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 \(\chi_{889}(79,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2667.eb
\(\chi_{2667}(79,\cdot)\) \(\chi_{2667}(88,\cdot)\) \(\chi_{2667}(121,\cdot)\) \(\chi_{2667}(142,\cdot)\) \(\chi_{2667}(247,\cdot)\) \(\chi_{2667}(289,\cdot)\) \(\chi_{2667}(298,\cdot)\) \(\chi_{2667}(394,\cdot)\) \(\chi_{2667}(529,\cdot)\) \(\chi_{2667}(550,\cdot)\) \(\chi_{2667}(592,\cdot)\) \(\chi_{2667}(676,\cdot)\) \(\chi_{2667}(793,\cdot)\) \(\chi_{2667}(844,\cdot)\) \(\chi_{2667}(877,\cdot)\) \(\chi_{2667}(907,\cdot)\) \(\chi_{2667}(919,\cdot)\) \(\chi_{2667}(1033,\cdot)\) \(\chi_{2667}(1087,\cdot)\) \(\chi_{2667}(1129,\cdot)\) \(\chi_{2667}(1213,\cdot)\) \(\chi_{2667}(1306,\cdot)\) \(\chi_{2667}(1423,\cdot)\) \(\chi_{2667}(1495,\cdot)\) \(\chi_{2667}(1558,\cdot)\) \(\chi_{2667}(1789,\cdot)\) \(\chi_{2667}(1852,\cdot)\) \(\chi_{2667}(2041,\cdot)\) \(\chi_{2667}(2104,\cdot)\) \(\chi_{2667}(2221,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((890,1144,2416)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{50}{63}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 2667 }(79, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{1}{3}\right)\) |