Basic properties
| Modulus: | \(6422\) | |
| Conductor: | \(3211\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3211}(311,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6422.co
\(\chi_{6422}(311,\cdot)\) \(\chi_{6422}(467,\cdot)\) \(\chi_{6422}(805,\cdot)\) \(\chi_{6422}(961,\cdot)\) \(\chi_{6422}(1299,\cdot)\) \(\chi_{6422}(1455,\cdot)\) \(\chi_{6422}(1793,\cdot)\) \(\chi_{6422}(1949,\cdot)\) \(\chi_{6422}(2287,\cdot)\) \(\chi_{6422}(2443,\cdot)\) \(\chi_{6422}(2781,\cdot)\) \(\chi_{6422}(2937,\cdot)\) \(\chi_{6422}(3275,\cdot)\) \(\chi_{6422}(3431,\cdot)\) \(\chi_{6422}(3769,\cdot)\) \(\chi_{6422}(3925,\cdot)\) \(\chi_{6422}(4263,\cdot)\) \(\chi_{6422}(4419,\cdot)\) \(\chi_{6422}(4757,\cdot)\) \(\chi_{6422}(4913,\cdot)\) \(\chi_{6422}(5251,\cdot)\) \(\chi_{6422}(5901,\cdot)\) \(\chi_{6422}(6239,\cdot)\) \(\chi_{6422}(6395,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((4903,4733)\) → \((e\left(\frac{23}{26}\right),e\left(\frac{1}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 6422 }(311, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{23}{39}\right)\) |