Basic properties
| Modulus: | \(8512\) | |
| Conductor: | \(1216\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(144\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1216}(1211,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8512.ma
\(\chi_{8512}(155,\cdot)\) \(\chi_{8512}(211,\cdot)\) \(\chi_{8512}(547,\cdot)\) \(\chi_{8512}(603,\cdot)\) \(\chi_{8512}(659,\cdot)\) \(\chi_{8512}(827,\cdot)\) \(\chi_{8512}(1219,\cdot)\) \(\chi_{8512}(1275,\cdot)\) \(\chi_{8512}(1611,\cdot)\) \(\chi_{8512}(1667,\cdot)\) \(\chi_{8512}(1723,\cdot)\) \(\chi_{8512}(1891,\cdot)\) \(\chi_{8512}(2283,\cdot)\) \(\chi_{8512}(2339,\cdot)\) \(\chi_{8512}(2675,\cdot)\) \(\chi_{8512}(2731,\cdot)\) \(\chi_{8512}(2787,\cdot)\) \(\chi_{8512}(2955,\cdot)\) \(\chi_{8512}(3347,\cdot)\) \(\chi_{8512}(3403,\cdot)\) \(\chi_{8512}(3739,\cdot)\) \(\chi_{8512}(3795,\cdot)\) \(\chi_{8512}(3851,\cdot)\) \(\chi_{8512}(4019,\cdot)\) \(\chi_{8512}(4411,\cdot)\) \(\chi_{8512}(4467,\cdot)\) \(\chi_{8512}(4803,\cdot)\) \(\chi_{8512}(4859,\cdot)\) \(\chi_{8512}(4915,\cdot)\) \(\chi_{8512}(5083,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{144})$ |
| Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((5055,6917,7297,3137)\) → \((-1,e\left(\frac{1}{16}\right),1,e\left(\frac{7}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 8512 }(4859, a) \) | \(1\) | \(1\) | \(e\left(\frac{107}{144}\right)\) | \(e\left(\frac{41}{144}\right)\) | \(e\left(\frac{35}{72}\right)\) | \(e\left(\frac{23}{48}\right)\) | \(e\left(\frac{127}{144}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{11}{72}\right)\) | \(e\left(\frac{41}{72}\right)\) | \(e\left(\frac{11}{48}\right)\) |