Basic properties
| Modulus: | \(8044\) | |
| Conductor: | \(2011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(67\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2011}(133,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8044.q
\(\chi_{8044}(133,\cdot)\) \(\chi_{8044}(321,\cdot)\) \(\chi_{8044}(445,\cdot)\) \(\chi_{8044}(857,\cdot)\) \(\chi_{8044}(1013,\cdot)\) \(\chi_{8044}(1077,\cdot)\) \(\chi_{8044}(1269,\cdot)\) \(\chi_{8044}(1333,\cdot)\) \(\chi_{8044}(1365,\cdot)\) \(\chi_{8044}(1561,\cdot)\) \(\chi_{8044}(1589,\cdot)\) \(\chi_{8044}(1593,\cdot)\) \(\chi_{8044}(1601,\cdot)\) \(\chi_{8044}(1625,\cdot)\) \(\chi_{8044}(1633,\cdot)\) \(\chi_{8044}(2085,\cdot)\) \(\chi_{8044}(2193,\cdot)\) \(\chi_{8044}(2289,\cdot)\) \(\chi_{8044}(2337,\cdot)\) \(\chi_{8044}(2353,\cdot)\) \(\chi_{8044}(2445,\cdot)\) \(\chi_{8044}(2473,\cdot)\) \(\chi_{8044}(2561,\cdot)\) \(\chi_{8044}(2565,\cdot)\) \(\chi_{8044}(2725,\cdot)\) \(\chi_{8044}(2765,\cdot)\) \(\chi_{8044}(2861,\cdot)\) \(\chi_{8044}(2877,\cdot)\) \(\chi_{8044}(3157,\cdot)\) \(\chi_{8044}(3297,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{67})$ |
| Fixed field: | Number field defined by a degree 67 polynomial |
Values on generators
\((4023,4025)\) → \((1,e\left(\frac{32}{67}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8044 }(133, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{67}\right)\) | \(e\left(\frac{5}{67}\right)\) | \(e\left(\frac{3}{67}\right)\) | \(e\left(\frac{64}{67}\right)\) | \(e\left(\frac{19}{67}\right)\) | \(e\left(\frac{41}{67}\right)\) | \(e\left(\frac{37}{67}\right)\) | \(e\left(\frac{49}{67}\right)\) | \(e\left(\frac{31}{67}\right)\) | \(e\left(\frac{35}{67}\right)\) |