↑

Properties

Label 1449.bw
Modulus $1449$
Conductor $1449$
Order $33$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath
Copy content comment:Define the Dirichlet character orbit
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1449, base_ring=CyclotomicField(66)) M = H._module chi = DirichletCharacter(H, M([44,44,6])) chi.galois_orbit()
 
Copy content gp:[g,chi] = znchar(Mod(25, 1449)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1449.25"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };
 

Basic properties

Modulus: \(1449\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(1449\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(33\)
Copy content comment:Order
 
Copy content sage:chi.multiplicative_order()
 
Copy content gp:charorder(g,chi)
 
Copy content magma:Order(chi);
 
Real: no
Copy content comment:Whether the character is real
 
Copy content sage:chi.multiplicative_order() <= 2
 
Copy content gp:charorder(g,chi) <= 2
 
Copy content magma:Order(chi) le 2;
 
Primitive: yes
Copy content comment:If the character is primitive
 
Copy content sage:chi.is_primitive()
 
Copy content gp:#znconreyconductor(g,chi)==1
 
Copy content magma:IsPrimitive(chi);
 
Minimal: yes
Parity: even
Copy content comment:Parity
 
Copy content sage:chi.is_odd()
 
Copy content gp:zncharisodd(g,chi)
 
Copy content magma:IsOdd(chi);
 

Related number fields

Field of values: \(\Q(\zeta_{33})\)
Fixed field: Number field defined by a degree 33 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(5\) \(8\) \(10\) \(11\) \(13\) \(16\) \(17\) \(19\)
\(\chi_{1449}(25,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{23}{33}\right)\)
\(\chi_{1449}(58,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{10}{33}\right)\)
\(\chi_{1449}(121,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{31}{33}\right)\)
\(\chi_{1449}(151,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{29}{33}\right)\)
\(\chi_{1449}(340,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{17}{33}\right)\)
\(\chi_{1449}(403,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{32}{33}\right)\)
\(\chi_{1449}(466,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{20}{33}\right)\)
\(\chi_{1449}(499,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{4}{33}\right)\)
\(\chi_{1449}(625,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{13}{33}\right)\)
\(\chi_{1449}(814,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{16}{33}\right)\)
\(\chi_{1449}(844,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{26}{33}\right)\)
\(\chi_{1449}(877,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{19}{33}\right)\)
\(\chi_{1449}(970,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{2}{33}\right)\)
\(\chi_{1449}(1066,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{25}{33}\right)\)
\(\chi_{1449}(1129,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{1}{33}\right)\)
\(\chi_{1449}(1159,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{5}{33}\right)\)
\(\chi_{1449}(1222,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{8}{33}\right)\)
\(\chi_{1449}(1255,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{7}{33}\right)\)
\(\chi_{1449}(1411,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{14}{33}\right)\)
\(\chi_{1449}(1444,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{28}{33}\right)\)