Properties

Conductor 1337
Order 190
Real No
Primitive No
Parity Odd
Orbit Label 4011.cc

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[34]
 
pari: [g,chi] = znchar(Mod(34,4011))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1337
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.cc
Orbit index = 55

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 ]
 

\(\chi_{4011}(13,\cdot)\) \(\chi_{4011}(34,\cdot)\) \(\chi_{4011}(97,\cdot)\) \(\chi_{4011}(118,\cdot)\) \(\chi_{4011}(349,\cdot)\) \(\chi_{4011}(391,\cdot)\) \(\chi_{4011}(433,\cdot)\) \(\chi_{4011}(454,\cdot)\) \(\chi_{4011}(517,\cdot)\) \(\chi_{4011}(538,\cdot)\) \(\chi_{4011}(706,\cdot)\) \(\chi_{4011}(790,\cdot)\) \(\chi_{4011}(832,\cdot)\) \(\chi_{4011}(958,\cdot)\) \(\chi_{4011}(979,\cdot)\) \(\chi_{4011}(1000,\cdot)\) \(\chi_{4011}(1063,\cdot)\) \(\chi_{4011}(1084,\cdot)\) \(\chi_{4011}(1189,\cdot)\) \(\chi_{4011}(1210,\cdot)\) \(\chi_{4011}(1231,\cdot)\) \(\chi_{4011}(1315,\cdot)\) \(\chi_{4011}(1357,\cdot)\) \(\chi_{4011}(1441,\cdot)\) \(\chi_{4011}(1546,\cdot)\) \(\chi_{4011}(1588,\cdot)\) \(\chi_{4011}(1609,\cdot)\) \(\chi_{4011}(1630,\cdot)\) \(\chi_{4011}(1672,\cdot)\) \(\chi_{4011}(1735,\cdot)\) ...

Inducing primitive character

\(\chi_{1337}(34,\cdot)\)

Values on generators

\((2675,2866,2311)\) → \((1,-1,e\left(\frac{71}{95}\right))\)

Values

-112458101113161719
\(-1\)\(1\)\(e\left(\frac{84}{95}\right)\)\(e\left(\frac{73}{95}\right)\)\(e\left(\frac{33}{38}\right)\)\(e\left(\frac{62}{95}\right)\)\(e\left(\frac{143}{190}\right)\)\(e\left(\frac{10}{19}\right)\)\(e\left(\frac{39}{190}\right)\)\(e\left(\frac{51}{95}\right)\)\(e\left(\frac{141}{190}\right)\)\(e\left(\frac{47}{190}\right)\)
value at  e.g. 2

Related number fields

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