↑

Properties

Label 1300.ct
Modulus $1300$
Conductor $1300$
Order $60$
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1300, base_ring=CyclotomicField(60)) M = H._module chi = DirichletCharacter(H, M([30,57,35])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(63,1300)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1300\)
Conductor: \(1300\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(60\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: yes
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{60})\)
Fixed field: Number field defined by a degree 60 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(7\) \(9\) \(11\) \(17\) \(19\) \(21\) \(23\) \(27\) \(29\)
\(\chi_{1300}(63,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{1300}(67,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{1300}(163,\cdot)\) \(-1\) \(1\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{1300}(227,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{23}{30}\right)\)
\(\chi_{1300}(323,\cdot)\) \(-1\) \(1\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{13}{30}\right)\)
\(\chi_{1300}(327,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{30}\right)\)
\(\chi_{1300}(423,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{23}{30}\right)\)
\(\chi_{1300}(487,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{1300}(583,\cdot)\) \(-1\) \(1\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{1300}(587,\cdot)\) \(-1\) \(1\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{1300}(683,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{1300}(747,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{1300}(847,\cdot)\) \(-1\) \(1\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{1300}(1103,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{1300}(1203,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{1300}(1267,\cdot)\) \(-1\) \(1\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{29}{30}\right)\)