# Properties

 Label 1441.bl Modulus $1441$ Conductor $131$ Order $65$ Real no Primitive no Minimal yes Parity even

# Related objects

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

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

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,74]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(12,1441))

pari: order = charorder(g,chi)

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

## Basic properties

 Modulus: $$1441$$ Conductor: $$131$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$65$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 131.g 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$12$$
$$\chi_{1441}(12,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{37}{65}\right)$$ $$e\left(\frac{64}{65}\right)$$ $$e\left(\frac{9}{65}\right)$$ $$e\left(\frac{12}{65}\right)$$ $$e\left(\frac{36}{65}\right)$$ $$e\left(\frac{42}{65}\right)$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{63}{65}\right)$$ $$e\left(\frac{49}{65}\right)$$ $$e\left(\frac{8}{65}\right)$$
$$\chi_{1441}(34,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{22}{65}\right)$$ $$e\left(\frac{24}{65}\right)$$ $$e\left(\frac{44}{65}\right)$$ $$e\left(\frac{37}{65}\right)$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{32}{65}\right)$$ $$e\left(\frac{1}{65}\right)$$ $$e\left(\frac{48}{65}\right)$$ $$e\left(\frac{59}{65}\right)$$ $$e\left(\frac{3}{65}\right)$$
$$\chi_{1441}(100,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{47}{65}\right)$$ $$e\left(\frac{4}{65}\right)$$ $$e\left(\frac{29}{65}\right)$$ $$e\left(\frac{17}{65}\right)$$ $$e\left(\frac{51}{65}\right)$$ $$e\left(\frac{27}{65}\right)$$ $$e\left(\frac{11}{65}\right)$$ $$e\left(\frac{8}{65}\right)$$ $$e\left(\frac{64}{65}\right)$$ $$e\left(\frac{33}{65}\right)$$
$$\chi_{1441}(144,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{9}{65}\right)$$ $$e\left(\frac{63}{65}\right)$$ $$e\left(\frac{18}{65}\right)$$ $$e\left(\frac{24}{65}\right)$$ $$e\left(\frac{7}{65}\right)$$ $$e\left(\frac{19}{65}\right)$$ $$e\left(\frac{27}{65}\right)$$ $$e\left(\frac{61}{65}\right)$$ $$e\left(\frac{33}{65}\right)$$ $$e\left(\frac{16}{65}\right)$$
$$\chi_{1441}(166,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{6}{65}\right)$$ $$e\left(\frac{42}{65}\right)$$ $$e\left(\frac{12}{65}\right)$$ $$e\left(\frac{16}{65}\right)$$ $$e\left(\frac{48}{65}\right)$$ $$e\left(\frac{56}{65}\right)$$ $$e\left(\frac{18}{65}\right)$$ $$e\left(\frac{19}{65}\right)$$ $$e\left(\frac{22}{65}\right)$$ $$e\left(\frac{54}{65}\right)$$
$$\chi_{1441}(177,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{12}{65}\right)$$ $$e\left(\frac{19}{65}\right)$$ $$e\left(\frac{24}{65}\right)$$ $$e\left(\frac{32}{65}\right)$$ $$e\left(\frac{31}{65}\right)$$ $$e\left(\frac{47}{65}\right)$$ $$e\left(\frac{36}{65}\right)$$ $$e\left(\frac{38}{65}\right)$$ $$e\left(\frac{44}{65}\right)$$ $$e\left(\frac{43}{65}\right)$$
$$\chi_{1441}(232,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{27}{65}\right)$$ $$e\left(\frac{59}{65}\right)$$ $$e\left(\frac{54}{65}\right)$$ $$e\left(\frac{7}{65}\right)$$ $$e\left(\frac{21}{65}\right)$$ $$e\left(\frac{57}{65}\right)$$ $$e\left(\frac{16}{65}\right)$$ $$e\left(\frac{53}{65}\right)$$ $$e\left(\frac{34}{65}\right)$$ $$e\left(\frac{48}{65}\right)$$
$$\chi_{1441}(254,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{34}{65}\right)$$ $$e\left(\frac{43}{65}\right)$$ $$e\left(\frac{3}{65}\right)$$ $$e\left(\frac{4}{65}\right)$$ $$e\left(\frac{12}{65}\right)$$ $$e\left(\frac{14}{65}\right)$$ $$e\left(\frac{37}{65}\right)$$ $$e\left(\frac{21}{65}\right)$$ $$e\left(\frac{38}{65}\right)$$ $$e\left(\frac{46}{65}\right)$$
$$\chi_{1441}(265,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{36}{65}\right)$$ $$e\left(\frac{57}{65}\right)$$ $$e\left(\frac{7}{65}\right)$$ $$e\left(\frac{31}{65}\right)$$ $$e\left(\frac{28}{65}\right)$$ $$e\left(\frac{11}{65}\right)$$ $$e\left(\frac{43}{65}\right)$$ $$e\left(\frac{49}{65}\right)$$ $$e\left(\frac{2}{65}\right)$$ $$e\left(\frac{64}{65}\right)$$
$$\chi_{1441}(287,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{62}{65}\right)$$ $$e\left(\frac{27}{65}\right)$$ $$e\left(\frac{36}{65}\right)$$ $$e\left(\frac{43}{65}\right)$$ $$e\left(\frac{61}{65}\right)$$ $$e\left(\frac{8}{65}\right)$$ $$e\left(\frac{59}{65}\right)$$ $$e\left(\frac{17}{65}\right)$$ $$e\left(\frac{24}{65}\right)$$
$$\chi_{1441}(298,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{8}{65}\right)$$ $$e\left(\frac{56}{65}\right)$$ $$e\left(\frac{16}{65}\right)$$ $$e\left(\frac{43}{65}\right)$$ $$e\left(\frac{64}{65}\right)$$ $$e\left(\frac{53}{65}\right)$$ $$e\left(\frac{24}{65}\right)$$ $$e\left(\frac{47}{65}\right)$$ $$e\left(\frac{51}{65}\right)$$ $$e\left(\frac{7}{65}\right)$$
$$\chi_{1441}(353,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{57}{65}\right)$$ $$e\left(\frac{9}{65}\right)$$ $$e\left(\frac{49}{65}\right)$$ $$e\left(\frac{22}{65}\right)$$ $$e\left(\frac{1}{65}\right)$$ $$e\left(\frac{12}{65}\right)$$ $$e\left(\frac{41}{65}\right)$$ $$e\left(\frac{18}{65}\right)$$ $$e\left(\frac{14}{65}\right)$$ $$e\left(\frac{58}{65}\right)$$
$$\chi_{1441}(364,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{58}{65}\right)$$ $$e\left(\frac{16}{65}\right)$$ $$e\left(\frac{51}{65}\right)$$ $$e\left(\frac{3}{65}\right)$$ $$e\left(\frac{9}{65}\right)$$ $$e\left(\frac{43}{65}\right)$$ $$e\left(\frac{44}{65}\right)$$ $$e\left(\frac{32}{65}\right)$$ $$e\left(\frac{61}{65}\right)$$ $$e\left(\frac{2}{65}\right)$$
$$\chi_{1441}(397,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{65}\right)$$ $$e\left(\frac{7}{65}\right)$$ $$e\left(\frac{2}{65}\right)$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{8}{65}\right)$$ $$e\left(\frac{31}{65}\right)$$ $$e\left(\frac{3}{65}\right)$$ $$e\left(\frac{14}{65}\right)$$ $$e\left(\frac{47}{65}\right)$$ $$e\left(\frac{9}{65}\right)$$
$$\chi_{1441}(408,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{59}{65}\right)$$ $$e\left(\frac{23}{65}\right)$$ $$e\left(\frac{53}{65}\right)$$ $$e\left(\frac{49}{65}\right)$$ $$e\left(\frac{17}{65}\right)$$ $$e\left(\frac{9}{65}\right)$$ $$e\left(\frac{47}{65}\right)$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{43}{65}\right)$$ $$e\left(\frac{11}{65}\right)$$
$$\chi_{1441}(441,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{38}{65}\right)$$ $$e\left(\frac{6}{65}\right)$$ $$e\left(\frac{11}{65}\right)$$ $$e\left(\frac{58}{65}\right)$$ $$e\left(\frac{44}{65}\right)$$ $$e\left(\frac{8}{65}\right)$$ $$e\left(\frac{49}{65}\right)$$ $$e\left(\frac{12}{65}\right)$$ $$e\left(\frac{31}{65}\right)$$ $$e\left(\frac{17}{65}\right)$$
$$\chi_{1441}(452,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{41}{65}\right)$$ $$e\left(\frac{27}{65}\right)$$ $$e\left(\frac{17}{65}\right)$$ $$e\left(\frac{1}{65}\right)$$ $$e\left(\frac{3}{65}\right)$$ $$e\left(\frac{36}{65}\right)$$ $$e\left(\frac{58}{65}\right)$$ $$e\left(\frac{54}{65}\right)$$ $$e\left(\frac{42}{65}\right)$$ $$e\left(\frac{44}{65}\right)$$
$$\chi_{1441}(474,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{14}{65}\right)$$ $$e\left(\frac{33}{65}\right)$$ $$e\left(\frac{28}{65}\right)$$ $$e\left(\frac{59}{65}\right)$$ $$e\left(\frac{47}{65}\right)$$ $$e\left(\frac{44}{65}\right)$$ $$e\left(\frac{42}{65}\right)$$ $$e\left(\frac{1}{65}\right)$$ $$e\left(\frac{8}{65}\right)$$ $$e\left(\frac{61}{65}\right)$$
$$\chi_{1441}(507,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{54}{65}\right)$$ $$e\left(\frac{53}{65}\right)$$ $$e\left(\frac{43}{65}\right)$$ $$e\left(\frac{14}{65}\right)$$ $$e\left(\frac{42}{65}\right)$$ $$e\left(\frac{49}{65}\right)$$ $$e\left(\frac{32}{65}\right)$$ $$e\left(\frac{41}{65}\right)$$ $$e\left(\frac{3}{65}\right)$$ $$e\left(\frac{31}{65}\right)$$
$$\chi_{1441}(518,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{4}{65}\right)$$ $$e\left(\frac{28}{65}\right)$$ $$e\left(\frac{8}{65}\right)$$ $$e\left(\frac{54}{65}\right)$$ $$e\left(\frac{32}{65}\right)$$ $$e\left(\frac{59}{65}\right)$$ $$e\left(\frac{12}{65}\right)$$ $$e\left(\frac{56}{65}\right)$$ $$e\left(\frac{58}{65}\right)$$ $$e\left(\frac{36}{65}\right)$$
$$\chi_{1441}(529,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{23}{65}\right)$$ $$e\left(\frac{31}{65}\right)$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{18}{65}\right)$$ $$e\left(\frac{54}{65}\right)$$ $$e\left(\frac{63}{65}\right)$$ $$e\left(\frac{4}{65}\right)$$ $$e\left(\frac{62}{65}\right)$$ $$e\left(\frac{41}{65}\right)$$ $$e\left(\frac{12}{65}\right)$$
$$\chi_{1441}(540,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{2}{65}\right)$$ $$e\left(\frac{14}{65}\right)$$ $$e\left(\frac{4}{65}\right)$$ $$e\left(\frac{27}{65}\right)$$ $$e\left(\frac{16}{65}\right)$$ $$e\left(\frac{62}{65}\right)$$ $$e\left(\frac{6}{65}\right)$$ $$e\left(\frac{28}{65}\right)$$ $$e\left(\frac{29}{65}\right)$$ $$e\left(\frac{18}{65}\right)$$
$$\chi_{1441}(551,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{43}{65}\right)$$ $$e\left(\frac{41}{65}\right)$$ $$e\left(\frac{21}{65}\right)$$ $$e\left(\frac{28}{65}\right)$$ $$e\left(\frac{19}{65}\right)$$ $$e\left(\frac{33}{65}\right)$$ $$e\left(\frac{64}{65}\right)$$ $$e\left(\frac{17}{65}\right)$$ $$e\left(\frac{6}{65}\right)$$ $$e\left(\frac{62}{65}\right)$$
$$\chi_{1441}(562,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{18}{65}\right)$$ $$e\left(\frac{61}{65}\right)$$ $$e\left(\frac{36}{65}\right)$$ $$e\left(\frac{48}{65}\right)$$ $$e\left(\frac{14}{65}\right)$$ $$e\left(\frac{38}{65}\right)$$ $$e\left(\frac{54}{65}\right)$$ $$e\left(\frac{57}{65}\right)$$ $$e\left(\frac{1}{65}\right)$$ $$e\left(\frac{32}{65}\right)$$
$$\chi_{1441}(573,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{31}{65}\right)$$ $$e\left(\frac{22}{65}\right)$$ $$e\left(\frac{62}{65}\right)$$ $$e\left(\frac{61}{65}\right)$$ $$e\left(\frac{53}{65}\right)$$ $$e\left(\frac{51}{65}\right)$$ $$e\left(\frac{28}{65}\right)$$ $$e\left(\frac{44}{65}\right)$$ $$e\left(\frac{27}{65}\right)$$ $$e\left(\frac{19}{65}\right)$$
$$\chi_{1441}(683,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{49}{65}\right)$$ $$e\left(\frac{18}{65}\right)$$ $$e\left(\frac{33}{65}\right)$$ $$e\left(\frac{44}{65}\right)$$ $$e\left(\frac{2}{65}\right)$$ $$e\left(\frac{24}{65}\right)$$ $$e\left(\frac{17}{65}\right)$$ $$e\left(\frac{36}{65}\right)$$ $$e\left(\frac{28}{65}\right)$$ $$e\left(\frac{51}{65}\right)$$
$$\chi_{1441}(749,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{53}{65}\right)$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{41}{65}\right)$$ $$e\left(\frac{33}{65}\right)$$ $$e\left(\frac{34}{65}\right)$$ $$e\left(\frac{18}{65}\right)$$ $$e\left(\frac{29}{65}\right)$$ $$e\left(\frac{27}{65}\right)$$ $$e\left(\frac{21}{65}\right)$$ $$e\left(\frac{22}{65}\right)$$
$$\chi_{1441}(760,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{42}{65}\right)$$ $$e\left(\frac{34}{65}\right)$$ $$e\left(\frac{19}{65}\right)$$ $$e\left(\frac{47}{65}\right)$$ $$e\left(\frac{11}{65}\right)$$ $$e\left(\frac{2}{65}\right)$$ $$e\left(\frac{61}{65}\right)$$ $$e\left(\frac{3}{65}\right)$$ $$e\left(\frac{24}{65}\right)$$ $$e\left(\frac{53}{65}\right)$$
$$\chi_{1441}(793,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{48}{65}\right)$$ $$e\left(\frac{11}{65}\right)$$ $$e\left(\frac{31}{65}\right)$$ $$e\left(\frac{63}{65}\right)$$ $$e\left(\frac{59}{65}\right)$$ $$e\left(\frac{58}{65}\right)$$ $$e\left(\frac{14}{65}\right)$$ $$e\left(\frac{22}{65}\right)$$ $$e\left(\frac{46}{65}\right)$$ $$e\left(\frac{42}{65}\right)$$
$$\chi_{1441}(903,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{16}{65}\right)$$ $$e\left(\frac{47}{65}\right)$$ $$e\left(\frac{32}{65}\right)$$ $$e\left(\frac{21}{65}\right)$$ $$e\left(\frac{63}{65}\right)$$ $$e\left(\frac{41}{65}\right)$$ $$e\left(\frac{48}{65}\right)$$ $$e\left(\frac{29}{65}\right)$$ $$e\left(\frac{37}{65}\right)$$ $$e\left(\frac{14}{65}\right)$$
$$\chi_{1441}(958,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{63}{65}\right)$$ $$e\left(\frac{51}{65}\right)$$ $$e\left(\frac{61}{65}\right)$$ $$e\left(\frac{38}{65}\right)$$ $$e\left(\frac{49}{65}\right)$$ $$e\left(\frac{3}{65}\right)$$ $$e\left(\frac{59}{65}\right)$$ $$e\left(\frac{37}{65}\right)$$ $$e\left(\frac{36}{65}\right)$$ $$e\left(\frac{47}{65}\right)$$