Basic properties
Modulus: | \(2667\) | |
Conductor: | \(889\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(63\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{889}(886,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2667.ec
\(\chi_{2667}(163,\cdot)\) \(\chi_{2667}(352,\cdot)\) \(\chi_{2667}(415,\cdot)\) \(\chi_{2667}(646,\cdot)\) \(\chi_{2667}(697,\cdot)\) \(\chi_{2667}(709,\cdot)\) \(\chi_{2667}(739,\cdot)\) \(\chi_{2667}(886,\cdot)\) \(\chi_{2667}(898,\cdot)\) \(\chi_{2667}(949,\cdot)\) \(\chi_{2667}(961,\cdot)\) \(\chi_{2667}(970,\cdot)\) \(\chi_{2667}(1192,\cdot)\) \(\chi_{2667}(1222,\cdot)\) \(\chi_{2667}(1264,\cdot)\) \(\chi_{2667}(1285,\cdot)\) \(\chi_{2667}(1339,\cdot)\) \(\chi_{2667}(1390,\cdot)\) \(\chi_{2667}(1432,\cdot)\) \(\chi_{2667}(1537,\cdot)\) \(\chi_{2667}(1612,\cdot)\) \(\chi_{2667}(1822,\cdot)\) \(\chi_{2667}(1936,\cdot)\) \(\chi_{2667}(2020,\cdot)\) \(\chi_{2667}(2053,\cdot)\) \(\chi_{2667}(2062,\cdot)\) \(\chi_{2667}(2074,\cdot)\) \(\chi_{2667}(2116,\cdot)\) \(\chi_{2667}(2200,\cdot)\) \(\chi_{2667}(2230,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((890,1144,2416)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{32}{63}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 2667 }(886, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{13}{63}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(1\) |