Properties

Label 7098.373
Modulus $7098$
Conductor $1183$
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([0,26,58]))
 
pari: [g,chi] = znchar(Mod(373,7098))
 

Basic properties

Modulus: \(7098\)
Conductor: \(1183\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(39\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1183}(373,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 7098.cr

\(\chi_{7098}(373,\cdot)\) \(\chi_{7098}(445,\cdot)\) \(\chi_{7098}(919,\cdot)\) \(\chi_{7098}(1465,\cdot)\) \(\chi_{7098}(1537,\cdot)\) \(\chi_{7098}(2011,\cdot)\) \(\chi_{7098}(2083,\cdot)\) \(\chi_{7098}(2629,\cdot)\) \(\chi_{7098}(3103,\cdot)\) \(\chi_{7098}(3175,\cdot)\) \(\chi_{7098}(3649,\cdot)\) \(\chi_{7098}(3721,\cdot)\) \(\chi_{7098}(4195,\cdot)\) \(\chi_{7098}(4267,\cdot)\) \(\chi_{7098}(4741,\cdot)\) \(\chi_{7098}(4813,\cdot)\) \(\chi_{7098}(5287,\cdot)\) \(\chi_{7098}(5359,\cdot)\) \(\chi_{7098}(5833,\cdot)\) \(\chi_{7098}(5905,\cdot)\) \(\chi_{7098}(6379,\cdot)\) \(\chi_{7098}(6451,\cdot)\) \(\chi_{7098}(6925,\cdot)\) \(\chi_{7098}(6997,\cdot)\)

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: 39.39.253721406991290895924770503111827676888647505643788160579278763946491805765758913183386148271215912203961.1

Values on generators

\((4733,5071,6931)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{29}{39}\right))\)

Values

\(-1\)\(1\)\(5\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)\(41\)
\(1\)\(1\)\(e\left(\frac{14}{39}\right)\)\(e\left(\frac{12}{13}\right)\)\(e\left(\frac{35}{39}\right)\)\(1\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{28}{39}\right)\)\(e\left(\frac{29}{39}\right)\)\(e\left(\frac{37}{39}\right)\)\(e\left(\frac{37}{39}\right)\)\(e\left(\frac{8}{39}\right)\)
value at e.g. 2