Properties

Conductor 1337
Order 570
Real No
Primitive No
Parity Odd
Orbit Label 4011.cg

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[10]
 
pari: [g,chi] = znchar(Mod(10,4011))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1337
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 570
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.cg
Orbit index = 59

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 ]
 

\(\chi_{4011}(10,\cdot)\) \(\chi_{4011}(40,\cdot)\) \(\chi_{4011}(103,\cdot)\) \(\chi_{4011}(115,\cdot)\) \(\chi_{4011}(199,\cdot)\) \(\chi_{4011}(208,\cdot)\) \(\chi_{4011}(241,\cdot)\) \(\chi_{4011}(250,\cdot)\) \(\chi_{4011}(271,\cdot)\) \(\chi_{4011}(283,\cdot)\) \(\chi_{4011}(325,\cdot)\) \(\chi_{4011}(397,\cdot)\) \(\chi_{4011}(409,\cdot)\) \(\chi_{4011}(430,\cdot)\) \(\chi_{4011}(460,\cdot)\) \(\chi_{4011}(472,\cdot)\) \(\chi_{4011}(502,\cdot)\) \(\chi_{4011}(544,\cdot)\) \(\chi_{4011}(577,\cdot)\) \(\chi_{4011}(586,\cdot)\) \(\chi_{4011}(607,\cdot)\) \(\chi_{4011}(619,\cdot)\) \(\chi_{4011}(640,\cdot)\) \(\chi_{4011}(670,\cdot)\) \(\chi_{4011}(691,\cdot)\) \(\chi_{4011}(703,\cdot)\) \(\chi_{4011}(745,\cdot)\) \(\chi_{4011}(766,\cdot)\) \(\chi_{4011}(787,\cdot)\) \(\chi_{4011}(829,\cdot)\) ...

Inducing primitive character

\(\chi_{1337}(10,\cdot)\)

Values on generators

\((2675,2866,2311)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{47}{95}\right))\)

Values

-112458101113161719
\(-1\)\(1\)\(e\left(\frac{29}{285}\right)\)\(e\left(\frac{58}{285}\right)\)\(e\left(\frac{65}{114}\right)\)\(e\left(\frac{29}{95}\right)\)\(e\left(\frac{383}{570}\right)\)\(e\left(\frac{41}{57}\right)\)\(e\left(\frac{173}{190}\right)\)\(e\left(\frac{116}{285}\right)\)\(e\left(\frac{371}{570}\right)\)\(e\left(\frac{187}{570}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{285})\)