Basic properties
| Modulus: | \(8112\) | |
| Conductor: | \(2704\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2704}(181,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8112.dx
\(\chi_{8112}(181,\cdot)\) \(\chi_{8112}(493,\cdot)\) \(\chi_{8112}(805,\cdot)\) \(\chi_{8112}(1117,\cdot)\) \(\chi_{8112}(1429,\cdot)\) \(\chi_{8112}(1741,\cdot)\) \(\chi_{8112}(2053,\cdot)\) \(\chi_{8112}(2677,\cdot)\) \(\chi_{8112}(2989,\cdot)\) \(\chi_{8112}(3301,\cdot)\) \(\chi_{8112}(3613,\cdot)\) \(\chi_{8112}(3925,\cdot)\) \(\chi_{8112}(4237,\cdot)\) \(\chi_{8112}(4549,\cdot)\) \(\chi_{8112}(4861,\cdot)\) \(\chi_{8112}(5173,\cdot)\) \(\chi_{8112}(5485,\cdot)\) \(\chi_{8112}(5797,\cdot)\) \(\chi_{8112}(6109,\cdot)\) \(\chi_{8112}(6733,\cdot)\) \(\chi_{8112}(7045,\cdot)\) \(\chi_{8112}(7357,\cdot)\) \(\chi_{8112}(7669,\cdot)\) \(\chi_{8112}(7981,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((5071,6085,2705,3889)\) → \((1,i,1,e\left(\frac{21}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8112 }(181, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(i\) | \(-1\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{23}{52}\right)\) |