Basic properties
Modulus: | \(2738\) | |
Conductor: | \(1369\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(37\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1369}(75,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2738.j
\(\chi_{2738}(75,\cdot)\) \(\chi_{2738}(149,\cdot)\) \(\chi_{2738}(223,\cdot)\) \(\chi_{2738}(297,\cdot)\) \(\chi_{2738}(371,\cdot)\) \(\chi_{2738}(445,\cdot)\) \(\chi_{2738}(519,\cdot)\) \(\chi_{2738}(593,\cdot)\) \(\chi_{2738}(667,\cdot)\) \(\chi_{2738}(741,\cdot)\) \(\chi_{2738}(815,\cdot)\) \(\chi_{2738}(889,\cdot)\) \(\chi_{2738}(963,\cdot)\) \(\chi_{2738}(1037,\cdot)\) \(\chi_{2738}(1111,\cdot)\) \(\chi_{2738}(1185,\cdot)\) \(\chi_{2738}(1259,\cdot)\) \(\chi_{2738}(1333,\cdot)\) \(\chi_{2738}(1407,\cdot)\) \(\chi_{2738}(1481,\cdot)\) \(\chi_{2738}(1555,\cdot)\) \(\chi_{2738}(1629,\cdot)\) \(\chi_{2738}(1703,\cdot)\) \(\chi_{2738}(1777,\cdot)\) \(\chi_{2738}(1851,\cdot)\) \(\chi_{2738}(1925,\cdot)\) \(\chi_{2738}(1999,\cdot)\) \(\chi_{2738}(2073,\cdot)\) \(\chi_{2738}(2147,\cdot)\) \(\chi_{2738}(2221,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{37})$ |
Fixed field: | 37.37.81381208133441979421709122744091225498491936628940230588748580298513087650630871328595025812353503688138712627681.1 |
Values on generators
\(1371\) → \(e\left(\frac{2}{37}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 2738 }(75, a) \) | \(1\) | \(1\) | \(e\left(\frac{36}{37}\right)\) | \(e\left(\frac{17}{37}\right)\) | \(e\left(\frac{23}{37}\right)\) | \(e\left(\frac{35}{37}\right)\) | \(e\left(\frac{24}{37}\right)\) | \(e\left(\frac{2}{37}\right)\) | \(e\left(\frac{16}{37}\right)\) | \(e\left(\frac{10}{37}\right)\) | \(e\left(\frac{33}{37}\right)\) | \(e\left(\frac{22}{37}\right)\) |