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 \(\chi_{3211}(49,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6422.cg
\(\chi_{6422}(49,\cdot)\) \(\chi_{6422}(121,\cdot)\) \(\chi_{6422}(543,\cdot)\) \(\chi_{6422}(615,\cdot)\) \(\chi_{6422}(1109,\cdot)\) \(\chi_{6422}(1531,\cdot)\) \(\chi_{6422}(1603,\cdot)\) \(\chi_{6422}(2025,\cdot)\) \(\chi_{6422}(2097,\cdot)\) \(\chi_{6422}(2519,\cdot)\) \(\chi_{6422}(2591,\cdot)\) \(\chi_{6422}(3013,\cdot)\) \(\chi_{6422}(3085,\cdot)\) \(\chi_{6422}(3507,\cdot)\) \(\chi_{6422}(3579,\cdot)\) \(\chi_{6422}(4001,\cdot)\) \(\chi_{6422}(4073,\cdot)\) \(\chi_{6422}(4495,\cdot)\) \(\chi_{6422}(4567,\cdot)\) \(\chi_{6422}(4989,\cdot)\) \(\chi_{6422}(5061,\cdot)\) \(\chi_{6422}(5483,\cdot)\) \(\chi_{6422}(5977,\cdot)\) \(\chi_{6422}(6049,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((4903,4733)\) → \((e\left(\frac{29}{78}\right),e\left(\frac{2}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 6422 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{39}\right)\) |