Basic properties
| Modulus: | \(8036\) | |
| Conductor: | \(8036\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | 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.dq
\(\chi_{8036}(255,\cdot)\) \(\chi_{8036}(647,\cdot)\) \(\chi_{8036}(747,\cdot)\) \(\chi_{8036}(1139,\cdot)\) \(\chi_{8036}(1895,\cdot)\) \(\chi_{8036}(2287,\cdot)\) \(\chi_{8036}(2551,\cdot)\) \(\chi_{8036}(2943,\cdot)\) \(\chi_{8036}(3043,\cdot)\) \(\chi_{8036}(3435,\cdot)\) \(\chi_{8036}(3699,\cdot)\) \(\chi_{8036}(4091,\cdot)\) \(\chi_{8036}(4191,\cdot)\) \(\chi_{8036}(4583,\cdot)\) \(\chi_{8036}(4847,\cdot)\) \(\chi_{8036}(5239,\cdot)\) \(\chi_{8036}(5339,\cdot)\) \(\chi_{8036}(5731,\cdot)\) \(\chi_{8036}(5995,\cdot)\) \(\chi_{8036}(6387,\cdot)\) \(\chi_{8036}(7143,\cdot)\) \(\chi_{8036}(7535,\cdot)\) \(\chi_{8036}(7635,\cdot)\) \(\chi_{8036}(8027,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((4019,493,785)\) → \((-1,e\left(\frac{41}{42}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 8036 }(1895, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{13}{21}\right)\) |