Basic properties
| Modulus: | \(6422\) | |
| Conductor: | \(3211\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(234\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3211}(1819,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6422.de
\(\chi_{6422}(51,\cdot)\) \(\chi_{6422}(129,\cdot)\) \(\chi_{6422}(155,\cdot)\) \(\chi_{6422}(181,\cdot)\) \(\chi_{6422}(363,\cdot)\) \(\chi_{6422}(545,\cdot)\) \(\chi_{6422}(623,\cdot)\) \(\chi_{6422}(649,\cdot)\) \(\chi_{6422}(831,\cdot)\) \(\chi_{6422}(857,\cdot)\) \(\chi_{6422}(1039,\cdot)\) \(\chi_{6422}(1117,\cdot)\) \(\chi_{6422}(1143,\cdot)\) \(\chi_{6422}(1169,\cdot)\) \(\chi_{6422}(1325,\cdot)\) \(\chi_{6422}(1533,\cdot)\) \(\chi_{6422}(1611,\cdot)\) \(\chi_{6422}(1637,\cdot)\) \(\chi_{6422}(1663,\cdot)\) \(\chi_{6422}(1819,\cdot)\) \(\chi_{6422}(1845,\cdot)\) \(\chi_{6422}(2105,\cdot)\) \(\chi_{6422}(2131,\cdot)\) \(\chi_{6422}(2157,\cdot)\) \(\chi_{6422}(2313,\cdot)\) \(\chi_{6422}(2339,\cdot)\) \(\chi_{6422}(2521,\cdot)\) \(\chi_{6422}(2599,\cdot)\) \(\chi_{6422}(2625,\cdot)\) \(\chi_{6422}(2651,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((4903,4733)\) → \((e\left(\frac{15}{26}\right),e\left(\frac{7}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 6422 }(1819, a) \) | \(-1\) | \(1\) | \(e\left(\frac{139}{234}\right)\) | \(e\left(\frac{97}{234}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{22}{117}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{1}{117}\right)\) | \(e\left(\frac{14}{117}\right)\) | \(e\left(\frac{77}{117}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{97}{117}\right)\) |