Basic properties
| Modulus: | \(8640\) | |
| Conductor: | \(864\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{864}(661,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8640.hp
\(\chi_{8640}(121,\cdot)\) \(\chi_{8640}(601,\cdot)\) \(\chi_{8640}(841,\cdot)\) \(\chi_{8640}(1321,\cdot)\) \(\chi_{8640}(1561,\cdot)\) \(\chi_{8640}(2041,\cdot)\) \(\chi_{8640}(2281,\cdot)\) \(\chi_{8640}(2761,\cdot)\) \(\chi_{8640}(3001,\cdot)\) \(\chi_{8640}(3481,\cdot)\) \(\chi_{8640}(3721,\cdot)\) \(\chi_{8640}(4201,\cdot)\) \(\chi_{8640}(4441,\cdot)\) \(\chi_{8640}(4921,\cdot)\) \(\chi_{8640}(5161,\cdot)\) \(\chi_{8640}(5641,\cdot)\) \(\chi_{8640}(5881,\cdot)\) \(\chi_{8640}(6361,\cdot)\) \(\chi_{8640}(6601,\cdot)\) \(\chi_{8640}(7081,\cdot)\) \(\chi_{8640}(7321,\cdot)\) \(\chi_{8640}(7801,\cdot)\) \(\chi_{8640}(8041,\cdot)\) \(\chi_{8640}(8521,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((2431,3781,6401,3457)\) → \((1,e\left(\frac{5}{8}\right),e\left(\frac{4}{9}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 8640 }(121, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{65}{72}\right)\) | \(e\left(\frac{67}{72}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{23}{72}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{11}{36}\right)\) |