chi = DirichletCharacter(H, M([0,4,7]))

chi.galois_orbit()

[g,chi] = znchar(Mod(37,273))

order = charorder(g,chi)

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

## Basic properties

 Modulus: $$273$$ Conductor: $$91$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$12$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 91.x sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Related number fields

 Field of values: $$\Q(\zeta_{12})$$ Fixed field: 12.0.10331448031704891637.1

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$8$$ $$10$$ $$11$$ $$16$$ $$17$$ $$19$$ $$20$$
$$\chi_{273}(37,\cdot)$$ $$-1$$ $$1$$ $$i$$ $$-1$$ $$e\left(\frac{11}{12}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{273}(46,\cdot)$$ $$-1$$ $$1$$ $$i$$ $$-1$$ $$e\left(\frac{7}{12}\right)$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{273}(184,\cdot)$$ $$-1$$ $$1$$ $$-i$$ $$-1$$ $$e\left(\frac{5}{12}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{273}(214,\cdot)$$ $$-1$$ $$1$$ $$-i$$ $$-1$$ $$e\left(\frac{1}{12}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$