Properties

Conductor 573
Order 190
Real No
Primitive No
Parity Even
Orbit Label 4011.bz

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[29]
 
pari: [g,chi] = znchar(Mod(29,4011))
 

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 = Even
Orbit label = 4011.bz
Orbit index = 52

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 ]
 

\(\chi_{4011}(29,\cdot)\) \(\chi_{4011}(71,\cdot)\) \(\chi_{4011}(113,\cdot)\) \(\chi_{4011}(176,\cdot)\) \(\chi_{4011}(302,\cdot)\) \(\chi_{4011}(323,\cdot)\) \(\chi_{4011}(365,\cdot)\) \(\chi_{4011}(470,\cdot)\) \(\chi_{4011}(533,\cdot)\) \(\chi_{4011}(617,\cdot)\) \(\chi_{4011}(785,\cdot)\) \(\chi_{4011}(806,\cdot)\) \(\chi_{4011}(827,\cdot)\) \(\chi_{4011}(869,\cdot)\) \(\chi_{4011}(890,\cdot)\) \(\chi_{4011}(932,\cdot)\) \(\chi_{4011}(953,\cdot)\) \(\chi_{4011}(974,\cdot)\) \(\chi_{4011}(1016,\cdot)\) \(\chi_{4011}(1079,\cdot)\) \(\chi_{4011}(1100,\cdot)\) \(\chi_{4011}(1142,\cdot)\) \(\chi_{4011}(1247,\cdot)\) \(\chi_{4011}(1289,\cdot)\) \(\chi_{4011}(1310,\cdot)\) \(\chi_{4011}(1394,\cdot)\) \(\chi_{4011}(1436,\cdot)\) \(\chi_{4011}(1478,\cdot)\) \(\chi_{4011}(1520,\cdot)\) \(\chi_{4011}(1604,\cdot)\) ...

Inducing primitive character

\(\chi_{573}(29,\cdot)\)

Values on generators

\((2675,2866,2311)\) → \((-1,1,e\left(\frac{33}{190}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{27}{190}\right)\)\(e\left(\frac{27}{95}\right)\)\(e\left(\frac{7}{38}\right)\)\(e\left(\frac{81}{190}\right)\)\(e\left(\frac{31}{95}\right)\)\(e\left(\frac{5}{19}\right)\)\(e\left(\frac{43}{95}\right)\)\(e\left(\frac{54}{95}\right)\)\(e\left(\frac{99}{190}\right)\)\(e\left(\frac{33}{190}\right)\)
value at  e.g. 2

Related number fields

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