# Properties

 Label 1441.bx Modulus $1441$ Conductor $1441$ Order $130$ 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([91,51]))

chi.galois_orbit()

[g,chi] = znchar(Mod(29,1441))

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: $$130$$ 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 130 polynomial (not computed)

## First 31 of 48 characters in Galois orbit

Character $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$12$$
$$\chi_{1441}(29,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{6}{65}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{12}{65}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{61}{65}\right)$$ $$e\left(\frac{73}{130}\right)$$ $$e\left(\frac{18}{65}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{61}{65}\right)$$ $$e\left(\frac{2}{65}\right)$$
$$\chi_{1441}(30,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{14}{65}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{28}{65}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{34}{65}\right)$$ $$e\left(\frac{127}{130}\right)$$ $$e\left(\frac{42}{65}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{34}{65}\right)$$ $$e\left(\frac{48}{65}\right)$$
$$\chi_{1441}(72,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{2}{65}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{4}{65}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{42}{65}\right)$$ $$e\left(\frac{111}{130}\right)$$ $$e\left(\frac{6}{65}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{42}{65}\right)$$ $$e\left(\frac{44}{65}\right)$$
$$\chi_{1441}(85,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{64}{65}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{63}{65}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{44}{65}\right)$$ $$e\left(\frac{107}{130}\right)$$ $$e\left(\frac{62}{65}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{44}{65}\right)$$ $$e\left(\frac{43}{65}\right)$$
$$\chi_{1441}(95,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{21}{65}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{42}{65}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{51}{65}\right)$$ $$e\left(\frac{93}{130}\right)$$ $$e\left(\frac{63}{65}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{51}{65}\right)$$ $$e\left(\frac{7}{65}\right)$$
$$\chi_{1441}(127,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{27}{65}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{54}{65}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{47}{65}\right)$$ $$e\left(\frac{101}{130}\right)$$ $$e\left(\frac{16}{65}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{47}{65}\right)$$ $$e\left(\frac{9}{65}\right)$$
$$\chi_{1441}(162,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{34}{65}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{3}{65}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{64}{65}\right)$$ $$e\left(\frac{67}{130}\right)$$ $$e\left(\frac{37}{65}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{64}{65}\right)$$ $$e\left(\frac{33}{65}\right)$$
$$\chi_{1441}(228,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{9}{65}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{18}{65}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{59}{65}\right)$$ $$e\left(\frac{77}{130}\right)$$ $$e\left(\frac{27}{65}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{59}{65}\right)$$ $$e\left(\frac{3}{65}\right)$$
$$\chi_{1441}(237,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{7}{65}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{14}{65}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{17}{65}\right)$$ $$e\left(\frac{31}{130}\right)$$ $$e\left(\frac{21}{65}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{17}{65}\right)$$ $$e\left(\frac{24}{65}\right)$$
$$\chi_{1441}(250,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{24}{65}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{48}{65}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{49}{65}\right)$$ $$e\left(\frac{97}{130}\right)$$ $$e\left(\frac{7}{65}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{49}{65}\right)$$ $$e\left(\frac{8}{65}\right)$$
$$\chi_{1441}(259,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{62}{65}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{59}{65}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{2}{65}\right)$$ $$e\left(\frac{61}{130}\right)$$ $$e\left(\frac{56}{65}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{2}{65}\right)$$ $$e\left(\frac{64}{65}\right)$$
$$\chi_{1441}(358,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{32}{65}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{64}{65}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{22}{65}\right)$$ $$e\left(\frac{21}{130}\right)$$ $$e\left(\frac{31}{65}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{22}{65}\right)$$ $$e\left(\frac{54}{65}\right)$$
$$\chi_{1441}(365,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{23}{65}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{28}{65}\right)$$ $$e\left(\frac{9}{130}\right)$$ $$e\left(\frac{4}{65}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{28}{65}\right)$$ $$e\left(\frac{51}{65}\right)$$
$$\chi_{1441}(459,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{19}{65}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{38}{65}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{9}{65}\right)$$ $$e\left(\frac{47}{130}\right)$$ $$e\left(\frac{57}{65}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{9}{65}\right)$$ $$e\left(\frac{28}{65}\right)$$
$$\chi_{1441}(481,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{49}{65}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{33}{65}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{54}{65}\right)$$ $$e\left(\frac{87}{130}\right)$$ $$e\left(\frac{17}{65}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{54}{65}\right)$$ $$e\left(\frac{38}{65}\right)$$
$$\chi_{1441}(513,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{41}{65}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{17}{65}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{16}{65}\right)$$ $$e\left(\frac{33}{130}\right)$$ $$e\left(\frac{58}{65}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{16}{65}\right)$$ $$e\left(\frac{57}{65}\right)$$
$$\chi_{1441}(530,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{43}{65}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{21}{65}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{58}{65}\right)$$ $$e\left(\frac{79}{130}\right)$$ $$e\left(\frac{64}{65}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{58}{65}\right)$$ $$e\left(\frac{36}{65}\right)$$
$$\chi_{1441}(534,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{17}{65}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{34}{65}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{32}{65}\right)$$ $$e\left(\frac{1}{130}\right)$$ $$e\left(\frac{51}{65}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{32}{65}\right)$$ $$e\left(\frac{49}{65}\right)$$
$$\chi_{1441}(541,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{28}{65}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{56}{65}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{3}{65}\right)$$ $$e\left(\frac{59}{130}\right)$$ $$e\left(\frac{19}{65}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{3}{65}\right)$$ $$e\left(\frac{31}{65}\right)$$
$$\chi_{1441}(574,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{53}{65}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{41}{65}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{8}{65}\right)$$ $$e\left(\frac{49}{130}\right)$$ $$e\left(\frac{29}{65}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{8}{65}\right)$$ $$e\left(\frac{61}{65}\right)$$
$$\chi_{1441}(578,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{37}{65}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{9}{65}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{62}{65}\right)$$ $$e\left(\frac{71}{130}\right)$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{62}{65}\right)$$ $$e\left(\frac{34}{65}\right)$$
$$\chi_{1441}(580,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{4}{65}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{8}{65}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{19}{65}\right)$$ $$e\left(\frac{27}{130}\right)$$ $$e\left(\frac{12}{65}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{19}{65}\right)$$ $$e\left(\frac{23}{65}\right)$$
$$\chi_{1441}(600,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{12}{65}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{24}{65}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{57}{65}\right)$$ $$e\left(\frac{81}{130}\right)$$ $$e\left(\frac{36}{65}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{57}{65}\right)$$ $$e\left(\frac{4}{65}\right)$$
$$\chi_{1441}(640,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{33}{65}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{1}{65}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{43}{65}\right)$$ $$e\left(\frac{109}{130}\right)$$ $$e\left(\frac{34}{65}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{43}{65}\right)$$ $$e\left(\frac{11}{65}\right)$$
$$\chi_{1441}(646,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{59}{65}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{53}{65}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{4}{65}\right)$$ $$e\left(\frac{57}{130}\right)$$ $$e\left(\frac{47}{65}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{4}{65}\right)$$ $$e\left(\frac{63}{65}\right)$$
$$\chi_{1441}(677,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{22}{65}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{44}{65}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{7}{65}\right)$$ $$e\left(\frac{51}{130}\right)$$ $$e\left(\frac{1}{65}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{7}{65}\right)$$ $$e\left(\frac{29}{65}\right)$$
$$\chi_{1441}(722,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{16}{65}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{32}{65}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{11}{65}\right)$$ $$e\left(\frac{43}{130}\right)$$ $$e\left(\frac{48}{65}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{11}{65}\right)$$ $$e\left(\frac{27}{65}\right)$$
$$\chi_{1441}(788,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{27}{65}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{56}{65}\right)$$ $$e\left(\frac{83}{130}\right)$$ $$e\left(\frac{8}{65}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{56}{65}\right)$$ $$e\left(\frac{37}{65}\right)$$
$$\chi_{1441}(794,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{8}{65}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{16}{65}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{38}{65}\right)$$ $$e\left(\frac{119}{130}\right)$$ $$e\left(\frac{24}{65}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{38}{65}\right)$$ $$e\left(\frac{46}{65}\right)$$
$$\chi_{1441}(876,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{11}{65}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{22}{65}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{36}{65}\right)$$ $$e\left(\frac{123}{130}\right)$$ $$e\left(\frac{33}{65}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{36}{65}\right)$$ $$e\left(\frac{47}{65}\right)$$
$$\chi_{1441}(904,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{48}{65}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{31}{65}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{33}{65}\right)$$ $$e\left(\frac{129}{130}\right)$$ $$e\left(\frac{14}{65}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{33}{65}\right)$$ $$e\left(\frac{16}{65}\right)$$