# Properties

 Label 1148.ci Modulus $1148$ Conductor $287$ Order $120$ Real no Primitive no Minimal yes Parity odd

# Related objects

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

sage: H = DirichletGroup(1148, base_ring=CyclotomicField(120))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,80,81]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(53,1148))

pari: order = charorder(g,chi)

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

## Basic properties

 Modulus: $$1148$$ Conductor: $$287$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$120$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 287.bf 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: $\Q(\zeta_{120})$ Fixed field: Number field defined by a degree 120 polynomial (not computed)

## First 31 of 32 characters in Galois orbit

Character $$-1$$ $$1$$ $$3$$ $$5$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$19$$ $$23$$ $$25$$
$$\chi_{1148}(53,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{83}{120}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{113}{120}\right)$$ $$e\left(\frac{49}{120}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{1148}(65,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{37}{120}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{7}{120}\right)$$ $$e\left(\frac{71}{120}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$
$$\chi_{1148}(93,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{67}{120}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{97}{120}\right)$$ $$e\left(\frac{41}{120}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$
$$\chi_{1148}(149,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{73}{120}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{43}{120}\right)$$ $$e\left(\frac{59}{120}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$
$$\chi_{1148}(177,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{79}{120}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{109}{120}\right)$$ $$e\left(\frac{77}{120}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$
$$\chi_{1148}(193,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{23}{120}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{53}{120}\right)$$ $$e\left(\frac{109}{120}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{1148}(233,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{19}{120}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{49}{120}\right)$$ $$e\left(\frac{17}{120}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$
$$\chi_{1148}(261,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{13}{120}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{103}{120}\right)$$ $$e\left(\frac{119}{120}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$
$$\chi_{1148}(317,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{120}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{37}{120}\right)$$ $$e\left(\frac{101}{120}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$
$$\chi_{1148}(345,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{97}{120}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{67}{120}\right)$$ $$e\left(\frac{11}{120}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$
$$\chi_{1148}(417,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{71}{120}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{101}{120}\right)$$ $$e\left(\frac{13}{120}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$
$$\chi_{1148}(429,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{120}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{91}{120}\right)$$ $$e\left(\frac{83}{120}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$
$$\chi_{1148}(445,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{29}{120}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{119}{120}\right)$$ $$e\left(\frac{7}{120}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$
$$\chi_{1148}(457,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{49}{120}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{19}{120}\right)$$ $$e\left(\frac{107}{120}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$
$$\chi_{1148}(473,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{101}{120}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{71}{120}\right)$$ $$e\left(\frac{103}{120}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$
$$\chi_{1148}(485,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{91}{120}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{1}{120}\right)$$ $$e\left(\frac{113}{120}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$
$$\chi_{1148}(557,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{77}{120}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{47}{120}\right)$$ $$e\left(\frac{31}{120}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$
$$\chi_{1148}(585,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{107}{120}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{17}{120}\right)$$ $$e\left(\frac{1}{120}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$
$$\chi_{1148}(641,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{113}{120}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{83}{120}\right)$$ $$e\left(\frac{19}{120}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{1148}(669,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{119}{120}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{29}{120}\right)$$ $$e\left(\frac{37}{120}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$
$$\chi_{1148}(709,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{43}{120}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{73}{120}\right)$$ $$e\left(\frac{89}{120}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$
$$\chi_{1148}(725,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{59}{120}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{89}{120}\right)$$ $$e\left(\frac{97}{120}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$
$$\chi_{1148}(753,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{53}{120}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{23}{120}\right)$$ $$e\left(\frac{79}{120}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{1148}(809,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{47}{120}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{77}{120}\right)$$ $$e\left(\frac{61}{120}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$
$$\chi_{1148}(837,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{17}{120}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{107}{120}\right)$$ $$e\left(\frac{91}{120}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$
$$\chi_{1148}(849,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{103}{120}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{13}{120}\right)$$ $$e\left(\frac{29}{120}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$
$$\chi_{1148}(921,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{41}{120}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{11}{120}\right)$$ $$e\left(\frac{43}{120}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$
$$\chi_{1148}(949,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{89}{120}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{59}{120}\right)$$ $$e\left(\frac{67}{120}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$
$$\chi_{1148}(977,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{120}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{41}{120}\right)$$ $$e\left(\frac{73}{120}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$
$$\chi_{1148}(1073,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{31}{120}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{61}{120}\right)$$ $$e\left(\frac{53}{120}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$
$$\chi_{1148}(1101,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{109}{120}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{79}{120}\right)$$ $$e\left(\frac{47}{120}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$