Basic properties
| Modulus: | \(8036\) | |
| Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(35\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2009}(57,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8036.cn
\(\chi_{8036}(57,\cdot)\) \(\chi_{8036}(141,\cdot)\) \(\chi_{8036}(365,\cdot)\) \(\chi_{8036}(953,\cdot)\) \(\chi_{8036}(1205,\cdot)\) \(\chi_{8036}(1289,\cdot)\) \(\chi_{8036}(1513,\cdot)\) \(\chi_{8036}(2101,\cdot)\) \(\chi_{8036}(2437,\cdot)\) \(\chi_{8036}(2661,\cdot)\) \(\chi_{8036}(3249,\cdot)\) \(\chi_{8036}(3501,\cdot)\) \(\chi_{8036}(3585,\cdot)\) \(\chi_{8036}(3809,\cdot)\) \(\chi_{8036}(4397,\cdot)\) \(\chi_{8036}(4649,\cdot)\) \(\chi_{8036}(4733,\cdot)\) \(\chi_{8036}(4957,\cdot)\) \(\chi_{8036}(5545,\cdot)\) \(\chi_{8036}(5797,\cdot)\) \(\chi_{8036}(6105,\cdot)\) \(\chi_{8036}(6693,\cdot)\) \(\chi_{8036}(6945,\cdot)\) \(\chi_{8036}(7029,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 35 polynomial |
Values on generators
\((4019,493,785)\) → \((1,e\left(\frac{6}{7}\right),e\left(\frac{3}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 8036 }(57, a) \) | \(1\) | \(1\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{4}{35}\right)\) |