Properties

Conductor 4025
Order 330
Real No
Primitive Yes
Parity Odd
Orbit Label 4025.di

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(4025)
 
sage: chi = H[31]
 
pari: [g,chi] = znchar(Mod(31,4025))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4025
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 330
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 = Odd
Orbit label = 4025.di
Orbit index = 87

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 ]
 

\(\chi_{4025}(31,\cdot)\) \(\chi_{4025}(96,\cdot)\) \(\chi_{4025}(131,\cdot)\) \(\chi_{4025}(236,\cdot)\) \(\chi_{4025}(271,\cdot)\) \(\chi_{4025}(311,\cdot)\) \(\chi_{4025}(381,\cdot)\) \(\chi_{4025}(416,\cdot)\) \(\chi_{4025}(446,\cdot)\) \(\chi_{4025}(486,\cdot)\) \(\chi_{4025}(556,\cdot)\) \(\chi_{4025}(591,\cdot)\) \(\chi_{4025}(656,\cdot)\) \(\chi_{4025}(696,\cdot)\) \(\chi_{4025}(731,\cdot)\) \(\chi_{4025}(761,\cdot)\) \(\chi_{4025}(831,\cdot)\) \(\chi_{4025}(836,\cdot)\) \(\chi_{4025}(906,\cdot)\) \(\chi_{4025}(936,\cdot)\) \(\chi_{4025}(1041,\cdot)\) \(\chi_{4025}(1116,\cdot)\) \(\chi_{4025}(1181,\cdot)\) \(\chi_{4025}(1186,\cdot)\) \(\chi_{4025}(1221,\cdot)\) \(\chi_{4025}(1291,\cdot)\) \(\chi_{4025}(1361,\cdot)\) \(\chi_{4025}(1396,\cdot)\) \(\chi_{4025}(1461,\cdot)\) \(\chi_{4025}(1531,\cdot)\) ...

Values on generators

\((2577,1151,3501)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{1}{6}\right),e\left(\frac{3}{11}\right))\)

Values

-1123468911121316
\(-1\)\(1\)\(e\left(\frac{46}{165}\right)\)\(e\left(\frac{109}{330}\right)\)\(e\left(\frac{92}{165}\right)\)\(e\left(\frac{67}{110}\right)\)\(e\left(\frac{46}{55}\right)\)\(e\left(\frac{109}{165}\right)\)\(e\left(\frac{86}{165}\right)\)\(e\left(\frac{293}{330}\right)\)\(e\left(\frac{101}{110}\right)\)\(e\left(\frac{19}{165}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{165})\)