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 \(\chi_{3211}(1199,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6422.dd
\(\chi_{6422}(3,\cdot)\) \(\chi_{6422}(165,\cdot)\) \(\chi_{6422}(185,\cdot)\) \(\chi_{6422}(211,\cdot)\) \(\chi_{6422}(243,\cdot)\) \(\chi_{6422}(295,\cdot)\) \(\chi_{6422}(497,\cdot)\) \(\chi_{6422}(659,\cdot)\) \(\chi_{6422}(679,\cdot)\) \(\chi_{6422}(705,\cdot)\) \(\chi_{6422}(737,\cdot)\) \(\chi_{6422}(789,\cdot)\) \(\chi_{6422}(1153,\cdot)\) \(\chi_{6422}(1173,\cdot)\) \(\chi_{6422}(1199,\cdot)\) \(\chi_{6422}(1231,\cdot)\) \(\chi_{6422}(1283,\cdot)\) \(\chi_{6422}(1485,\cdot)\) \(\chi_{6422}(1647,\cdot)\) \(\chi_{6422}(1693,\cdot)\) \(\chi_{6422}(1725,\cdot)\) \(\chi_{6422}(1777,\cdot)\) \(\chi_{6422}(1979,\cdot)\) \(\chi_{6422}(2141,\cdot)\) \(\chi_{6422}(2161,\cdot)\) \(\chi_{6422}(2187,\cdot)\) \(\chi_{6422}(2271,\cdot)\) \(\chi_{6422}(2473,\cdot)\) \(\chi_{6422}(2635,\cdot)\) \(\chi_{6422}(2655,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((4903,4733)\) → \((e\left(\frac{1}{39}\right),e\left(\frac{1}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 6422 }(1199, a) \) | \(-1\) | \(1\) | \(e\left(\frac{211}{234}\right)\) | \(e\left(\frac{14}{117}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{94}{117}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{5}{234}\right)\) | \(e\left(\frac{35}{117}\right)\) | \(e\left(\frac{229}{234}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{28}{117}\right)\) |