Basic properties
| Modulus: | \(35937\) | |
| Conductor: | \(35937\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1089\) | 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 35937.cf
\(\chi_{35937}(34,\cdot)\) \(\chi_{35937}(67,\cdot)\) \(\chi_{35937}(133,\cdot)\) \(\chi_{35937}(166,\cdot)\) \(\chi_{35937}(232,\cdot)\) \(\chi_{35937}(265,\cdot)\) \(\chi_{35937}(331,\cdot)\) \(\chi_{35937}(430,\cdot)\) \(\chi_{35937}(463,\cdot)\) \(\chi_{35937}(529,\cdot)\) \(\chi_{35937}(562,\cdot)\) \(\chi_{35937}(628,\cdot)\) \(\chi_{35937}(661,\cdot)\) \(\chi_{35937}(760,\cdot)\) \(\chi_{35937}(826,\cdot)\) \(\chi_{35937}(859,\cdot)\) \(\chi_{35937}(925,\cdot)\) \(\chi_{35937}(958,\cdot)\) \(\chi_{35937}(1024,\cdot)\) \(\chi_{35937}(1057,\cdot)\) \(\chi_{35937}(1123,\cdot)\) \(\chi_{35937}(1156,\cdot)\) \(\chi_{35937}(1222,\cdot)\) \(\chi_{35937}(1255,\cdot)\) \(\chi_{35937}(1321,\cdot)\) \(\chi_{35937}(1354,\cdot)\) \(\chi_{35937}(1420,\cdot)\) \(\chi_{35937}(1519,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{1089})$ |
| Fixed field: | Number field defined by a degree 1089 polynomial (not computed) |
Values on generators
\((22628,13312)\) → \((e\left(\frac{8}{9}\right),e\left(\frac{16}{121}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 35937 }(34, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{1089}\right)\) | \(e\left(\frac{46}{1089}\right)\) | \(e\left(\frac{844}{1089}\right)\) | \(e\left(\frac{953}{1089}\right)\) | \(e\left(\frac{23}{363}\right)\) | \(e\left(\frac{289}{363}\right)\) | \(e\left(\frac{1003}{1089}\right)\) | \(e\left(\frac{976}{1089}\right)\) | \(e\left(\frac{92}{1089}\right)\) | \(e\left(\frac{130}{363}\right)\) |