Basic properties
| Modulus: | \(3136\) | |
| Conductor: | \(1568\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(56\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1568}(267,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3136.cj
\(\chi_{3136}(71,\cdot)\) \(\chi_{3136}(183,\cdot)\) \(\chi_{3136}(407,\cdot)\) \(\chi_{3136}(519,\cdot)\) \(\chi_{3136}(631,\cdot)\) \(\chi_{3136}(743,\cdot)\) \(\chi_{3136}(855,\cdot)\) \(\chi_{3136}(967,\cdot)\) \(\chi_{3136}(1191,\cdot)\) \(\chi_{3136}(1303,\cdot)\) \(\chi_{3136}(1415,\cdot)\) \(\chi_{3136}(1527,\cdot)\) \(\chi_{3136}(1639,\cdot)\) \(\chi_{3136}(1751,\cdot)\) \(\chi_{3136}(1975,\cdot)\) \(\chi_{3136}(2087,\cdot)\) \(\chi_{3136}(2199,\cdot)\) \(\chi_{3136}(2311,\cdot)\) \(\chi_{3136}(2423,\cdot)\) \(\chi_{3136}(2535,\cdot)\) \(\chi_{3136}(2759,\cdot)\) \(\chi_{3136}(2871,\cdot)\) \(\chi_{3136}(2983,\cdot)\) \(\chi_{3136}(3095,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{56})$ |
| Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((1471,197,1473)\) → \((-1,e\left(\frac{5}{8}\right),e\left(\frac{4}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 3136 }(71, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{56}\right)\) | \(e\left(\frac{11}{56}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{27}{56}\right)\) | \(e\left(\frac{13}{56}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{11}{28}\right)\) |