Basic properties
| Modulus: | \(8640\) | |
| Conductor: | \(8640\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(144\) | 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 8640.hz
\(\chi_{8640}(59,\cdot)\) \(\chi_{8640}(299,\cdot)\) \(\chi_{8640}(419,\cdot)\) \(\chi_{8640}(659,\cdot)\) \(\chi_{8640}(779,\cdot)\) \(\chi_{8640}(1019,\cdot)\) \(\chi_{8640}(1139,\cdot)\) \(\chi_{8640}(1379,\cdot)\) \(\chi_{8640}(1499,\cdot)\) \(\chi_{8640}(1739,\cdot)\) \(\chi_{8640}(1859,\cdot)\) \(\chi_{8640}(2099,\cdot)\) \(\chi_{8640}(2219,\cdot)\) \(\chi_{8640}(2459,\cdot)\) \(\chi_{8640}(2579,\cdot)\) \(\chi_{8640}(2819,\cdot)\) \(\chi_{8640}(2939,\cdot)\) \(\chi_{8640}(3179,\cdot)\) \(\chi_{8640}(3299,\cdot)\) \(\chi_{8640}(3539,\cdot)\) \(\chi_{8640}(3659,\cdot)\) \(\chi_{8640}(3899,\cdot)\) \(\chi_{8640}(4019,\cdot)\) \(\chi_{8640}(4259,\cdot)\) \(\chi_{8640}(4379,\cdot)\) \(\chi_{8640}(4619,\cdot)\) \(\chi_{8640}(4739,\cdot)\) \(\chi_{8640}(4979,\cdot)\) \(\chi_{8640}(5099,\cdot)\) \(\chi_{8640}(5339,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{144})$ |
| Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((2431,3781,6401,3457)\) → \((-1,e\left(\frac{1}{16}\right),e\left(\frac{5}{18}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 8640 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{72}\right)\) | \(e\left(\frac{61}{144}\right)\) | \(e\left(\frac{95}{144}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{13}{48}\right)\) | \(e\left(\frac{67}{72}\right)\) | \(e\left(\frac{139}{144}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{35}{48}\right)\) | \(e\left(\frac{43}{72}\right)\) |