Basic properties
| Modulus: | \(8036\) | |
| Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2009}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8036.dp
\(\chi_{8036}(9,\cdot)\) \(\chi_{8036}(401,\cdot)\) \(\chi_{8036}(501,\cdot)\) \(\chi_{8036}(893,\cdot)\) \(\chi_{8036}(1649,\cdot)\) \(\chi_{8036}(2041,\cdot)\) \(\chi_{8036}(2305,\cdot)\) \(\chi_{8036}(2697,\cdot)\) \(\chi_{8036}(2797,\cdot)\) \(\chi_{8036}(3189,\cdot)\) \(\chi_{8036}(3453,\cdot)\) \(\chi_{8036}(3845,\cdot)\) \(\chi_{8036}(3945,\cdot)\) \(\chi_{8036}(4337,\cdot)\) \(\chi_{8036}(4601,\cdot)\) \(\chi_{8036}(4993,\cdot)\) \(\chi_{8036}(5093,\cdot)\) \(\chi_{8036}(5485,\cdot)\) \(\chi_{8036}(5749,\cdot)\) \(\chi_{8036}(6141,\cdot)\) \(\chi_{8036}(6897,\cdot)\) \(\chi_{8036}(7289,\cdot)\) \(\chi_{8036}(7389,\cdot)\) \(\chi_{8036}(7781,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((4019,493,785)\) → \((1,e\left(\frac{1}{21}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 8036 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{16}{21}\right)\) |