Basic properties
| Modulus: | \(6069\) | |
| Conductor: | \(289\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(136\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{289}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6069.ck
\(\chi_{6069}(43,\cdot)\) \(\chi_{6069}(127,\cdot)\) \(\chi_{6069}(253,\cdot)\) \(\chi_{6069}(274,\cdot)\) \(\chi_{6069}(400,\cdot)\) \(\chi_{6069}(484,\cdot)\) \(\chi_{6069}(610,\cdot)\) \(\chi_{6069}(631,\cdot)\) \(\chi_{6069}(841,\cdot)\) \(\chi_{6069}(967,\cdot)\) \(\chi_{6069}(988,\cdot)\) \(\chi_{6069}(1114,\cdot)\) \(\chi_{6069}(1198,\cdot)\) \(\chi_{6069}(1324,\cdot)\) \(\chi_{6069}(1345,\cdot)\) \(\chi_{6069}(1471,\cdot)\) \(\chi_{6069}(1681,\cdot)\) \(\chi_{6069}(1702,\cdot)\) \(\chi_{6069}(1828,\cdot)\) \(\chi_{6069}(1912,\cdot)\) \(\chi_{6069}(2038,\cdot)\) \(\chi_{6069}(2059,\cdot)\) \(\chi_{6069}(2185,\cdot)\) \(\chi_{6069}(2269,\cdot)\) \(\chi_{6069}(2395,\cdot)\) \(\chi_{6069}(2416,\cdot)\) \(\chi_{6069}(2542,\cdot)\) \(\chi_{6069}(2626,\cdot)\) \(\chi_{6069}(2752,\cdot)\) \(\chi_{6069}(2773,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{136})$ |
| Fixed field: | Number field defined by a degree 136 polynomial (not computed) |
Values on generators
\((2024,4336,3760)\) → \((1,1,e\left(\frac{113}{136}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(19\) | \(20\) |
| \( \chi_{ 6069 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{68}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{37}{136}\right)\) | \(e\left(\frac{41}{68}\right)\) | \(e\left(\frac{19}{136}\right)\) | \(e\left(\frac{15}{136}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{43}{68}\right)\) | \(e\left(\frac{1}{136}\right)\) |