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 \(\chi_{3211}(27,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6422.ck
\(\chi_{6422}(27,\cdot)\) \(\chi_{6422}(183,\cdot)\) \(\chi_{6422}(521,\cdot)\) \(\chi_{6422}(1171,\cdot)\) \(\chi_{6422}(1509,\cdot)\) \(\chi_{6422}(1665,\cdot)\) \(\chi_{6422}(2003,\cdot)\) \(\chi_{6422}(2159,\cdot)\) \(\chi_{6422}(2497,\cdot)\) \(\chi_{6422}(2653,\cdot)\) \(\chi_{6422}(2991,\cdot)\) \(\chi_{6422}(3147,\cdot)\) \(\chi_{6422}(3485,\cdot)\) \(\chi_{6422}(3641,\cdot)\) \(\chi_{6422}(3979,\cdot)\) \(\chi_{6422}(4135,\cdot)\) \(\chi_{6422}(4473,\cdot)\) \(\chi_{6422}(4629,\cdot)\) \(\chi_{6422}(4967,\cdot)\) \(\chi_{6422}(5123,\cdot)\) \(\chi_{6422}(5461,\cdot)\) \(\chi_{6422}(5617,\cdot)\) \(\chi_{6422}(5955,\cdot)\) \(\chi_{6422}(6111,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((4903,4733)\) → \((e\left(\frac{5}{13}\right),e\left(\frac{1}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 6422 }(27, a) \) | \(-1\) | \(1\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{10}{39}\right)\) |