Properties

Label 6001.35
Modulus $6001$
Conductor $353$
Order $44$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(6001)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,7]))
 
pari: [g,chi] = znchar(Mod(35,6001))
 

Basic properties

Modulus: \(6001\)
Conductor: \(353\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{353}(35,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6001.co

\(\chi_{6001}(35,\cdot)\) \(\chi_{6001}(171,\cdot)\) \(\chi_{6001}(868,\cdot)\) \(\chi_{6001}(1055,\cdot)\) \(\chi_{6001}(1123,\cdot)\) \(\chi_{6001}(1378,\cdot)\) \(\chi_{6001}(1446,\cdot)\) \(\chi_{6001}(1701,\cdot)\) \(\chi_{6001}(1769,\cdot)\) \(\chi_{6001}(1956,\cdot)\) \(\chi_{6001}(2653,\cdot)\) \(\chi_{6001}(2789,\cdot)\) \(\chi_{6001}(2959,\cdot)\) \(\chi_{6001}(3265,\cdot)\) \(\chi_{6001}(3384,\cdot)\) \(\chi_{6001}(4115,\cdot)\) \(\chi_{6001}(4710,\cdot)\) \(\chi_{6001}(5441,\cdot)\) \(\chi_{6001}(5560,\cdot)\) \(\chi_{6001}(5866,\cdot)\)

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

Values on generators

\((2825,3180)\) → \((1,e\left(\frac{7}{44}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{7}{44}\right)\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{7}{44}\right)\)\(i\)\(-i\)\(e\left(\frac{3}{11}\right)\)\(e\left(\frac{7}{22}\right)\)\(i\)\(e\left(\frac{6}{11}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{44})\)
Fixed field: 44.44.35835406203814951479694647910185633079666581776176301713385706009212329177523219833640506320292452723709900577.1