Properties

Label 2001.1114
Modulus $2001$
Conductor $667$
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(2001, base_ring=CyclotomicField(44))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,6,11]))
 
pari: [g,chi] = znchar(Mod(1114,2001))
 

Basic properties

Modulus: \(2001\)
Conductor: \(667\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{667}(447,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2001.bh

\(\chi_{2001}(157,\cdot)\) \(\chi_{2001}(244,\cdot)\) \(\chi_{2001}(481,\cdot)\) \(\chi_{2001}(592,\cdot)\) \(\chi_{2001}(655,\cdot)\) \(\chi_{2001}(766,\cdot)\) \(\chi_{2001}(916,\cdot)\) \(\chi_{2001}(940,\cdot)\) \(\chi_{2001}(1003,\cdot)\) \(\chi_{2001}(1027,\cdot)\) \(\chi_{2001}(1114,\cdot)\) \(\chi_{2001}(1201,\cdot)\) \(\chi_{2001}(1351,\cdot)\) \(\chi_{2001}(1525,\cdot)\) \(\chi_{2001}(1699,\cdot)\) \(\chi_{2001}(1723,\cdot)\) \(\chi_{2001}(1786,\cdot)\) \(\chi_{2001}(1873,\cdot)\) \(\chi_{2001}(1897,\cdot)\) \(\chi_{2001}(1960,\cdot)\)

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: 44.44.2829456642779506738660199294300931896594438764890376623447387777021003184630861677846958804464951379972781.1

Values on generators

\((668,1132,553)\) → \((1,e\left(\frac{3}{22}\right),i)\)

Values

\(-1\)\(1\)\(2\)\(4\)\(5\)\(7\)\(8\)\(10\)\(11\)\(13\)\(14\)\(16\)
\(1\)\(1\)\(e\left(\frac{23}{44}\right)\)\(e\left(\frac{1}{22}\right)\)\(e\left(\frac{7}{11}\right)\)\(e\left(\frac{13}{22}\right)\)\(e\left(\frac{25}{44}\right)\)\(e\left(\frac{7}{44}\right)\)\(e\left(\frac{21}{44}\right)\)\(e\left(\frac{9}{22}\right)\)\(e\left(\frac{5}{44}\right)\)\(e\left(\frac{1}{11}\right)\)
value at e.g. 2