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 \(\chi_{4320}(1723,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8640.hj
\(\chi_{8640}(103,\cdot)\) \(\chi_{8640}(247,\cdot)\) \(\chi_{8640}(583,\cdot)\) \(\chi_{8640}(727,\cdot)\) \(\chi_{8640}(1543,\cdot)\) \(\chi_{8640}(1687,\cdot)\) \(\chi_{8640}(2023,\cdot)\) \(\chi_{8640}(2167,\cdot)\) \(\chi_{8640}(2983,\cdot)\) \(\chi_{8640}(3127,\cdot)\) \(\chi_{8640}(3463,\cdot)\) \(\chi_{8640}(3607,\cdot)\) \(\chi_{8640}(4423,\cdot)\) \(\chi_{8640}(4567,\cdot)\) \(\chi_{8640}(4903,\cdot)\) \(\chi_{8640}(5047,\cdot)\) \(\chi_{8640}(5863,\cdot)\) \(\chi_{8640}(6007,\cdot)\) \(\chi_{8640}(6343,\cdot)\) \(\chi_{8640}(6487,\cdot)\) \(\chi_{8640}(7303,\cdot)\) \(\chi_{8640}(7447,\cdot)\) \(\chi_{8640}(7783,\cdot)\) \(\chi_{8640}(7927,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((2431,3781,6401,3457)\) → \((-1,e\left(\frac{1}{8}\right),e\left(\frac{7}{9}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 8640 }(103, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{17}{72}\right)\) | \(e\left(\frac{25}{72}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{47}{72}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{35}{36}\right)\) |