Properties

Label 3549.dg
Modulus $3549$
Conductor $1183$
Order $78$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(3549, base_ring=CyclotomicField(78))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,52,9]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(25,3549))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(3549\)
Conductor: \(1183\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(78\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 1183.bs
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: $\Q(\zeta_{39})$
Fixed field: Number field defined by a degree 78 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(5\) \(8\) \(10\) \(11\) \(16\) \(17\) \(19\) \(20\)
\(\chi_{3549}(25,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{78}\right)\) \(e\left(\frac{35}{39}\right)\) \(e\left(\frac{29}{78}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{32}{39}\right)\) \(e\left(\frac{43}{78}\right)\) \(e\left(\frac{31}{39}\right)\) \(e\left(\frac{20}{39}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{26}\right)\)
\(\chi_{3549}(142,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{78}\right)\) \(e\left(\frac{4}{39}\right)\) \(e\left(\frac{49}{78}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{7}{39}\right)\) \(e\left(\frac{35}{78}\right)\) \(e\left(\frac{8}{39}\right)\) \(e\left(\frac{19}{39}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{19}{26}\right)\)
\(\chi_{3549}(298,\cdot)\) \(1\) \(1\) \(e\left(\frac{71}{78}\right)\) \(e\left(\frac{32}{39}\right)\) \(e\left(\frac{41}{78}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{17}{39}\right)\) \(e\left(\frac{7}{78}\right)\) \(e\left(\frac{25}{39}\right)\) \(e\left(\frac{35}{39}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{9}{26}\right)\)
\(\chi_{3549}(415,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{78}\right)\) \(e\left(\frac{1}{39}\right)\) \(e\left(\frac{61}{78}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{31}{39}\right)\) \(e\left(\frac{77}{78}\right)\) \(e\left(\frac{2}{39}\right)\) \(e\left(\frac{34}{39}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{21}{26}\right)\)
\(\chi_{3549}(571,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{78}\right)\) \(e\left(\frac{29}{39}\right)\) \(e\left(\frac{53}{78}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{2}{39}\right)\) \(e\left(\frac{49}{78}\right)\) \(e\left(\frac{19}{39}\right)\) \(e\left(\frac{11}{39}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{26}\right)\)
\(\chi_{3549}(688,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{78}\right)\) \(e\left(\frac{37}{39}\right)\) \(e\left(\frac{73}{78}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{16}{39}\right)\) \(e\left(\frac{41}{78}\right)\) \(e\left(\frac{35}{39}\right)\) \(e\left(\frac{10}{39}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{23}{26}\right)\)
\(\chi_{3549}(961,\cdot)\) \(1\) \(1\) \(e\left(\frac{73}{78}\right)\) \(e\left(\frac{34}{39}\right)\) \(e\left(\frac{7}{78}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{1}{39}\right)\) \(e\left(\frac{5}{78}\right)\) \(e\left(\frac{29}{39}\right)\) \(e\left(\frac{25}{39}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{25}{26}\right)\)
\(\chi_{3549}(1117,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{78}\right)\) \(e\left(\frac{23}{39}\right)\) \(e\left(\frac{77}{78}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{11}{39}\right)\) \(e\left(\frac{55}{78}\right)\) \(e\left(\frac{7}{39}\right)\) \(e\left(\frac{2}{39}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{15}{26}\right)\)
\(\chi_{3549}(1234,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{78}\right)\) \(e\left(\frac{31}{39}\right)\) \(e\left(\frac{19}{78}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{25}{39}\right)\) \(e\left(\frac{47}{78}\right)\) \(e\left(\frac{23}{39}\right)\) \(e\left(\frac{1}{39}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{26}\right)\)
\(\chi_{3549}(1390,\cdot)\) \(1\) \(1\) \(e\left(\frac{59}{78}\right)\) \(e\left(\frac{20}{39}\right)\) \(e\left(\frac{11}{78}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{35}{39}\right)\) \(e\left(\frac{19}{78}\right)\) \(e\left(\frac{1}{39}\right)\) \(e\left(\frac{17}{39}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{26}\right)\)
\(\chi_{3549}(1507,\cdot)\) \(1\) \(1\) \(e\left(\frac{67}{78}\right)\) \(e\left(\frac{28}{39}\right)\) \(e\left(\frac{31}{78}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{10}{39}\right)\) \(e\left(\frac{11}{78}\right)\) \(e\left(\frac{17}{39}\right)\) \(e\left(\frac{16}{39}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{26}\right)\)
\(\chi_{3549}(1663,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{78}\right)\) \(e\left(\frac{17}{39}\right)\) \(e\left(\frac{23}{78}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{20}{39}\right)\) \(e\left(\frac{61}{78}\right)\) \(e\left(\frac{34}{39}\right)\) \(e\left(\frac{32}{39}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{19}{26}\right)\)
\(\chi_{3549}(1780,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{78}\right)\) \(e\left(\frac{25}{39}\right)\) \(e\left(\frac{43}{78}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{34}{39}\right)\) \(e\left(\frac{53}{78}\right)\) \(e\left(\frac{11}{39}\right)\) \(e\left(\frac{31}{39}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{26}\right)\)
\(\chi_{3549}(1936,\cdot)\) \(1\) \(1\) \(e\left(\frac{53}{78}\right)\) \(e\left(\frac{14}{39}\right)\) \(e\left(\frac{35}{78}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{5}{39}\right)\) \(e\left(\frac{25}{78}\right)\) \(e\left(\frac{28}{39}\right)\) \(e\left(\frac{8}{39}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{21}{26}\right)\)
\(\chi_{3549}(2053,\cdot)\) \(1\) \(1\) \(e\left(\frac{61}{78}\right)\) \(e\left(\frac{22}{39}\right)\) \(e\left(\frac{55}{78}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{19}{39}\right)\) \(e\left(\frac{17}{78}\right)\) \(e\left(\frac{5}{39}\right)\) \(e\left(\frac{7}{39}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{26}\right)\)
\(\chi_{3549}(2209,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{78}\right)\) \(e\left(\frac{11}{39}\right)\) \(e\left(\frac{47}{78}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{29}{39}\right)\) \(e\left(\frac{67}{78}\right)\) \(e\left(\frac{22}{39}\right)\) \(e\left(\frac{23}{39}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{23}{26}\right)\)
\(\chi_{3549}(2326,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{78}\right)\) \(e\left(\frac{19}{39}\right)\) \(e\left(\frac{67}{78}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{4}{39}\right)\) \(e\left(\frac{59}{78}\right)\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{22}{39}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{9}{26}\right)\)
\(\chi_{3549}(2482,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{78}\right)\) \(e\left(\frac{8}{39}\right)\) \(e\left(\frac{59}{78}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{14}{39}\right)\) \(e\left(\frac{31}{78}\right)\) \(e\left(\frac{16}{39}\right)\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{25}{26}\right)\)
\(\chi_{3549}(2599,\cdot)\) \(1\) \(1\) \(e\left(\frac{55}{78}\right)\) \(e\left(\frac{16}{39}\right)\) \(e\left(\frac{1}{78}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{28}{39}\right)\) \(e\left(\frac{23}{78}\right)\) \(e\left(\frac{32}{39}\right)\) \(e\left(\frac{37}{39}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{26}\right)\)
\(\chi_{3549}(2755,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{78}\right)\) \(e\left(\frac{5}{39}\right)\) \(e\left(\frac{71}{78}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{73}{78}\right)\) \(e\left(\frac{10}{39}\right)\) \(e\left(\frac{14}{39}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{26}\right)\)
\(\chi_{3549}(3028,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{78}\right)\) \(e\left(\frac{2}{39}\right)\) \(e\left(\frac{5}{78}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{23}{39}\right)\) \(e\left(\frac{37}{78}\right)\) \(e\left(\frac{4}{39}\right)\) \(e\left(\frac{29}{39}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{26}\right)\)
\(\chi_{3549}(3145,\cdot)\) \(1\) \(1\) \(e\left(\frac{49}{78}\right)\) \(e\left(\frac{10}{39}\right)\) \(e\left(\frac{25}{78}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{37}{39}\right)\) \(e\left(\frac{29}{78}\right)\) \(e\left(\frac{20}{39}\right)\) \(e\left(\frac{28}{39}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{15}{26}\right)\)
\(\chi_{3549}(3301,\cdot)\) \(1\) \(1\) \(e\left(\frac{77}{78}\right)\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{17}{78}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{8}{39}\right)\) \(e\left(\frac{1}{78}\right)\) \(e\left(\frac{37}{39}\right)\) \(e\left(\frac{5}{39}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{26}\right)\)
\(\chi_{3549}(3418,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{78}\right)\) \(e\left(\frac{7}{39}\right)\) \(e\left(\frac{37}{78}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{22}{39}\right)\) \(e\left(\frac{71}{78}\right)\) \(e\left(\frac{14}{39}\right)\) \(e\left(\frac{4}{39}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{17}{26}\right)\)