Properties

Label 3549.cu
Modulus $3549$
Conductor $1183$
Order $52$
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(52))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,26,49]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(34,3549))
 
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: \(52\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 1183.bn
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: $\Q(\zeta_{52})$
Fixed field: Number field defined by a degree 52 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(5\) \(8\) \(10\) \(11\) \(16\) \(17\) \(19\) \(20\)
\(\chi_{3549}(34,\cdot)\) \(1\) \(1\) \(e\left(\frac{49}{52}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{51}{52}\right)\) \(e\left(\frac{43}{52}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{3}{52}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(-i\) \(e\left(\frac{45}{52}\right)\)
\(\chi_{3549}(265,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{52}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{49}{52}\right)\) \(e\left(\frac{25}{52}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{9}{52}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{3}{13}\right)\) \(i\) \(e\left(\frac{31}{52}\right)\)
\(\chi_{3549}(307,\cdot)\) \(1\) \(1\) \(e\left(\frac{33}{52}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{11}{52}\right)\) \(e\left(\frac{47}{52}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{19}{52}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{2}{13}\right)\) \(-i\) \(e\left(\frac{25}{52}\right)\)
\(\chi_{3549}(538,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{52}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{37}{52}\right)\) \(e\left(\frac{21}{52}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{45}{52}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{2}{13}\right)\) \(i\) \(e\left(\frac{51}{52}\right)\)
\(\chi_{3549}(580,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{52}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{23}{52}\right)\) \(e\left(\frac{51}{52}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{35}{52}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{3}{13}\right)\) \(-i\) \(e\left(\frac{5}{52}\right)\)
\(\chi_{3549}(811,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{52}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{25}{52}\right)\) \(e\left(\frac{17}{52}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{29}{52}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(i\) \(e\left(\frac{19}{52}\right)\)
\(\chi_{3549}(853,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{52}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{35}{52}\right)\) \(e\left(\frac{3}{52}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{51}{52}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(-i\) \(e\left(\frac{37}{52}\right)\)
\(\chi_{3549}(1126,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{52}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{47}{52}\right)\) \(e\left(\frac{7}{52}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{15}{52}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{5}{13}\right)\) \(-i\) \(e\left(\frac{17}{52}\right)\)
\(\chi_{3549}(1357,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{52}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{1}{52}\right)\) \(e\left(\frac{9}{52}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{49}{52}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{12}{13}\right)\) \(i\) \(e\left(\frac{7}{52}\right)\)
\(\chi_{3549}(1399,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{52}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{7}{52}\right)\) \(e\left(\frac{11}{52}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{31}{52}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{6}{13}\right)\) \(-i\) \(e\left(\frac{49}{52}\right)\)
\(\chi_{3549}(1630,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{52}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{41}{52}\right)\) \(e\left(\frac{5}{52}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{33}{52}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{11}{13}\right)\) \(i\) \(e\left(\frac{27}{52}\right)\)
\(\chi_{3549}(1672,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{52}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{19}{52}\right)\) \(e\left(\frac{15}{52}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{47}{52}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(-i\) \(e\left(\frac{29}{52}\right)\)
\(\chi_{3549}(1903,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{52}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{29}{52}\right)\) \(e\left(\frac{1}{52}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{17}{52}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(i\) \(e\left(\frac{47}{52}\right)\)
\(\chi_{3549}(1945,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{52}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{31}{52}\right)\) \(e\left(\frac{19}{52}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{11}{52}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{8}{13}\right)\) \(-i\) \(e\left(\frac{9}{52}\right)\)
\(\chi_{3549}(2176,\cdot)\) \(1\) \(1\) \(e\left(\frac{51}{52}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{17}{52}\right)\) \(e\left(\frac{49}{52}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{1}{52}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{9}{13}\right)\) \(i\) \(e\left(\frac{15}{52}\right)\)
\(\chi_{3549}(2218,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{52}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{43}{52}\right)\) \(e\left(\frac{23}{52}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{27}{52}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{9}{13}\right)\) \(-i\) \(e\left(\frac{41}{52}\right)\)
\(\chi_{3549}(2449,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{52}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{5}{52}\right)\) \(e\left(\frac{45}{52}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{37}{52}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{8}{13}\right)\) \(i\) \(e\left(\frac{35}{52}\right)\)
\(\chi_{3549}(2491,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{52}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{3}{52}\right)\) \(e\left(\frac{27}{52}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{43}{52}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(-i\) \(e\left(\frac{21}{52}\right)\)
\(\chi_{3549}(2722,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{52}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{45}{52}\right)\) \(e\left(\frac{41}{52}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{21}{52}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(i\) \(e\left(\frac{3}{52}\right)\)
\(\chi_{3549}(2764,\cdot)\) \(1\) \(1\) \(e\left(\frac{45}{52}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{15}{52}\right)\) \(e\left(\frac{31}{52}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{7}{52}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{11}{13}\right)\) \(-i\) \(e\left(\frac{1}{52}\right)\)
\(\chi_{3549}(2995,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{52}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{33}{52}\right)\) \(e\left(\frac{37}{52}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{5}{52}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{6}{13}\right)\) \(i\) \(e\left(\frac{23}{52}\right)\)
\(\chi_{3549}(3037,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{52}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{27}{52}\right)\) \(e\left(\frac{35}{52}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{23}{52}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{12}{13}\right)\) \(-i\) \(e\left(\frac{33}{52}\right)\)
\(\chi_{3549}(3268,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{52}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{21}{52}\right)\) \(e\left(\frac{33}{52}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{41}{52}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{5}{13}\right)\) \(i\) \(e\left(\frac{43}{52}\right)\)
\(\chi_{3549}(3541,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{52}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{9}{52}\right)\) \(e\left(\frac{29}{52}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{25}{52}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(i\) \(e\left(\frac{11}{52}\right)\)