Basic properties
Modulus: | \(373\) | |
Conductor: | \(373\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(93\) | 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.i
\(\chi_{373}(9,\cdot)\) \(\chi_{373}(16,\cdot)\) \(\chi_{373}(21,\cdot)\) \(\chi_{373}(28,\cdot)\) \(\chi_{373}(29,\cdot)\) \(\chi_{373}(38,\cdot)\) \(\chi_{373}(39,\cdot)\) \(\chi_{373}(40,\cdot)\) \(\chi_{373}(46,\cdot)\) \(\chi_{373}(51,\cdot)\) \(\chi_{373}(52,\cdot)\) \(\chi_{373}(66,\cdot)\) \(\chi_{373}(68,\cdot)\) \(\chi_{373}(70,\cdot)\) \(\chi_{373}(73,\cdot)\) \(\chi_{373}(81,\cdot)\) \(\chi_{373}(83,\cdot)\) \(\chi_{373}(93,\cdot)\) \(\chi_{373}(94,\cdot)\) \(\chi_{373}(95,\cdot)\) \(\chi_{373}(100,\cdot)\) \(\chi_{373}(101,\cdot)\) \(\chi_{373}(107,\cdot)\) \(\chi_{373}(108,\cdot)\) \(\chi_{373}(115,\cdot)\) \(\chi_{373}(124,\cdot)\) \(\chi_{373}(130,\cdot)\) \(\chi_{373}(148,\cdot)\) \(\chi_{373}(165,\cdot)\) \(\chi_{373}(170,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{93})$ |
Fixed field: | Number field defined by a degree 93 polynomial |
Values on generators
\(2\) → \(e\left(\frac{55}{93}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 373 }(179, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{93}\right)\) | \(e\left(\frac{70}{93}\right)\) | \(e\left(\frac{17}{93}\right)\) | \(e\left(\frac{88}{93}\right)\) | \(e\left(\frac{32}{93}\right)\) | \(e\left(\frac{3}{31}\right)\) | \(e\left(\frac{24}{31}\right)\) | \(e\left(\frac{47}{93}\right)\) | \(e\left(\frac{50}{93}\right)\) | \(e\left(\frac{83}{93}\right)\) |