Basic properties
| Modulus: | \(6422\) | |
| Conductor: | \(3211\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3211}(87,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6422.cd
\(\chi_{6422}(87,\cdot)\) \(\chi_{6422}(159,\cdot)\) \(\chi_{6422}(581,\cdot)\) \(\chi_{6422}(1075,\cdot)\) \(\chi_{6422}(1147,\cdot)\) \(\chi_{6422}(1569,\cdot)\) \(\chi_{6422}(1641,\cdot)\) \(\chi_{6422}(2063,\cdot)\) \(\chi_{6422}(2135,\cdot)\) \(\chi_{6422}(2629,\cdot)\) \(\chi_{6422}(3051,\cdot)\) \(\chi_{6422}(3123,\cdot)\) \(\chi_{6422}(3545,\cdot)\) \(\chi_{6422}(3617,\cdot)\) \(\chi_{6422}(4039,\cdot)\) \(\chi_{6422}(4111,\cdot)\) \(\chi_{6422}(4533,\cdot)\) \(\chi_{6422}(4605,\cdot)\) \(\chi_{6422}(5027,\cdot)\) \(\chi_{6422}(5099,\cdot)\) \(\chi_{6422}(5521,\cdot)\) \(\chi_{6422}(5593,\cdot)\) \(\chi_{6422}(6015,\cdot)\) \(\chi_{6422}(6087,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((4903,4733)\) → \((e\left(\frac{2}{39}\right),e\left(\frac{2}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 6422 }(87, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(1\) | \(e\left(\frac{10}{39}\right)\) |