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Properties

Label 1740.ch
Modulus $1740$
Conductor $87$
Order $28$
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(1740, base_ring=CyclotomicField(28)) M = H._module chi = DirichletCharacter(H, M([0,14,0,13])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(101,1740)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1740\)
Conductor: \(87\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(28\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 87.k
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: \(\Q(\zeta_{28})\)
Fixed field: \(\Q(\zeta_{87})^+\)

Characters in Galois orbit

Character \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{1740}(101,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(i\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{11}{28}\right)\) \(-i\) \(e\left(\frac{1}{28}\right)\)
\(\chi_{1740}(221,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(-i\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{5}{28}\right)\) \(i\) \(e\left(\frac{3}{28}\right)\)
\(\chi_{1740}(461,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(-i\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{1}{28}\right)\) \(i\) \(e\left(\frac{23}{28}\right)\)
\(\chi_{1740}(641,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(i\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{15}{28}\right)\) \(-i\) \(e\left(\frac{9}{28}\right)\)
\(\chi_{1740}(881,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(i\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{19}{28}\right)\) \(-i\) \(e\left(\frac{17}{28}\right)\)
\(\chi_{1740}(1001,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(-i\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{25}{28}\right)\) \(i\) \(e\left(\frac{15}{28}\right)\)
\(\chi_{1740}(1121,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(i\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{27}{28}\right)\) \(-i\) \(e\left(\frac{5}{28}\right)\)
\(\chi_{1740}(1181,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(i\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{23}{28}\right)\) \(-i\) \(e\left(\frac{25}{28}\right)\)
\(\chi_{1740}(1361,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(-i\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{17}{28}\right)\) \(i\) \(e\left(\frac{27}{28}\right)\)
\(\chi_{1740}(1481,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(i\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{3}{28}\right)\) \(-i\) \(e\left(\frac{13}{28}\right)\)
\(\chi_{1740}(1661,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(-i\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{9}{28}\right)\) \(i\) \(e\left(\frac{11}{28}\right)\)
\(\chi_{1740}(1721,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(-i\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{13}{28}\right)\) \(i\) \(e\left(\frac{19}{28}\right)\)