Basic properties
| Modulus: | \(1648\) | |
| Conductor: | \(824\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(102\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{824}(437,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1648.bp
\(\chi_{1648}(25,\cdot)\) \(\chi_{1648}(41,\cdot)\) \(\chi_{1648}(105,\cdot)\) \(\chi_{1648}(121,\cdot)\) \(\chi_{1648}(153,\cdot)\) \(\chi_{1648}(185,\cdot)\) \(\chi_{1648}(201,\cdot)\) \(\chi_{1648}(265,\cdot)\) \(\chi_{1648}(297,\cdot)\) \(\chi_{1648}(313,\cdot)\) \(\chi_{1648}(345,\cdot)\) \(\chi_{1648}(361,\cdot)\) \(\chi_{1648}(377,\cdot)\) \(\chi_{1648}(441,\cdot)\) \(\chi_{1648}(553,\cdot)\) \(\chi_{1648}(633,\cdot)\) \(\chi_{1648}(681,\cdot)\) \(\chi_{1648}(841,\cdot)\) \(\chi_{1648}(857,\cdot)\) \(\chi_{1648}(873,\cdot)\) \(\chi_{1648}(921,\cdot)\) \(\chi_{1648}(953,\cdot)\) \(\chi_{1648}(985,\cdot)\) \(\chi_{1648}(1049,\cdot)\) \(\chi_{1648}(1113,\cdot)\) \(\chi_{1648}(1161,\cdot)\) \(\chi_{1648}(1193,\cdot)\) \(\chi_{1648}(1225,\cdot)\) \(\chi_{1648}(1449,\cdot)\) \(\chi_{1648}(1497,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((207,1237,417)\) → \((1,-1,e\left(\frac{1}{51}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1648 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{34}\right)\) | \(e\left(\frac{53}{102}\right)\) | \(e\left(\frac{4}{51}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{71}{102}\right)\) | \(e\left(\frac{31}{34}\right)\) | \(e\left(\frac{40}{51}\right)\) | \(e\left(\frac{19}{51}\right)\) | \(e\left(\frac{7}{102}\right)\) | \(e\left(\frac{35}{102}\right)\) |