Basic properties
| Modulus: | \(8036\) | |
| Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(105\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2009}(1369,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8036.ds
\(\chi_{8036}(37,\cdot)\) \(\chi_{8036}(221,\cdot)\) \(\chi_{8036}(305,\cdot)\) \(\chi_{8036}(529,\cdot)\) \(\chi_{8036}(625,\cdot)\) \(\chi_{8036}(877,\cdot)\) \(\chi_{8036}(1117,\cdot)\) \(\chi_{8036}(1185,\cdot)\) \(\chi_{8036}(1369,\cdot)\) \(\chi_{8036}(1453,\cdot)\) \(\chi_{8036}(1677,\cdot)\) \(\chi_{8036}(1773,\cdot)\) \(\chi_{8036}(2025,\cdot)\) \(\chi_{8036}(2109,\cdot)\) \(\chi_{8036}(2265,\cdot)\) \(\chi_{8036}(2601,\cdot)\) \(\chi_{8036}(2825,\cdot)\) \(\chi_{8036}(3173,\cdot)\) \(\chi_{8036}(3257,\cdot)\) \(\chi_{8036}(3413,\cdot)\) \(\chi_{8036}(3481,\cdot)\) \(\chi_{8036}(3665,\cdot)\) \(\chi_{8036}(3749,\cdot)\) \(\chi_{8036}(3973,\cdot)\) \(\chi_{8036}(4069,\cdot)\) \(\chi_{8036}(4321,\cdot)\) \(\chi_{8036}(4405,\cdot)\) \(\chi_{8036}(4561,\cdot)\) \(\chi_{8036}(4629,\cdot)\) \(\chi_{8036}(4813,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((4019,493,785)\) → \((1,e\left(\frac{11}{21}\right),e\left(\frac{3}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 8036 }(1369, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{41}{105}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{94}{105}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{82}{105}\right)\) |