Properties

Conductor 4011
Order 190
Real No
Primitive Yes
Parity Even
Orbit Label 4011.by

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[20]
 
pari: [g,chi] = znchar(Mod(20,4011))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4011
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 = Yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 4011.by
Orbit index = 51

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 ]
 

\(\chi_{4011}(20,\cdot)\) \(\chi_{4011}(104,\cdot)\) \(\chi_{4011}(209,\cdot)\) \(\chi_{4011}(251,\cdot)\) \(\chi_{4011}(272,\cdot)\) \(\chi_{4011}(293,\cdot)\) \(\chi_{4011}(335,\cdot)\) \(\chi_{4011}(398,\cdot)\) \(\chi_{4011}(461,\cdot)\) \(\chi_{4011}(482,\cdot)\) \(\chi_{4011}(545,\cdot)\) \(\chi_{4011}(650,\cdot)\) \(\chi_{4011}(671,\cdot)\) \(\chi_{4011}(776,\cdot)\) \(\chi_{4011}(818,\cdot)\) \(\chi_{4011}(839,\cdot)\) \(\chi_{4011}(860,\cdot)\) \(\chi_{4011}(881,\cdot)\) \(\chi_{4011}(902,\cdot)\) \(\chi_{4011}(965,\cdot)\) \(\chi_{4011}(1070,\cdot)\) \(\chi_{4011}(1154,\cdot)\) \(\chi_{4011}(1196,\cdot)\) \(\chi_{4011}(1238,\cdot)\) \(\chi_{4011}(1280,\cdot)\) \(\chi_{4011}(1364,\cdot)\) \(\chi_{4011}(1385,\cdot)\) \(\chi_{4011}(1427,\cdot)\) \(\chi_{4011}(1532,\cdot)\) \(\chi_{4011}(1574,\cdot)\) ...

Values on generators

\((2675,2866,2311)\) → \((-1,-1,e\left(\frac{69}{95}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{87}{190}\right)\)\(e\left(\frac{87}{95}\right)\)\(e\left(\frac{6}{19}\right)\)\(e\left(\frac{71}{190}\right)\)\(e\left(\frac{147}{190}\right)\)\(e\left(\frac{9}{38}\right)\)\(e\left(\frac{161}{190}\right)\)\(e\left(\frac{79}{95}\right)\)\(e\left(\frac{17}{95}\right)\)\(e\left(\frac{43}{190}\right)\)
value at  e.g. 2

Related number fields

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