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 \(\chi_{2888}(1515,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5776.cl
\(\chi_{5776}(71,\cdot)\) \(\chi_{5776}(135,\cdot)\) \(\chi_{5776}(167,\cdot)\) \(\chi_{5776}(231,\cdot)\) \(\chi_{5776}(279,\cdot)\) \(\chi_{5776}(295,\cdot)\) \(\chi_{5776}(375,\cdot)\) \(\chi_{5776}(439,\cdot)\) \(\chi_{5776}(471,\cdot)\) \(\chi_{5776}(535,\cdot)\) \(\chi_{5776}(583,\cdot)\) \(\chi_{5776}(599,\cdot)\) \(\chi_{5776}(679,\cdot)\) \(\chi_{5776}(743,\cdot)\) \(\chi_{5776}(775,\cdot)\) \(\chi_{5776}(839,\cdot)\) \(\chi_{5776}(887,\cdot)\) \(\chi_{5776}(903,\cdot)\) \(\chi_{5776}(983,\cdot)\) \(\chi_{5776}(1047,\cdot)\) \(\chi_{5776}(1079,\cdot)\) \(\chi_{5776}(1143,\cdot)\) \(\chi_{5776}(1191,\cdot)\) \(\chi_{5776}(1207,\cdot)\) \(\chi_{5776}(1287,\cdot)\) \(\chi_{5776}(1351,\cdot)\) \(\chi_{5776}(1383,\cdot)\) \(\chi_{5776}(1447,\cdot)\) \(\chi_{5776}(1495,\cdot)\) \(\chi_{5776}(1511,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((5055,1445,2529)\) → \((-1,-1,e\left(\frac{79}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 5776 }(71, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{342}\right)\) | \(e\left(\frac{31}{342}\right)\) | \(e\left(\frac{17}{114}\right)\) | \(e\left(\frac{37}{171}\right)\) | \(e\left(\frac{32}{57}\right)\) | \(e\left(\frac{85}{171}\right)\) | \(e\left(\frac{34}{171}\right)\) | \(e\left(\frac{35}{171}\right)\) | \(e\left(\frac{44}{171}\right)\) | \(e\left(\frac{77}{342}\right)\) |