Basic properties
| Modulus: | \(8788\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(165,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8788.q
\(\chi_{8788}(529,\cdot)\) \(\chi_{8788}(653,\cdot)\) \(\chi_{8788}(1205,\cdot)\) \(\chi_{8788}(1329,\cdot)\) \(\chi_{8788}(1881,\cdot)\) \(\chi_{8788}(2005,\cdot)\) \(\chi_{8788}(2557,\cdot)\) \(\chi_{8788}(2681,\cdot)\) \(\chi_{8788}(3909,\cdot)\) \(\chi_{8788}(4033,\cdot)\) \(\chi_{8788}(4585,\cdot)\) \(\chi_{8788}(4709,\cdot)\) \(\chi_{8788}(5261,\cdot)\) \(\chi_{8788}(5385,\cdot)\) \(\chi_{8788}(5937,\cdot)\) \(\chi_{8788}(6061,\cdot)\) \(\chi_{8788}(6613,\cdot)\) \(\chi_{8788}(6737,\cdot)\) \(\chi_{8788}(7289,\cdot)\) \(\chi_{8788}(7413,\cdot)\) \(\chi_{8788}(7965,\cdot)\) \(\chi_{8788}(8089,\cdot)\) \(\chi_{8788}(8641,\cdot)\) \(\chi_{8788}(8765,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((4395,6593)\) → \((1,e\left(\frac{20}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 8788 }(7289, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{2}{3}\right)\) |