Properties

Conductor 3004
Order 150
Real No
Primitive Yes
Parity Even
Orbit Label 3004.y

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(3004)
 
sage: chi = H[223]
 
pari: [g,chi] = znchar(Mod(223,3004))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 3004
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 150
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 = 3004.y
Orbit index = 25

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 ]
 

\(\chi_{3004}(11,\cdot)\) \(\chi_{3004}(83,\cdot)\) \(\chi_{3004}(223,\cdot)\) \(\chi_{3004}(243,\cdot)\) \(\chi_{3004}(251,\cdot)\) \(\chi_{3004}(379,\cdot)\) \(\chi_{3004}(455,\cdot)\) \(\chi_{3004}(467,\cdot)\) \(\chi_{3004}(551,\cdot)\) \(\chi_{3004}(567,\cdot)\) \(\chi_{3004}(571,\cdot)\) \(\chi_{3004}(699,\cdot)\) \(\chi_{3004}(719,\cdot)\) \(\chi_{3004}(859,\cdot)\) \(\chi_{3004}(863,\cdot)\) \(\chi_{3004}(871,\cdot)\) \(\chi_{3004}(1031,\cdot)\) \(\chi_{3004}(1051,\cdot)\) \(\chi_{3004}(1103,\cdot)\) \(\chi_{3004}(1195,\cdot)\) \(\chi_{3004}(1203,\cdot)\) \(\chi_{3004}(1339,\cdot)\) \(\chi_{3004}(1371,\cdot)\) \(\chi_{3004}(1383,\cdot)\) \(\chi_{3004}(1395,\cdot)\) \(\chi_{3004}(1631,\cdot)\) \(\chi_{3004}(1875,\cdot)\) \(\chi_{3004}(1879,\cdot)\) \(\chi_{3004}(2059,\cdot)\) \(\chi_{3004}(2063,\cdot)\) ...

Values on generators

\((1503,1505)\) → \((-1,e\left(\frac{101}{150}\right))\)

Values

-113579111315171921
\(1\)\(1\)\(e\left(\frac{13}{75}\right)\)\(e\left(\frac{43}{75}\right)\)\(e\left(\frac{21}{25}\right)\)\(e\left(\frac{26}{75}\right)\)\(e\left(\frac{14}{15}\right)\)\(e\left(\frac{4}{75}\right)\)\(e\left(\frac{56}{75}\right)\)\(e\left(\frac{79}{150}\right)\)\(e\left(\frac{143}{150}\right)\)\(e\left(\frac{1}{75}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{75})\)