Properties

Label 980.bi
Modulus $980$
Conductor $245$
Order $28$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(980, base_ring=CyclotomicField(28))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,21,22]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(13,980))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(980\)
Conductor: \(245\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(28\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 245.s
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{28})\)
Fixed field: 28.28.857574960063654015836849375042748140931725025177001953125.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(9\) \(11\) \(13\) \(17\) \(19\) \(23\) \(27\) \(29\) \(31\)
\(\chi_{980}(13,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{11}{28}\right)\) \(1\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(-1\)
\(\chi_{980}(153,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{23}{28}\right)\) \(1\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(-1\)
\(\chi_{980}(237,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{5}{28}\right)\) \(1\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(-1\)
\(\chi_{980}(377,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{17}{28}\right)\) \(1\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(-1\)
\(\chi_{980}(433,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{19}{28}\right)\) \(1\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(-1\)
\(\chi_{980}(517,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{1}{28}\right)\) \(1\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(-1\)
\(\chi_{980}(573,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{3}{28}\right)\) \(1\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(-1\)
\(\chi_{980}(657,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{13}{28}\right)\) \(1\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(-1\)
\(\chi_{980}(713,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{15}{28}\right)\) \(1\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(-1\)
\(\chi_{980}(797,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{25}{28}\right)\) \(1\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(-1\)
\(\chi_{980}(853,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{27}{28}\right)\) \(1\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(-1\)
\(\chi_{980}(937,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{9}{28}\right)\) \(1\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(-1\)