Basic properties
| Modulus: | \(6422\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(81,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6422.cb
\(\chi_{6422}(419,\cdot)\) \(\chi_{6422}(685,\cdot)\) \(\chi_{6422}(913,\cdot)\) \(\chi_{6422}(1179,\cdot)\) \(\chi_{6422}(1407,\cdot)\) \(\chi_{6422}(1673,\cdot)\) \(\chi_{6422}(1901,\cdot)\) \(\chi_{6422}(2167,\cdot)\) \(\chi_{6422}(2395,\cdot)\) \(\chi_{6422}(2661,\cdot)\) \(\chi_{6422}(2889,\cdot)\) \(\chi_{6422}(3155,\cdot)\) \(\chi_{6422}(3383,\cdot)\) \(\chi_{6422}(3649,\cdot)\) \(\chi_{6422}(3877,\cdot)\) \(\chi_{6422}(4143,\cdot)\) \(\chi_{6422}(4637,\cdot)\) \(\chi_{6422}(4865,\cdot)\) \(\chi_{6422}(5131,\cdot)\) \(\chi_{6422}(5359,\cdot)\) \(\chi_{6422}(5625,\cdot)\) \(\chi_{6422}(5853,\cdot)\) \(\chi_{6422}(6119,\cdot)\) \(\chi_{6422}(6347,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((4903,4733)\) → \((e\left(\frac{7}{39}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 6422 }(419, a) \) | \(1\) | \(1\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{3}{13}\right)\) |