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 \(\chi_{3211}(131,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6422.ct
\(\chi_{6422}(131,\cdot)\) \(\chi_{6422}(157,\cdot)\) \(\chi_{6422}(313,\cdot)\) \(\chi_{6422}(365,\cdot)\) \(\chi_{6422}(443,\cdot)\) \(\chi_{6422}(625,\cdot)\) \(\chi_{6422}(651,\cdot)\) \(\chi_{6422}(807,\cdot)\) \(\chi_{6422}(833,\cdot)\) \(\chi_{6422}(859,\cdot)\) \(\chi_{6422}(937,\cdot)\) \(\chi_{6422}(1119,\cdot)\) \(\chi_{6422}(1145,\cdot)\) \(\chi_{6422}(1301,\cdot)\) \(\chi_{6422}(1327,\cdot)\) \(\chi_{6422}(1431,\cdot)\) \(\chi_{6422}(1613,\cdot)\) \(\chi_{6422}(1639,\cdot)\) \(\chi_{6422}(1795,\cdot)\) \(\chi_{6422}(1821,\cdot)\) \(\chi_{6422}(1847,\cdot)\) \(\chi_{6422}(1925,\cdot)\) \(\chi_{6422}(2107,\cdot)\) \(\chi_{6422}(2133,\cdot)\) \(\chi_{6422}(2289,\cdot)\) \(\chi_{6422}(2315,\cdot)\) \(\chi_{6422}(2341,\cdot)\) \(\chi_{6422}(2419,\cdot)\) \(\chi_{6422}(2601,\cdot)\) \(\chi_{6422}(2627,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 117 polynomial (not computed) |
Values on generators
\((4903,4733)\) → \((e\left(\frac{12}{13}\right),e\left(\frac{5}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 6422 }(131, a) \) | \(1\) | \(1\) | \(e\left(\frac{80}{117}\right)\) | \(e\left(\frac{23}{117}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{43}{117}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{103}{117}\right)\) | \(e\left(\frac{38}{117}\right)\) | \(e\left(\frac{92}{117}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{46}{117}\right)\) |