Basic properties
| Modulus: | \(9408\) | |
| Conductor: | \(9408\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(336\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9408.fw
\(\chi_{9408}(11,\cdot)\) \(\chi_{9408}(107,\cdot)\) \(\chi_{9408}(179,\cdot)\) \(\chi_{9408}(347,\cdot)\) \(\chi_{9408}(443,\cdot)\) \(\chi_{9408}(515,\cdot)\) \(\chi_{9408}(611,\cdot)\) \(\chi_{9408}(683,\cdot)\) \(\chi_{9408}(779,\cdot)\) \(\chi_{9408}(947,\cdot)\) \(\chi_{9408}(1019,\cdot)\) \(\chi_{9408}(1115,\cdot)\) \(\chi_{9408}(1187,\cdot)\) \(\chi_{9408}(1283,\cdot)\) \(\chi_{9408}(1355,\cdot)\) \(\chi_{9408}(1523,\cdot)\) \(\chi_{9408}(1619,\cdot)\) \(\chi_{9408}(1691,\cdot)\) \(\chi_{9408}(1787,\cdot)\) \(\chi_{9408}(1859,\cdot)\) \(\chi_{9408}(1955,\cdot)\) \(\chi_{9408}(2123,\cdot)\) \(\chi_{9408}(2195,\cdot)\) \(\chi_{9408}(2291,\cdot)\) \(\chi_{9408}(2363,\cdot)\) \(\chi_{9408}(2459,\cdot)\) \(\chi_{9408}(2531,\cdot)\) \(\chi_{9408}(2699,\cdot)\) \(\chi_{9408}(2795,\cdot)\) \(\chi_{9408}(2867,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{336})$ |
| Fixed field: | Number field defined by a degree 336 polynomial (not computed) |
Values on generators
\((1471,6469,3137,4609)\) → \((-1,e\left(\frac{5}{16}\right),-1,e\left(\frac{20}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 9408 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{145}{336}\right)\) | \(e\left(\frac{221}{336}\right)\) | \(e\left(\frac{13}{112}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{1}{48}\right)\) | \(e\left(\frac{95}{168}\right)\) | \(e\left(\frac{145}{168}\right)\) | \(e\left(\frac{9}{112}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{97}{336}\right)\) |