Basic properties
| Modulus: | \(9408\) | |
| Conductor: | \(4704\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(168\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4704}(2963,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9408.fu
\(\chi_{9408}(23,\cdot)\) \(\chi_{9408}(359,\cdot)\) \(\chi_{9408}(599,\cdot)\) \(\chi_{9408}(695,\cdot)\) \(\chi_{9408}(935,\cdot)\) \(\chi_{9408}(1031,\cdot)\) \(\chi_{9408}(1271,\cdot)\) \(\chi_{9408}(1367,\cdot)\) \(\chi_{9408}(1607,\cdot)\) \(\chi_{9408}(1703,\cdot)\) \(\chi_{9408}(1943,\cdot)\) \(\chi_{9408}(2279,\cdot)\) \(\chi_{9408}(2375,\cdot)\) \(\chi_{9408}(2711,\cdot)\) \(\chi_{9408}(2951,\cdot)\) \(\chi_{9408}(3047,\cdot)\) \(\chi_{9408}(3287,\cdot)\) \(\chi_{9408}(3383,\cdot)\) \(\chi_{9408}(3623,\cdot)\) \(\chi_{9408}(3719,\cdot)\) \(\chi_{9408}(3959,\cdot)\) \(\chi_{9408}(4055,\cdot)\) \(\chi_{9408}(4295,\cdot)\) \(\chi_{9408}(4631,\cdot)\) \(\chi_{9408}(4727,\cdot)\) \(\chi_{9408}(5063,\cdot)\) \(\chi_{9408}(5303,\cdot)\) \(\chi_{9408}(5399,\cdot)\) \(\chi_{9408}(5639,\cdot)\) \(\chi_{9408}(5735,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{168})$ |
| Fixed field: | Number field defined by a degree 168 polynomial (not computed) |
Values on generators
\((1471,6469,3137,4609)\) → \((-1,e\left(\frac{7}{8}\right),-1,e\left(\frac{19}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 9408 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{103}{168}\right)\) | \(e\left(\frac{95}{168}\right)\) | \(e\left(\frac{55}{56}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{23}{56}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{139}{168}\right)\) |