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Properties

Label 18054.673
Modulus $18054$
Conductor $9027$
Order $1392$
Real no
Primitive no
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(18054, base_ring=CyclotomicField(1392)) M = H._module chi = DirichletCharacter(H, M([928,261,1272]))
 
Copy content gp:[g,chi] = znchar(Mod(673, 18054))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("18054.673");
 

Basic properties

Modulus: \(18054\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(9027\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(1392\)
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: no, induced from \(\chi_{9027}(673,\cdot)\)
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 18054.cz

\(\chi_{18054}(31,\cdot)\) \(\chi_{18054}(61,\cdot)\) \(\chi_{18054}(97,\cdot)\) \(\chi_{18054}(211,\cdot)\) \(\chi_{18054}(283,\cdot)\) \(\chi_{18054}(301,\cdot)\) \(\chi_{18054}(313,\cdot)\) \(\chi_{18054}(337,\cdot)\) \(\chi_{18054}(367,\cdot)\) \(\chi_{18054}(385,\cdot)\) \(\chi_{18054}(445,\cdot)\) \(\chi_{18054}(571,\cdot)\) \(\chi_{18054}(583,\cdot)\) \(\chi_{18054}(601,\cdot)\) \(\chi_{18054}(673,\cdot)\) \(\chi_{18054}(691,\cdot)\) \(\chi_{18054}(745,\cdot)\) \(\chi_{18054}(751,\cdot)\) \(\chi_{18054}(805,\cdot)\) \(\chi_{18054}(823,\cdot)\) \(\chi_{18054}(895,\cdot)\) \(\chi_{18054}(925,\cdot)\) \(\chi_{18054}(1057,\cdot)\) \(\chi_{18054}(1093,\cdot)\) \(\chi_{18054}(1129,\cdot)\) \(\chi_{18054}(1159,\cdot)\) \(\chi_{18054}(1213,\cdot)\) \(\chi_{18054}(1219,\cdot)\) \(\chi_{18054}(1321,\cdot)\) \(\chi_{18054}(1363,\cdot)\) ...

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: $\Q(\zeta_{1392})$
Fixed field: Number field defined by a degree 1392 polynomial (not computed)

Values on generators

\((16049,13807,13159)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{3}{16}\right),e\left(\frac{53}{58}\right))\)

First values

\(a\) \(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\( \chi_{ 18054 }(673, a) \) \(1\)\(1\)\(e\left(\frac{1049}{1392}\right)\)\(e\left(\frac{247}{1392}\right)\)\(e\left(\frac{1147}{1392}\right)\)\(e\left(\frac{71}{348}\right)\)\(e\left(\frac{81}{232}\right)\)\(e\left(\frac{1187}{1392}\right)\)\(e\left(\frac{353}{696}\right)\)\(e\left(\frac{961}{1392}\right)\)\(e\left(\frac{1109}{1392}\right)\)\(e\left(\frac{27}{29}\right)\)
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)
 
\( \chi_{ 18054 }(673,a) \;\) at \(\;a = \) e.g. 2