Basic properties
| Modulus: | \(6422\) | |
| Conductor: | \(3211\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3211}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6422.cv
\(\chi_{6422}(7,\cdot)\) \(\chi_{6422}(11,\cdot)\) \(\chi_{6422}(45,\cdot)\) \(\chi_{6422}(353,\cdot)\) \(\chi_{6422}(501,\cdot)\) \(\chi_{6422}(505,\cdot)\) \(\chi_{6422}(539,\cdot)\) \(\chi_{6422}(847,\cdot)\) \(\chi_{6422}(999,\cdot)\) \(\chi_{6422}(1341,\cdot)\) \(\chi_{6422}(1489,\cdot)\) \(\chi_{6422}(1493,\cdot)\) \(\chi_{6422}(1527,\cdot)\) \(\chi_{6422}(1835,\cdot)\) \(\chi_{6422}(1983,\cdot)\) \(\chi_{6422}(1987,\cdot)\) \(\chi_{6422}(2021,\cdot)\) \(\chi_{6422}(2329,\cdot)\) \(\chi_{6422}(2477,\cdot)\) \(\chi_{6422}(2481,\cdot)\) \(\chi_{6422}(2515,\cdot)\) \(\chi_{6422}(2823,\cdot)\) \(\chi_{6422}(2971,\cdot)\) \(\chi_{6422}(2975,\cdot)\) \(\chi_{6422}(3009,\cdot)\) \(\chi_{6422}(3317,\cdot)\) \(\chi_{6422}(3465,\cdot)\) \(\chi_{6422}(3503,\cdot)\) \(\chi_{6422}(3811,\cdot)\) \(\chi_{6422}(3959,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((4903,4733)\) → \((e\left(\frac{107}{156}\right),e\left(\frac{1}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 6422 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{79}{156}\right)\) | \(e\left(\frac{61}{156}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{101}{156}\right)\) | \(e\left(\frac{139}{156}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{121}{156}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{78}\right)\) |