Basic properties
| Modulus: | \(9408\) | |
| Conductor: | \(3136\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(336\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3136}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9408.gc
\(\chi_{9408}(37,\cdot)\) \(\chi_{9408}(109,\cdot)\) \(\chi_{9408}(205,\cdot)\) \(\chi_{9408}(277,\cdot)\) \(\chi_{9408}(445,\cdot)\) \(\chi_{9408}(541,\cdot)\) \(\chi_{9408}(613,\cdot)\) \(\chi_{9408}(709,\cdot)\) \(\chi_{9408}(781,\cdot)\) \(\chi_{9408}(877,\cdot)\) \(\chi_{9408}(1045,\cdot)\) \(\chi_{9408}(1117,\cdot)\) \(\chi_{9408}(1213,\cdot)\) \(\chi_{9408}(1285,\cdot)\) \(\chi_{9408}(1381,\cdot)\) \(\chi_{9408}(1453,\cdot)\) \(\chi_{9408}(1621,\cdot)\) \(\chi_{9408}(1717,\cdot)\) \(\chi_{9408}(1789,\cdot)\) \(\chi_{9408}(1885,\cdot)\) \(\chi_{9408}(1957,\cdot)\) \(\chi_{9408}(2053,\cdot)\) \(\chi_{9408}(2221,\cdot)\) \(\chi_{9408}(2293,\cdot)\) \(\chi_{9408}(2389,\cdot)\) \(\chi_{9408}(2461,\cdot)\) \(\chi_{9408}(2557,\cdot)\) \(\chi_{9408}(2629,\cdot)\) \(\chi_{9408}(2797,\cdot)\) \(\chi_{9408}(2893,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{336})$ |
| Fixed field: | Number field defined by a degree 336 polynomial (not computed) |
Values on generators
\((1471,6469,3137,4609)\) → \((1,e\left(\frac{9}{16}\right),1,e\left(\frac{16}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 9408 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{221}{336}\right)\) | \(e\left(\frac{97}{336}\right)\) | \(e\left(\frac{65}{112}\right)\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{29}{48}\right)\) | \(e\left(\frac{139}{168}\right)\) | \(e\left(\frac{53}{168}\right)\) | \(e\left(\frac{101}{112}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{149}{336}\right)\) |