Basic properties
| Modulus: | \(8640\) | |
| Conductor: | \(4320\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4320}(3283,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8640.hn
\(\chi_{8640}(7,\cdot)\) \(\chi_{8640}(823,\cdot)\) \(\chi_{8640}(967,\cdot)\) \(\chi_{8640}(1303,\cdot)\) \(\chi_{8640}(1447,\cdot)\) \(\chi_{8640}(2263,\cdot)\) \(\chi_{8640}(2407,\cdot)\) \(\chi_{8640}(2743,\cdot)\) \(\chi_{8640}(2887,\cdot)\) \(\chi_{8640}(3703,\cdot)\) \(\chi_{8640}(3847,\cdot)\) \(\chi_{8640}(4183,\cdot)\) \(\chi_{8640}(4327,\cdot)\) \(\chi_{8640}(5143,\cdot)\) \(\chi_{8640}(5287,\cdot)\) \(\chi_{8640}(5623,\cdot)\) \(\chi_{8640}(5767,\cdot)\) \(\chi_{8640}(6583,\cdot)\) \(\chi_{8640}(6727,\cdot)\) \(\chi_{8640}(7063,\cdot)\) \(\chi_{8640}(7207,\cdot)\) \(\chi_{8640}(8023,\cdot)\) \(\chi_{8640}(8167,\cdot)\) \(\chi_{8640}(8503,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((2431,3781,6401,3457)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{2}{9}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 8640 }(7063, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{55}{72}\right)\) | \(e\left(\frac{11}{72}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{25}{72}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{1}{36}\right)\) |