Basic properties
| Modulus: | \(25857\) | |
| Conductor: | \(25857\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(312\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 25857.lt
\(\chi_{25857}(25,\cdot)\) \(\chi_{25857}(376,\cdot)\) \(\chi_{25857}(610,\cdot)\) \(\chi_{25857}(688,\cdot)\) \(\chi_{25857}(961,\cdot)\) \(\chi_{25857}(1039,\cdot)\) \(\chi_{25857}(1273,\cdot)\) \(\chi_{25857}(1624,\cdot)\) \(\chi_{25857}(2014,\cdot)\) \(\chi_{25857}(2599,\cdot)\) \(\chi_{25857}(2677,\cdot)\) \(\chi_{25857}(2950,\cdot)\) \(\chi_{25857}(3028,\cdot)\) \(\chi_{25857}(3262,\cdot)\) \(\chi_{25857}(3613,\cdot)\) \(\chi_{25857}(4003,\cdot)\) \(\chi_{25857}(4354,\cdot)\) \(\chi_{25857}(4588,\cdot)\) \(\chi_{25857}(4666,\cdot)\) \(\chi_{25857}(4939,\cdot)\) \(\chi_{25857}(5017,\cdot)\) \(\chi_{25857}(5251,\cdot)\) \(\chi_{25857}(5602,\cdot)\) \(\chi_{25857}(5992,\cdot)\) \(\chi_{25857}(6343,\cdot)\) \(\chi_{25857}(6577,\cdot)\) \(\chi_{25857}(6655,\cdot)\) \(\chi_{25857}(7006,\cdot)\) \(\chi_{25857}(7240,\cdot)\) \(\chi_{25857}(7591,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{312})$ |
| Fixed field: | Number field defined by a degree 312 polynomial (not computed) |
Values on generators
\((14366,14536,19774)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{3}{26}\right),e\left(\frac{5}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(19\) |
| \( \chi_{ 25857 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{156}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{155}{312}\right)\) | \(e\left(\frac{277}{312}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{3}{104}\right)\) | \(e\left(\frac{289}{312}\right)\) | \(e\left(\frac{131}{312}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(i\) |