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 \(\chi_{3211}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6422.cs
\(\chi_{6422}(9,\cdot)\) \(\chi_{6422}(55,\cdot)\) \(\chi_{6422}(61,\cdot)\) \(\chi_{6422}(81,\cdot)\) \(\chi_{6422}(139,\cdot)\) \(\chi_{6422}(263,\cdot)\) \(\chi_{6422}(503,\cdot)\) \(\chi_{6422}(549,\cdot)\) \(\chi_{6422}(555,\cdot)\) \(\chi_{6422}(575,\cdot)\) \(\chi_{6422}(633,\cdot)\) \(\chi_{6422}(757,\cdot)\) \(\chi_{6422}(997,\cdot)\) \(\chi_{6422}(1043,\cdot)\) \(\chi_{6422}(1049,\cdot)\) \(\chi_{6422}(1069,\cdot)\) \(\chi_{6422}(1127,\cdot)\) \(\chi_{6422}(1251,\cdot)\) \(\chi_{6422}(1491,\cdot)\) \(\chi_{6422}(1537,\cdot)\) \(\chi_{6422}(1563,\cdot)\) \(\chi_{6422}(1621,\cdot)\) \(\chi_{6422}(1745,\cdot)\) \(\chi_{6422}(1985,\cdot)\) \(\chi_{6422}(2031,\cdot)\) \(\chi_{6422}(2037,\cdot)\) \(\chi_{6422}(2057,\cdot)\) \(\chi_{6422}(2115,\cdot)\) \(\chi_{6422}(2239,\cdot)\) \(\chi_{6422}(2479,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 117 polynomial (not computed) |
Values on generators
\((4903,4733)\) → \((e\left(\frac{23}{39}\right),e\left(\frac{4}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 6422 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{106}{117}\right)\) | \(e\left(\frac{49}{117}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{95}{117}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{38}{117}\right)\) | \(e\left(\frac{64}{117}\right)\) | \(e\left(\frac{79}{117}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{98}{117}\right)\) |