Basic properties
| Modulus: | \(43904\) | |
| Conductor: | \(784\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{784}(395,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 43904.ct
\(\chi_{43904}(31,\cdot)\) \(\chi_{43904}(607,\cdot)\) \(\chi_{43904}(3167,\cdot)\) \(\chi_{43904}(3743,\cdot)\) \(\chi_{43904}(6303,\cdot)\) \(\chi_{43904}(9439,\cdot)\) \(\chi_{43904}(10015,\cdot)\) \(\chi_{43904}(12575,\cdot)\) \(\chi_{43904}(13151,\cdot)\) \(\chi_{43904}(15711,\cdot)\) \(\chi_{43904}(16287,\cdot)\) \(\chi_{43904}(19423,\cdot)\) \(\chi_{43904}(21983,\cdot)\) \(\chi_{43904}(22559,\cdot)\) \(\chi_{43904}(25119,\cdot)\) \(\chi_{43904}(25695,\cdot)\) \(\chi_{43904}(28255,\cdot)\) \(\chi_{43904}(31391,\cdot)\) \(\chi_{43904}(31967,\cdot)\) \(\chi_{43904}(34527,\cdot)\) \(\chi_{43904}(35103,\cdot)\) \(\chi_{43904}(37663,\cdot)\) \(\chi_{43904}(38239,\cdot)\) \(\chi_{43904}(41375,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((17151,9605,17153)\) → \((-1,i,e\left(\frac{1}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 43904 }(6303, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{37}{42}\right)\) |