Basic properties
| Modulus: | \(35937\) | |
| Conductor: | \(35937\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2178\) | 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 35937.ck
\(\chi_{35937}(43,\cdot)\) \(\chi_{35937}(76,\cdot)\) \(\chi_{35937}(142,\cdot)\) \(\chi_{35937}(175,\cdot)\) \(\chi_{35937}(274,\cdot)\) \(\chi_{35937}(340,\cdot)\) \(\chi_{35937}(373,\cdot)\) \(\chi_{35937}(439,\cdot)\) \(\chi_{35937}(472,\cdot)\) \(\chi_{35937}(538,\cdot)\) \(\chi_{35937}(571,\cdot)\) \(\chi_{35937}(637,\cdot)\) \(\chi_{35937}(670,\cdot)\) \(\chi_{35937}(736,\cdot)\) \(\chi_{35937}(769,\cdot)\) \(\chi_{35937}(835,\cdot)\) \(\chi_{35937}(868,\cdot)\) \(\chi_{35937}(934,\cdot)\) \(\chi_{35937}(1033,\cdot)\) \(\chi_{35937}(1066,\cdot)\) \(\chi_{35937}(1132,\cdot)\) \(\chi_{35937}(1165,\cdot)\) \(\chi_{35937}(1231,\cdot)\) \(\chi_{35937}(1264,\cdot)\) \(\chi_{35937}(1363,\cdot)\) \(\chi_{35937}(1429,\cdot)\) \(\chi_{35937}(1462,\cdot)\) \(\chi_{35937}(1528,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{1089})$ |
| Fixed field: | Number field defined by a degree 2178 polynomial (not computed) |
Values on generators
\((22628,13312)\) → \((e\left(\frac{2}{9}\right),e\left(\frac{49}{242}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 35937 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{925}{2178}\right)\) | \(e\left(\frac{925}{1089}\right)\) | \(e\left(\frac{400}{1089}\right)\) | \(e\left(\frac{733}{2178}\right)\) | \(e\left(\frac{199}{726}\right)\) | \(e\left(\frac{575}{726}\right)\) | \(e\left(\frac{2081}{2178}\right)\) | \(e\left(\frac{829}{1089}\right)\) | \(e\left(\frac{761}{1089}\right)\) | \(e\left(\frac{383}{726}\right)\) |