Basic properties
| Modulus: | \(367\) | |
| Conductor: | \(367\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(122\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 367.f
\(\chi_{367}(3,\cdot)\) \(\chi_{367}(5,\cdot)\) \(\chi_{367}(21,\cdot)\) \(\chi_{367}(24,\cdot)\) \(\chi_{367}(27,\cdot)\) \(\chi_{367}(29,\cdot)\) \(\chi_{367}(35,\cdot)\) \(\chi_{367}(38,\cdot)\) \(\chi_{367}(40,\cdot)\) \(\chi_{367}(44,\cdot)\) \(\chi_{367}(45,\cdot)\) \(\chi_{367}(68,\cdot)\) \(\chi_{367}(75,\cdot)\) \(\chi_{367}(86,\cdot)\) \(\chi_{367}(109,\cdot)\) \(\chi_{367}(125,\cdot)\) \(\chi_{367}(138,\cdot)\) \(\chi_{367}(141,\cdot)\) \(\chi_{367}(142,\cdot)\) \(\chi_{367}(147,\cdot)\) \(\chi_{367}(156,\cdot)\) \(\chi_{367}(158,\cdot)\) \(\chi_{367}(163,\cdot)\) \(\chi_{367}(167,\cdot)\) \(\chi_{367}(168,\cdot)\) \(\chi_{367}(177,\cdot)\) \(\chi_{367}(189,\cdot)\) \(\chi_{367}(192,\cdot)\) \(\chi_{367}(203,\cdot)\) \(\chi_{367}(216,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{61})$ |
| Fixed field: | Number field defined by a degree 122 polynomial (not computed) |
Values on generators
\(6\) → \(e\left(\frac{25}{122}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 367 }(3, a) \) | \(-1\) | \(1\) | \(e\left(\frac{51}{61}\right)\) | \(e\left(\frac{45}{122}\right)\) | \(e\left(\frac{41}{61}\right)\) | \(e\left(\frac{87}{122}\right)\) | \(e\left(\frac{25}{122}\right)\) | \(e\left(\frac{28}{61}\right)\) | \(e\left(\frac{31}{61}\right)\) | \(e\left(\frac{45}{61}\right)\) | \(e\left(\frac{67}{122}\right)\) | \(e\left(\frac{49}{122}\right)\) |