Basic properties
| Modulus: | \(10037\) | |
| Conductor: | \(10037\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(5018\) | 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 10037.k
\(\chi_{10037}(4,\cdot)\) \(\chi_{10037}(6,\cdot)\) \(\chi_{10037}(13,\cdot)\) \(\chi_{10037}(14,\cdot)\) \(\chi_{10037}(15,\cdot)\) \(\chi_{10037}(19,\cdot)\) \(\chi_{10037}(21,\cdot)\) \(\chi_{10037}(23,\cdot)\) \(\chi_{10037}(25,\cdot)\) \(\chi_{10037}(34,\cdot)\) \(\chi_{10037}(35,\cdot)\) \(\chi_{10037}(44,\cdot)\) \(\chi_{10037}(49,\cdot)\) \(\chi_{10037}(51,\cdot)\) \(\chi_{10037}(64,\cdot)\) \(\chi_{10037}(66,\cdot)\) \(\chi_{10037}(67,\cdot)\) \(\chi_{10037}(73,\cdot)\) \(\chi_{10037}(85,\cdot)\) \(\chi_{10037}(94,\cdot)\) \(\chi_{10037}(96,\cdot)\) \(\chi_{10037}(99,\cdot)\) \(\chi_{10037}(106,\cdot)\) \(\chi_{10037}(110,\cdot)\) \(\chi_{10037}(119,\cdot)\) \(\chi_{10037}(122,\cdot)\) \(\chi_{10037}(129,\cdot)\) \(\chi_{10037}(131,\cdot)\) \(\chi_{10037}(143,\cdot)\) \(\chi_{10037}(144,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{2509})$ |
| Fixed field: | Number field defined by a degree 5018 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{1}{5018}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 10037 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{5018}\right)\) | \(e\left(\frac{237}{386}\right)\) | \(e\left(\frac{1}{2509}\right)\) | \(e\left(\frac{4861}{5018}\right)\) | \(e\left(\frac{1541}{2509}\right)\) | \(e\left(\frac{567}{5018}\right)\) | \(e\left(\frac{3}{5018}\right)\) | \(e\left(\frac{44}{193}\right)\) | \(e\left(\frac{187}{193}\right)\) | \(e\left(\frac{907}{2509}\right)\) |