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Properties

Label 261.u
Modulus $261$
Conductor $261$
Order $42$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(261, base_ring=CyclotomicField(42)) M = H._module chi = DirichletCharacter(H, M([14,3])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(4,261)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(261\)
Conductor: \(261\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(42\)
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: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{21})\)
Fixed field: 42.42.565343212441678035532894502003808167878401992443661947648452445739810658542578516149.1

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(11\) \(13\) \(14\) \(16\)
\(\chi_{261}(4,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{13}{21}\right)\)
\(\chi_{261}(13,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{19}{21}\right)\)
\(\chi_{261}(22,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{1}{21}\right)\)
\(\chi_{261}(34,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{17}{21}\right)\)
\(\chi_{261}(67,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{16}{21}\right)\)
\(\chi_{261}(121,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{10}{21}\right)\)
\(\chi_{261}(151,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{11}{21}\right)\)
\(\chi_{261}(178,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{20}{21}\right)\)
\(\chi_{261}(187,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{5}{21}\right)\)
\(\chi_{261}(196,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{8}{21}\right)\)
\(\chi_{261}(238,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{4}{21}\right)\)
\(\chi_{261}(241,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{2}{21}\right)\)