Basic properties
| Modulus: | \(8036\) | |
| Conductor: | \(8036\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(56\) | 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.da
\(\chi_{8036}(407,\cdot)\) \(\chi_{8036}(519,\cdot)\) \(\chi_{8036}(547,\cdot)\) \(\chi_{8036}(659,\cdot)\) \(\chi_{8036}(1555,\cdot)\) \(\chi_{8036}(1695,\cdot)\) \(\chi_{8036}(1807,\cdot)\) \(\chi_{8036}(2703,\cdot)\) \(\chi_{8036}(2815,\cdot)\) \(\chi_{8036}(2955,\cdot)\) \(\chi_{8036}(3851,\cdot)\) \(\chi_{8036}(3963,\cdot)\) \(\chi_{8036}(3991,\cdot)\) \(\chi_{8036}(4103,\cdot)\) \(\chi_{8036}(5111,\cdot)\) \(\chi_{8036}(5139,\cdot)\) \(\chi_{8036}(5251,\cdot)\) \(\chi_{8036}(6147,\cdot)\) \(\chi_{8036}(6259,\cdot)\) \(\chi_{8036}(6287,\cdot)\) \(\chi_{8036}(6399,\cdot)\) \(\chi_{8036}(7295,\cdot)\) \(\chi_{8036}(7407,\cdot)\) \(\chi_{8036}(7435,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{56})$ |
| Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((4019,493,785)\) → \((-1,e\left(\frac{5}{7}\right),e\left(\frac{7}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 8036 }(407, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{56}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{39}{56}\right)\) | \(e\left(\frac{39}{56}\right)\) | \(e\left(\frac{17}{56}\right)\) | \(e\left(\frac{41}{56}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{13}{14}\right)\) |