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.mo
\(\chi_{25857}(2,\cdot)\) \(\chi_{25857}(32,\cdot)\) \(\chi_{25857}(59,\cdot)\) \(\chi_{25857}(128,\cdot)\) \(\chi_{25857}(236,\cdot)\) \(\chi_{25857}(1181,\cdot)\) \(\chi_{25857}(1787,\cdot)\) \(\chi_{25857}(1991,\cdot)\) \(\chi_{25857}(2021,\cdot)\) \(\chi_{25857}(2048,\cdot)\) \(\chi_{25857}(2225,\cdot)\) \(\chi_{25857}(2984,\cdot)\) \(\chi_{25857}(3170,\cdot)\) \(\chi_{25857}(3776,\cdot)\) \(\chi_{25857}(3980,\cdot)\) \(\chi_{25857}(4010,\cdot)\) \(\chi_{25857}(4106,\cdot)\) \(\chi_{25857}(4214,\cdot)\) \(\chi_{25857}(4973,\cdot)\) \(\chi_{25857}(5969,\cdot)\) \(\chi_{25857}(5999,\cdot)\) \(\chi_{25857}(6026,\cdot)\) \(\chi_{25857}(6095,\cdot)\) \(\chi_{25857}(6203,\cdot)\) \(\chi_{25857}(6962,\cdot)\) \(\chi_{25857}(7148,\cdot)\) \(\chi_{25857}(7754,\cdot)\) \(\chi_{25857}(7958,\cdot)\) \(\chi_{25857}(7988,\cdot)\) \(\chi_{25857}(8015,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{312})$ |
| Fixed field: | Number field defined by a degree 312 polynomial (not computed) |
Values on generators
\((14366,14536,19774)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{5}{156}\right),e\left(\frac{3}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(19\) |
| \( \chi_{ 25857 }(32, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{103}{312}\right)\) | \(e\left(\frac{277}{312}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{139}{312}\right)\) | \(e\left(\frac{79}{104}\right)\) | \(e\left(\frac{1}{312}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{1}{3}\right)\) |