Basic properties
| Modulus: | \(8036\) | |
| Conductor: | \(8036\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | 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 8036.ei
\(\chi_{8036}(187,\cdot)\) \(\chi_{8036}(271,\cdot)\) \(\chi_{8036}(523,\cdot)\) \(\chi_{8036}(843,\cdot)\) \(\chi_{8036}(927,\cdot)\) \(\chi_{8036}(1111,\cdot)\) \(\chi_{8036}(1179,\cdot)\) \(\chi_{8036}(1335,\cdot)\) \(\chi_{8036}(1419,\cdot)\) \(\chi_{8036}(1671,\cdot)\) \(\chi_{8036}(1767,\cdot)\) \(\chi_{8036}(2075,\cdot)\) \(\chi_{8036}(2259,\cdot)\) \(\chi_{8036}(2327,\cdot)\) \(\chi_{8036}(2483,\cdot)\) \(\chi_{8036}(2819,\cdot)\) \(\chi_{8036}(2915,\cdot)\) \(\chi_{8036}(3139,\cdot)\) \(\chi_{8036}(3223,\cdot)\) \(\chi_{8036}(3407,\cdot)\) \(\chi_{8036}(3475,\cdot)\) \(\chi_{8036}(3631,\cdot)\) \(\chi_{8036}(3715,\cdot)\) \(\chi_{8036}(3967,\cdot)\) \(\chi_{8036}(4063,\cdot)\) \(\chi_{8036}(4287,\cdot)\) \(\chi_{8036}(4371,\cdot)\) \(\chi_{8036}(4555,\cdot)\) \(\chi_{8036}(4623,\cdot)\) \(\chi_{8036}(4779,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((4019,493,785)\) → \((-1,e\left(\frac{23}{42}\right),e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 8036 }(187, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{143}{210}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{11}{105}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{41}{105}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{149}{210}\right)\) | \(e\left(\frac{38}{105}\right)\) |