Basic properties
| Modulus: | \(8018\) | |
| Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(63\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4009}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8018.cy
\(\chi_{8018}(43,\cdot)\) \(\chi_{8018}(73,\cdot)\) \(\chi_{8018}(101,\cdot)\) \(\chi_{8018}(161,\cdot)\) \(\chi_{8018}(245,\cdot)\) \(\chi_{8018}(389,\cdot)\) \(\chi_{8018}(917,\cdot)\) \(\chi_{8018}(1023,\cdot)\) \(\chi_{8018}(1309,\cdot)\) \(\chi_{8018}(1657,\cdot)\) \(\chi_{8018}(1849,\cdot)\) \(\chi_{8018}(1867,\cdot)\) \(\chi_{8018}(2077,\cdot)\) \(\chi_{8018}(2183,\cdot)\) \(\chi_{8018}(2797,\cdot)\) \(\chi_{8018}(3133,\cdot)\) \(\chi_{8018}(3139,\cdot)\) \(\chi_{8018}(3493,\cdot)\) \(\chi_{8018}(3899,\cdot)\) \(\chi_{8018}(4189,\cdot)\) \(\chi_{8018}(4337,\cdot)\) \(\chi_{8018}(5329,\cdot)\) \(\chi_{8018}(5603,\cdot)\) \(\chi_{8018}(5647,\cdot)\) \(\chi_{8018}(5659,\cdot)\) \(\chi_{8018}(5671,\cdot)\) \(\chi_{8018}(5875,\cdot)\) \(\chi_{8018}(5877,\cdot)\) \(\chi_{8018}(6153,\cdot)\) \(\chi_{8018}(6431,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((2111,1901)\) → \((e\left(\frac{8}{9}\right),e\left(\frac{8}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 8018 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{63}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{7}{9}\right)\) |