Basic properties
| Modulus: | \(1340\) | |
| Conductor: | \(1340\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | 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 1340.bv
\(\chi_{1340}(7,\cdot)\) \(\chi_{1340}(63,\cdot)\) \(\chi_{1340}(87,\cdot)\) \(\chi_{1340}(147,\cdot)\) \(\chi_{1340}(203,\cdot)\) \(\chi_{1340}(247,\cdot)\) \(\chi_{1340}(347,\cdot)\) \(\chi_{1340}(363,\cdot)\) \(\chi_{1340}(367,\cdot)\) \(\chi_{1340}(383,\cdot)\) \(\chi_{1340}(443,\cdot)\) \(\chi_{1340}(463,\cdot)\) \(\chi_{1340}(487,\cdot)\) \(\chi_{1340}(503,\cdot)\) \(\chi_{1340}(543,\cdot)\) \(\chi_{1340}(547,\cdot)\) \(\chi_{1340}(567,\cdot)\) \(\chi_{1340}(587,\cdot)\) \(\chi_{1340}(623,\cdot)\) \(\chi_{1340}(647,\cdot)\) \(\chi_{1340}(683,\cdot)\) \(\chi_{1340}(727,\cdot)\) \(\chi_{1340}(783,\cdot)\) \(\chi_{1340}(787,\cdot)\) \(\chi_{1340}(867,\cdot)\) \(\chi_{1340}(883,\cdot)\) \(\chi_{1340}(903,\cdot)\) \(\chi_{1340}(1007,\cdot)\) \(\chi_{1340}(1023,\cdot)\) \(\chi_{1340}(1083,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((671,537,1141)\) → \((-1,i,e\left(\frac{1}{66}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 1340 }(1007, a) \) | \(-1\) | \(1\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{13}{132}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{5}{132}\right)\) | \(e\left(\frac{29}{132}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{89}{132}\right)\) | \(e\left(\frac{23}{44}\right)\) |