# Properties

 Label 8470.cb Modulus $8470$ Conductor $605$ Order $44$ Real no Primitive no Minimal yes Parity even

# Learn more

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

sage: H = DirichletGroup(8470, base_ring=CyclotomicField(44))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([33,0,10]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(43,8470))

pari: order = charorder(g,chi)

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

## Basic properties

 Modulus: $$8470$$ Conductor: $$605$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$44$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 605.r sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$3$$ $$9$$ $$13$$ $$17$$ $$19$$ $$23$$ $$27$$ $$29$$ $$31$$ $$37$$
$$\chi_{8470}(43,\cdot)$$ $$1$$ $$1$$ $$i$$ $$-1$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$-i$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{13}{44}\right)$$
$$\chi_{8470}(197,\cdot)$$ $$1$$ $$1$$ $$-i$$ $$-1$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$i$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{31}{44}\right)$$
$$\chi_{8470}(813,\cdot)$$ $$1$$ $$1$$ $$i$$ $$-1$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$-i$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{37}{44}\right)$$
$$\chi_{8470}(1583,\cdot)$$ $$1$$ $$1$$ $$i$$ $$-1$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$-i$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{17}{44}\right)$$
$$\chi_{8470}(1737,\cdot)$$ $$1$$ $$1$$ $$-i$$ $$-1$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$i$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{35}{44}\right)$$
$$\chi_{8470}(2353,\cdot)$$ $$1$$ $$1$$ $$i$$ $$-1$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$-i$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{41}{44}\right)$$
$$\chi_{8470}(2507,\cdot)$$ $$1$$ $$1$$ $$-i$$ $$-1$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$i$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{15}{44}\right)$$
$$\chi_{8470}(3123,\cdot)$$ $$1$$ $$1$$ $$i$$ $$-1$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$-i$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{21}{44}\right)$$
$$\chi_{8470}(3277,\cdot)$$ $$1$$ $$1$$ $$-i$$ $$-1$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$i$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{39}{44}\right)$$
$$\chi_{8470}(3893,\cdot)$$ $$1$$ $$1$$ $$i$$ $$-1$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$-i$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{1}{44}\right)$$
$$\chi_{8470}(4047,\cdot)$$ $$1$$ $$1$$ $$-i$$ $$-1$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$i$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{19}{44}\right)$$
$$\chi_{8470}(4663,\cdot)$$ $$1$$ $$1$$ $$i$$ $$-1$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$-i$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{25}{44}\right)$$
$$\chi_{8470}(4817,\cdot)$$ $$1$$ $$1$$ $$-i$$ $$-1$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$i$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{43}{44}\right)$$
$$\chi_{8470}(5433,\cdot)$$ $$1$$ $$1$$ $$i$$ $$-1$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$-i$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{44}\right)$$
$$\chi_{8470}(5587,\cdot)$$ $$1$$ $$1$$ $$-i$$ $$-1$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$i$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{23}{44}\right)$$
$$\chi_{8470}(6203,\cdot)$$ $$1$$ $$1$$ $$i$$ $$-1$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$-i$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{29}{44}\right)$$
$$\chi_{8470}(6357,\cdot)$$ $$1$$ $$1$$ $$-i$$ $$-1$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$i$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{44}\right)$$
$$\chi_{8470}(6973,\cdot)$$ $$1$$ $$1$$ $$i$$ $$-1$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$-i$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{9}{44}\right)$$
$$\chi_{8470}(7127,\cdot)$$ $$1$$ $$1$$ $$-i$$ $$-1$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$i$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{27}{44}\right)$$
$$\chi_{8470}(7897,\cdot)$$ $$1$$ $$1$$ $$-i$$ $$-1$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$i$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{44}\right)$$