Basic properties
| Modulus: | \(8036\) | |
| Conductor: | \(8036\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | 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.dh
\(\chi_{8036}(139,\cdot)\) \(\chi_{8036}(223,\cdot)\) \(\chi_{8036}(447,\cdot)\) \(\chi_{8036}(1035,\cdot)\) \(\chi_{8036}(1287,\cdot)\) \(\chi_{8036}(1595,\cdot)\) \(\chi_{8036}(2183,\cdot)\) \(\chi_{8036}(2435,\cdot)\) \(\chi_{8036}(2519,\cdot)\) \(\chi_{8036}(3583,\cdot)\) \(\chi_{8036}(3667,\cdot)\) \(\chi_{8036}(3891,\cdot)\) \(\chi_{8036}(4479,\cdot)\) \(\chi_{8036}(4731,\cdot)\) \(\chi_{8036}(4815,\cdot)\) \(\chi_{8036}(5039,\cdot)\) \(\chi_{8036}(5627,\cdot)\) \(\chi_{8036}(5963,\cdot)\) \(\chi_{8036}(6187,\cdot)\) \(\chi_{8036}(6775,\cdot)\) \(\chi_{8036}(7027,\cdot)\) \(\chi_{8036}(7111,\cdot)\) \(\chi_{8036}(7335,\cdot)\) \(\chi_{8036}(7923,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((4019,493,785)\) → \((-1,e\left(\frac{5}{14}\right),e\left(\frac{3}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 8036 }(139, a) \) | \(1\) | \(1\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{4}{35}\right)\) |