Basic properties
| Modulus: | \(1610\) | |
| Conductor: | \(805\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{805}(107,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1610.bt
\(\chi_{1610}(37,\cdot)\) \(\chi_{1610}(53,\cdot)\) \(\chi_{1610}(67,\cdot)\) \(\chi_{1610}(107,\cdot)\) \(\chi_{1610}(247,\cdot)\) \(\chi_{1610}(263,\cdot)\) \(\chi_{1610}(333,\cdot)\) \(\chi_{1610}(373,\cdot)\) \(\chi_{1610}(387,\cdot)\) \(\chi_{1610}(457,\cdot)\) \(\chi_{1610}(513,\cdot)\) \(\chi_{1610}(527,\cdot)\) \(\chi_{1610}(543,\cdot)\) \(\chi_{1610}(557,\cdot)\) \(\chi_{1610}(613,\cdot)\) \(\chi_{1610}(697,\cdot)\) \(\chi_{1610}(723,\cdot)\) \(\chi_{1610}(753,\cdot)\) \(\chi_{1610}(793,\cdot)\) \(\chi_{1610}(893,\cdot)\) \(\chi_{1610}(907,\cdot)\) \(\chi_{1610}(963,\cdot)\) \(\chi_{1610}(977,\cdot)\) \(\chi_{1610}(1003,\cdot)\) \(\chi_{1610}(1017,\cdot)\) \(\chi_{1610}(1033,\cdot)\) \(\chi_{1610}(1073,\cdot)\) \(\chi_{1610}(1157,\cdot)\) \(\chi_{1610}(1187,\cdot)\) \(\chi_{1610}(1213,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((967,1151,281)\) → \((i,e\left(\frac{1}{3}\right),e\left(\frac{17}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(27\) | \(29\) | \(31\) | \(33\) |
| \( \chi_{ 1610 }(107, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{132}\right)\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{131}{132}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{97}{132}\right)\) |