Basic properties
| Modulus: | \(5929\) | |
| Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(105\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{539}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5929.bm
\(\chi_{5929}(9,\cdot)\) \(\chi_{5929}(81,\cdot)\) \(\chi_{5929}(130,\cdot)\) \(\chi_{5929}(366,\cdot)\) \(\chi_{5929}(487,\cdot)\) \(\chi_{5929}(632,\cdot)\) \(\chi_{5929}(807,\cdot)\) \(\chi_{5929}(856,\cdot)\) \(\chi_{5929}(928,\cdot)\) \(\chi_{5929}(977,\cdot)\) \(\chi_{5929}(1213,\cdot)\) \(\chi_{5929}(1334,\cdot)\) \(\chi_{5929}(1479,\cdot)\) \(\chi_{5929}(1600,\cdot)\) \(\chi_{5929}(1654,\cdot)\) \(\chi_{5929}(1703,\cdot)\) \(\chi_{5929}(1775,\cdot)\) \(\chi_{5929}(1824,\cdot)\) \(\chi_{5929}(2060,\cdot)\) \(\chi_{5929}(2181,\cdot)\) \(\chi_{5929}(2326,\cdot)\) \(\chi_{5929}(2447,\cdot)\) \(\chi_{5929}(2501,\cdot)\) \(\chi_{5929}(2550,\cdot)\) \(\chi_{5929}(2622,\cdot)\) \(\chi_{5929}(2671,\cdot)\) \(\chi_{5929}(2907,\cdot)\) \(\chi_{5929}(3028,\cdot)\) \(\chi_{5929}(3173,\cdot)\) \(\chi_{5929}(3294,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((1816,2059)\) → \((e\left(\frac{1}{21}\right),e\left(\frac{3}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 5929 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{89}{105}\right)\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{6}{35}\right)\) |