Basic properties
| Modulus: | \(6422\) | |
| Conductor: | \(3211\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(117\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3211}(35,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6422.cu
\(\chi_{6422}(35,\cdot)\) \(\chi_{6422}(237,\cdot)\) \(\chi_{6422}(289,\cdot)\) \(\chi_{6422}(321,\cdot)\) \(\chi_{6422}(347,\cdot)\) \(\chi_{6422}(367,\cdot)\) \(\chi_{6422}(731,\cdot)\) \(\chi_{6422}(783,\cdot)\) \(\chi_{6422}(815,\cdot)\) \(\chi_{6422}(841,\cdot)\) \(\chi_{6422}(861,\cdot)\) \(\chi_{6422}(1023,\cdot)\) \(\chi_{6422}(1225,\cdot)\) \(\chi_{6422}(1277,\cdot)\) \(\chi_{6422}(1309,\cdot)\) \(\chi_{6422}(1335,\cdot)\) \(\chi_{6422}(1355,\cdot)\) \(\chi_{6422}(1517,\cdot)\) \(\chi_{6422}(1719,\cdot)\) \(\chi_{6422}(1771,\cdot)\) \(\chi_{6422}(1803,\cdot)\) \(\chi_{6422}(1829,\cdot)\) \(\chi_{6422}(1849,\cdot)\) \(\chi_{6422}(2011,\cdot)\) \(\chi_{6422}(2213,\cdot)\) \(\chi_{6422}(2265,\cdot)\) \(\chi_{6422}(2297,\cdot)\) \(\chi_{6422}(2323,\cdot)\) \(\chi_{6422}(2505,\cdot)\) \(\chi_{6422}(2707,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 117 polynomial (not computed) |
Values on generators
\((4903,4733)\) → \((e\left(\frac{29}{39}\right),e\left(\frac{2}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 6422 }(35, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{117}\right)\) | \(e\left(\frac{29}{117}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{22}{117}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{40}{117}\right)\) | \(e\left(\frac{92}{117}\right)\) | \(e\left(\frac{116}{117}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{58}{117}\right)\) |