Basic properties
| Modulus: | \(8670\) | |
| 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 \(\chi_{289}(121,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8670.cl
\(\chi_{8670}(121,\cdot)\) \(\chi_{8670}(151,\cdot)\) \(\chi_{8670}(331,\cdot)\) \(\chi_{8670}(451,\cdot)\) \(\chi_{8670}(631,\cdot)\) \(\chi_{8670}(661,\cdot)\) \(\chi_{8670}(841,\cdot)\) \(\chi_{8670}(961,\cdot)\) \(\chi_{8670}(1141,\cdot)\) \(\chi_{8670}(1171,\cdot)\) \(\chi_{8670}(1351,\cdot)\) \(\chi_{8670}(1471,\cdot)\) \(\chi_{8670}(1651,\cdot)\) \(\chi_{8670}(1681,\cdot)\) \(\chi_{8670}(1861,\cdot)\) \(\chi_{8670}(1981,\cdot)\) \(\chi_{8670}(2161,\cdot)\) \(\chi_{8670}(2191,\cdot)\) \(\chi_{8670}(2371,\cdot)\) \(\chi_{8670}(2671,\cdot)\) \(\chi_{8670}(2701,\cdot)\) \(\chi_{8670}(2881,\cdot)\) \(\chi_{8670}(3001,\cdot)\) \(\chi_{8670}(3181,\cdot)\) \(\chi_{8670}(3211,\cdot)\) \(\chi_{8670}(3391,\cdot)\) \(\chi_{8670}(3511,\cdot)\) \(\chi_{8670}(3691,\cdot)\) \(\chi_{8670}(3721,\cdot)\) \(\chi_{8670}(3901,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{136})$ |
| Fixed field: | Number field defined by a degree 136 polynomial (not computed) |
Values on generators
\((2891,6937,6361)\) → \((1,1,e\left(\frac{23}{136}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8670 }(121, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{136}\right)\) | \(e\left(\frac{121}{136}\right)\) | \(e\left(\frac{5}{34}\right)\) | \(e\left(\frac{25}{68}\right)\) | \(e\left(\frac{97}{136}\right)\) | \(e\left(\frac{19}{136}\right)\) | \(e\left(\frac{71}{136}\right)\) | \(e\left(\frac{111}{136}\right)\) | \(e\left(\frac{125}{136}\right)\) | \(e\left(\frac{15}{68}\right)\) |