Basic properties
Modulus: | \(367\) | |
Conductor: | \(367\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(61\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 367.e
\(\chi_{367}(7,\cdot)\) \(\chi_{367}(8,\cdot)\) \(\chi_{367}(9,\cdot)\) \(\chi_{367}(15,\cdot)\) \(\chi_{367}(25,\cdot)\) \(\chi_{367}(46,\cdot)\) \(\chi_{367}(47,\cdot)\) \(\chi_{367}(49,\cdot)\) \(\chi_{367}(52,\cdot)\) \(\chi_{367}(56,\cdot)\) \(\chi_{367}(59,\cdot)\) \(\chi_{367}(63,\cdot)\) \(\chi_{367}(64,\cdot)\) \(\chi_{367}(72,\cdot)\) \(\chi_{367}(74,\cdot)\) \(\chi_{367}(81,\cdot)\) \(\chi_{367}(87,\cdot)\) \(\chi_{367}(101,\cdot)\) \(\chi_{367}(105,\cdot)\) \(\chi_{367}(106,\cdot)\) \(\chi_{367}(107,\cdot)\) \(\chi_{367}(114,\cdot)\) \(\chi_{367}(120,\cdot)\) \(\chi_{367}(122,\cdot)\) \(\chi_{367}(124,\cdot)\) \(\chi_{367}(132,\cdot)\) \(\chi_{367}(134,\cdot)\) \(\chi_{367}(135,\cdot)\) \(\chi_{367}(137,\cdot)\) \(\chi_{367}(145,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{61})$ |
Fixed field: | Number field defined by a degree 61 polynomial |
Values on generators
\(6\) → \(e\left(\frac{27}{61}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 367 }(63, a) \) | \(1\) | \(1\) | \(e\left(\frac{15}{61}\right)\) | \(e\left(\frac{12}{61}\right)\) | \(e\left(\frac{30}{61}\right)\) | \(e\left(\frac{11}{61}\right)\) | \(e\left(\frac{27}{61}\right)\) | \(e\left(\frac{19}{61}\right)\) | \(e\left(\frac{45}{61}\right)\) | \(e\left(\frac{24}{61}\right)\) | \(e\left(\frac{26}{61}\right)\) | \(e\left(\frac{9}{61}\right)\) |