Properties

Label 2205.cx
Modulus $2205$
Conductor $735$
Order $28$
Real no
Primitive no
Minimal yes
Parity odd

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(2205, base_ring=CyclotomicField(28))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([14,7,22]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(62,2205))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(2205\)
Conductor: \(735\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(28\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 735.bk
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{28})\)
Fixed field: 28.0.4101754449160695184473159618498838032884071911945819854736328125.1

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(8\) \(11\) \(13\) \(16\) \(17\) \(19\) \(22\) \(23\)
\(\chi_{2205}(62,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{11}{28}\right)\) \(1\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{3}{28}\right)\)
\(\chi_{2205}(188,\cdot)\) \(-1\) \(1\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{28}\right)\) \(1\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{9}{28}\right)\)
\(\chi_{2205}(377,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{28}\right)\) \(1\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{11}{28}\right)\)
\(\chi_{2205}(503,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{25}{28}\right)\) \(1\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{17}{28}\right)\)
\(\chi_{2205}(692,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{23}{28}\right)\) \(1\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{19}{28}\right)\)
\(\chi_{2205}(818,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{17}{28}\right)\) \(1\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{25}{28}\right)\)
\(\chi_{2205}(1007,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{15}{28}\right)\) \(1\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{27}{28}\right)\)
\(\chi_{2205}(1133,\cdot)\) \(-1\) \(1\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{9}{28}\right)\) \(1\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{5}{28}\right)\)
\(\chi_{2205}(1448,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{28}\right)\) \(1\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{13}{28}\right)\)
\(\chi_{2205}(1637,\cdot)\) \(-1\) \(1\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{27}{28}\right)\) \(1\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{15}{28}\right)\)
\(\chi_{2205}(1952,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{19}{28}\right)\) \(1\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{23}{28}\right)\)
\(\chi_{2205}(2078,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{13}{28}\right)\) \(1\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{1}{28}\right)\)