Properties

Conductor 573
Order 190
Real No
Primitive No
Parity Odd
Orbit Label 4011.ca

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[50]
 
pari: [g,chi] = znchar(Mod(50,4011))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 573
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.ca
Orbit index = 53

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 ]
 

\(\chi_{4011}(8,\cdot)\) \(\chi_{4011}(50,\cdot)\) \(\chi_{4011}(92,\cdot)\) \(\chi_{4011}(134,\cdot)\) \(\chi_{4011}(218,\cdot)\) \(\chi_{4011}(239,\cdot)\) \(\chi_{4011}(281,\cdot)\) \(\chi_{4011}(386,\cdot)\) \(\chi_{4011}(428,\cdot)\) \(\chi_{4011}(449,\cdot)\) \(\chi_{4011}(512,\cdot)\) \(\chi_{4011}(554,\cdot)\) \(\chi_{4011}(575,\cdot)\) \(\chi_{4011}(596,\cdot)\) \(\chi_{4011}(638,\cdot)\) \(\chi_{4011}(659,\cdot)\) \(\chi_{4011}(701,\cdot)\) \(\chi_{4011}(722,\cdot)\) \(\chi_{4011}(743,\cdot)\) \(\chi_{4011}(911,\cdot)\) \(\chi_{4011}(995,\cdot)\) \(\chi_{4011}(1058,\cdot)\) \(\chi_{4011}(1163,\cdot)\) \(\chi_{4011}(1205,\cdot)\) \(\chi_{4011}(1226,\cdot)\) \(\chi_{4011}(1352,\cdot)\) \(\chi_{4011}(1415,\cdot)\) \(\chi_{4011}(1457,\cdot)\) \(\chi_{4011}(1499,\cdot)\) \(\chi_{4011}(1541,\cdot)\) ...

Inducing primitive character

\(\chi_{573}(50,\cdot)\)

Values on generators

\((2675,2866,2311)\) → \((-1,1,e\left(\frac{72}{95}\right))\)

Values

-112458101113161719
\(-1\)\(1\)\(e\left(\frac{161}{190}\right)\)\(e\left(\frac{66}{95}\right)\)\(e\left(\frac{15}{38}\right)\)\(e\left(\frac{103}{190}\right)\)\(e\left(\frac{23}{95}\right)\)\(e\left(\frac{35}{38}\right)\)\(e\left(\frac{84}{95}\right)\)\(e\left(\frac{37}{95}\right)\)\(e\left(\frac{147}{190}\right)\)\(e\left(\frac{72}{95}\right)\)
value at  e.g. 2

Related number fields

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