↑

Properties

Label 44100.md
Modulus $44100$
Conductor $2100$
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(44100, base_ring=CyclotomicField(60)) M = H._module chi = DirichletCharacter(H, M([30,30,21,10])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(1403,44100)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(44100\)
Conductor: \(2100\)
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 2100.do
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 \(-1\) \(1\) \(11\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{44100}(1403,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{2}{5}\right)\) \(-i\)
\(\chi_{44100}(3167,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(i\)
\(\chi_{44100}(10223,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{1}{5}\right)\) \(-i\)
\(\chi_{44100}(11987,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{4}{5}\right)\) \(i\)
\(\chi_{44100}(12563,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{4}{5}\right)\) \(-i\)
\(\chi_{44100}(14327,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{1}{5}\right)\) \(i\)
\(\chi_{44100}(21383,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(-i\)
\(\chi_{44100}(23147,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{2}{5}\right)\) \(i\)
\(\chi_{44100}(27863,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{4}{5}\right)\) \(-i\)
\(\chi_{44100}(29627,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{1}{5}\right)\) \(i\)
\(\chi_{44100}(30203,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{2}{5}\right)\) \(-i\)
\(\chi_{44100}(31967,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(i\)
\(\chi_{44100}(36683,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(-i\)
\(\chi_{44100}(38447,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{2}{5}\right)\) \(i\)
\(\chi_{44100}(39023,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{1}{5}\right)\) \(-i\)
\(\chi_{44100}(40787,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{4}{5}\right)\) \(i\)