Basic properties
| Modulus: | \(2667\) | |
| Conductor: | \(127\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(63\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{127}(21,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2667.ea
\(\chi_{2667}(148,\cdot)\) \(\chi_{2667}(169,\cdot)\) \(\chi_{2667}(211,\cdot)\) \(\chi_{2667}(295,\cdot)\) \(\chi_{2667}(316,\cdot)\) \(\chi_{2667}(358,\cdot)\) \(\chi_{2667}(463,\cdot)\) \(\chi_{2667}(505,\cdot)\) \(\chi_{2667}(526,\cdot)\) \(\chi_{2667}(568,\cdot)\) \(\chi_{2667}(589,\cdot)\) \(\chi_{2667}(652,\cdot)\) \(\chi_{2667}(841,\cdot)\) \(\chi_{2667}(883,\cdot)\) \(\chi_{2667}(904,\cdot)\) \(\chi_{2667}(925,\cdot)\) \(\chi_{2667}(1009,\cdot)\) \(\chi_{2667}(1051,\cdot)\) \(\chi_{2667}(1114,\cdot)\) \(\chi_{2667}(1156,\cdot)\) \(\chi_{2667}(1177,\cdot)\) \(\chi_{2667}(1408,\cdot)\) \(\chi_{2667}(1471,\cdot)\) \(\chi_{2667}(1555,\cdot)\) \(\chi_{2667}(1639,\cdot)\) \(\chi_{2667}(1660,\cdot)\) \(\chi_{2667}(1681,\cdot)\) \(\chi_{2667}(1723,\cdot)\) \(\chi_{2667}(1849,\cdot)\) \(\chi_{2667}(1891,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((890,1144,2416)\) → \((1,1,e\left(\frac{58}{63}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 2667 }(148, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{34}{63}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{1}{3}\right)\) |