Basic properties
| Modulus: | \(8788\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(44,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8788.r
\(\chi_{8788}(437,\cdot)\) \(\chi_{8788}(577,\cdot)\) \(\chi_{8788}(1113,\cdot)\) \(\chi_{8788}(1253,\cdot)\) \(\chi_{8788}(1789,\cdot)\) \(\chi_{8788}(1929,\cdot)\) \(\chi_{8788}(2465,\cdot)\) \(\chi_{8788}(2605,\cdot)\) \(\chi_{8788}(3141,\cdot)\) \(\chi_{8788}(3281,\cdot)\) \(\chi_{8788}(3817,\cdot)\) \(\chi_{8788}(3957,\cdot)\) \(\chi_{8788}(4493,\cdot)\) \(\chi_{8788}(5169,\cdot)\) \(\chi_{8788}(5309,\cdot)\) \(\chi_{8788}(5845,\cdot)\) \(\chi_{8788}(5985,\cdot)\) \(\chi_{8788}(6521,\cdot)\) \(\chi_{8788}(6661,\cdot)\) \(\chi_{8788}(7197,\cdot)\) \(\chi_{8788}(7337,\cdot)\) \(\chi_{8788}(7873,\cdot)\) \(\chi_{8788}(8013,\cdot)\) \(\chi_{8788}(8689,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((4395,6593)\) → \((1,e\left(\frac{35}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 8788 }(8689, a) \) | \(-1\) | \(1\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(-i\) | \(e\left(\frac{25}{52}\right)\) | \(-1\) |