Basic properties
Modulus: | \(5776\) | |
Conductor: | \(2888\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(342\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2888}(1453,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5776.cn
\(\chi_{5776}(9,\cdot)\) \(\chi_{5776}(25,\cdot)\) \(\chi_{5776}(73,\cdot)\) \(\chi_{5776}(137,\cdot)\) \(\chi_{5776}(169,\cdot)\) \(\chi_{5776}(233,\cdot)\) \(\chi_{5776}(313,\cdot)\) \(\chi_{5776}(329,\cdot)\) \(\chi_{5776}(377,\cdot)\) \(\chi_{5776}(441,\cdot)\) \(\chi_{5776}(473,\cdot)\) \(\chi_{5776}(537,\cdot)\) \(\chi_{5776}(617,\cdot)\) \(\chi_{5776}(633,\cdot)\) \(\chi_{5776}(681,\cdot)\) \(\chi_{5776}(745,\cdot)\) \(\chi_{5776}(777,\cdot)\) \(\chi_{5776}(841,\cdot)\) \(\chi_{5776}(921,\cdot)\) \(\chi_{5776}(937,\cdot)\) \(\chi_{5776}(985,\cdot)\) \(\chi_{5776}(1049,\cdot)\) \(\chi_{5776}(1081,\cdot)\) \(\chi_{5776}(1225,\cdot)\) \(\chi_{5776}(1241,\cdot)\) \(\chi_{5776}(1289,\cdot)\) \(\chi_{5776}(1353,\cdot)\) \(\chi_{5776}(1385,\cdot)\) \(\chi_{5776}(1449,\cdot)\) \(\chi_{5776}(1529,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{171})$ |
Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((5055,1445,2529)\) → \((1,-1,e\left(\frac{139}{171}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 5776 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{167}{342}\right)\) | \(e\left(\frac{29}{342}\right)\) | \(e\left(\frac{53}{57}\right)\) | \(e\left(\frac{167}{171}\right)\) | \(e\left(\frac{47}{114}\right)\) | \(e\left(\frac{319}{342}\right)\) | \(e\left(\frac{98}{171}\right)\) | \(e\left(\frac{121}{171}\right)\) | \(e\left(\frac{143}{342}\right)\) | \(e\left(\frac{116}{171}\right)\) |