Basic properties
| Modulus: | \(2888\) | |
| Conductor: | \(2888\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(342\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2888.bu
\(\chi_{2888}(13,\cdot)\) \(\chi_{2888}(21,\cdot)\) \(\chi_{2888}(29,\cdot)\) \(\chi_{2888}(53,\cdot)\) \(\chi_{2888}(109,\cdot)\) \(\chi_{2888}(117,\cdot)\) \(\chi_{2888}(165,\cdot)\) \(\chi_{2888}(173,\cdot)\) \(\chi_{2888}(181,\cdot)\) \(\chi_{2888}(205,\cdot)\) \(\chi_{2888}(261,\cdot)\) \(\chi_{2888}(269,\cdot)\) \(\chi_{2888}(317,\cdot)\) \(\chi_{2888}(325,\cdot)\) \(\chi_{2888}(357,\cdot)\) \(\chi_{2888}(413,\cdot)\) \(\chi_{2888}(421,\cdot)\) \(\chi_{2888}(469,\cdot)\) \(\chi_{2888}(485,\cdot)\) \(\chi_{2888}(509,\cdot)\) \(\chi_{2888}(565,\cdot)\) \(\chi_{2888}(573,\cdot)\) \(\chi_{2888}(621,\cdot)\) \(\chi_{2888}(629,\cdot)\) \(\chi_{2888}(637,\cdot)\) \(\chi_{2888}(661,\cdot)\) \(\chi_{2888}(717,\cdot)\) \(\chi_{2888}(725,\cdot)\) \(\chi_{2888}(773,\cdot)\) \(\chi_{2888}(781,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((2167,1445,2529)\) → \((1,-1,e\left(\frac{83}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 2888 }(53, a) \) | \(-1\) | \(1\) | \(e\left(\frac{40}{171}\right)\) | \(e\left(\frac{275}{342}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{80}{171}\right)\) | \(e\left(\frac{29}{114}\right)\) | \(e\left(\frac{59}{171}\right)\) | \(e\left(\frac{13}{342}\right)\) | \(e\left(\frac{145}{171}\right)\) | \(e\left(\frac{109}{171}\right)\) | \(e\left(\frac{74}{171}\right)\) |