Basic properties
| Modulus: | \(8640\) | |
| Conductor: | \(1728\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(144\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1728}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8640.hw
\(\chi_{8640}(61,\cdot)\) \(\chi_{8640}(301,\cdot)\) \(\chi_{8640}(421,\cdot)\) \(\chi_{8640}(661,\cdot)\) \(\chi_{8640}(781,\cdot)\) \(\chi_{8640}(1021,\cdot)\) \(\chi_{8640}(1141,\cdot)\) \(\chi_{8640}(1381,\cdot)\) \(\chi_{8640}(1501,\cdot)\) \(\chi_{8640}(1741,\cdot)\) \(\chi_{8640}(1861,\cdot)\) \(\chi_{8640}(2101,\cdot)\) \(\chi_{8640}(2221,\cdot)\) \(\chi_{8640}(2461,\cdot)\) \(\chi_{8640}(2581,\cdot)\) \(\chi_{8640}(2821,\cdot)\) \(\chi_{8640}(2941,\cdot)\) \(\chi_{8640}(3181,\cdot)\) \(\chi_{8640}(3301,\cdot)\) \(\chi_{8640}(3541,\cdot)\) \(\chi_{8640}(3661,\cdot)\) \(\chi_{8640}(3901,\cdot)\) \(\chi_{8640}(4021,\cdot)\) \(\chi_{8640}(4261,\cdot)\) \(\chi_{8640}(4381,\cdot)\) \(\chi_{8640}(4621,\cdot)\) \(\chi_{8640}(4741,\cdot)\) \(\chi_{8640}(4981,\cdot)\) \(\chi_{8640}(5101,\cdot)\) \(\chi_{8640}(5341,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{144})$ |
| Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((2431,3781,6401,3457)\) → \((1,e\left(\frac{3}{16}\right),e\left(\frac{8}{9}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 8640 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{72}\right)\) | \(e\left(\frac{71}{144}\right)\) | \(e\left(\frac{133}{144}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{47}{48}\right)\) | \(e\left(\frac{29}{72}\right)\) | \(e\left(\frac{137}{144}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{1}{48}\right)\) | \(e\left(\frac{53}{72}\right)\) |