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.co
\(\chi_{1037}(15,\cdot)\) \(\chi_{1037}(25,\cdot)\) \(\chi_{1037}(42,\cdot)\) \(\chi_{1037}(76,\cdot)\) \(\chi_{1037}(77,\cdot)\) \(\chi_{1037}(83,\cdot)\) \(\chi_{1037}(117,\cdot)\) \(\chi_{1037}(134,\cdot)\) \(\chi_{1037}(138,\cdot)\) \(\chi_{1037}(144,\cdot)\) \(\chi_{1037}(178,\cdot)\) \(\chi_{1037}(179,\cdot)\) \(\chi_{1037}(195,\cdot)\) \(\chi_{1037}(240,\cdot)\) \(\chi_{1037}(321,\cdot)\) \(\chi_{1037}(382,\cdot)\) \(\chi_{1037}(423,\cdot)\) \(\chi_{1037}(484,\cdot)\) \(\chi_{1037}(757,\cdot)\) \(\chi_{1037}(774,\cdot)\) \(\chi_{1037}(808,\cdot)\) \(\chi_{1037}(818,\cdot)\) \(\chi_{1037}(835,\cdot)\) \(\chi_{1037}(869,\cdot)\) \(\chi_{1037}(876,\cdot)\) \(\chi_{1037}(910,\cdot)\) \(\chi_{1037}(927,\cdot)\) \(\chi_{1037}(937,\cdot)\) \(\chi_{1037}(971,\cdot)\) \(\chi_{1037}(988,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((428,307)\) → \((e\left(\frac{7}{8}\right),e\left(\frac{11}{15}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1037 }(818, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{1}{8}\right)\) |