Properties

Label 7098.211
Modulus $7098$
Conductor $169$
Order $39$
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(7098, base_ring=CyclotomicField(78))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,0,38]))
 
pari: [g,chi] = znchar(Mod(211,7098))
 

Basic properties

Modulus: \(7098\)
Conductor: \(169\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(39\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{169}(42,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 7098.cq

\(\chi_{7098}(211,\cdot)\) \(\chi_{7098}(295,\cdot)\) \(\chi_{7098}(757,\cdot)\) \(\chi_{7098}(841,\cdot)\) \(\chi_{7098}(1303,\cdot)\) \(\chi_{7098}(1387,\cdot)\) \(\chi_{7098}(1849,\cdot)\) \(\chi_{7098}(1933,\cdot)\) \(\chi_{7098}(2395,\cdot)\) \(\chi_{7098}(2479,\cdot)\) \(\chi_{7098}(2941,\cdot)\) \(\chi_{7098}(3025,\cdot)\) \(\chi_{7098}(3487,\cdot)\) \(\chi_{7098}(4117,\cdot)\) \(\chi_{7098}(4579,\cdot)\) \(\chi_{7098}(4663,\cdot)\) \(\chi_{7098}(5125,\cdot)\) \(\chi_{7098}(5209,\cdot)\) \(\chi_{7098}(5671,\cdot)\) \(\chi_{7098}(5755,\cdot)\) \(\chi_{7098}(6217,\cdot)\) \(\chi_{7098}(6301,\cdot)\) \(\chi_{7098}(6763,\cdot)\) \(\chi_{7098}(6847,\cdot)\)

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

Related number fields

Field of values: $\Q(\zeta_{39})$
Fixed field: 39.39.27027636582498189040621249864144468324898507852136260989871841246090732111847218889.1

Values on generators

\((4733,5071,6931)\) → \((1,1,e\left(\frac{19}{39}\right))\)

Values

\(-1\)\(1\)\(5\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)\(41\)
\(1\)\(1\)\(e\left(\frac{5}{13}\right)\)\(e\left(\frac{7}{39}\right)\)\(e\left(\frac{5}{39}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{10}{13}\right)\)\(e\left(\frac{19}{39}\right)\)\(e\left(\frac{3}{13}\right)\)\(e\left(\frac{22}{39}\right)\)\(e\left(\frac{16}{39}\right)\)
value at e.g. 2