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 \(\chi_{3211}(235,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6422.cc
\(\chi_{6422}(235,\cdot)\) \(\chi_{6422}(391,\cdot)\) \(\chi_{6422}(729,\cdot)\) \(\chi_{6422}(885,\cdot)\) \(\chi_{6422}(1223,\cdot)\) \(\chi_{6422}(1379,\cdot)\) \(\chi_{6422}(1717,\cdot)\) \(\chi_{6422}(1873,\cdot)\) \(\chi_{6422}(2211,\cdot)\) \(\chi_{6422}(2861,\cdot)\) \(\chi_{6422}(3199,\cdot)\) \(\chi_{6422}(3355,\cdot)\) \(\chi_{6422}(3693,\cdot)\) \(\chi_{6422}(3849,\cdot)\) \(\chi_{6422}(4187,\cdot)\) \(\chi_{6422}(4343,\cdot)\) \(\chi_{6422}(4681,\cdot)\) \(\chi_{6422}(4837,\cdot)\) \(\chi_{6422}(5175,\cdot)\) \(\chi_{6422}(5331,\cdot)\) \(\chi_{6422}(5669,\cdot)\) \(\chi_{6422}(5825,\cdot)\) \(\chi_{6422}(6163,\cdot)\) \(\chi_{6422}(6319,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((4903,4733)\) → \((e\left(\frac{6}{13}\right),e\left(\frac{1}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 6422 }(235, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{38}{39}\right)\) |