Basic properties
| Modulus: | \(1568\) | |
| Conductor: | \(1568\) | 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 1568.cd
\(\chi_{1568}(29,\cdot)\) \(\chi_{1568}(85,\cdot)\) \(\chi_{1568}(141,\cdot)\) \(\chi_{1568}(253,\cdot)\) \(\chi_{1568}(309,\cdot)\) \(\chi_{1568}(365,\cdot)\) \(\chi_{1568}(421,\cdot)\) \(\chi_{1568}(477,\cdot)\) \(\chi_{1568}(533,\cdot)\) \(\chi_{1568}(645,\cdot)\) \(\chi_{1568}(701,\cdot)\) \(\chi_{1568}(757,\cdot)\) \(\chi_{1568}(813,\cdot)\) \(\chi_{1568}(869,\cdot)\) \(\chi_{1568}(925,\cdot)\) \(\chi_{1568}(1037,\cdot)\) \(\chi_{1568}(1093,\cdot)\) \(\chi_{1568}(1149,\cdot)\) \(\chi_{1568}(1205,\cdot)\) \(\chi_{1568}(1261,\cdot)\) \(\chi_{1568}(1317,\cdot)\) \(\chi_{1568}(1429,\cdot)\) \(\chi_{1568}(1485,\cdot)\) \(\chi_{1568}(1541,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{56})$ |
| Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((1471,197,1473)\) → \((1,e\left(\frac{3}{8}\right),e\left(\frac{3}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 1568 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{56}\right)\) | \(e\left(\frac{45}{56}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{1}{56}\right)\) | \(e\left(\frac{43}{56}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{17}{28}\right)\) |