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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1340.bt
\(\chi_{1340}(23,\cdot)\) \(\chi_{1340}(47,\cdot)\) \(\chi_{1340}(83,\cdot)\) \(\chi_{1340}(103,\cdot)\) \(\chi_{1340}(123,\cdot)\) \(\chi_{1340}(127,\cdot)\) \(\chi_{1340}(167,\cdot)\) \(\chi_{1340}(183,\cdot)\) \(\chi_{1340}(207,\cdot)\) \(\chi_{1340}(227,\cdot)\) \(\chi_{1340}(287,\cdot)\) \(\chi_{1340}(303,\cdot)\) \(\chi_{1340}(307,\cdot)\) \(\chi_{1340}(323,\cdot)\) \(\chi_{1340}(423,\cdot)\) \(\chi_{1340}(467,\cdot)\) \(\chi_{1340}(523,\cdot)\) \(\chi_{1340}(583,\cdot)\) \(\chi_{1340}(607,\cdot)\) \(\chi_{1340}(663,\cdot)\) \(\chi_{1340}(687,\cdot)\) \(\chi_{1340}(703,\cdot)\) \(\chi_{1340}(743,\cdot)\) \(\chi_{1340}(747,\cdot)\) \(\chi_{1340}(763,\cdot)\) \(\chi_{1340}(823,\cdot)\) \(\chi_{1340}(827,\cdot)\) \(\chi_{1340}(843,\cdot)\) \(\chi_{1340}(887,\cdot)\) \(\chi_{1340}(907,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((671,537,1141)\) → \((-1,i,e\left(\frac{17}{33}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 1340 }(467, a) \) | \(1\) | \(1\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{79}{132}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{71}{132}\right)\) | \(e\left(\frac{29}{132}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{89}{132}\right)\) | \(e\left(\frac{1}{44}\right)\) |