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Properties

Label 60515.4422
Modulus $60515$
Conductor $60515$
Order $252$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

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Show commands: Magma / Pari/GP / SageMath
Copy content comment:Define the Dirichlet character
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(60515, base_ring=CyclotomicField(252)) M = H._module chi = DirichletCharacter(H, M([63,66,21,98]))
 
Copy content gp:[g,chi] = znchar(Mod(4422, 60515))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("60515.4422");
 

Basic properties

Modulus: \(60515\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(60515\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(252\)
Copy content comment:Order
 
Copy content sage:chi.multiplicative_order()
 
Copy content gp:charorder(g,chi)
 
Copy content magma:Order(chi);
 
Real: no
Copy content comment:Whether the character is real
 
Copy content sage:chi.multiplicative_order() <= 2
 
Copy content gp:charorder(g,chi) <= 2
 
Copy content magma:Order(chi) le 2;
 
Primitive: yes
Copy content comment:If the character is primitive
 
Copy content sage:chi.is_primitive()
 
Copy content gp:#znconreyconductor(g,chi)==1
 
Copy content magma:IsPrimitive(chi);
 
Minimal: yes
Parity: even
Copy content comment:Parity
 
Copy content sage:chi.is_odd()
 
Copy content gp:zncharisodd(g,chi)
 
Copy content magma:IsOdd(chi);
 

Galois orbit 60515.ckm

\(\chi_{60515}(782,\cdot)\) \(\chi_{60515}(1237,\cdot)\) \(\chi_{60515}(1363,\cdot)\) \(\chi_{60515}(1592,\cdot)\) \(\chi_{60515}(2502,\cdot)\) \(\chi_{60515}(3867,\cdot)\) \(\chi_{60515}(4422,\cdot)\) \(\chi_{60515}(4518,\cdot)\) \(\chi_{60515}(5428,\cdot)\) \(\chi_{60515}(6368,\cdot)\) \(\chi_{60515}(6823,\cdot)\) \(\chi_{60515}(9882,\cdot)\) \(\chi_{60515}(10008,\cdot)\) \(\chi_{60515}(10237,\cdot)\) \(\chi_{60515}(11147,\cdot)\) \(\chi_{60515}(12512,\cdot)\) \(\chi_{60515}(13067,\cdot)\) \(\chi_{60515}(14073,\cdot)\) \(\chi_{60515}(15438,\cdot)\) \(\chi_{60515}(15468,\cdot)\) \(\chi_{60515}(18072,\cdot)\) \(\chi_{60515}(18527,\cdot)\) \(\chi_{60515}(18653,\cdot)\) \(\chi_{60515}(18882,\cdot)\) \(\chi_{60515}(19792,\cdot)\) \(\chi_{60515}(21157,\cdot)\) \(\chi_{60515}(21712,\cdot)\) \(\chi_{60515}(21808,\cdot)\) \(\chi_{60515}(23658,\cdot)\) \(\chi_{60515}(24083,\cdot)\) ...

Copy content comment:Galois orbit
 
Copy content sage:chi.galois_orbit()
 
Copy content gp:order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 
Copy content magma:order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };
 

Related number fields

Field of values: $\Q(\zeta_{252})$
Fixed field: Number field defined by a degree 252 polynomial (not computed)

Values on generators

\((24207,12351,4656,25481)\) → \((i,e\left(\frac{11}{42}\right),e\left(\frac{1}{12}\right),e\left(\frac{7}{18}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(8\)\(9\)\(11\)\(12\)\(16\)\(17\)
\( \chi_{ 60515 }(4422, a) \) \(1\)\(1\)\(e\left(\frac{67}{126}\right)\)\(e\left(\frac{101}{252}\right)\)\(e\left(\frac{4}{63}\right)\)\(e\left(\frac{235}{252}\right)\)\(e\left(\frac{25}{42}\right)\)\(e\left(\frac{101}{126}\right)\)\(e\left(\frac{61}{84}\right)\)\(e\left(\frac{13}{28}\right)\)\(e\left(\frac{8}{63}\right)\)\(e\left(\frac{215}{252}\right)\)
Copy content comment:Value of chi at x
 
Copy content sage:chi(x)
 
Copy content gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
 
Copy content magma:chi(x)
 
\( \chi_{ 60515 }(4422,a) \;\) at \(\;a = \) e.g. 2