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.ca
\(\chi_{1568}(27,\cdot)\) \(\chi_{1568}(83,\cdot)\) \(\chi_{1568}(139,\cdot)\) \(\chi_{1568}(251,\cdot)\) \(\chi_{1568}(307,\cdot)\) \(\chi_{1568}(363,\cdot)\) \(\chi_{1568}(419,\cdot)\) \(\chi_{1568}(475,\cdot)\) \(\chi_{1568}(531,\cdot)\) \(\chi_{1568}(643,\cdot)\) \(\chi_{1568}(699,\cdot)\) \(\chi_{1568}(755,\cdot)\) \(\chi_{1568}(811,\cdot)\) \(\chi_{1568}(867,\cdot)\) \(\chi_{1568}(923,\cdot)\) \(\chi_{1568}(1035,\cdot)\) \(\chi_{1568}(1091,\cdot)\) \(\chi_{1568}(1147,\cdot)\) \(\chi_{1568}(1203,\cdot)\) \(\chi_{1568}(1259,\cdot)\) \(\chi_{1568}(1315,\cdot)\) \(\chi_{1568}(1427,\cdot)\) \(\chi_{1568}(1483,\cdot)\) \(\chi_{1568}(1539,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{56})$ |
| Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((1471,197,1473)\) → \((-1,e\left(\frac{1}{8}\right),e\left(\frac{1}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 1568 }(27, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{56}\right)\) | \(e\left(\frac{11}{56}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{55}{56}\right)\) | \(e\left(\frac{13}{56}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{11}{28}\right)\) |