Basic properties
| Modulus: | \(9408\) | |
| 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 \(\chi_{1568}(643,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9408.et
\(\chi_{9408}(55,\cdot)\) \(\chi_{9408}(727,\cdot)\) \(\chi_{9408}(1063,\cdot)\) \(\chi_{9408}(1399,\cdot)\) \(\chi_{9408}(1735,\cdot)\) \(\chi_{9408}(2071,\cdot)\) \(\chi_{9408}(2407,\cdot)\) \(\chi_{9408}(3079,\cdot)\) \(\chi_{9408}(3415,\cdot)\) \(\chi_{9408}(3751,\cdot)\) \(\chi_{9408}(4087,\cdot)\) \(\chi_{9408}(4423,\cdot)\) \(\chi_{9408}(4759,\cdot)\) \(\chi_{9408}(5431,\cdot)\) \(\chi_{9408}(5767,\cdot)\) \(\chi_{9408}(6103,\cdot)\) \(\chi_{9408}(6439,\cdot)\) \(\chi_{9408}(6775,\cdot)\) \(\chi_{9408}(7111,\cdot)\) \(\chi_{9408}(7783,\cdot)\) \(\chi_{9408}(8119,\cdot)\) \(\chi_{9408}(8455,\cdot)\) \(\chi_{9408}(8791,\cdot)\) \(\chi_{9408}(9127,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{56})$ |
| Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((1471,6469,3137,4609)\) → \((-1,e\left(\frac{3}{8}\right),1,e\left(\frac{9}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 9408 }(55, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{56}\right)\) | \(e\left(\frac{5}{56}\right)\) | \(e\left(\frac{47}{56}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{39}{56}\right)\) | \(1\) | \(e\left(\frac{53}{56}\right)\) |