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
\((2167,1445,2529)\) → \((-1,-1,e\left(\frac{139}{342}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 2888 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{169}{342}\right)\) | \(e\left(\frac{271}{342}\right)\) | \(e\left(\frac{53}{114}\right)\) | \(e\left(\frac{169}{171}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{37}{171}\right)\) | \(e\left(\frac{49}{171}\right)\) | \(e\left(\frac{146}{171}\right)\) | \(e\left(\frac{164}{171}\right)\) | \(e\left(\frac{287}{342}\right)\) |