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.hu
\(\chi_{6031}(68,\cdot)\) \(\chi_{6031}(80,\cdot)\) \(\chi_{6031}(117,\cdot)\) \(\chi_{6031}(154,\cdot)\) \(\chi_{6031}(302,\cdot)\) \(\chi_{6031}(376,\cdot)\) \(\chi_{6031}(401,\cdot)\) \(\chi_{6031}(438,\cdot)\) \(\chi_{6031}(450,\cdot)\) \(\chi_{6031}(475,\cdot)\) \(\chi_{6031}(561,\cdot)\) \(\chi_{6031}(598,\cdot)\) \(\chi_{6031}(672,\cdot)\) \(\chi_{6031}(697,\cdot)\) \(\chi_{6031}(734,\cdot)\) \(\chi_{6031}(746,\cdot)\) \(\chi_{6031}(857,\cdot)\) \(\chi_{6031}(882,\cdot)\) \(\chi_{6031}(894,\cdot)\) \(\chi_{6031}(931,\cdot)\) \(\chi_{6031}(968,\cdot)\) \(\chi_{6031}(1030,\cdot)\) \(\chi_{6031}(1067,\cdot)\) \(\chi_{6031}(1079,\cdot)\) \(\chi_{6031}(1153,\cdot)\) \(\chi_{6031}(1289,\cdot)\) \(\chi_{6031}(1412,\cdot)\) \(\chi_{6031}(1474,\cdot)\) \(\chi_{6031}(1486,\cdot)\) \(\chi_{6031}(1511,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{324})$ |
| Fixed field: | Number field defined by a degree 324 polynomial (not computed) |
Values on generators
\((816,5218)\) → \((i,e\left(\frac{59}{162}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6031 }(68, a) \) | \(1\) | \(1\) | \(e\left(\frac{199}{324}\right)\) | \(e\left(\frac{23}{81}\right)\) | \(e\left(\frac{37}{162}\right)\) | \(e\left(\frac{23}{108}\right)\) | \(e\left(\frac{97}{108}\right)\) | \(e\left(\frac{95}{162}\right)\) | \(e\left(\frac{91}{108}\right)\) | \(e\left(\frac{46}{81}\right)\) | \(e\left(\frac{67}{81}\right)\) | \(e\left(\frac{50}{81}\right)\) |