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 \(\chi_{3211}(53,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6422.dj
\(\chi_{6422}(53,\cdot)\) \(\chi_{6422}(79,\cdot)\) \(\chi_{6422}(105,\cdot)\) \(\chi_{6422}(261,\cdot)\) \(\chi_{6422}(287,\cdot)\) \(\chi_{6422}(469,\cdot)\) \(\chi_{6422}(547,\cdot)\) \(\chi_{6422}(573,\cdot)\) \(\chi_{6422}(599,\cdot)\) \(\chi_{6422}(755,\cdot)\) \(\chi_{6422}(781,\cdot)\) \(\chi_{6422}(963,\cdot)\) \(\chi_{6422}(1041,\cdot)\) \(\chi_{6422}(1067,\cdot)\) \(\chi_{6422}(1093,\cdot)\) \(\chi_{6422}(1249,\cdot)\) \(\chi_{6422}(1275,\cdot)\) \(\chi_{6422}(1457,\cdot)\) \(\chi_{6422}(1535,\cdot)\) \(\chi_{6422}(1561,\cdot)\) \(\chi_{6422}(1587,\cdot)\) \(\chi_{6422}(1743,\cdot)\) \(\chi_{6422}(1769,\cdot)\) \(\chi_{6422}(1951,\cdot)\) \(\chi_{6422}(2055,\cdot)\) \(\chi_{6422}(2081,\cdot)\) \(\chi_{6422}(2237,\cdot)\) \(\chi_{6422}(2263,\cdot)\) \(\chi_{6422}(2445,\cdot)\) \(\chi_{6422}(2523,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((4903,4733)\) → \((e\left(\frac{10}{13}\right),e\left(\frac{11}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 6422 }(53, a) \) | \(-1\) | \(1\) | \(e\left(\frac{77}{234}\right)\) | \(e\left(\frac{82}{117}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{77}{117}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{7}{234}\right)\) | \(e\left(\frac{49}{117}\right)\) | \(e\left(\frac{71}{234}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{47}{117}\right)\) |