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.ib
\(\chi_{8640}(229,\cdot)\) \(\chi_{8640}(349,\cdot)\) \(\chi_{8640}(589,\cdot)\) \(\chi_{8640}(709,\cdot)\) \(\chi_{8640}(949,\cdot)\) \(\chi_{8640}(1069,\cdot)\) \(\chi_{8640}(1309,\cdot)\) \(\chi_{8640}(1429,\cdot)\) \(\chi_{8640}(1669,\cdot)\) \(\chi_{8640}(1789,\cdot)\) \(\chi_{8640}(2029,\cdot)\) \(\chi_{8640}(2149,\cdot)\) \(\chi_{8640}(2389,\cdot)\) \(\chi_{8640}(2509,\cdot)\) \(\chi_{8640}(2749,\cdot)\) \(\chi_{8640}(2869,\cdot)\) \(\chi_{8640}(3109,\cdot)\) \(\chi_{8640}(3229,\cdot)\) \(\chi_{8640}(3469,\cdot)\) \(\chi_{8640}(3589,\cdot)\) \(\chi_{8640}(3829,\cdot)\) \(\chi_{8640}(3949,\cdot)\) \(\chi_{8640}(4189,\cdot)\) \(\chi_{8640}(4309,\cdot)\) \(\chi_{8640}(4549,\cdot)\) \(\chi_{8640}(4669,\cdot)\) \(\chi_{8640}(4909,\cdot)\) \(\chi_{8640}(5029,\cdot)\) \(\chi_{8640}(5269,\cdot)\) \(\chi_{8640}(5389,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{144})$ |
| Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((2431,3781,6401,3457)\) → \((1,e\left(\frac{9}{16}\right),e\left(\frac{4}{9}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 8640 }(229, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{72}\right)\) | \(e\left(\frac{85}{144}\right)\) | \(e\left(\frac{71}{144}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{13}{48}\right)\) | \(e\left(\frac{19}{72}\right)\) | \(e\left(\frac{91}{144}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{31}{72}\right)\) |