Basic properties
| Modulus: | \(2888\) | |
| Conductor: | \(1444\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(342\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1444}(55,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2888.bp
\(\chi_{2888}(23,\cdot)\) \(\chi_{2888}(47,\cdot)\) \(\chi_{2888}(55,\cdot)\) \(\chi_{2888}(63,\cdot)\) \(\chi_{2888}(111,\cdot)\) \(\chi_{2888}(119,\cdot)\) \(\chi_{2888}(175,\cdot)\) \(\chi_{2888}(199,\cdot)\) \(\chi_{2888}(207,\cdot)\) \(\chi_{2888}(215,\cdot)\) \(\chi_{2888}(263,\cdot)\) \(\chi_{2888}(271,\cdot)\) \(\chi_{2888}(327,\cdot)\) \(\chi_{2888}(351,\cdot)\) \(\chi_{2888}(359,\cdot)\) \(\chi_{2888}(367,\cdot)\) \(\chi_{2888}(479,\cdot)\) \(\chi_{2888}(503,\cdot)\) \(\chi_{2888}(511,\cdot)\) \(\chi_{2888}(519,\cdot)\) \(\chi_{2888}(567,\cdot)\) \(\chi_{2888}(575,\cdot)\) \(\chi_{2888}(631,\cdot)\) \(\chi_{2888}(655,\cdot)\) \(\chi_{2888}(663,\cdot)\) \(\chi_{2888}(671,\cdot)\) \(\chi_{2888}(719,\cdot)\) \(\chi_{2888}(727,\cdot)\) \(\chi_{2888}(783,\cdot)\) \(\chi_{2888}(807,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((2167,1445,2529)\) → \((-1,1,e\left(\frac{167}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 2888 }(55, a) \) | \(-1\) | \(1\) | \(e\left(\frac{85}{342}\right)\) | \(e\left(\frac{98}{171}\right)\) | \(e\left(\frac{113}{114}\right)\) | \(e\left(\frac{85}{171}\right)\) | \(e\left(\frac{13}{114}\right)\) | \(e\left(\frac{52}{171}\right)\) | \(e\left(\frac{281}{342}\right)\) | \(e\left(\frac{122}{171}\right)\) | \(e\left(\frac{41}{171}\right)\) | \(e\left(\frac{29}{342}\right)\) |