Basic properties
| Modulus: | \(9408\) | |
| Conductor: | \(9408\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(112\) | 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.fm
\(\chi_{9408}(125,\cdot)\) \(\chi_{9408}(461,\cdot)\) \(\chi_{9408}(629,\cdot)\) \(\chi_{9408}(797,\cdot)\) \(\chi_{9408}(965,\cdot)\) \(\chi_{9408}(1133,\cdot)\) \(\chi_{9408}(1301,\cdot)\) \(\chi_{9408}(1637,\cdot)\) \(\chi_{9408}(1805,\cdot)\) \(\chi_{9408}(1973,\cdot)\) \(\chi_{9408}(2141,\cdot)\) \(\chi_{9408}(2309,\cdot)\) \(\chi_{9408}(2477,\cdot)\) \(\chi_{9408}(2813,\cdot)\) \(\chi_{9408}(2981,\cdot)\) \(\chi_{9408}(3149,\cdot)\) \(\chi_{9408}(3317,\cdot)\) \(\chi_{9408}(3485,\cdot)\) \(\chi_{9408}(3653,\cdot)\) \(\chi_{9408}(3989,\cdot)\) \(\chi_{9408}(4157,\cdot)\) \(\chi_{9408}(4325,\cdot)\) \(\chi_{9408}(4493,\cdot)\) \(\chi_{9408}(4661,\cdot)\) \(\chi_{9408}(4829,\cdot)\) \(\chi_{9408}(5165,\cdot)\) \(\chi_{9408}(5333,\cdot)\) \(\chi_{9408}(5501,\cdot)\) \(\chi_{9408}(5669,\cdot)\) \(\chi_{9408}(5837,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{112})$ |
| Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\((1471,6469,3137,4609)\) → \((1,e\left(\frac{3}{16}\right),-1,e\left(\frac{1}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 9408 }(125, a) \) | \(1\) | \(1\) | \(e\left(\frac{85}{112}\right)\) | \(e\left(\frac{33}{112}\right)\) | \(e\left(\frac{19}{112}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{47}{56}\right)\) | \(e\left(\frac{29}{56}\right)\) | \(e\left(\frac{95}{112}\right)\) | \(1\) | \(e\left(\frac{109}{112}\right)\) |