Basic properties
| Modulus: | \(2385\) | |
| Conductor: | \(2385\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2385.cr
\(\chi_{2385}(167,\cdot)\) \(\chi_{2385}(338,\cdot)\) \(\chi_{2385}(353,\cdot)\) \(\chi_{2385}(392,\cdot)\) \(\chi_{2385}(443,\cdot)\) \(\chi_{2385}(482,\cdot)\) \(\chi_{2385}(518,\cdot)\) \(\chi_{2385}(527,\cdot)\) \(\chi_{2385}(533,\cdot)\) \(\chi_{2385}(542,\cdot)\) \(\chi_{2385}(578,\cdot)\) \(\chi_{2385}(617,\cdot)\) \(\chi_{2385}(668,\cdot)\) \(\chi_{2385}(707,\cdot)\) \(\chi_{2385}(722,\cdot)\) \(\chi_{2385}(893,\cdot)\) \(\chi_{2385}(1082,\cdot)\) \(\chi_{2385}(1127,\cdot)\) \(\chi_{2385}(1148,\cdot)\) \(\chi_{2385}(1217,\cdot)\) \(\chi_{2385}(1238,\cdot)\) \(\chi_{2385}(1298,\cdot)\) \(\chi_{2385}(1328,\cdot)\) \(\chi_{2385}(1337,\cdot)\) \(\chi_{2385}(1352,\cdot)\) \(\chi_{2385}(1373,\cdot)\) \(\chi_{2385}(1433,\cdot)\) \(\chi_{2385}(1463,\cdot)\) \(\chi_{2385}(1517,\cdot)\) \(\chi_{2385}(1523,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1856,1432,1486)\) → \((e\left(\frac{1}{6}\right),-i,e\left(\frac{9}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 2385 }(353, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{131}{156}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{115}{156}\right)\) | \(e\left(\frac{145}{156}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{47}{52}\right)\) |