Basic properties
| Modulus: | \(373\) | |
| Conductor: | \(373\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(186\) | 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 373.k
\(\chi_{373}(3,\cdot)\) \(\chi_{373}(4,\cdot)\) \(\chi_{373}(10,\cdot)\) \(\chi_{373}(25,\cdot)\) \(\chi_{373}(36,\cdot)\) \(\chi_{373}(37,\cdot)\) \(\chi_{373}(48,\cdot)\) \(\chi_{373}(59,\cdot)\) \(\chi_{373}(63,\cdot)\) \(\chi_{373}(71,\cdot)\) \(\chi_{373}(90,\cdot)\) \(\chi_{373}(103,\cdot)\) \(\chi_{373}(106,\cdot)\) \(\chi_{373}(112,\cdot)\) \(\chi_{373}(114,\cdot)\) \(\chi_{373}(116,\cdot)\) \(\chi_{373}(117,\cdot)\) \(\chi_{373}(120,\cdot)\) \(\chi_{373}(121,\cdot)\) \(\chi_{373}(122,\cdot)\) \(\chi_{373}(123,\cdot)\) \(\chi_{373}(134,\cdot)\) \(\chi_{373}(138,\cdot)\) \(\chi_{373}(147,\cdot)\) \(\chi_{373}(153,\cdot)\) \(\chi_{373}(164,\cdot)\) \(\chi_{373}(181,\cdot)\) \(\chi_{373}(194,\cdot)\) \(\chi_{373}(196,\cdot)\) \(\chi_{373}(198,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{93})$ |
| Fixed field: | Number field defined by a degree 186 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{131}{186}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 373 }(147, a) \) | \(1\) | \(1\) | \(e\left(\frac{131}{186}\right)\) | \(e\left(\frac{58}{93}\right)\) | \(e\left(\frac{38}{93}\right)\) | \(e\left(\frac{5}{186}\right)\) | \(e\left(\frac{61}{186}\right)\) | \(e\left(\frac{14}{31}\right)\) | \(e\left(\frac{7}{62}\right)\) | \(e\left(\frac{23}{93}\right)\) | \(e\left(\frac{68}{93}\right)\) | \(e\left(\frac{103}{186}\right)\) |