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Properties

Label 880.ck
Modulus $880$
Conductor $176$
Order $20$
Real no
Primitive no
Minimal yes
Parity odd

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(880, base_ring=CyclotomicField(20)) M = H._module chi = DirichletCharacter(H, M([0,15,0,18])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(61,880)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(880\)
Conductor: \(176\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(20\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 176.u
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: \(\Q(\zeta_{20})\)
Fixed field: 20.0.200317132330035063121671003054276608.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(7\) \(9\) \(13\) \(17\) \(19\) \(21\) \(23\) \(27\) \(29\)
\(\chi_{880}(61,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(i\) \(-1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{11}{20}\right)\)
\(\chi_{880}(101,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(-i\) \(-1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{9}{20}\right)\)
\(\chi_{880}(261,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(-i\) \(-1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{17}{20}\right)\)
\(\chi_{880}(381,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(i\) \(-1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{20}\right)\)
\(\chi_{880}(501,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(-i\) \(-1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{20}\right)\)
\(\chi_{880}(541,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(i\) \(-1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{19}{20}\right)\)
\(\chi_{880}(701,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(i\) \(-1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{20}\right)\)
\(\chi_{880}(821,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(-i\) \(-1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{13}{20}\right)\)