Basic properties
| Modulus: | \(8112\) | |
| Conductor: | \(1352\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1352}(683,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8112.fo
\(\chi_{8112}(7,\cdot)\) \(\chi_{8112}(487,\cdot)\) \(\chi_{8112}(535,\cdot)\) \(\chi_{8112}(583,\cdot)\) \(\chi_{8112}(631,\cdot)\) \(\chi_{8112}(1111,\cdot)\) \(\chi_{8112}(1159,\cdot)\) \(\chi_{8112}(1207,\cdot)\) \(\chi_{8112}(1255,\cdot)\) \(\chi_{8112}(1735,\cdot)\) \(\chi_{8112}(1783,\cdot)\) \(\chi_{8112}(1831,\cdot)\) \(\chi_{8112}(1879,\cdot)\) \(\chi_{8112}(2359,\cdot)\) \(\chi_{8112}(2407,\cdot)\) \(\chi_{8112}(2503,\cdot)\) \(\chi_{8112}(2983,\cdot)\) \(\chi_{8112}(3031,\cdot)\) \(\chi_{8112}(3079,\cdot)\) \(\chi_{8112}(3127,\cdot)\) \(\chi_{8112}(3607,\cdot)\) \(\chi_{8112}(3655,\cdot)\) \(\chi_{8112}(3703,\cdot)\) \(\chi_{8112}(3751,\cdot)\) \(\chi_{8112}(4231,\cdot)\) \(\chi_{8112}(4279,\cdot)\) \(\chi_{8112}(4327,\cdot)\) \(\chi_{8112}(4855,\cdot)\) \(\chi_{8112}(4903,\cdot)\) \(\chi_{8112}(4951,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((5071,6085,2705,3889)\) → \((-1,-1,1,e\left(\frac{107}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8112 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{139}{156}\right)\) | \(e\left(\frac{101}{156}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{22}{39}\right)\) |