Basic properties
| Modulus: | \(1369\) | |
| Conductor: | \(1369\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(37\) | 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 1369.j
\(\chi_{1369}(38,\cdot)\) \(\chi_{1369}(75,\cdot)\) \(\chi_{1369}(112,\cdot)\) \(\chi_{1369}(149,\cdot)\) \(\chi_{1369}(186,\cdot)\) \(\chi_{1369}(223,\cdot)\) \(\chi_{1369}(260,\cdot)\) \(\chi_{1369}(297,\cdot)\) \(\chi_{1369}(334,\cdot)\) \(\chi_{1369}(371,\cdot)\) \(\chi_{1369}(408,\cdot)\) \(\chi_{1369}(445,\cdot)\) \(\chi_{1369}(482,\cdot)\) \(\chi_{1369}(519,\cdot)\) \(\chi_{1369}(556,\cdot)\) \(\chi_{1369}(593,\cdot)\) \(\chi_{1369}(630,\cdot)\) \(\chi_{1369}(667,\cdot)\) \(\chi_{1369}(704,\cdot)\) \(\chi_{1369}(741,\cdot)\) \(\chi_{1369}(778,\cdot)\) \(\chi_{1369}(815,\cdot)\) \(\chi_{1369}(852,\cdot)\) \(\chi_{1369}(889,\cdot)\) \(\chi_{1369}(926,\cdot)\) \(\chi_{1369}(963,\cdot)\) \(\chi_{1369}(1000,\cdot)\) \(\chi_{1369}(1037,\cdot)\) \(\chi_{1369}(1074,\cdot)\) \(\chi_{1369}(1111,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{37})$ |
| Fixed field: | 37.37.81381208133441979421709122744091225498491936628940230588748580298513087650630871328595025812353503688138712627681.1 |
Values on generators
\(2\) → \(e\left(\frac{22}{37}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1369 }(815, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{37}\right)\) | \(e\left(\frac{26}{37}\right)\) | \(e\left(\frac{7}{37}\right)\) | \(e\left(\frac{2}{37}\right)\) | \(e\left(\frac{11}{37}\right)\) | \(e\left(\frac{31}{37}\right)\) | \(e\left(\frac{29}{37}\right)\) | \(e\left(\frac{15}{37}\right)\) | \(e\left(\frac{24}{37}\right)\) | \(e\left(\frac{5}{37}\right)\) |