Properties

Label 1840.101
Modulus $1840$
Conductor $368$
Order $44$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1840, base_ring=CyclotomicField(44))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,11,0,20]))
 
pari: [g,chi] = znchar(Mod(101,1840))
 

Basic properties

Modulus: \(1840\)
Conductor: \(368\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{368}(101,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1840.cv

\(\chi_{1840}(101,\cdot)\) \(\chi_{1840}(141,\cdot)\) \(\chi_{1840}(261,\cdot)\) \(\chi_{1840}(301,\cdot)\) \(\chi_{1840}(381,\cdot)\) \(\chi_{1840}(501,\cdot)\) \(\chi_{1840}(541,\cdot)\) \(\chi_{1840}(581,\cdot)\) \(\chi_{1840}(821,\cdot)\) \(\chi_{1840}(901,\cdot)\) \(\chi_{1840}(1021,\cdot)\) \(\chi_{1840}(1061,\cdot)\) \(\chi_{1840}(1181,\cdot)\) \(\chi_{1840}(1221,\cdot)\) \(\chi_{1840}(1301,\cdot)\) \(\chi_{1840}(1421,\cdot)\) \(\chi_{1840}(1461,\cdot)\) \(\chi_{1840}(1501,\cdot)\) \(\chi_{1840}(1741,\cdot)\) \(\chi_{1840}(1821,\cdot)\)

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: \(\Q(\zeta_{44})\)
Fixed field: 44.44.7829660228065619245582194641412012312544945884150589900838471630076269829766255604192509952.1

Values on generators

\((1151,1381,737,1201)\) → \((1,i,1,e\left(\frac{5}{11}\right))\)

Values

\(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(17\)\(19\)\(21\)\(27\)\(29\)
\(1\)\(1\)\(e\left(\frac{1}{44}\right)\)\(e\left(\frac{3}{22}\right)\)\(e\left(\frac{1}{22}\right)\)\(e\left(\frac{15}{44}\right)\)\(e\left(\frac{5}{44}\right)\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{25}{44}\right)\)\(e\left(\frac{7}{44}\right)\)\(e\left(\frac{3}{44}\right)\)\(e\left(\frac{41}{44}\right)\)
value at e.g. 2