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Properties

Label 1740.cf
Modulus $1740$
Conductor $1740$
Order $28$
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(1740, base_ring=CyclotomicField(28)) M = H._module chi = DirichletCharacter(H, M([14,14,14,5])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(119,1740)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1740\)
Conductor: \(1740\)
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: 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: \(\Q(\zeta_{28})\)
Fixed field: Number field defined by a degree 28 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{1740}(119,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(-i\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{1}{28}\right)\) \(-i\) \(e\left(\frac{9}{28}\right)\)
\(\chi_{1740}(359,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(-i\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{5}{28}\right)\) \(-i\) \(e\left(\frac{17}{28}\right)\)
\(\chi_{1740}(479,\cdot)\) \(-1\) \(1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(i\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{11}{28}\right)\) \(i\) \(e\left(\frac{15}{28}\right)\)
\(\chi_{1740}(599,\cdot)\) \(-1\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{2}{7}\right)\) \(-i\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{13}{28}\right)\) \(-i\) \(e\left(\frac{5}{28}\right)\)
\(\chi_{1740}(659,\cdot)\) \(-1\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(-i\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{9}{28}\right)\) \(-i\) \(e\left(\frac{25}{28}\right)\)
\(\chi_{1740}(839,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{1}{7}\right)\) \(i\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{3}{28}\right)\) \(i\) \(e\left(\frac{27}{28}\right)\)
\(\chi_{1740}(959,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{1}{7}\right)\) \(-i\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{17}{28}\right)\) \(-i\) \(e\left(\frac{13}{28}\right)\)
\(\chi_{1740}(1139,\cdot)\) \(-1\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(i\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{23}{28}\right)\) \(i\) \(e\left(\frac{11}{28}\right)\)
\(\chi_{1740}(1199,\cdot)\) \(-1\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{2}{7}\right)\) \(i\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{27}{28}\right)\) \(i\) \(e\left(\frac{19}{28}\right)\)
\(\chi_{1740}(1319,\cdot)\) \(-1\) \(1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(-i\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{25}{28}\right)\) \(-i\) \(e\left(\frac{1}{28}\right)\)
\(\chi_{1740}(1439,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(i\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{19}{28}\right)\) \(i\) \(e\left(\frac{3}{28}\right)\)
\(\chi_{1740}(1679,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(i\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{15}{28}\right)\) \(i\) \(e\left(\frac{23}{28}\right)\)