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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2888.br
\(\chi_{2888}(3,\cdot)\) \(\chi_{2888}(51,\cdot)\) \(\chi_{2888}(59,\cdot)\) \(\chi_{2888}(67,\cdot)\) \(\chi_{2888}(91,\cdot)\) \(\chi_{2888}(147,\cdot)\) \(\chi_{2888}(155,\cdot)\) \(\chi_{2888}(203,\cdot)\) \(\chi_{2888}(211,\cdot)\) \(\chi_{2888}(219,\cdot)\) \(\chi_{2888}(243,\cdot)\) \(\chi_{2888}(355,\cdot)\) \(\chi_{2888}(363,\cdot)\) \(\chi_{2888}(371,\cdot)\) \(\chi_{2888}(395,\cdot)\) \(\chi_{2888}(451,\cdot)\) \(\chi_{2888}(459,\cdot)\) \(\chi_{2888}(507,\cdot)\) \(\chi_{2888}(515,\cdot)\) \(\chi_{2888}(523,\cdot)\) \(\chi_{2888}(547,\cdot)\) \(\chi_{2888}(603,\cdot)\) \(\chi_{2888}(611,\cdot)\) \(\chi_{2888}(659,\cdot)\) \(\chi_{2888}(667,\cdot)\) \(\chi_{2888}(675,\cdot)\) \(\chi_{2888}(699,\cdot)\) \(\chi_{2888}(755,\cdot)\) \(\chi_{2888}(763,\cdot)\) \(\chi_{2888}(811,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((2167,1445,2529)\) → \((-1,-1,e\left(\frac{269}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 2888 }(67, a) \) | \(1\) | \(1\) | \(e\left(\frac{113}{342}\right)\) | \(e\left(\frac{335}{342}\right)\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{113}{171}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{47}{171}\right)\) | \(e\left(\frac{53}{171}\right)\) | \(e\left(\frac{130}{171}\right)\) | \(e\left(\frac{139}{171}\right)\) | \(e\left(\frac{115}{342}\right)\) |