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 \(\chi_{3211}(425,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6422.ca
\(\chi_{6422}(425,\cdot)\) \(\chi_{6422}(809,\cdot)\) \(\chi_{6422}(919,\cdot)\) \(\chi_{6422}(1303,\cdot)\) \(\chi_{6422}(1413,\cdot)\) \(\chi_{6422}(1797,\cdot)\) \(\chi_{6422}(1907,\cdot)\) \(\chi_{6422}(2291,\cdot)\) \(\chi_{6422}(2401,\cdot)\) \(\chi_{6422}(2785,\cdot)\) \(\chi_{6422}(3279,\cdot)\) \(\chi_{6422}(3389,\cdot)\) \(\chi_{6422}(3773,\cdot)\) \(\chi_{6422}(3883,\cdot)\) \(\chi_{6422}(4267,\cdot)\) \(\chi_{6422}(4377,\cdot)\) \(\chi_{6422}(4761,\cdot)\) \(\chi_{6422}(4871,\cdot)\) \(\chi_{6422}(5255,\cdot)\) \(\chi_{6422}(5365,\cdot)\) \(\chi_{6422}(5749,\cdot)\) \(\chi_{6422}(5859,\cdot)\) \(\chi_{6422}(6243,\cdot)\) \(\chi_{6422}(6353,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((4903,4733)\) → \((e\left(\frac{2}{39}\right),e\left(\frac{1}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 6422 }(425, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{23}{39}\right)\) |