Basic properties
Modulus: | \(4998\) | |
Conductor: | \(2499\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2499}(47,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4998.cp
\(\chi_{4998}(47,\cdot)\) \(\chi_{4998}(89,\cdot)\) \(\chi_{4998}(353,\cdot)\) \(\chi_{4998}(395,\cdot)\) \(\chi_{4998}(761,\cdot)\) \(\chi_{4998}(1067,\cdot)\) \(\chi_{4998}(1475,\cdot)\) \(\chi_{4998}(1517,\cdot)\) \(\chi_{4998}(1781,\cdot)\) \(\chi_{4998}(1823,\cdot)\) \(\chi_{4998}(2189,\cdot)\) \(\chi_{4998}(2231,\cdot)\) \(\chi_{4998}(2495,\cdot)\) \(\chi_{4998}(2537,\cdot)\) \(\chi_{4998}(2903,\cdot)\) \(\chi_{4998}(2945,\cdot)\) \(\chi_{4998}(3209,\cdot)\) \(\chi_{4998}(3251,\cdot)\) \(\chi_{4998}(3617,\cdot)\) \(\chi_{4998}(3659,\cdot)\) \(\chi_{4998}(3923,\cdot)\) \(\chi_{4998}(3965,\cdot)\) \(\chi_{4998}(4373,\cdot)\) \(\chi_{4998}(4679,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1667,2551,4117)\) → \((-1,e\left(\frac{5}{42}\right),i)\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 4998 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{1}{28}\right)\) |