Properties

Label 3630.47
Modulus $3630$
Conductor $1815$
Order $220$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(3630)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([110,55,196]))
 
pari: [g,chi] = znchar(Mod(47,3630))
 

Basic properties

Modulus: \(3630\)
Conductor: \(1815\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(220\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1815}(47,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3630.bt

\(\chi_{3630}(47,\cdot)\) \(\chi_{3630}(53,\cdot)\) \(\chi_{3630}(113,\cdot)\) \(\chi_{3630}(137,\cdot)\) \(\chi_{3630}(203,\cdot)\) \(\chi_{3630}(257,\cdot)\) \(\chi_{3630}(317,\cdot)\) \(\chi_{3630}(377,\cdot)\) \(\chi_{3630}(383,\cdot)\) \(\chi_{3630}(443,\cdot)\) \(\chi_{3630}(467,\cdot)\) \(\chi_{3630}(533,\cdot)\) \(\chi_{3630}(587,\cdot)\) \(\chi_{3630}(647,\cdot)\) \(\chi_{3630}(653,\cdot)\) \(\chi_{3630}(707,\cdot)\) \(\chi_{3630}(713,\cdot)\) \(\chi_{3630}(773,\cdot)\) \(\chi_{3630}(797,\cdot)\) \(\chi_{3630}(863,\cdot)\) \(\chi_{3630}(917,\cdot)\) \(\chi_{3630}(983,\cdot)\) \(\chi_{3630}(1037,\cdot)\) \(\chi_{3630}(1043,\cdot)\) \(\chi_{3630}(1103,\cdot)\) \(\chi_{3630}(1127,\cdot)\) \(\chi_{3630}(1193,\cdot)\) \(\chi_{3630}(1247,\cdot)\) \(\chi_{3630}(1307,\cdot)\) \(\chi_{3630}(1313,\cdot)\) ...

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Values on generators

\((1211,727,3511)\) → \((-1,i,e\left(\frac{49}{55}\right))\)

Values

\(-1\)\(1\)\(7\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{107}{220}\right)\)\(e\left(\frac{161}{220}\right)\)\(e\left(\frac{89}{220}\right)\)\(e\left(\frac{49}{110}\right)\)\(e\left(\frac{27}{44}\right)\)\(e\left(\frac{8}{55}\right)\)\(e\left(\frac{34}{55}\right)\)\(e\left(\frac{147}{220}\right)\)\(e\left(\frac{109}{110}\right)\)\(e\left(\frac{1}{44}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{220})$
Fixed field: Number field defined by a degree 220 polynomial