Basic properties
| Modulus: | \(10037\) | |
| Conductor: | \(10037\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(772\) | 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 10037.i
\(\chi_{10037}(3,\cdot)\) \(\chi_{10037}(27,\cdot)\) \(\chi_{10037}(30,\cdot)\) \(\chi_{10037}(47,\cdot)\) \(\chi_{10037}(95,\cdot)\) \(\chi_{10037}(111,\cdot)\) \(\chi_{10037}(118,\cdot)\) \(\chi_{10037}(134,\cdot)\) \(\chi_{10037}(156,\cdot)\) \(\chi_{10037}(205,\cdot)\) \(\chi_{10037}(243,\cdot)\) \(\chi_{10037}(249,\cdot)\) \(\chi_{10037}(258,\cdot)\) \(\chi_{10037}(270,\cdot)\) \(\chi_{10037}(272,\cdot)\) \(\chi_{10037}(278,\cdot)\) \(\chi_{10037}(300,\cdot)\) \(\chi_{10037}(341,\cdot)\) \(\chi_{10037}(377,\cdot)\) \(\chi_{10037}(391,\cdot)\) \(\chi_{10037}(423,\cdot)\) \(\chi_{10037}(426,\cdot)\) \(\chi_{10037}(443,\cdot)\) \(\chi_{10037}(470,\cdot)\) \(\chi_{10037}(479,\cdot)\) \(\chi_{10037}(491,\cdot)\) \(\chi_{10037}(494,\cdot)\) \(\chi_{10037}(537,\cdot)\) \(\chi_{10037}(579,\cdot)\) \(\chi_{10037}(583,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{772})$ |
| Fixed field: | Number field defined by a degree 772 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{711}{772}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 10037 }(27, a) \) | \(-1\) | \(1\) | \(e\left(\frac{711}{772}\right)\) | \(e\left(\frac{427}{772}\right)\) | \(e\left(\frac{325}{386}\right)\) | \(e\left(\frac{699}{772}\right)\) | \(e\left(\frac{183}{386}\right)\) | \(e\left(\frac{539}{772}\right)\) | \(e\left(\frac{589}{772}\right)\) | \(e\left(\frac{41}{386}\right)\) | \(e\left(\frac{319}{386}\right)\) | \(e\left(\frac{32}{193}\right)\) |