Properties

Conductor 191
Order 95
Real No
Primitive No
Parity Even
Orbit Label 4011.bp

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[43]
 
pari: [g,chi] = znchar(Mod(43,4011))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 191
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 95
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.bp
Orbit index = 42

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 ]
 

\(\chi_{4011}(43,\cdot)\) \(\chi_{4011}(64,\cdot)\) \(\chi_{4011}(85,\cdot)\) \(\chi_{4011}(169,\cdot)\) \(\chi_{4011}(211,\cdot)\) \(\chi_{4011}(295,\cdot)\) \(\chi_{4011}(400,\cdot)\) \(\chi_{4011}(442,\cdot)\) \(\chi_{4011}(463,\cdot)\) \(\chi_{4011}(484,\cdot)\) \(\chi_{4011}(526,\cdot)\) \(\chi_{4011}(589,\cdot)\) \(\chi_{4011}(652,\cdot)\) \(\chi_{4011}(673,\cdot)\) \(\chi_{4011}(736,\cdot)\) \(\chi_{4011}(841,\cdot)\) \(\chi_{4011}(862,\cdot)\) \(\chi_{4011}(967,\cdot)\) \(\chi_{4011}(1009,\cdot)\) \(\chi_{4011}(1030,\cdot)\) \(\chi_{4011}(1051,\cdot)\) \(\chi_{4011}(1072,\cdot)\) \(\chi_{4011}(1093,\cdot)\) \(\chi_{4011}(1156,\cdot)\) \(\chi_{4011}(1261,\cdot)\) \(\chi_{4011}(1345,\cdot)\) \(\chi_{4011}(1387,\cdot)\) \(\chi_{4011}(1429,\cdot)\) \(\chi_{4011}(1471,\cdot)\) \(\chi_{4011}(1555,\cdot)\) ...

Inducing primitive character

\(\chi_{191}(43,\cdot)\)

Values on generators

\((2675,2866,2311)\) → \((1,1,e\left(\frac{4}{95}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{81}{95}\right)\)\(e\left(\frac{67}{95}\right)\)\(e\left(\frac{2}{19}\right)\)\(e\left(\frac{53}{95}\right)\)\(e\left(\frac{91}{95}\right)\)\(e\left(\frac{11}{19}\right)\)\(e\left(\frac{68}{95}\right)\)\(e\left(\frac{39}{95}\right)\)\(e\left(\frac{12}{95}\right)\)\(e\left(\frac{4}{95}\right)\)
value at  e.g. 2

Related number fields

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