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.ib
\(\chi_{6031}(20,\cdot)\) \(\chi_{6031}(129,\cdot)\) \(\chi_{6031}(130,\cdot)\) \(\chi_{6031}(153,\cdot)\) \(\chi_{6031}(264,\cdot)\) \(\chi_{6031}(291,\cdot)\) \(\chi_{6031}(405,\cdot)\) \(\chi_{6031}(557,\cdot)\) \(\chi_{6031}(605,\cdot)\) \(\chi_{6031}(725,\cdot)\) \(\chi_{6031}(759,\cdot)\) \(\chi_{6031}(760,\cdot)\) \(\chi_{6031}(834,\cdot)\) \(\chi_{6031}(890,\cdot)\) \(\chi_{6031}(927,\cdot)\) \(\chi_{6031}(944,\cdot)\) \(\chi_{6031}(1023,\cdot)\) \(\chi_{6031}(1051,\cdot)\) \(\chi_{6031}(1115,\cdot)\) \(\chi_{6031}(1263,\cdot)\) \(\chi_{6031}(1367,\cdot)\) \(\chi_{6031}(1386,\cdot)\) \(\chi_{6031}(1537,\cdot)\) \(\chi_{6031}(1682,\cdot)\) \(\chi_{6031}(1697,\cdot)\) \(\chi_{6031}(1724,\cdot)\) \(\chi_{6031}(1800,\cdot)\) \(\chi_{6031}(1811,\cdot)\) \(\chi_{6031}(1882,\cdot)\) \(\chi_{6031}(1941,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{324})$ |
| Fixed field: | Number field defined by a degree 324 polynomial (not computed) |
Values on generators
\((816,5218)\) → \((e\left(\frac{25}{36}\right),e\left(\frac{17}{162}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6031 }(20, a) \) | \(1\) | \(1\) | \(e\left(\frac{259}{324}\right)\) | \(e\left(\frac{53}{81}\right)\) | \(e\left(\frac{97}{162}\right)\) | \(e\left(\frac{59}{108}\right)\) | \(e\left(\frac{49}{108}\right)\) | \(e\left(\frac{143}{162}\right)\) | \(e\left(\frac{43}{108}\right)\) | \(e\left(\frac{25}{81}\right)\) | \(e\left(\frac{28}{81}\right)\) | \(e\left(\frac{62}{81}\right)\) |