Basic properties
| Modulus: | \(6031\) | |
| Conductor: | \(6031\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(324\) | 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 6031.hl
\(\chi_{6031}(50,\cdot)\) \(\chi_{6031}(52,\cdot)\) \(\chi_{6031}(106,\cdot)\) \(\chi_{6031}(116,\cdot)\) \(\chi_{6031}(242,\cdot)\) \(\chi_{6031}(257,\cdot)\) \(\chi_{6031}(311,\cdot)\) \(\chi_{6031}(328,\cdot)\) \(\chi_{6031}(355,\cdot)\) \(\chi_{6031}(402,\cdot)\) \(\chi_{6031}(446,\cdot)\) \(\chi_{6031}(463,\cdot)\) \(\chi_{6031}(531,\cdot)\) \(\chi_{6031}(611,\cdot)\) \(\chi_{6031}(681,\cdot)\) \(\chi_{6031}(720,\cdot)\) \(\chi_{6031}(827,\cdot)\) \(\chi_{6031}(943,\cdot)\) \(\chi_{6031}(964,\cdot)\) \(\chi_{6031}(1053,\cdot)\) \(\chi_{6031}(1090,\cdot)\) \(\chi_{6031}(1204,\cdot)\) \(\chi_{6031}(1271,\cdot)\) \(\chi_{6031}(1428,\cdot)\) \(\chi_{6031}(1478,\cdot)\) \(\chi_{6031}(1512,\cdot)\) \(\chi_{6031}(1626,\cdot)\) \(\chi_{6031}(1648,\cdot)\) \(\chi_{6031}(1650,\cdot)\) \(\chi_{6031}(1754,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{324})$ |
| Fixed field: | Number field defined by a degree 324 polynomial (not computed) |
Values on generators
\((816,5218)\) → \((e\left(\frac{11}{36}\right),e\left(\frac{31}{162}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6031 }(50, a) \) | \(1\) | \(1\) | \(e\left(\frac{161}{324}\right)\) | \(e\left(\frac{22}{81}\right)\) | \(e\left(\frac{161}{162}\right)\) | \(e\left(\frac{97}{108}\right)\) | \(e\left(\frac{83}{108}\right)\) | \(e\left(\frac{121}{162}\right)\) | \(e\left(\frac{53}{108}\right)\) | \(e\left(\frac{44}{81}\right)\) | \(e\left(\frac{32}{81}\right)\) | \(e\left(\frac{13}{81}\right)\) |