Properties

Label 8034.101
Modulus $8034$
Conductor $4017$
Order $102$
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(8034)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([51,85,95]))
 
pari: [g,chi] = znchar(Mod(101,8034))
 

Basic properties

Modulus: \(8034\)
Conductor: \(4017\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(102\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{4017}(101,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8034.df

\(\chi_{8034}(101,\cdot)\) \(\chi_{8034}(173,\cdot)\) \(\chi_{8034}(251,\cdot)\) \(\chi_{8034}(569,\cdot)\) \(\chi_{8034}(875,\cdot)\) \(\chi_{8034}(1115,\cdot)\) \(\chi_{8034}(1271,\cdot)\) \(\chi_{8034}(2045,\cdot)\) \(\chi_{8034}(2207,\cdot)\) \(\chi_{8034}(2753,\cdot)\) \(\chi_{8034}(3065,\cdot)\) \(\chi_{8034}(3611,\cdot)\) \(\chi_{8034}(3689,\cdot)\) \(\chi_{8034}(3761,\cdot)\) \(\chi_{8034}(4001,\cdot)\) \(\chi_{8034}(4079,\cdot)\) \(\chi_{8034}(4781,\cdot)\) \(\chi_{8034}(4853,\cdot)\) \(\chi_{8034}(5009,\cdot)\) \(\chi_{8034}(5087,\cdot)\) \(\chi_{8034}(5327,\cdot)\) \(\chi_{8034}(5555,\cdot)\) \(\chi_{8034}(5633,\cdot)\) \(\chi_{8034}(5639,\cdot)\) \(\chi_{8034}(5789,\cdot)\) \(\chi_{8034}(5867,\cdot)\) \(\chi_{8034}(6803,\cdot)\) \(\chi_{8034}(7193,\cdot)\) \(\chi_{8034}(7427,\cdot)\) \(\chi_{8034}(7745,\cdot)\) ...

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

\((5357,1237,5773)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{95}{102}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\(1\)\(1\)\(e\left(\frac{95}{102}\right)\)\(e\left(\frac{91}{102}\right)\)\(e\left(\frac{5}{34}\right)\)\(e\left(\frac{37}{102}\right)\)\(e\left(\frac{23}{34}\right)\)\(e\left(\frac{19}{102}\right)\)\(e\left(\frac{44}{51}\right)\)\(e\left(\frac{95}{102}\right)\)\(e\left(\frac{10}{17}\right)\)\(e\left(\frac{14}{17}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{51})$
Fixed field: Number field defined by a degree 102 polynomial