Basic properties
| Modulus: | \(4704\) | |
| Conductor: | \(1568\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(168\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1568}(115,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4704.eu
\(\chi_{4704}(115,\cdot)\) \(\chi_{4704}(187,\cdot)\) \(\chi_{4704}(283,\cdot)\) \(\chi_{4704}(355,\cdot)\) \(\chi_{4704}(451,\cdot)\) \(\chi_{4704}(523,\cdot)\) \(\chi_{4704}(691,\cdot)\) \(\chi_{4704}(787,\cdot)\) \(\chi_{4704}(859,\cdot)\) \(\chi_{4704}(955,\cdot)\) \(\chi_{4704}(1027,\cdot)\) \(\chi_{4704}(1123,\cdot)\) \(\chi_{4704}(1291,\cdot)\) \(\chi_{4704}(1363,\cdot)\) \(\chi_{4704}(1459,\cdot)\) \(\chi_{4704}(1531,\cdot)\) \(\chi_{4704}(1627,\cdot)\) \(\chi_{4704}(1699,\cdot)\) \(\chi_{4704}(1867,\cdot)\) \(\chi_{4704}(1963,\cdot)\) \(\chi_{4704}(2035,\cdot)\) \(\chi_{4704}(2131,\cdot)\) \(\chi_{4704}(2203,\cdot)\) \(\chi_{4704}(2299,\cdot)\) \(\chi_{4704}(2467,\cdot)\) \(\chi_{4704}(2539,\cdot)\) \(\chi_{4704}(2635,\cdot)\) \(\chi_{4704}(2707,\cdot)\) \(\chi_{4704}(2803,\cdot)\) \(\chi_{4704}(2875,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{168})$ |
| Fixed field: | Number field defined by a degree 168 polynomial (not computed) |
Values on generators
\((1471,1765,3137,4609)\) → \((-1,e\left(\frac{7}{8}\right),1,e\left(\frac{25}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 4704 }(115, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{168}\right)\) | \(e\left(\frac{115}{168}\right)\) | \(e\left(\frac{43}{56}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{19}{56}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{155}{168}\right)\) |