Basic properties
| Modulus: | \(8020\) | |
| Conductor: | \(1604\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1604}(171,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8020.cv
\(\chi_{8020}(171,\cdot)\) \(\chi_{8020}(631,\cdot)\) \(\chi_{8020}(991,\cdot)\) \(\chi_{8020}(1251,\cdot)\) \(\chi_{8020}(1271,\cdot)\) \(\chi_{8020}(1311,\cdot)\) \(\chi_{8020}(1351,\cdot)\) \(\chi_{8020}(1451,\cdot)\) \(\chi_{8020}(1571,\cdot)\) \(\chi_{8020}(2031,\cdot)\) \(\chi_{8020}(2251,\cdot)\) \(\chi_{8020}(2731,\cdot)\) \(\chi_{8020}(2891,\cdot)\) \(\chi_{8020}(3051,\cdot)\) \(\chi_{8020}(3451,\cdot)\) \(\chi_{8020}(3751,\cdot)\) \(\chi_{8020}(3891,\cdot)\) \(\chi_{8020}(4931,\cdot)\) \(\chi_{8020}(5071,\cdot)\) \(\chi_{8020}(5371,\cdot)\) \(\chi_{8020}(5771,\cdot)\) \(\chi_{8020}(5931,\cdot)\) \(\chi_{8020}(6091,\cdot)\) \(\chi_{8020}(6571,\cdot)\) \(\chi_{8020}(6791,\cdot)\) \(\chi_{8020}(7251,\cdot)\) \(\chi_{8020}(7371,\cdot)\) \(\chi_{8020}(7471,\cdot)\) \(\chi_{8020}(7511,\cdot)\) \(\chi_{8020}(7551,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((4011,6417,7221)\) → \((-1,1,e\left(\frac{33}{80}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 8020 }(171, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{47}{80}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{59}{80}\right)\) |