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Properties

Label 3060.fl
Modulus $3060$
Conductor $765$
Order $48$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3060, base_ring=CyclotomicField(48)) M = H._module chi = DirichletCharacter(H, M([0,32,36,27])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(133,3060)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(3060\)
Conductor: \(765\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(48\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 765.cs
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{48})\)
Fixed field: Number field defined by a degree 48 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(7\) \(11\) \(13\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{3060}(133,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{1}{24}\right)\)
\(\chi_{3060}(517,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{11}{24}\right)\)
\(\chi_{3060}(853,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{1}{24}\right)\)
\(\chi_{3060}(877,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{11}{24}\right)\)
\(\chi_{3060}(913,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{5}{24}\right)\)
\(\chi_{3060}(997,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{7}{24}\right)\)
\(\chi_{3060}(1093,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{5}{24}\right)\)
\(\chi_{3060}(1417,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{23}{24}\right)\)
\(\chi_{3060}(1537,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{19}{24}\right)\)
\(\chi_{3060}(1897,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{19}{24}\right)\)
\(\chi_{3060}(1933,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{13}{24}\right)\)
\(\chi_{3060}(2113,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{13}{24}\right)\)
\(\chi_{3060}(2173,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{17}{24}\right)\)
\(\chi_{3060}(2437,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{7}{24}\right)\)
\(\chi_{3060}(2893,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{17}{24}\right)\)
\(\chi_{3060}(3037,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{23}{24}\right)\)