Basic properties
Modulus: | \(4998\) | |
Conductor: | \(833\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(112\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{833}(139,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4998.cr
\(\chi_{4998}(139,\cdot)\) \(\chi_{4998}(181,\cdot)\) \(\chi_{4998}(265,\cdot)\) \(\chi_{4998}(517,\cdot)\) \(\chi_{4998}(601,\cdot)\) \(\chi_{4998}(643,\cdot)\) \(\chi_{4998}(811,\cdot)\) \(\chi_{4998}(853,\cdot)\) \(\chi_{4998}(895,\cdot)\) \(\chi_{4998}(1231,\cdot)\) \(\chi_{4998}(1315,\cdot)\) \(\chi_{4998}(1357,\cdot)\) \(\chi_{4998}(1399,\cdot)\) \(\chi_{4998}(1525,\cdot)\) \(\chi_{4998}(1609,\cdot)\) \(\chi_{4998}(1693,\cdot)\) \(\chi_{4998}(1945,\cdot)\) \(\chi_{4998}(2029,\cdot)\) \(\chi_{4998}(2071,\cdot)\) \(\chi_{4998}(2113,\cdot)\) \(\chi_{4998}(2239,\cdot)\) \(\chi_{4998}(2281,\cdot)\) \(\chi_{4998}(2323,\cdot)\) \(\chi_{4998}(2407,\cdot)\) \(\chi_{4998}(2659,\cdot)\) \(\chi_{4998}(2785,\cdot)\) \(\chi_{4998}(2827,\cdot)\) \(\chi_{4998}(2953,\cdot)\) \(\chi_{4998}(2995,\cdot)\) \(\chi_{4998}(3121,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{112})$ |
Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\((1667,2551,4117)\) → \((1,e\left(\frac{5}{14}\right),e\left(\frac{1}{16}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 4998 }(139, a) \) | \(1\) | \(1\) | \(e\left(\frac{75}{112}\right)\) | \(e\left(\frac{81}{112}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{57}{112}\right)\) | \(e\left(\frac{19}{56}\right)\) | \(e\left(\frac{27}{112}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{55}{112}\right)\) | \(e\left(\frac{5}{112}\right)\) |