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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1568.cb
\(\chi_{1568}(43,\cdot)\) \(\chi_{1568}(155,\cdot)\) \(\chi_{1568}(211,\cdot)\) \(\chi_{1568}(267,\cdot)\) \(\chi_{1568}(323,\cdot)\) \(\chi_{1568}(379,\cdot)\) \(\chi_{1568}(435,\cdot)\) \(\chi_{1568}(547,\cdot)\) \(\chi_{1568}(603,\cdot)\) \(\chi_{1568}(659,\cdot)\) \(\chi_{1568}(715,\cdot)\) \(\chi_{1568}(771,\cdot)\) \(\chi_{1568}(827,\cdot)\) \(\chi_{1568}(939,\cdot)\) \(\chi_{1568}(995,\cdot)\) \(\chi_{1568}(1051,\cdot)\) \(\chi_{1568}(1107,\cdot)\) \(\chi_{1568}(1163,\cdot)\) \(\chi_{1568}(1219,\cdot)\) \(\chi_{1568}(1331,\cdot)\) \(\chi_{1568}(1387,\cdot)\) \(\chi_{1568}(1443,\cdot)\) \(\chi_{1568}(1499,\cdot)\) \(\chi_{1568}(1555,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{56})$ |
| Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((1471,197,1473)\) → \((-1,e\left(\frac{5}{8}\right),e\left(\frac{1}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 1568 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{56}\right)\) | \(e\left(\frac{43}{56}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{19}{56}\right)\) | \(e\left(\frac{5}{56}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{15}{28}\right)\) |