Properties

Label 6001.94
Modulus $6001$
Conductor $6001$
Order $176$
Real no
Primitive yes
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([22,15]))
 
pari: [g,chi] = znchar(Mod(94,6001))
 

Basic properties

Modulus: \(6001\)
Conductor: \(6001\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(176\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6001.dg

\(\chi_{6001}(94,\cdot)\) \(\chi_{6001}(155,\cdot)\) \(\chi_{6001}(196,\cdot)\) \(\chi_{6001}(281,\cdot)\) \(\chi_{6001}(576,\cdot)\) \(\chi_{6001}(688,\cdot)\) \(\chi_{6001}(994,\cdot)\) \(\chi_{6001}(1131,\cdot)\) \(\chi_{6001}(1141,\cdot)\) \(\chi_{6001}(1216,\cdot)\) \(\chi_{6001}(1226,\cdot)\) \(\chi_{6001}(1243,\cdot)\) \(\chi_{6001}(1256,\cdot)\) \(\chi_{6001}(1260,\cdot)\) \(\chi_{6001}(1318,\cdot)\) \(\chi_{6001}(1334,\cdot)\) \(\chi_{6001}(1488,\cdot)\) \(\chi_{6001}(1505,\cdot)\) \(\chi_{6001}(1532,\cdot)\) \(\chi_{6001}(1600,\cdot)\) \(\chi_{6001}(1742,\cdot)\) \(\chi_{6001}(1804,\cdot)\) \(\chi_{6001}(1851,\cdot)\) \(\chi_{6001}(1878,\cdot)\) \(\chi_{6001}(1929,\cdot)\) \(\chi_{6001}(1974,\cdot)\) \(\chi_{6001}(2072,\cdot)\) \(\chi_{6001}(2099,\cdot)\) \(\chi_{6001}(2127,\cdot)\) \(\chi_{6001}(2133,\cdot)\) ...

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

\((2825,3180)\) → \((e\left(\frac{1}{8}\right),e\left(\frac{15}{176}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{8}{11}\right)\)\(e\left(\frac{37}{176}\right)\)\(e\left(\frac{5}{11}\right)\)\(e\left(\frac{169}{176}\right)\)\(e\left(\frac{15}{16}\right)\)\(e\left(\frac{13}{16}\right)\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{37}{88}\right)\)\(e\left(\frac{11}{16}\right)\)\(e\left(\frac{87}{88}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{176})$
Fixed field: Number field defined by a degree 176 polynomial