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
\(6\) → \(e\left(\frac{55}{122}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 367 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{39}{61}\right)\) | \(e\left(\frac{99}{122}\right)\) | \(e\left(\frac{17}{61}\right)\) | \(e\left(\frac{45}{122}\right)\) | \(e\left(\frac{55}{122}\right)\) | \(e\left(\frac{25}{61}\right)\) | \(e\left(\frac{56}{61}\right)\) | \(e\left(\frac{38}{61}\right)\) | \(e\left(\frac{1}{122}\right)\) | \(e\left(\frac{59}{122}\right)\) |