Properties

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

Related objects

Learn more

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([104,72]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(3,1441))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

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