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Properties

Label 1655.bi
Modulus $1655$
Conductor $1655$
Order $66$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

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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(1655, base_ring=CyclotomicField(66)) M = H._module chi = DirichletCharacter(H, M([33,32])) chi.galois_orbit()
 
Copy content gp:[g,chi] = znchar(Mod(79, 1655)) 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("1655.79"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };
 

Basic properties

Modulus: \(1655\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(1655\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(66\)
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 66 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(7\) \(8\) \(9\) \(11\) \(12\) \(13\)
\(\chi_{1655}(79,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{17}{22}\right)\) \(-1\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{53}{66}\right)\)
\(\chi_{1655}(89,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{21}{22}\right)\) \(-1\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{37}{66}\right)\)
\(\chi_{1655}(169,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{15}{22}\right)\) \(-1\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{61}{66}\right)\)
\(\chi_{1655}(219,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{15}{22}\right)\) \(-1\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{17}{66}\right)\)
\(\chi_{1655}(259,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{13}{22}\right)\) \(-1\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{25}{66}\right)\)
\(\chi_{1655}(284,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{7}{22}\right)\) \(-1\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{5}{66}\right)\)
\(\chi_{1655}(419,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{5}{22}\right)\) \(-1\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{13}{66}\right)\)
\(\chi_{1655}(494,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{5}{22}\right)\) \(-1\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{35}{66}\right)\)
\(\chi_{1655}(529,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{7}{22}\right)\) \(-1\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{49}{66}\right)\)
\(\chi_{1655}(554,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{3}{22}\right)\) \(-1\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{43}{66}\right)\)
\(\chi_{1655}(614,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{1}{22}\right)\) \(-1\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{7}{66}\right)\)
\(\chi_{1655}(639,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{9}{22}\right)\) \(-1\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{41}{66}\right)\)
\(\chi_{1655}(649,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{13}{22}\right)\) \(-1\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{47}{66}\right)\)
\(\chi_{1655}(794,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{17}{22}\right)\) \(-1\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{31}{66}\right)\)
\(\chi_{1655}(874,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{1}{22}\right)\) \(-1\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{29}{66}\right)\)
\(\chi_{1655}(959,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{19}{22}\right)\) \(-1\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{1}{66}\right)\)
\(\chi_{1655}(1124,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{21}{22}\right)\) \(-1\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{59}{66}\right)\)
\(\chi_{1655}(1139,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{3}{22}\right)\) \(-1\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{65}{66}\right)\)
\(\chi_{1655}(1419,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{19}{22}\right)\) \(-1\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{23}{66}\right)\)
\(\chi_{1655}(1604,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{9}{22}\right)\) \(-1\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{19}{66}\right)\)