Properties

Label 1441.by
Modulus $1441$
Conductor $1441$
Order $130$
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([13,1]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(2,1441))
 
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: \(130\)
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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(12\)
\(\chi_{1441}(2,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{65}\right)\) \(e\left(\frac{23}{65}\right)\) \(e\left(\frac{14}{65}\right)\) \(e\left(\frac{49}{65}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{57}{130}\right)\) \(e\left(\frac{21}{65}\right)\) \(e\left(\frac{46}{65}\right)\) \(e\left(\frac{56}{65}\right)\) \(e\left(\frac{37}{65}\right)\)
\(\chi_{1441}(8,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{65}\right)\) \(e\left(\frac{4}{65}\right)\) \(e\left(\frac{42}{65}\right)\) \(e\left(\frac{17}{65}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{41}{130}\right)\) \(e\left(\frac{63}{65}\right)\) \(e\left(\frac{8}{65}\right)\) \(e\left(\frac{38}{65}\right)\) \(e\left(\frac{46}{65}\right)\)
\(\chi_{1441}(90,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{65}\right)\) \(e\left(\frac{38}{65}\right)\) \(e\left(\frac{9}{65}\right)\) \(e\left(\frac{64}{65}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{97}{130}\right)\) \(e\left(\frac{46}{65}\right)\) \(e\left(\frac{11}{65}\right)\) \(e\left(\frac{36}{65}\right)\) \(e\left(\frac{47}{65}\right)\)
\(\chi_{1441}(106,\cdot)\) \(1\) \(1\) \(e\left(\frac{59}{65}\right)\) \(e\left(\frac{36}{65}\right)\) \(e\left(\frac{53}{65}\right)\) \(e\left(\frac{23}{65}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{109}{130}\right)\) \(e\left(\frac{47}{65}\right)\) \(e\left(\frac{7}{65}\right)\) \(e\left(\frac{17}{65}\right)\) \(e\left(\frac{24}{65}\right)\)
\(\chi_{1441}(118,\cdot)\) \(1\) \(1\) \(e\left(\frac{61}{65}\right)\) \(e\left(\frac{24}{65}\right)\) \(e\left(\frac{57}{65}\right)\) \(e\left(\frac{37}{65}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{51}{130}\right)\) \(e\left(\frac{53}{65}\right)\) \(e\left(\frac{48}{65}\right)\) \(e\left(\frac{33}{65}\right)\) \(e\left(\frac{16}{65}\right)\)
\(\chi_{1441}(128,\cdot)\) \(1\) \(1\) \(e\left(\frac{49}{65}\right)\) \(e\left(\frac{31}{65}\right)\) \(e\left(\frac{33}{65}\right)\) \(e\left(\frac{18}{65}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{9}{130}\right)\) \(e\left(\frac{17}{65}\right)\) \(e\left(\frac{62}{65}\right)\) \(e\left(\frac{2}{65}\right)\) \(e\left(\frac{64}{65}\right)\)
\(\chi_{1441}(171,\cdot)\) \(1\) \(1\) \(e\left(\frac{18}{65}\right)\) \(e\left(\frac{22}{65}\right)\) \(e\left(\frac{36}{65}\right)\) \(e\left(\frac{61}{65}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{63}{130}\right)\) \(e\left(\frac{54}{65}\right)\) \(e\left(\frac{44}{65}\right)\) \(e\left(\frac{14}{65}\right)\) \(e\left(\frac{58}{65}\right)\)
\(\chi_{1441}(227,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{65}\right)\) \(e\left(\frac{16}{65}\right)\) \(e\left(\frac{38}{65}\right)\) \(e\left(\frac{3}{65}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{99}{130}\right)\) \(e\left(\frac{57}{65}\right)\) \(e\left(\frac{32}{65}\right)\) \(e\left(\frac{22}{65}\right)\) \(e\left(\frac{54}{65}\right)\)
\(\chi_{1441}(255,\cdot)\) \(1\) \(1\) \(e\left(\frac{22}{65}\right)\) \(e\left(\frac{63}{65}\right)\) \(e\left(\frac{44}{65}\right)\) \(e\left(\frac{24}{65}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{77}{130}\right)\) \(e\left(\frac{1}{65}\right)\) \(e\left(\frac{61}{65}\right)\) \(e\left(\frac{46}{65}\right)\) \(e\left(\frac{42}{65}\right)\)
\(\chi_{1441}(292,\cdot)\) \(1\) \(1\) \(e\left(\frac{53}{65}\right)\) \(e\left(\frac{7}{65}\right)\) \(e\left(\frac{41}{65}\right)\) \(e\left(\frac{46}{65}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{23}{130}\right)\) \(e\left(\frac{29}{65}\right)\) \(e\left(\frac{14}{65}\right)\) \(e\left(\frac{34}{65}\right)\) \(e\left(\frac{48}{65}\right)\)
\(\chi_{1441}(299,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{65}\right)\) \(e\left(\frac{33}{65}\right)\) \(e\left(\frac{54}{65}\right)\) \(e\left(\frac{59}{65}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{127}{130}\right)\) \(e\left(\frac{16}{65}\right)\) \(e\left(\frac{1}{65}\right)\) \(e\left(\frac{21}{65}\right)\) \(e\left(\frac{22}{65}\right)\)
\(\chi_{1441}(347,\cdot)\) \(1\) \(1\) \(e\left(\frac{38}{65}\right)\) \(e\left(\frac{32}{65}\right)\) \(e\left(\frac{11}{65}\right)\) \(e\left(\frac{6}{65}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{3}{130}\right)\) \(e\left(\frac{49}{65}\right)\) \(e\left(\frac{64}{65}\right)\) \(e\left(\frac{44}{65}\right)\) \(e\left(\frac{43}{65}\right)\)
\(\chi_{1441}(349,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{65}\right)\) \(e\left(\frac{34}{65}\right)\) \(e\left(\frac{32}{65}\right)\) \(e\left(\frac{47}{65}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{121}{130}\right)\) \(e\left(\frac{48}{65}\right)\) \(e\left(\frac{3}{65}\right)\) \(e\left(\frac{63}{65}\right)\) \(e\left(\frac{1}{65}\right)\)
\(\chi_{1441}(360,\cdot)\) \(1\) \(1\) \(e\left(\frac{51}{65}\right)\) \(e\left(\frac{19}{65}\right)\) \(e\left(\frac{37}{65}\right)\) \(e\left(\frac{32}{65}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{81}{130}\right)\) \(e\left(\frac{23}{65}\right)\) \(e\left(\frac{38}{65}\right)\) \(e\left(\frac{18}{65}\right)\) \(e\left(\frac{56}{65}\right)\)
\(\chi_{1441}(403,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{65}\right)\) \(e\left(\frac{41}{65}\right)\) \(e\left(\frac{8}{65}\right)\) \(e\left(\frac{28}{65}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{79}{130}\right)\) \(e\left(\frac{12}{65}\right)\) \(e\left(\frac{17}{65}\right)\) \(e\left(\frac{32}{65}\right)\) \(e\left(\frac{49}{65}\right)\)
\(\chi_{1441}(424,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{65}\right)\) \(e\left(\frac{17}{65}\right)\) \(e\left(\frac{16}{65}\right)\) \(e\left(\frac{56}{65}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{93}{130}\right)\) \(e\left(\frac{24}{65}\right)\) \(e\left(\frac{34}{65}\right)\) \(e\left(\frac{64}{65}\right)\) \(e\left(\frac{33}{65}\right)\)
\(\chi_{1441}(447,\cdot)\) \(1\) \(1\) \(e\left(\frac{24}{65}\right)\) \(e\left(\frac{51}{65}\right)\) \(e\left(\frac{48}{65}\right)\) \(e\left(\frac{38}{65}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{19}{130}\right)\) \(e\left(\frac{7}{65}\right)\) \(e\left(\frac{37}{65}\right)\) \(e\left(\frac{62}{65}\right)\) \(e\left(\frac{34}{65}\right)\)
\(\chi_{1441}(469,\cdot)\) \(1\) \(1\) \(e\left(\frac{64}{65}\right)\) \(e\left(\frac{6}{65}\right)\) \(e\left(\frac{63}{65}\right)\) \(e\left(\frac{58}{65}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{29}{130}\right)\) \(e\left(\frac{62}{65}\right)\) \(e\left(\frac{12}{65}\right)\) \(e\left(\frac{57}{65}\right)\) \(e\left(\frac{4}{65}\right)\)
\(\chi_{1441}(486,\cdot)\) \(1\) \(1\) \(e\left(\frac{57}{65}\right)\) \(e\left(\frac{48}{65}\right)\) \(e\left(\frac{49}{65}\right)\) \(e\left(\frac{9}{65}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{37}{130}\right)\) \(e\left(\frac{41}{65}\right)\) \(e\left(\frac{31}{65}\right)\) \(e\left(\frac{1}{65}\right)\) \(e\left(\frac{32}{65}\right)\)
\(\chi_{1441}(490,\cdot)\) \(1\) \(1\) \(e\left(\frac{48}{65}\right)\) \(e\left(\frac{37}{65}\right)\) \(e\left(\frac{31}{65}\right)\) \(e\left(\frac{11}{65}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{103}{130}\right)\) \(e\left(\frac{14}{65}\right)\) \(e\left(\frac{9}{65}\right)\) \(e\left(\frac{59}{65}\right)\) \(e\left(\frac{3}{65}\right)\)
\(\chi_{1441}(497,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{65}\right)\) \(e\left(\frac{28}{65}\right)\) \(e\left(\frac{34}{65}\right)\) \(e\left(\frac{54}{65}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{27}{130}\right)\) \(e\left(\frac{51}{65}\right)\) \(e\left(\frac{56}{65}\right)\) \(e\left(\frac{6}{65}\right)\) \(e\left(\frac{62}{65}\right)\)
\(\chi_{1441}(503,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{65}\right)\) \(e\left(\frac{29}{65}\right)\) \(e\left(\frac{12}{65}\right)\) \(e\left(\frac{42}{65}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{21}{130}\right)\) \(e\left(\frac{18}{65}\right)\) \(e\left(\frac{58}{65}\right)\) \(e\left(\frac{48}{65}\right)\) \(e\left(\frac{41}{65}\right)\)
\(\chi_{1441}(512,\cdot)\) \(1\) \(1\) \(e\left(\frac{63}{65}\right)\) \(e\left(\frac{12}{65}\right)\) \(e\left(\frac{61}{65}\right)\) \(e\left(\frac{51}{65}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{123}{130}\right)\) \(e\left(\frac{59}{65}\right)\) \(e\left(\frac{24}{65}\right)\) \(e\left(\frac{49}{65}\right)\) \(e\left(\frac{8}{65}\right)\)
\(\chi_{1441}(519,\cdot)\) \(1\) \(1\) \(e\left(\frac{62}{65}\right)\) \(e\left(\frac{18}{65}\right)\) \(e\left(\frac{59}{65}\right)\) \(e\left(\frac{44}{65}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{87}{130}\right)\) \(e\left(\frac{56}{65}\right)\) \(e\left(\frac{36}{65}\right)\) \(e\left(\frac{41}{65}\right)\) \(e\left(\frac{12}{65}\right)\)
\(\chi_{1441}(546,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{65}\right)\) \(e\left(\frac{11}{65}\right)\) \(e\left(\frac{18}{65}\right)\) \(e\left(\frac{63}{65}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{129}{130}\right)\) \(e\left(\frac{27}{65}\right)\) \(e\left(\frac{22}{65}\right)\) \(e\left(\frac{7}{65}\right)\) \(e\left(\frac{29}{65}\right)\)
\(\chi_{1441}(547,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{65}\right)\) \(e\left(\frac{9}{65}\right)\) \(e\left(\frac{62}{65}\right)\) \(e\left(\frac{22}{65}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{11}{130}\right)\) \(e\left(\frac{28}{65}\right)\) \(e\left(\frac{18}{65}\right)\) \(e\left(\frac{53}{65}\right)\) \(e\left(\frac{6}{65}\right)\)
\(\chi_{1441}(607,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{65}\right)\) \(e\left(\frac{58}{65}\right)\) \(e\left(\frac{24}{65}\right)\) \(e\left(\frac{19}{65}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{107}{130}\right)\) \(e\left(\frac{36}{65}\right)\) \(e\left(\frac{51}{65}\right)\) \(e\left(\frac{31}{65}\right)\) \(e\left(\frac{17}{65}\right)\)
\(\chi_{1441}(635,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{65}\right)\) \(e\left(\frac{64}{65}\right)\) \(e\left(\frac{22}{65}\right)\) \(e\left(\frac{12}{65}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{71}{130}\right)\) \(e\left(\frac{33}{65}\right)\) \(e\left(\frac{63}{65}\right)\) \(e\left(\frac{23}{65}\right)\) \(e\left(\frac{21}{65}\right)\)
\(\chi_{1441}(684,\cdot)\) \(1\) \(1\) \(e\left(\frac{32}{65}\right)\) \(e\left(\frac{3}{65}\right)\) \(e\left(\frac{64}{65}\right)\) \(e\left(\frac{29}{65}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{47}{130}\right)\) \(e\left(\frac{31}{65}\right)\) \(e\left(\frac{6}{65}\right)\) \(e\left(\frac{61}{65}\right)\) \(e\left(\frac{2}{65}\right)\)
\(\chi_{1441}(721,\cdot)\) \(1\) \(1\) \(e\left(\frac{58}{65}\right)\) \(e\left(\frac{42}{65}\right)\) \(e\left(\frac{51}{65}\right)\) \(e\left(\frac{16}{65}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{73}{130}\right)\) \(e\left(\frac{44}{65}\right)\) \(e\left(\frac{19}{65}\right)\) \(e\left(\frac{9}{65}\right)\) \(e\left(\frac{28}{65}\right)\)
\(\chi_{1441}(743,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{65}\right)\) \(e\left(\frac{57}{65}\right)\) \(e\left(\frac{46}{65}\right)\) \(e\left(\frac{31}{65}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{113}{130}\right)\) \(e\left(\frac{4}{65}\right)\) \(e\left(\frac{49}{65}\right)\) \(e\left(\frac{54}{65}\right)\) \(e\left(\frac{38}{65}\right)\)