Properties

Conductor 4025
Order 110
Real No
Primitive Yes
Parity Odd
Orbit Label 4025.cw

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[41]
 
pari: [g,chi] = znchar(Mod(41,4025))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4025
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 110
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.cw
Orbit index = 75

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 ]
 

\(\chi_{4025}(6,\cdot)\) \(\chi_{4025}(41,\cdot)\) \(\chi_{4025}(146,\cdot)\) \(\chi_{4025}(216,\cdot)\) \(\chi_{4025}(496,\cdot)\) \(\chi_{4025}(531,\cdot)\) \(\chi_{4025}(671,\cdot)\) \(\chi_{4025}(706,\cdot)\) \(\chi_{4025}(811,\cdot)\) \(\chi_{4025}(846,\cdot)\) \(\chi_{4025}(1021,\cdot)\) \(\chi_{4025}(1231,\cdot)\) \(\chi_{4025}(1336,\cdot)\) \(\chi_{4025}(1406,\cdot)\) \(\chi_{4025}(1511,\cdot)\) \(\chi_{4025}(1616,\cdot)\) \(\chi_{4025}(1756,\cdot)\) \(\chi_{4025}(2036,\cdot)\) \(\chi_{4025}(2106,\cdot)\) \(\chi_{4025}(2141,\cdot)\) \(\chi_{4025}(2211,\cdot)\) \(\chi_{4025}(2281,\cdot)\) \(\chi_{4025}(2316,\cdot)\) \(\chi_{4025}(2421,\cdot)\) \(\chi_{4025}(2456,\cdot)\) \(\chi_{4025}(2561,\cdot)\) \(\chi_{4025}(2631,\cdot)\) \(\chi_{4025}(2841,\cdot)\) \(\chi_{4025}(2911,\cdot)\) \(\chi_{4025}(2946,\cdot)\) ...

Values on generators

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

Values

-1123468911121316
\(-1\)\(1\)\(e\left(\frac{16}{55}\right)\)\(e\left(\frac{69}{110}\right)\)\(e\left(\frac{32}{55}\right)\)\(e\left(\frac{101}{110}\right)\)\(e\left(\frac{48}{55}\right)\)\(e\left(\frac{14}{55}\right)\)\(e\left(\frac{6}{55}\right)\)\(e\left(\frac{23}{110}\right)\)\(e\left(\frac{103}{110}\right)\)\(e\left(\frac{9}{55}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{55})\)