Basic properties
Modulus: | \(2667\) | |
Conductor: | \(889\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{889}(55,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2667.ef
\(\chi_{2667}(55,\cdot)\) \(\chi_{2667}(97,\cdot)\) \(\chi_{2667}(118,\cdot)\) \(\chi_{2667}(139,\cdot)\) \(\chi_{2667}(223,\cdot)\) \(\chi_{2667}(307,\cdot)\) \(\chi_{2667}(370,\cdot)\) \(\chi_{2667}(601,\cdot)\) \(\chi_{2667}(622,\cdot)\) \(\chi_{2667}(664,\cdot)\) \(\chi_{2667}(727,\cdot)\) \(\chi_{2667}(769,\cdot)\) \(\chi_{2667}(853,\cdot)\) \(\chi_{2667}(874,\cdot)\) \(\chi_{2667}(895,\cdot)\) \(\chi_{2667}(937,\cdot)\) \(\chi_{2667}(1126,\cdot)\) \(\chi_{2667}(1189,\cdot)\) \(\chi_{2667}(1210,\cdot)\) \(\chi_{2667}(1252,\cdot)\) \(\chi_{2667}(1273,\cdot)\) \(\chi_{2667}(1315,\cdot)\) \(\chi_{2667}(1420,\cdot)\) \(\chi_{2667}(1462,\cdot)\) \(\chi_{2667}(1483,\cdot)\) \(\chi_{2667}(1567,\cdot)\) \(\chi_{2667}(1609,\cdot)\) \(\chi_{2667}(1630,\cdot)\) \(\chi_{2667}(1861,\cdot)\) \(\chi_{2667}(2071,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((890,1144,2416)\) → \((1,-1,e\left(\frac{29}{126}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 2667 }(55, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{17}{126}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{31}{126}\right)\) | \(e\left(\frac{5}{6}\right)\) |