Basic properties
Modulus: | \(373\) | |
Conductor: | \(373\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(124\) | 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 373.j
\(\chi_{373}(8,\cdot)\) \(\chi_{373}(18,\cdot)\) \(\chi_{373}(19,\cdot)\) \(\chi_{373}(20,\cdot)\) \(\chi_{373}(23,\cdot)\) \(\chi_{373}(33,\cdot)\) \(\chi_{373}(45,\cdot)\) \(\chi_{373}(50,\cdot)\) \(\chi_{373}(56,\cdot)\) \(\chi_{373}(58,\cdot)\) \(\chi_{373}(67,\cdot)\) \(\chi_{373}(74,\cdot)\) \(\chi_{373}(96,\cdot)\) \(\chi_{373}(97,\cdot)\) \(\chi_{373}(113,\cdot)\) \(\chi_{373}(125,\cdot)\) \(\chi_{373}(126,\cdot)\) \(\chi_{373}(129,\cdot)\) \(\chi_{373}(133,\cdot)\) \(\chi_{373}(136,\cdot)\) \(\chi_{373}(139,\cdot)\) \(\chi_{373}(140,\cdot)\) \(\chi_{373}(142,\cdot)\) \(\chi_{373}(145,\cdot)\) \(\chi_{373}(146,\cdot)\) \(\chi_{373}(157,\cdot)\) \(\chi_{373}(161,\cdot)\) \(\chi_{373}(167,\cdot)\) \(\chi_{373}(176,\cdot)\) \(\chi_{373}(185,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{124})$ |
Fixed field: | Number field defined by a degree 124 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{43}{124}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 373 }(136, a) \) | \(-1\) | \(1\) | \(e\left(\frac{43}{124}\right)\) | \(e\left(\frac{33}{62}\right)\) | \(e\left(\frac{43}{62}\right)\) | \(e\left(\frac{75}{124}\right)\) | \(e\left(\frac{109}{124}\right)\) | \(e\left(\frac{41}{62}\right)\) | \(e\left(\frac{5}{124}\right)\) | \(e\left(\frac{2}{31}\right)\) | \(e\left(\frac{59}{62}\right)\) | \(e\left(\frac{119}{124}\right)\) |