Basic properties
| Modulus: | \(2667\) | |
| Conductor: | \(889\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(63\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{889}(163,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2667.ec
\(\chi_{2667}(163,\cdot)\) \(\chi_{2667}(352,\cdot)\) \(\chi_{2667}(415,\cdot)\) \(\chi_{2667}(646,\cdot)\) \(\chi_{2667}(697,\cdot)\) \(\chi_{2667}(709,\cdot)\) \(\chi_{2667}(739,\cdot)\) \(\chi_{2667}(886,\cdot)\) \(\chi_{2667}(898,\cdot)\) \(\chi_{2667}(949,\cdot)\) \(\chi_{2667}(961,\cdot)\) \(\chi_{2667}(970,\cdot)\) \(\chi_{2667}(1192,\cdot)\) \(\chi_{2667}(1222,\cdot)\) \(\chi_{2667}(1264,\cdot)\) \(\chi_{2667}(1285,\cdot)\) \(\chi_{2667}(1339,\cdot)\) \(\chi_{2667}(1390,\cdot)\) \(\chi_{2667}(1432,\cdot)\) \(\chi_{2667}(1537,\cdot)\) \(\chi_{2667}(1612,\cdot)\) \(\chi_{2667}(1822,\cdot)\) \(\chi_{2667}(1936,\cdot)\) \(\chi_{2667}(2020,\cdot)\) \(\chi_{2667}(2053,\cdot)\) \(\chi_{2667}(2062,\cdot)\) \(\chi_{2667}(2074,\cdot)\) \(\chi_{2667}(2116,\cdot)\) \(\chi_{2667}(2200,\cdot)\) \(\chi_{2667}(2230,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((890,1144,2416)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{10}{63}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 2667 }(163, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(1\) |