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Properties

Label 128.l
Modulus $128$
Conductor $128$
Order $32$
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(128, base_ring=CyclotomicField(32)) M = H._module chi = DirichletCharacter(H, M([16,3])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(3,128)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(128\)
Conductor: \(128\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(32\)
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: \(\Q(\zeta_{32})\)
Fixed field: 32.0.3138550867693340381917894711603833208051177722232017256448.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(21\)
\(\chi_{128}(3,\cdot)\) \(-1\) \(1\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{7}{32}\right)\)
\(\chi_{128}(11,\cdot)\) \(-1\) \(1\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{17}{32}\right)\)
\(\chi_{128}(19,\cdot)\) \(-1\) \(1\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{11}{32}\right)\)
\(\chi_{128}(27,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{21}{32}\right)\)
\(\chi_{128}(35,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{15}{32}\right)\)
\(\chi_{128}(43,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{25}{32}\right)\)
\(\chi_{128}(51,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{19}{32}\right)\)
\(\chi_{128}(59,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{29}{32}\right)\)
\(\chi_{128}(67,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{23}{32}\right)\)
\(\chi_{128}(75,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{1}{32}\right)\)
\(\chi_{128}(83,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{27}{32}\right)\)
\(\chi_{128}(91,\cdot)\) \(-1\) \(1\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{5}{32}\right)\)
\(\chi_{128}(99,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{31}{32}\right)\)
\(\chi_{128}(107,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{9}{32}\right)\)
\(\chi_{128}(115,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{3}{32}\right)\)
\(\chi_{128}(123,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{13}{32}\right)\)