Properties

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

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1441, base_ring=CyclotomicField(130))
 
M = H._module
 
chi = DirichletCharacter(H, M([104,16]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(36,1441))
 
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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(12\)
\(\chi_{1441}(36,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{17}{65}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{56}{65}\right)\) \(e\left(\frac{12}{65}\right)\) \(e\left(\frac{27}{65}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{34}{65}\right)\) \(e\left(\frac{51}{65}\right)\) \(e\left(\frac{7}{65}\right)\)
\(\chi_{1441}(102,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{42}{65}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{16}{65}\right)\) \(e\left(\frac{22}{65}\right)\) \(e\left(\frac{17}{65}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{19}{65}\right)\) \(e\left(\frac{61}{65}\right)\) \(e\left(\frac{2}{65}\right)\)
\(\chi_{1441}(147,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{53}{65}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{14}{65}\right)\) \(e\left(\frac{3}{65}\right)\) \(e\left(\frac{23}{65}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{41}{65}\right)\) \(e\left(\frac{29}{65}\right)\) \(e\left(\frac{18}{65}\right)\)
\(\chi_{1441}(159,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{31}{65}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{18}{65}\right)\) \(e\left(\frac{41}{65}\right)\) \(e\left(\frac{11}{65}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{62}{65}\right)\) \(e\left(\frac{28}{65}\right)\) \(e\left(\frac{51}{65}\right)\)
\(\chi_{1441}(179,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{32}{65}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{6}{65}\right)\) \(e\left(\frac{57}{65}\right)\) \(e\left(\frac{47}{65}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{64}{65}\right)\) \(e\left(\frac{31}{65}\right)\) \(e\left(\frac{17}{65}\right)\)
\(\chi_{1441}(240,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{24}{65}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{37}{65}\right)\) \(e\left(\frac{59}{65}\right)\) \(e\left(\frac{19}{65}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{48}{65}\right)\) \(e\left(\frac{7}{65}\right)\) \(e\left(\frac{29}{65}\right)\)
\(\chi_{1441}(267,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{57}{65}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{31}{65}\right)\) \(e\left(\frac{2}{65}\right)\) \(e\left(\frac{37}{65}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{49}{65}\right)\) \(e\left(\frac{41}{65}\right)\) \(e\left(\frac{12}{65}\right)\)
\(\chi_{1441}(289,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{2}{65}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{41}{65}\right)\) \(e\left(\frac{32}{65}\right)\) \(e\left(\frac{7}{65}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{4}{65}\right)\) \(e\left(\frac{6}{65}\right)\) \(e\left(\frac{62}{65}\right)\)
\(\chi_{1441}(300,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{22}{65}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{61}{65}\right)\) \(e\left(\frac{27}{65}\right)\) \(e\left(\frac{12}{65}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{44}{65}\right)\) \(e\left(\frac{1}{65}\right)\) \(e\left(\frac{32}{65}\right)\)
\(\chi_{1441}(317,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{19}{65}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{32}{65}\right)\) \(e\left(\frac{44}{65}\right)\) \(e\left(\frac{34}{65}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{38}{65}\right)\) \(e\left(\frac{57}{65}\right)\) \(e\left(\frac{4}{65}\right)\)
\(\chi_{1441}(339,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{64}{65}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{12}{65}\right)\) \(e\left(\frac{49}{65}\right)\) \(e\left(\frac{29}{65}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{63}{65}\right)\) \(e\left(\frac{62}{65}\right)\) \(e\left(\frac{34}{65}\right)\)
\(\chi_{1441}(367,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{8}{65}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{34}{65}\right)\) \(e\left(\frac{63}{65}\right)\) \(e\left(\frac{28}{65}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{16}{65}\right)\) \(e\left(\frac{24}{65}\right)\) \(e\left(\frac{53}{65}\right)\)
\(\chi_{1441}(383,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{54}{65}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{2}{65}\right)\) \(e\left(\frac{19}{65}\right)\) \(e\left(\frac{59}{65}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{43}{65}\right)\) \(e\left(\frac{32}{65}\right)\) \(e\left(\frac{49}{65}\right)\)
\(\chi_{1441}(487,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{7}{65}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{46}{65}\right)\) \(e\left(\frac{47}{65}\right)\) \(e\left(\frac{57}{65}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{14}{65}\right)\) \(e\left(\frac{21}{65}\right)\) \(e\left(\frac{22}{65}\right)\)
\(\chi_{1441}(531,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{37}{65}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{11}{65}\right)\) \(e\left(\frac{7}{65}\right)\) \(e\left(\frac{32}{65}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{9}{65}\right)\) \(e\left(\frac{46}{65}\right)\) \(e\left(\frac{42}{65}\right)\)
\(\chi_{1441}(544,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{51}{65}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{38}{65}\right)\) \(e\left(\frac{36}{65}\right)\) \(e\left(\frac{16}{65}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{37}{65}\right)\) \(e\left(\frac{23}{65}\right)\) \(e\left(\frac{21}{65}\right)\)
\(\chi_{1441}(559,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{29}{65}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{42}{65}\right)\) \(e\left(\frac{9}{65}\right)\) \(e\left(\frac{4}{65}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{58}{65}\right)\) \(e\left(\frac{22}{65}\right)\) \(e\left(\frac{54}{65}\right)\)
\(\chi_{1441}(632,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{61}{65}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{48}{65}\right)\) \(e\left(\frac{1}{65}\right)\) \(e\left(\frac{51}{65}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{57}{65}\right)\) \(e\left(\frac{53}{65}\right)\) \(e\left(\frac{6}{65}\right)\)
\(\chi_{1441}(658,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{44}{65}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{57}{65}\right)\) \(e\left(\frac{54}{65}\right)\) \(e\left(\frac{24}{65}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{23}{65}\right)\) \(e\left(\frac{2}{65}\right)\) \(e\left(\frac{64}{65}\right)\)
\(\chi_{1441}(664,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{23}{65}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{49}{65}\right)\) \(e\left(\frac{43}{65}\right)\) \(e\left(\frac{48}{65}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{46}{65}\right)\) \(e\left(\frac{4}{65}\right)\) \(e\left(\frac{63}{65}\right)\)
\(\chi_{1441}(676,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{16}{65}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{3}{65}\right)\) \(e\left(\frac{61}{65}\right)\) \(e\left(\frac{56}{65}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{32}{65}\right)\) \(e\left(\frac{48}{65}\right)\) \(e\left(\frac{41}{65}\right)\)
\(\chi_{1441}(680,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{49}{65}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{62}{65}\right)\) \(e\left(\frac{4}{65}\right)\) \(e\left(\frac{9}{65}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{33}{65}\right)\) \(e\left(\frac{17}{65}\right)\) \(e\left(\frac{24}{65}\right)\)
\(\chi_{1441}(696,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{12}{65}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{51}{65}\right)\) \(e\left(\frac{62}{65}\right)\) \(e\left(\frac{42}{65}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{24}{65}\right)\) \(e\left(\frac{36}{65}\right)\) \(e\left(\frac{47}{65}\right)\)
\(\chi_{1441}(730,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{28}{65}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{54}{65}\right)\) \(e\left(\frac{58}{65}\right)\) \(e\left(\frac{33}{65}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{56}{65}\right)\) \(e\left(\frac{19}{65}\right)\) \(e\left(\frac{23}{65}\right)\)
\(\chi_{1441}(784,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{62}{65}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{36}{65}\right)\) \(e\left(\frac{17}{65}\right)\) \(e\left(\frac{22}{65}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{59}{65}\right)\) \(e\left(\frac{56}{65}\right)\) \(e\left(\frac{37}{65}\right)\)
\(\chi_{1441}(790,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{59}{65}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{7}{65}\right)\) \(e\left(\frac{34}{65}\right)\) \(e\left(\frac{44}{65}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{53}{65}\right)\) \(e\left(\frac{47}{65}\right)\) \(e\left(\frac{9}{65}\right)\)
\(\chi_{1441}(819,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{6}{65}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{58}{65}\right)\) \(e\left(\frac{31}{65}\right)\) \(e\left(\frac{21}{65}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{12}{65}\right)\) \(e\left(\frac{18}{65}\right)\) \(e\left(\frac{56}{65}\right)\)
\(\chi_{1441}(829,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{18}{65}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{44}{65}\right)\) \(e\left(\frac{28}{65}\right)\) \(e\left(\frac{63}{65}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{36}{65}\right)\) \(e\left(\frac{54}{65}\right)\) \(e\left(\frac{38}{65}\right)\)
\(\chi_{1441}(830,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{21}{65}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{8}{65}\right)\) \(e\left(\frac{11}{65}\right)\) \(e\left(\frac{41}{65}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{42}{65}\right)\) \(e\left(\frac{63}{65}\right)\) \(e\left(\frac{1}{65}\right)\)
\(\chi_{1441}(845,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{14}{65}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{27}{65}\right)\) \(e\left(\frac{29}{65}\right)\) \(e\left(\frac{49}{65}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{28}{65}\right)\) \(e\left(\frac{42}{65}\right)\) \(e\left(\frac{44}{65}\right)\)
\(\chi_{1441}(850,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{47}{65}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{21}{65}\right)\) \(e\left(\frac{37}{65}\right)\) \(e\left(\frac{2}{65}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{29}{65}\right)\) \(e\left(\frac{11}{65}\right)\) \(e\left(\frac{27}{65}\right)\)