Basic properties
| Modulus: | \(8001\) | |
| Conductor: | \(8001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(63\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8001.lk
\(\chi_{8001}(970,\cdot)\) \(\chi_{8001}(1192,\cdot)\) \(\chi_{8001}(1222,\cdot)\) \(\chi_{8001}(1285,\cdot)\) \(\chi_{8001}(1537,\cdot)\) \(\chi_{8001}(1822,\cdot)\) \(\chi_{8001}(2074,\cdot)\) \(\chi_{8001}(2200,\cdot)\) \(\chi_{8001}(2230,\cdot)\) \(\chi_{8001}(2356,\cdot)\) \(\chi_{8001}(2830,\cdot)\) \(\chi_{8001}(3019,\cdot)\) \(\chi_{8001}(3082,\cdot)\) \(\chi_{8001}(3364,\cdot)\) \(\chi_{8001}(3553,\cdot)\) \(\chi_{8001}(3616,\cdot)\) \(\chi_{8001}(3931,\cdot)\) \(\chi_{8001}(4057,\cdot)\) \(\chi_{8001}(4279,\cdot)\) \(\chi_{8001}(4687,\cdot)\) \(\chi_{8001}(4720,\cdot)\) \(\chi_{8001}(4783,\cdot)\) \(\chi_{8001}(4939,\cdot)\) \(\chi_{8001}(5035,\cdot)\) \(\chi_{8001}(5098,\cdot)\) \(\chi_{8001}(5224,\cdot)\) \(\chi_{8001}(5980,\cdot)\) \(\chi_{8001}(6043,\cdot)\) \(\chi_{8001}(6073,\cdot)\) \(\chi_{8001}(6232,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((3557,1144,7750)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{2}{3}\right),e\left(\frac{2}{63}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8001 }(970, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{55}{63}\right)\) | \(1\) |