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 \(\chi_{3211}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6422.dg
\(\chi_{6422}(17,\cdot)\) \(\chi_{6422}(43,\cdot)\) \(\chi_{6422}(101,\cdot)\) \(\chi_{6422}(225,\cdot)\) \(\chi_{6422}(465,\cdot)\) \(\chi_{6422}(511,\cdot)\) \(\chi_{6422}(517,\cdot)\) \(\chi_{6422}(537,\cdot)\) \(\chi_{6422}(595,\cdot)\) \(\chi_{6422}(719,\cdot)\) \(\chi_{6422}(959,\cdot)\) \(\chi_{6422}(1005,\cdot)\) \(\chi_{6422}(1011,\cdot)\) \(\chi_{6422}(1031,\cdot)\) \(\chi_{6422}(1089,\cdot)\) \(\chi_{6422}(1213,\cdot)\) \(\chi_{6422}(1453,\cdot)\) \(\chi_{6422}(1505,\cdot)\) \(\chi_{6422}(1525,\cdot)\) \(\chi_{6422}(1583,\cdot)\) \(\chi_{6422}(1707,\cdot)\) \(\chi_{6422}(1947,\cdot)\) \(\chi_{6422}(1993,\cdot)\) \(\chi_{6422}(1999,\cdot)\) \(\chi_{6422}(2019,\cdot)\) \(\chi_{6422}(2077,\cdot)\) \(\chi_{6422}(2201,\cdot)\) \(\chi_{6422}(2441,\cdot)\) \(\chi_{6422}(2487,\cdot)\) \(\chi_{6422}(2493,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((4903,4733)\) → \((e\left(\frac{73}{78}\right),e\left(\frac{5}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 6422 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{117}\right)\) | \(e\left(\frac{73}{234}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{64}{117}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{137}{234}\right)\) | \(e\left(\frac{23}{117}\right)\) | \(e\left(\frac{175}{234}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{73}{117}\right)\) |