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 \(\chi_{4320}(3949,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8640.he
\(\chi_{8640}(169,\cdot)\) \(\chi_{8640}(409,\cdot)\) \(\chi_{8640}(889,\cdot)\) \(\chi_{8640}(1129,\cdot)\) \(\chi_{8640}(1609,\cdot)\) \(\chi_{8640}(1849,\cdot)\) \(\chi_{8640}(2329,\cdot)\) \(\chi_{8640}(2569,\cdot)\) \(\chi_{8640}(3049,\cdot)\) \(\chi_{8640}(3289,\cdot)\) \(\chi_{8640}(3769,\cdot)\) \(\chi_{8640}(4009,\cdot)\) \(\chi_{8640}(4489,\cdot)\) \(\chi_{8640}(4729,\cdot)\) \(\chi_{8640}(5209,\cdot)\) \(\chi_{8640}(5449,\cdot)\) \(\chi_{8640}(5929,\cdot)\) \(\chi_{8640}(6169,\cdot)\) \(\chi_{8640}(6649,\cdot)\) \(\chi_{8640}(6889,\cdot)\) \(\chi_{8640}(7369,\cdot)\) \(\chi_{8640}(7609,\cdot)\) \(\chi_{8640}(8089,\cdot)\) \(\chi_{8640}(8329,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((2431,3781,6401,3457)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{8}{9}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 8640 }(169, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{67}{72}\right)\) | \(e\left(\frac{53}{72}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{37}{72}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{13}{36}\right)\) |