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.dl
\(\chi_{8036}(1007,\cdot)\) \(\chi_{8036}(1091,\cdot)\) \(\chi_{8036}(1343,\cdot)\) \(\chi_{8036}(1931,\cdot)\) \(\chi_{8036}(2239,\cdot)\) \(\chi_{8036}(2491,\cdot)\) \(\chi_{8036}(3079,\cdot)\) \(\chi_{8036}(3303,\cdot)\) \(\chi_{8036}(3387,\cdot)\) \(\chi_{8036}(3639,\cdot)\) \(\chi_{8036}(4227,\cdot)\) \(\chi_{8036}(4451,\cdot)\) \(\chi_{8036}(4535,\cdot)\) \(\chi_{8036}(4787,\cdot)\) \(\chi_{8036}(5375,\cdot)\) \(\chi_{8036}(5599,\cdot)\) \(\chi_{8036}(5935,\cdot)\) \(\chi_{8036}(6523,\cdot)\) \(\chi_{8036}(6747,\cdot)\) \(\chi_{8036}(6831,\cdot)\) \(\chi_{8036}(7083,\cdot)\) \(\chi_{8036}(7671,\cdot)\) \(\chi_{8036}(7895,\cdot)\) \(\chi_{8036}(7979,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((4019,493,785)\) → \((-1,e\left(\frac{1}{14}\right),e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 8036 }(1007, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{26}{35}\right)\) |