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.hm
\(\chi_{6031}(42,\cdot)\) \(\chi_{6031}(94,\cdot)\) \(\chi_{6031}(183,\cdot)\) \(\chi_{6031}(235,\cdot)\) \(\chi_{6031}(272,\cdot)\) \(\chi_{6031}(338,\cdot)\) \(\chi_{6031}(392,\cdot)\) \(\chi_{6031}(609,\cdot)\) \(\chi_{6031}(642,\cdot)\) \(\chi_{6031}(718,\cdot)\) \(\chi_{6031}(753,\cdot)\) \(\chi_{6031}(758,\cdot)\) \(\chi_{6031}(782,\cdot)\) \(\chi_{6031}(923,\cdot)\) \(\chi_{6031}(980,\cdot)\) \(\chi_{6031}(997,\cdot)\) \(\chi_{6031}(1054,\cdot)\) \(\chi_{6031}(1127,\cdot)\) \(\chi_{6031}(1208,\cdot)\) \(\chi_{6031}(1223,\cdot)\) \(\chi_{6031}(1280,\cdot)\) \(\chi_{6031}(1315,\cdot)\) \(\chi_{6031}(1393,\cdot)\) \(\chi_{6031}(1411,\cdot)\) \(\chi_{6031}(1463,\cdot)\) \(\chi_{6031}(1519,\cdot)\) \(\chi_{6031}(1573,\cdot)\) \(\chi_{6031}(1596,\cdot)\) \(\chi_{6031}(1604,\cdot)\) \(\chi_{6031}(1606,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{324})$ |
| Fixed field: | Number field defined by a degree 324 polynomial (not computed) |
Values on generators
\((816,5218)\) → \((e\left(\frac{23}{36}\right),e\left(\frac{13}{162}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6031 }(42, a) \) | \(1\) | \(1\) | \(e\left(\frac{233}{324}\right)\) | \(e\left(\frac{58}{81}\right)\) | \(e\left(\frac{71}{162}\right)\) | \(e\left(\frac{97}{108}\right)\) | \(e\left(\frac{47}{108}\right)\) | \(e\left(\frac{49}{162}\right)\) | \(e\left(\frac{17}{108}\right)\) | \(e\left(\frac{35}{81}\right)\) | \(e\left(\frac{50}{81}\right)\) | \(e\left(\frac{76}{81}\right)\) |