Basic properties
| Modulus: | \(7942\) | |
| Conductor: | \(3971\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(342\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3971}(21,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7942.bm
\(\chi_{7942}(21,\cdot)\) \(\chi_{7942}(109,\cdot)\) \(\chi_{7942}(219,\cdot)\) \(\chi_{7942}(241,\cdot)\) \(\chi_{7942}(395,\cdot)\) \(\chi_{7942}(439,\cdot)\) \(\chi_{7942}(527,\cdot)\) \(\chi_{7942}(637,\cdot)\) \(\chi_{7942}(659,\cdot)\) \(\chi_{7942}(725,\cdot)\) \(\chi_{7942}(813,\cdot)\) \(\chi_{7942}(857,\cdot)\) \(\chi_{7942}(945,\cdot)\) \(\chi_{7942}(1077,\cdot)\) \(\chi_{7942}(1143,\cdot)\) \(\chi_{7942}(1231,\cdot)\) \(\chi_{7942}(1275,\cdot)\) \(\chi_{7942}(1363,\cdot)\) \(\chi_{7942}(1473,\cdot)\) \(\chi_{7942}(1495,\cdot)\) \(\chi_{7942}(1561,\cdot)\) \(\chi_{7942}(1649,\cdot)\) \(\chi_{7942}(1693,\cdot)\) \(\chi_{7942}(1781,\cdot)\) \(\chi_{7942}(1891,\cdot)\) \(\chi_{7942}(1913,\cdot)\) \(\chi_{7942}(1979,\cdot)\) \(\chi_{7942}(2111,\cdot)\) \(\chi_{7942}(2199,\cdot)\) \(\chi_{7942}(2309,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((5777,6139)\) → \((-1,e\left(\frac{289}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 7942 }(21, a) \) | \(1\) | \(1\) | \(e\left(\frac{157}{342}\right)\) | \(e\left(\frac{8}{171}\right)\) | \(e\left(\frac{29}{114}\right)\) | \(e\left(\frac{157}{171}\right)\) | \(e\left(\frac{88}{171}\right)\) | \(e\left(\frac{173}{342}\right)\) | \(e\left(\frac{163}{342}\right)\) | \(e\left(\frac{122}{171}\right)\) | \(e\left(\frac{64}{171}\right)\) | \(e\left(\frac{16}{171}\right)\) |