Basic properties
| Modulus: | \(722\) | |
| Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(342\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{361}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 722.l
\(\chi_{722}(3,\cdot)\) \(\chi_{722}(13,\cdot)\) \(\chi_{722}(15,\cdot)\) \(\chi_{722}(21,\cdot)\) \(\chi_{722}(29,\cdot)\) \(\chi_{722}(33,\cdot)\) \(\chi_{722}(41,\cdot)\) \(\chi_{722}(51,\cdot)\) \(\chi_{722}(53,\cdot)\) \(\chi_{722}(59,\cdot)\) \(\chi_{722}(67,\cdot)\) \(\chi_{722}(71,\cdot)\) \(\chi_{722}(79,\cdot)\) \(\chi_{722}(89,\cdot)\) \(\chi_{722}(91,\cdot)\) \(\chi_{722}(97,\cdot)\) \(\chi_{722}(105,\cdot)\) \(\chi_{722}(109,\cdot)\) \(\chi_{722}(117,\cdot)\) \(\chi_{722}(129,\cdot)\) \(\chi_{722}(135,\cdot)\) \(\chi_{722}(143,\cdot)\) \(\chi_{722}(147,\cdot)\) \(\chi_{722}(155,\cdot)\) \(\chi_{722}(165,\cdot)\) \(\chi_{722}(167,\cdot)\) \(\chi_{722}(173,\cdot)\) \(\chi_{722}(181,\cdot)\) \(\chi_{722}(185,\cdot)\) \(\chi_{722}(193,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\(363\) → \(e\left(\frac{17}{342}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 722 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{311}{342}\right)\) | \(e\left(\frac{91}{171}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{140}{171}\right)\) | \(e\left(\frac{4}{57}\right)\) | \(e\left(\frac{121}{342}\right)\) | \(e\left(\frac{151}{342}\right)\) | \(e\left(\frac{40}{171}\right)\) | \(e\left(\frac{125}{342}\right)\) | \(e\left(\frac{44}{171}\right)\) |