# Properties

 Label 896.bs Modulus $896$ Conductor $896$ Order $96$ Real no Primitive yes Minimal yes Parity odd

# Related objects

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

sage: H = DirichletGroup(896, base_ring=CyclotomicField(96))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([48,63,64]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(11,896))

pari: order = charorder(g,chi)

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

## Basic properties

 Modulus: $$896$$ Conductor: $$896$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$96$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes 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: $\Q(\zeta_{96})$ Fixed field: Number field defined by a degree 96 polynomial

## First 31 of 32 characters in Galois orbit

Character $$-1$$ $$1$$ $$3$$ $$5$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$19$$ $$23$$ $$25$$
$$\chi_{896}(11,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{13}{96}\right)$$ $$e\left(\frac{95}{96}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{91}{96}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{89}{96}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{47}{48}\right)$$
$$\chi_{896}(51,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{71}{96}\right)$$ $$e\left(\frac{61}{96}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{17}{96}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{43}{96}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{13}{48}\right)$$
$$\chi_{896}(67,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{91}{96}\right)$$ $$e\left(\frac{89}{96}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{61}{96}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{47}{96}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{41}{48}\right)$$
$$\chi_{896}(107,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{96}\right)$$ $$e\left(\frac{7}{96}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{35}{96}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{49}{96}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{7}{48}\right)$$
$$\chi_{896}(123,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{25}{96}\right)$$ $$e\left(\frac{35}{96}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{79}{96}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{53}{96}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{35}{48}\right)$$
$$\chi_{896}(163,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{83}{96}\right)$$ $$e\left(\frac{1}{96}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{5}{96}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{7}{96}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{1}{48}\right)$$
$$\chi_{896}(179,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{7}{96}\right)$$ $$e\left(\frac{29}{96}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{49}{96}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{11}{96}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{29}{48}\right)$$
$$\chi_{896}(219,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{17}{96}\right)$$ $$e\left(\frac{43}{96}\right)$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{23}{96}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{13}{96}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{43}{48}\right)$$
$$\chi_{896}(235,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{37}{96}\right)$$ $$e\left(\frac{71}{96}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{67}{96}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{17}{96}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{23}{48}\right)$$
$$\chi_{896}(275,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{95}{96}\right)$$ $$e\left(\frac{37}{96}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{89}{96}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{67}{96}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{37}{48}\right)$$
$$\chi_{896}(291,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{19}{96}\right)$$ $$e\left(\frac{65}{96}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{37}{96}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{71}{96}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{17}{48}\right)$$
$$\chi_{896}(331,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{29}{96}\right)$$ $$e\left(\frac{79}{96}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{11}{96}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{73}{96}\right)$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{31}{48}\right)$$
$$\chi_{896}(347,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{49}{96}\right)$$ $$e\left(\frac{11}{96}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{55}{96}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{77}{96}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{11}{48}\right)$$
$$\chi_{896}(387,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{11}{96}\right)$$ $$e\left(\frac{73}{96}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{77}{96}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{31}{96}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{25}{48}\right)$$
$$\chi_{896}(403,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{31}{96}\right)$$ $$e\left(\frac{5}{96}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{25}{96}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{35}{96}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{5}{48}\right)$$
$$\chi_{896}(443,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{41}{96}\right)$$ $$e\left(\frac{19}{96}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{95}{96}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{37}{96}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{19}{48}\right)$$
$$\chi_{896}(459,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{61}{96}\right)$$ $$e\left(\frac{47}{96}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{43}{96}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{41}{96}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{47}{48}\right)$$
$$\chi_{896}(499,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{23}{96}\right)$$ $$e\left(\frac{13}{96}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{65}{96}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{91}{96}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{13}{48}\right)$$
$$\chi_{896}(515,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{43}{96}\right)$$ $$e\left(\frac{41}{96}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{13}{96}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{95}{96}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{41}{48}\right)$$
$$\chi_{896}(555,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{53}{96}\right)$$ $$e\left(\frac{55}{96}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{83}{96}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{1}{96}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{7}{48}\right)$$
$$\chi_{896}(571,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{73}{96}\right)$$ $$e\left(\frac{83}{96}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{31}{96}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{5}{96}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{35}{48}\right)$$
$$\chi_{896}(611,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{35}{96}\right)$$ $$e\left(\frac{49}{96}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{53}{96}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{55}{96}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{1}{48}\right)$$
$$\chi_{896}(627,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{55}{96}\right)$$ $$e\left(\frac{77}{96}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{1}{96}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{59}{96}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{29}{48}\right)$$
$$\chi_{896}(667,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{65}{96}\right)$$ $$e\left(\frac{91}{96}\right)$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{71}{96}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{61}{96}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{43}{48}\right)$$
$$\chi_{896}(683,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{85}{96}\right)$$ $$e\left(\frac{23}{96}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{19}{96}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{65}{96}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{23}{48}\right)$$
$$\chi_{896}(723,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{47}{96}\right)$$ $$e\left(\frac{85}{96}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{41}{96}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{19}{96}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{37}{48}\right)$$
$$\chi_{896}(739,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{67}{96}\right)$$ $$e\left(\frac{17}{96}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{85}{96}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{23}{96}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{17}{48}\right)$$
$$\chi_{896}(779,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{77}{96}\right)$$ $$e\left(\frac{31}{96}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{59}{96}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{25}{96}\right)$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{31}{48}\right)$$
$$\chi_{896}(795,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{96}\right)$$ $$e\left(\frac{59}{96}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{7}{96}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{29}{96}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{11}{48}\right)$$
$$\chi_{896}(835,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{59}{96}\right)$$ $$e\left(\frac{25}{96}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{29}{96}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{79}{96}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{25}{48}\right)$$
$$\chi_{896}(851,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{79}{96}\right)$$ $$e\left(\frac{53}{96}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{73}{96}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{83}{96}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{5}{48}\right)$$