Basic properties
| Modulus: | \(1037\) | |
| Conductor: | \(1037\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | 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 1037.cn
\(\chi_{1037}(19,\cdot)\) \(\chi_{1037}(36,\cdot)\) \(\chi_{1037}(49,\cdot)\) \(\chi_{1037}(66,\cdot)\) \(\chi_{1037}(100,\cdot)\) \(\chi_{1037}(110,\cdot)\) \(\chi_{1037}(127,\cdot)\) \(\chi_{1037}(161,\cdot)\) \(\chi_{1037}(168,\cdot)\) \(\chi_{1037}(202,\cdot)\) \(\chi_{1037}(219,\cdot)\) \(\chi_{1037}(229,\cdot)\) \(\chi_{1037}(263,\cdot)\) \(\chi_{1037}(280,\cdot)\) \(\chi_{1037}(553,\cdot)\) \(\chi_{1037}(614,\cdot)\) \(\chi_{1037}(655,\cdot)\) \(\chi_{1037}(716,\cdot)\) \(\chi_{1037}(797,\cdot)\) \(\chi_{1037}(842,\cdot)\) \(\chi_{1037}(858,\cdot)\) \(\chi_{1037}(859,\cdot)\) \(\chi_{1037}(893,\cdot)\) \(\chi_{1037}(899,\cdot)\) \(\chi_{1037}(903,\cdot)\) \(\chi_{1037}(920,\cdot)\) \(\chi_{1037}(954,\cdot)\) \(\chi_{1037}(960,\cdot)\) \(\chi_{1037}(961,\cdot)\) \(\chi_{1037}(995,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((428,307)\) → \((e\left(\frac{5}{8}\right),e\left(\frac{19}{30}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1037 }(110, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{97}{120}\right)\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{7}{8}\right)\) |