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Properties

Label 164025.de
Modulus $164025$
Conductor $18225$
Order $4860$
Real no
Primitive no
Minimal no
Parity odd

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(164025, base_ring=CyclotomicField(4860)) M = H._module chi = DirichletCharacter(H, M([2060,1701])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(28,164025)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(164025\)
Conductor: \(18225\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(4860\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 18225.ct
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: $\Q(\zeta_{4860})$
Fixed field: Number field defined by a degree 4860 polynomial (not computed)

First 12 of 1296 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(7\) \(8\) \(11\) \(13\) \(14\) \(16\) \(17\) \(19\)
\(\chi_{164025}(28,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3761}{4860}\right)\) \(e\left(\frac{1331}{2430}\right)\) \(e\left(\frac{733}{972}\right)\) \(e\left(\frac{521}{1620}\right)\) \(e\left(\frac{674}{1215}\right)\) \(e\left(\frac{1819}{4860}\right)\) \(e\left(\frac{1283}{2430}\right)\) \(e\left(\frac{116}{1215}\right)\) \(e\left(\frac{871}{1620}\right)\) \(e\left(\frac{73}{810}\right)\)
\(\chi_{164025}(217,\cdot)\) \(-1\) \(1\) \(e\left(\frac{2899}{4860}\right)\) \(e\left(\frac{469}{2430}\right)\) \(e\left(\frac{167}{972}\right)\) \(e\left(\frac{1279}{1620}\right)\) \(e\left(\frac{316}{1215}\right)\) \(e\left(\frac{2861}{4860}\right)\) \(e\left(\frac{1867}{2430}\right)\) \(e\left(\frac{469}{1215}\right)\) \(e\left(\frac{1109}{1620}\right)\) \(e\left(\frac{557}{810}\right)\)
\(\chi_{164025}(298,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3733}{4860}\right)\) \(e\left(\frac{1303}{2430}\right)\) \(e\left(\frac{665}{972}\right)\) \(e\left(\frac{493}{1620}\right)\) \(e\left(\frac{637}{1215}\right)\) \(e\left(\frac{4187}{4860}\right)\) \(e\left(\frac{1099}{2430}\right)\) \(e\left(\frac{88}{1215}\right)\) \(e\left(\frac{563}{1620}\right)\) \(e\left(\frac{209}{810}\right)\)
\(\chi_{164025}(352,\cdot)\) \(-1\) \(1\) \(e\left(\frac{4343}{4860}\right)\) \(e\left(\frac{1913}{2430}\right)\) \(e\left(\frac{619}{972}\right)\) \(e\left(\frac{1103}{1620}\right)\) \(e\left(\frac{662}{1215}\right)\) \(e\left(\frac{157}{4860}\right)\) \(e\left(\frac{1289}{2430}\right)\) \(e\left(\frac{698}{1215}\right)\) \(e\left(\frac{793}{1620}\right)\) \(e\left(\frac{139}{810}\right)\)
\(\chi_{164025}(433,\cdot)\) \(-1\) \(1\) \(e\left(\frac{2909}{4860}\right)\) \(e\left(\frac{479}{2430}\right)\) \(e\left(\frac{469}{972}\right)\) \(e\left(\frac{1289}{1620}\right)\) \(e\left(\frac{416}{1215}\right)\) \(e\left(\frac{3751}{4860}\right)\) \(e\left(\frac{197}{2430}\right)\) \(e\left(\frac{479}{1215}\right)\) \(e\left(\frac{1219}{1620}\right)\) \(e\left(\frac{277}{810}\right)\)
\(\chi_{164025}(622,\cdot)\) \(-1\) \(1\) \(e\left(\frac{751}{4860}\right)\) \(e\left(\frac{751}{2430}\right)\) \(e\left(\frac{227}{972}\right)\) \(e\left(\frac{751}{1620}\right)\) \(e\left(\frac{949}{1215}\right)\) \(e\left(\frac{1229}{4860}\right)\) \(e\left(\frac{943}{2430}\right)\) \(e\left(\frac{751}{1215}\right)\) \(e\left(\frac{161}{1620}\right)\) \(e\left(\frac{113}{810}\right)\)
\(\chi_{164025}(703,\cdot)\) \(-1\) \(1\) \(e\left(\frac{4501}{4860}\right)\) \(e\left(\frac{2071}{2430}\right)\) \(e\left(\frac{725}{972}\right)\) \(e\left(\frac{1261}{1620}\right)\) \(e\left(\frac{784}{1215}\right)\) \(e\left(\frac{4499}{4860}\right)\) \(e\left(\frac{1633}{2430}\right)\) \(e\left(\frac{856}{1215}\right)\) \(e\left(\frac{911}{1620}\right)\) \(e\left(\frac{413}{810}\right)\)
\(\chi_{164025}(838,\cdot)\) \(-1\) \(1\) \(e\left(\frac{2057}{4860}\right)\) \(e\left(\frac{2057}{2430}\right)\) \(e\left(\frac{205}{972}\right)\) \(e\left(\frac{437}{1620}\right)\) \(e\left(\frac{158}{1215}\right)\) \(e\left(\frac{823}{4860}\right)\) \(e\left(\frac{1541}{2430}\right)\) \(e\left(\frac{842}{1215}\right)\) \(e\left(\frac{1567}{1620}\right)\) \(e\left(\frac{481}{810}\right)\)
\(\chi_{164025}(1027,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3463}{4860}\right)\) \(e\left(\frac{1033}{2430}\right)\) \(e\left(\frac{287}{972}\right)\) \(e\left(\frac{223}{1620}\right)\) \(e\left(\frac{367}{1215}\right)\) \(e\left(\frac{4457}{4860}\right)\) \(e\left(\frac{19}{2430}\right)\) \(e\left(\frac{1033}{1215}\right)\) \(e\left(\frac{833}{1620}\right)\) \(e\left(\frac{479}{810}\right)\)
\(\chi_{164025}(1108,\cdot)\) \(-1\) \(1\) \(e\left(\frac{409}{4860}\right)\) \(e\left(\frac{409}{2430}\right)\) \(e\left(\frac{785}{972}\right)\) \(e\left(\frac{409}{1620}\right)\) \(e\left(\frac{931}{1215}\right)\) \(e\left(\frac{4811}{4860}\right)\) \(e\left(\frac{2167}{2430}\right)\) \(e\left(\frac{409}{1215}\right)\) \(e\left(\frac{1259}{1620}\right)\) \(e\left(\frac{617}{810}\right)\)
\(\chi_{164025}(1162,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1667}{4860}\right)\) \(e\left(\frac{1667}{2430}\right)\) \(e\left(\frac{91}{972}\right)\) \(e\left(\frac{47}{1620}\right)\) \(e\left(\frac{1118}{1215}\right)\) \(e\left(\frac{133}{4860}\right)\) \(e\left(\frac{1061}{2430}\right)\) \(e\left(\frac{452}{1215}\right)\) \(e\left(\frac{517}{1620}\right)\) \(e\left(\frac{61}{810}\right)\)
\(\chi_{164025}(1513,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1177}{4860}\right)\) \(e\left(\frac{1177}{2430}\right)\) \(e\left(\frac{845}{972}\right)\) \(e\left(\frac{1177}{1620}\right)\) \(e\left(\frac{1078}{1215}\right)\) \(e\left(\frac{263}{4860}\right)\) \(e\left(\frac{271}{2430}\right)\) \(e\left(\frac{1177}{1215}\right)\) \(e\left(\frac{1607}{1620}\right)\) \(e\left(\frac{11}{810}\right)\)