Basic properties
| Modulus: | \(2888\) | |
| Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(342\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{361}(41,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2888.bv
\(\chi_{2888}(33,\cdot)\) \(\chi_{2888}(41,\cdot)\) \(\chi_{2888}(89,\cdot)\) \(\chi_{2888}(97,\cdot)\) \(\chi_{2888}(105,\cdot)\) \(\chi_{2888}(129,\cdot)\) \(\chi_{2888}(185,\cdot)\) \(\chi_{2888}(193,\cdot)\) \(\chi_{2888}(241,\cdot)\) \(\chi_{2888}(249,\cdot)\) \(\chi_{2888}(257,\cdot)\) \(\chi_{2888}(281,\cdot)\) \(\chi_{2888}(337,\cdot)\) \(\chi_{2888}(345,\cdot)\) \(\chi_{2888}(393,\cdot)\) \(\chi_{2888}(401,\cdot)\) \(\chi_{2888}(409,\cdot)\) \(\chi_{2888}(433,\cdot)\) \(\chi_{2888}(489,\cdot)\) \(\chi_{2888}(497,\cdot)\) \(\chi_{2888}(545,\cdot)\) \(\chi_{2888}(553,\cdot)\) \(\chi_{2888}(561,\cdot)\) \(\chi_{2888}(585,\cdot)\) \(\chi_{2888}(641,\cdot)\) \(\chi_{2888}(649,\cdot)\) \(\chi_{2888}(697,\cdot)\) \(\chi_{2888}(705,\cdot)\) \(\chi_{2888}(713,\cdot)\) \(\chi_{2888}(737,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((2167,1445,2529)\) → \((1,1,e\left(\frac{67}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 2888 }(41, a) \) | \(-1\) | \(1\) | \(e\left(\frac{79}{342}\right)\) | \(e\left(\frac{77}{171}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{79}{171}\right)\) | \(e\left(\frac{56}{57}\right)\) | \(e\left(\frac{155}{342}\right)\) | \(e\left(\frac{233}{342}\right)\) | \(e\left(\frac{47}{171}\right)\) | \(e\left(\frac{211}{342}\right)\) | \(e\left(\frac{103}{171}\right)\) |