Basic properties
| Modulus: | \(8788\) | |
| Conductor: | \(676\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{676}(83,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8788.s
\(\chi_{8788}(99,\cdot)\) \(\chi_{8788}(775,\cdot)\) \(\chi_{8788}(915,\cdot)\) \(\chi_{8788}(1451,\cdot)\) \(\chi_{8788}(1591,\cdot)\) \(\chi_{8788}(2127,\cdot)\) \(\chi_{8788}(2267,\cdot)\) \(\chi_{8788}(2803,\cdot)\) \(\chi_{8788}(2943,\cdot)\) \(\chi_{8788}(3479,\cdot)\) \(\chi_{8788}(3619,\cdot)\) \(\chi_{8788}(4295,\cdot)\) \(\chi_{8788}(4831,\cdot)\) \(\chi_{8788}(4971,\cdot)\) \(\chi_{8788}(5507,\cdot)\) \(\chi_{8788}(5647,\cdot)\) \(\chi_{8788}(6183,\cdot)\) \(\chi_{8788}(6323,\cdot)\) \(\chi_{8788}(6859,\cdot)\) \(\chi_{8788}(6999,\cdot)\) \(\chi_{8788}(7535,\cdot)\) \(\chi_{8788}(7675,\cdot)\) \(\chi_{8788}(8211,\cdot)\) \(\chi_{8788}(8351,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((4395,6593)\) → \((-1,e\left(\frac{15}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 8788 }(6999, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(i\) | \(e\left(\frac{33}{52}\right)\) | \(1\) |