# Properties

 Label 8470.bm Modulus $8470$ Conductor $847$ Order $22$ Real no Primitive no Minimal yes Parity even

# Related objects

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

sage: H = DirichletGroup(8470, base_ring=CyclotomicField(22))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,11,3]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(461,8470))

pari: order = charorder(g,chi)

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

## Basic properties

 Modulus: $$8470$$ Conductor: $$847$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$22$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 847.p sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Related number fields

 Field of values: $$\Q(\zeta_{11})$$ Fixed field: 22.22.9844157004354856615879058544553513429399461246097373.1

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$3$$ $$9$$ $$13$$ $$17$$ $$19$$ $$23$$ $$27$$ $$29$$ $$31$$ $$37$$
$$\chi_{8470}(461,\cdot)$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$-1$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{8470}(1231,\cdot)$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$-1$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$
$$\chi_{8470}(2001,\cdot)$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$-1$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$
$$\chi_{8470}(2771,\cdot)$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$-1$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$
$$\chi_{8470}(3541,\cdot)$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$-1$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{8470}(4311,\cdot)$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$-1$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{8470}(5851,\cdot)$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$-1$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$
$$\chi_{8470}(6621,\cdot)$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$-1$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{8470}(7391,\cdot)$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$-1$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$
$$\chi_{8470}(8161,\cdot)$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$-1$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$