Basic properties
| Modulus: | \(8036\) | |
| Conductor: | \(8036\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(140\) | 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.dz
\(\chi_{8036}(251,\cdot)\) \(\chi_{8036}(279,\cdot)\) \(\chi_{8036}(307,\cdot)\) \(\chi_{8036}(531,\cdot)\) \(\chi_{8036}(699,\cdot)\) \(\chi_{8036}(923,\cdot)\) \(\chi_{8036}(951,\cdot)\) \(\chi_{8036}(1399,\cdot)\) \(\chi_{8036}(1427,\cdot)\) \(\chi_{8036}(1455,\cdot)\) \(\chi_{8036}(1679,\cdot)\) \(\chi_{8036}(1847,\cdot)\) \(\chi_{8036}(2071,\cdot)\) \(\chi_{8036}(2099,\cdot)\) \(\chi_{8036}(2127,\cdot)\) \(\chi_{8036}(2575,\cdot)\) \(\chi_{8036}(2603,\cdot)\) \(\chi_{8036}(2827,\cdot)\) \(\chi_{8036}(2995,\cdot)\) \(\chi_{8036}(3219,\cdot)\) \(\chi_{8036}(3247,\cdot)\) \(\chi_{8036}(3275,\cdot)\) \(\chi_{8036}(3695,\cdot)\) \(\chi_{8036}(3751,\cdot)\) \(\chi_{8036}(3975,\cdot)\) \(\chi_{8036}(4143,\cdot)\) \(\chi_{8036}(4367,\cdot)\) \(\chi_{8036}(4395,\cdot)\) \(\chi_{8036}(4423,\cdot)\) \(\chi_{8036}(4843,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((4019,493,785)\) → \((-1,e\left(\frac{3}{14}\right),e\left(\frac{17}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 8036 }(1455, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{87}{140}\right)\) | \(e\left(\frac{59}{140}\right)\) | \(e\left(\frac{53}{140}\right)\) | \(e\left(\frac{57}{140}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{29}{35}\right)\) |