↑

Properties

Label 8450.bu
Modulus $8450$
Conductor $325$
Order $60$
Real no
Primitive no
Minimal no
Parity even

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8450, base_ring=CyclotomicField(60)) M = H._module chi = DirichletCharacter(H, M([3,35])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(427,8450)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(8450\)
Conductor: \(325\)
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: no, induced from 325.bi
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
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 \(-1\) \(1\) \(3\) \(7\) \(9\) \(11\) \(17\) \(19\) \(21\) \(23\) \(27\) \(29\)
\(\chi_{8450}(427,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{13}{30}\right)\)
\(\chi_{8450}(1033,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{8450}(1263,\cdot)\) \(1\) \(1\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{8450}(2117,\cdot)\) \(1\) \(1\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{8450}(2347,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{8450}(2723,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{23}{30}\right)\)
\(\chi_{8450}(2953,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{8450}(4037,\cdot)\) \(1\) \(1\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{8450}(4413,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{8450}(5497,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{8450}(5727,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{23}{30}\right)\)
\(\chi_{8450}(6103,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{8450}(6333,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{8450}(7187,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{8450}(7417,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{8450}(8023,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{30}\right)\)