# Properties

 Label 1441.bj Modulus $1441$ Conductor $1441$ Order $65$ Real no Primitive yes Minimal yes Parity even

# Related objects

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

H = DirichletGroup(1441, base_ring=CyclotomicField(130))

M = H._module

chi = DirichletCharacter(H, M([104,72]))

chi.galois_orbit()

[g,chi] = znchar(Mod(3,1441))

order = charorder(g,chi)

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

## Basic properties

 Modulus: $$1441$$ Conductor: $$1441$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$65$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes 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: $\Q(\zeta_{65})$ Fixed field: Number field defined by a degree 65 polynomial

## First 31 of 48 characters in Galois orbit

Character $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$12$$
$$\chi_{1441}(3,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{23}{65}\right)$$ $$e\left(\frac{18}{65}\right)$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{44}{65}\right)$$ $$e\left(\frac{41}{65}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{4}{65}\right)$$ $$e\left(\frac{36}{65}\right)$$ $$e\left(\frac{2}{65}\right)$$ $$e\left(\frac{64}{65}\right)$$
$$\chi_{1441}(5,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{49}{65}\right)$$ $$e\left(\frac{44}{65}\right)$$ $$e\left(\frac{33}{65}\right)$$ $$e\left(\frac{57}{65}\right)$$ $$e\left(\frac{28}{65}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{17}{65}\right)$$ $$e\left(\frac{23}{65}\right)$$ $$e\left(\frac{41}{65}\right)$$ $$e\left(\frac{12}{65}\right)$$
$$\chi_{1441}(9,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{36}{65}\right)$$ $$e\left(\frac{27}{65}\right)$$ $$e\left(\frac{23}{65}\right)$$ $$e\left(\frac{17}{65}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{8}{65}\right)$$ $$e\left(\frac{7}{65}\right)$$ $$e\left(\frac{4}{65}\right)$$ $$e\left(\frac{63}{65}\right)$$
$$\chi_{1441}(15,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{7}{65}\right)$$ $$e\left(\frac{62}{65}\right)$$ $$e\left(\frac{14}{65}\right)$$ $$e\left(\frac{36}{65}\right)$$ $$e\left(\frac{4}{65}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{21}{65}\right)$$ $$e\left(\frac{59}{65}\right)$$ $$e\left(\frac{43}{65}\right)$$ $$e\left(\frac{11}{65}\right)$$
$$\chi_{1441}(25,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{33}{65}\right)$$ $$e\left(\frac{23}{65}\right)$$ $$e\left(\frac{1}{65}\right)$$ $$e\left(\frac{49}{65}\right)$$ $$e\left(\frac{56}{65}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{34}{65}\right)$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{17}{65}\right)$$ $$e\left(\frac{24}{65}\right)$$
$$\chi_{1441}(27,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{4}{65}\right)$$ $$e\left(\frac{54}{65}\right)$$ $$e\left(\frac{8}{65}\right)$$ $$e\left(\frac{2}{65}\right)$$ $$e\left(\frac{58}{65}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{12}{65}\right)$$ $$e\left(\frac{43}{65}\right)$$ $$e\left(\frac{6}{65}\right)$$ $$e\left(\frac{62}{65}\right)$$
$$\chi_{1441}(38,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{44}{65}\right)$$ $$e\left(\frac{9}{65}\right)$$ $$e\left(\frac{23}{65}\right)$$ $$e\left(\frac{22}{65}\right)$$ $$e\left(\frac{53}{65}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{2}{65}\right)$$ $$e\left(\frac{18}{65}\right)$$ $$e\left(\frac{1}{65}\right)$$ $$e\left(\frac{32}{65}\right)$$
$$\chi_{1441}(75,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{56}{65}\right)$$ $$e\left(\frac{41}{65}\right)$$ $$e\left(\frac{47}{65}\right)$$ $$e\left(\frac{28}{65}\right)$$ $$e\left(\frac{32}{65}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{38}{65}\right)$$ $$e\left(\frac{17}{65}\right)$$ $$e\left(\frac{19}{65}\right)$$ $$e\left(\frac{23}{65}\right)$$
$$\chi_{1441}(81,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{27}{65}\right)$$ $$e\left(\frac{7}{65}\right)$$ $$e\left(\frac{54}{65}\right)$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{34}{65}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{16}{65}\right)$$ $$e\left(\frac{14}{65}\right)$$ $$e\left(\frac{8}{65}\right)$$ $$e\left(\frac{61}{65}\right)$$
$$\chi_{1441}(114,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{2}{65}\right)$$ $$e\left(\frac{27}{65}\right)$$ $$e\left(\frac{4}{65}\right)$$ $$e\left(\frac{1}{65}\right)$$ $$e\left(\frac{29}{65}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{6}{65}\right)$$ $$e\left(\frac{54}{65}\right)$$ $$e\left(\frac{3}{65}\right)$$ $$e\left(\frac{31}{65}\right)$$
$$\chi_{1441}(125,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{17}{65}\right)$$ $$e\left(\frac{2}{65}\right)$$ $$e\left(\frac{34}{65}\right)$$ $$e\left(\frac{41}{65}\right)$$ $$e\left(\frac{19}{65}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{51}{65}\right)$$ $$e\left(\frac{4}{65}\right)$$ $$e\left(\frac{58}{65}\right)$$ $$e\left(\frac{36}{65}\right)$$
$$\chi_{1441}(135,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{53}{65}\right)$$ $$e\left(\frac{33}{65}\right)$$ $$e\left(\frac{41}{65}\right)$$ $$e\left(\frac{59}{65}\right)$$ $$e\left(\frac{21}{65}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{29}{65}\right)$$ $$e\left(\frac{1}{65}\right)$$ $$e\left(\frac{47}{65}\right)$$ $$e\left(\frac{9}{65}\right)$$
$$\chi_{1441}(174,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{36}{65}\right)$$ $$e\left(\frac{31}{65}\right)$$ $$e\left(\frac{7}{65}\right)$$ $$e\left(\frac{18}{65}\right)$$ $$e\left(\frac{2}{65}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{43}{65}\right)$$ $$e\left(\frac{62}{65}\right)$$ $$e\left(\frac{54}{65}\right)$$ $$e\left(\frac{38}{65}\right)$$
$$\chi_{1441}(190,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{28}{65}\right)$$ $$e\left(\frac{53}{65}\right)$$ $$e\left(\frac{56}{65}\right)$$ $$e\left(\frac{14}{65}\right)$$ $$e\left(\frac{16}{65}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{19}{65}\right)$$ $$e\left(\frac{41}{65}\right)$$ $$e\left(\frac{42}{65}\right)$$ $$e\left(\frac{44}{65}\right)$$
$$\chi_{1441}(196,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{6}{65}\right)$$ $$e\left(\frac{16}{65}\right)$$ $$e\left(\frac{12}{65}\right)$$ $$e\left(\frac{3}{65}\right)$$ $$e\left(\frac{22}{65}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{18}{65}\right)$$ $$e\left(\frac{32}{65}\right)$$ $$e\left(\frac{9}{65}\right)$$ $$e\left(\frac{28}{65}\right)$$
$$\chi_{1441}(225,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{14}{65}\right)$$ $$e\left(\frac{59}{65}\right)$$ $$e\left(\frac{28}{65}\right)$$ $$e\left(\frac{7}{65}\right)$$ $$e\left(\frac{8}{65}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{42}{65}\right)$$ $$e\left(\frac{53}{65}\right)$$ $$e\left(\frac{21}{65}\right)$$ $$e\left(\frac{22}{65}\right)$$
$$\chi_{1441}(269,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{9}{65}\right)$$ $$e\left(\frac{24}{65}\right)$$ $$e\left(\frac{18}{65}\right)$$ $$e\left(\frac{37}{65}\right)$$ $$e\left(\frac{33}{65}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{27}{65}\right)$$ $$e\left(\frac{48}{65}\right)$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{42}{65}\right)$$
$$\chi_{1441}(290,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{62}{65}\right)$$ $$e\left(\frac{57}{65}\right)$$ $$e\left(\frac{59}{65}\right)$$ $$e\left(\frac{31}{65}\right)$$ $$e\left(\frac{54}{65}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{56}{65}\right)$$ $$e\left(\frac{49}{65}\right)$$ $$e\left(\frac{28}{65}\right)$$ $$e\left(\frac{51}{65}\right)$$
$$\chi_{1441}(311,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{18}{65}\right)$$ $$e\left(\frac{48}{65}\right)$$ $$e\left(\frac{36}{65}\right)$$ $$e\left(\frac{9}{65}\right)$$ $$e\left(\frac{1}{65}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{54}{65}\right)$$ $$e\left(\frac{31}{65}\right)$$ $$e\left(\frac{27}{65}\right)$$ $$e\left(\frac{19}{65}\right)$$
$$\chi_{1441}(405,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{11}{65}\right)$$ $$e\left(\frac{51}{65}\right)$$ $$e\left(\frac{22}{65}\right)$$ $$e\left(\frac{38}{65}\right)$$ $$e\left(\frac{62}{65}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{33}{65}\right)$$ $$e\left(\frac{37}{65}\right)$$ $$e\left(\frac{49}{65}\right)$$ $$e\left(\frac{8}{65}\right)$$
$$\chi_{1441}(427,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{61}{65}\right)$$ $$e\left(\frac{11}{65}\right)$$ $$e\left(\frac{57}{65}\right)$$ $$e\left(\frac{63}{65}\right)$$ $$e\left(\frac{7}{65}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{53}{65}\right)$$ $$e\left(\frac{22}{65}\right)$$ $$e\left(\frac{59}{65}\right)$$ $$e\left(\frac{3}{65}\right)$$
$$\chi_{1441}(434,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{24}{65}\right)$$ $$e\left(\frac{64}{65}\right)$$ $$e\left(\frac{48}{65}\right)$$ $$e\left(\frac{12}{65}\right)$$ $$e\left(\frac{23}{65}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{7}{65}\right)$$ $$e\left(\frac{63}{65}\right)$$ $$e\left(\frac{36}{65}\right)$$ $$e\left(\frac{47}{65}\right)$$
$$\chi_{1441}(493,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{21}{65}\right)$$ $$e\left(\frac{56}{65}\right)$$ $$e\left(\frac{42}{65}\right)$$ $$e\left(\frac{43}{65}\right)$$ $$e\left(\frac{12}{65}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{63}{65}\right)$$ $$e\left(\frac{47}{65}\right)$$ $$e\left(\frac{64}{65}\right)$$ $$e\left(\frac{33}{65}\right)$$
$$\chi_{1441}(522,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{59}{65}\right)$$ $$e\left(\frac{49}{65}\right)$$ $$e\left(\frac{53}{65}\right)$$ $$e\left(\frac{62}{65}\right)$$ $$e\left(\frac{43}{65}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{47}{65}\right)$$ $$e\left(\frac{33}{65}\right)$$ $$e\left(\frac{56}{65}\right)$$ $$e\left(\frac{37}{65}\right)$$
$$\chi_{1441}(570,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{51}{65}\right)$$ $$e\left(\frac{6}{65}\right)$$ $$e\left(\frac{37}{65}\right)$$ $$e\left(\frac{58}{65}\right)$$ $$e\left(\frac{57}{65}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{23}{65}\right)$$ $$e\left(\frac{12}{65}\right)$$ $$e\left(\frac{44}{65}\right)$$ $$e\left(\frac{43}{65}\right)$$
$$\chi_{1441}(588,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{29}{65}\right)$$ $$e\left(\frac{34}{65}\right)$$ $$e\left(\frac{58}{65}\right)$$ $$e\left(\frac{47}{65}\right)$$ $$e\left(\frac{63}{65}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{22}{65}\right)$$ $$e\left(\frac{3}{65}\right)$$ $$e\left(\frac{11}{65}\right)$$ $$e\left(\frac{27}{65}\right)$$
$$\chi_{1441}(625,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{65}\right)$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{2}{65}\right)$$ $$e\left(\frac{33}{65}\right)$$ $$e\left(\frac{47}{65}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{3}{65}\right)$$ $$e\left(\frac{27}{65}\right)$$ $$e\left(\frac{34}{65}\right)$$ $$e\left(\frac{48}{65}\right)$$
$$\chi_{1441}(641,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{3}{65}\right)$$ $$e\left(\frac{8}{65}\right)$$ $$e\left(\frac{6}{65}\right)$$ $$e\left(\frac{34}{65}\right)$$ $$e\left(\frac{11}{65}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{9}{65}\right)$$ $$e\left(\frac{16}{65}\right)$$ $$e\left(\frac{37}{65}\right)$$ $$e\left(\frac{14}{65}\right)$$
$$\chi_{1441}(675,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{37}{65}\right)$$ $$e\left(\frac{12}{65}\right)$$ $$e\left(\frac{9}{65}\right)$$ $$e\left(\frac{51}{65}\right)$$ $$e\left(\frac{49}{65}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{24}{65}\right)$$ $$e\left(\frac{23}{65}\right)$$ $$e\left(\frac{21}{65}\right)$$
$$\chi_{1441}(729,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{8}{65}\right)$$ $$e\left(\frac{43}{65}\right)$$ $$e\left(\frac{16}{65}\right)$$ $$e\left(\frac{4}{65}\right)$$ $$e\left(\frac{51}{65}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{24}{65}\right)$$ $$e\left(\frac{21}{65}\right)$$ $$e\left(\frac{12}{65}\right)$$ $$e\left(\frac{59}{65}\right)$$
$$\chi_{1441}(746,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{31}{65}\right)$$ $$e\left(\frac{61}{65}\right)$$ $$e\left(\frac{62}{65}\right)$$ $$e\left(\frac{48}{65}\right)$$ $$e\left(\frac{27}{65}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{28}{65}\right)$$ $$e\left(\frac{57}{65}\right)$$ $$e\left(\frac{14}{65}\right)$$ $$e\left(\frac{58}{65}\right)$$