Basic properties
| Modulus: | \(10037\) | |
| Conductor: | \(10037\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(386\) | 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.h
\(\chi_{10037}(9,\cdot)\) \(\chi_{10037}(10,\cdot)\) \(\chi_{10037}(37,\cdot)\) \(\chi_{10037}(83,\cdot)\) \(\chi_{10037}(86,\cdot)\) \(\chi_{10037}(141,\cdot)\) \(\chi_{10037}(193,\cdot)\) \(\chi_{10037}(224,\cdot)\) \(\chi_{10037}(271,\cdot)\) \(\chi_{10037}(354,\cdot)\) \(\chi_{10037}(468,\cdot)\) \(\chi_{10037}(499,\cdot)\) \(\chi_{10037}(508,\cdot)\) \(\chi_{10037}(520,\cdot)\) \(\chi_{10037}(599,\cdot)\) \(\chi_{10037}(615,\cdot)\) \(\chi_{10037}(704,\cdot)\) \(\chi_{10037}(729,\cdot)\) \(\chi_{10037}(810,\cdot)\) \(\chi_{10037}(816,\cdot)\) \(\chi_{10037}(834,\cdot)\) \(\chi_{10037}(900,\cdot)\) \(\chi_{10037}(1000,\cdot)\) \(\chi_{10037}(1037,\cdot)\) \(\chi_{10037}(1106,\cdot)\) \(\chi_{10037}(1121,\cdot)\) \(\chi_{10037}(1131,\cdot)\) \(\chi_{10037}(1151,\cdot)\) \(\chi_{10037}(1278,\cdot)\) \(\chi_{10037}(1304,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{193})$ |
| Fixed field: | Number field defined by a degree 386 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{237}{386}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 10037 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{237}{386}\right)\) | \(e\left(\frac{271}{386}\right)\) | \(e\left(\frac{44}{193}\right)\) | \(e\left(\frac{233}{386}\right)\) | \(e\left(\frac{61}{193}\right)\) | \(e\left(\frac{51}{386}\right)\) | \(e\left(\frac{325}{386}\right)\) | \(e\left(\frac{78}{193}\right)\) | \(e\left(\frac{42}{193}\right)\) | \(e\left(\frac{150}{193}\right)\) |