Basic properties
| Modulus: | \(8001\) | |
| Conductor: | \(1143\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(63\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1143}(169,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8001.lo
\(\chi_{8001}(169,\cdot)\) \(\chi_{8001}(295,\cdot)\) \(\chi_{8001}(589,\cdot)\) \(\chi_{8001}(841,\cdot)\) \(\chi_{8001}(904,\cdot)\) \(\chi_{8001}(925,\cdot)\) \(\chi_{8001}(1114,\cdot)\) \(\chi_{8001}(1156,\cdot)\) \(\chi_{8001}(1177,\cdot)\) \(\chi_{8001}(1849,\cdot)\) \(\chi_{8001}(1975,\cdot)\) \(\chi_{8001}(2374,\cdot)\) \(\chi_{8001}(2815,\cdot)\) \(\chi_{8001}(2878,\cdot)\) \(\chi_{8001}(2983,\cdot)\) \(\chi_{8001}(3130,\cdot)\) \(\chi_{8001}(3172,\cdot)\) \(\chi_{8001}(3193,\cdot)\) \(\chi_{8001}(3235,\cdot)\) \(\chi_{8001}(3319,\cdot)\) \(\chi_{8001}(3550,\cdot)\) \(\chi_{8001}(3676,\cdot)\) \(\chi_{8001}(4075,\cdot)\) \(\chi_{8001}(4138,\cdot)\) \(\chi_{8001}(4306,\cdot)\) \(\chi_{8001}(4327,\cdot)\) \(\chi_{8001}(4390,\cdot)\) \(\chi_{8001}(4558,\cdot)\) \(\chi_{8001}(4768,\cdot)\) \(\chi_{8001}(5692,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((3557,1144,7750)\) → \((e\left(\frac{2}{3}\right),1,e\left(\frac{31}{63}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8001 }(169, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{1}{3}\right)\) |