Properties

Conductor 191
Order 190
Real No
Primitive No
Parity Odd
Orbit Label 4011.cb

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(4011)
 
sage: chi = H[22]
 
pari: [g,chi] = znchar(Mod(22,4011))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 191
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 190
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Odd
Orbit label = 4011.cb
Orbit index = 54

Galois orbit

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

\(\chi_{4011}(22,\cdot)\) \(\chi_{4011}(106,\cdot)\) \(\chi_{4011}(127,\cdot)\) \(\chi_{4011}(148,\cdot)\) \(\chi_{4011}(253,\cdot)\) \(\chi_{4011}(274,\cdot)\) \(\chi_{4011}(337,\cdot)\) \(\chi_{4011}(358,\cdot)\) \(\chi_{4011}(379,\cdot)\) \(\chi_{4011}(505,\cdot)\) \(\chi_{4011}(547,\cdot)\) \(\chi_{4011}(631,\cdot)\) \(\chi_{4011}(799,\cdot)\) \(\chi_{4011}(820,\cdot)\) \(\chi_{4011}(883,\cdot)\) \(\chi_{4011}(904,\cdot)\) \(\chi_{4011}(946,\cdot)\) \(\chi_{4011}(988,\cdot)\) \(\chi_{4011}(1219,\cdot)\) \(\chi_{4011}(1240,\cdot)\) \(\chi_{4011}(1303,\cdot)\) \(\chi_{4011}(1324,\cdot)\) \(\chi_{4011}(1366,\cdot)\) \(\chi_{4011}(1408,\cdot)\) \(\chi_{4011}(1450,\cdot)\) \(\chi_{4011}(1513,\cdot)\) \(\chi_{4011}(1639,\cdot)\) \(\chi_{4011}(1660,\cdot)\) \(\chi_{4011}(1702,\cdot)\) \(\chi_{4011}(1807,\cdot)\) ...

Inducing primitive character

\(\chi_{191}(22,\cdot)\)

Values on generators

\((2675,2866,2311)\) → \((1,1,e\left(\frac{129}{190}\right))\)

Values

-112458101113161719
\(-1\)\(1\)\(e\left(\frac{83}{95}\right)\)\(e\left(\frac{71}{95}\right)\)\(e\left(\frac{18}{19}\right)\)\(e\left(\frac{59}{95}\right)\)\(e\left(\frac{78}{95}\right)\)\(e\left(\frac{27}{38}\right)\)\(e\left(\frac{4}{95}\right)\)\(e\left(\frac{47}{95}\right)\)\(e\left(\frac{51}{95}\right)\)\(e\left(\frac{129}{190}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{95})\)