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 \(\chi_{4009}(465,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8018.da
\(\chi_{8018}(465,\cdot)\) \(\chi_{8018}(595,\cdot)\) \(\chi_{8018}(1005,\cdot)\) \(\chi_{8018}(1089,\cdot)\) \(\chi_{8018}(1233,\cdot)\) \(\chi_{8018}(1339,\cdot)\) \(\chi_{8018}(2153,\cdot)\) \(\chi_{8018}(2227,\cdot)\) \(\chi_{8018}(2289,\cdot)\) \(\chi_{8018}(2923,\cdot)\) \(\chi_{8018}(3027,\cdot)\) \(\chi_{8018}(3767,\cdot)\) \(\chi_{8018}(3977,\cdot)\) \(\chi_{8018}(4063,\cdot)\) \(\chi_{8018}(4393,\cdot)\) \(\chi_{8018}(4405,\cdot)\) \(\chi_{8018}(4759,\cdot)\) \(\chi_{8018}(4887,\cdot)\) \(\chi_{8018}(4907,\cdot)\) \(\chi_{8018}(5033,\cdot)\) \(\chi_{8018}(5165,\cdot)\) \(\chi_{8018}(5249,\cdot)\) \(\chi_{8018}(5951,\cdot)\) \(\chi_{8018}(6009,\cdot)\) \(\chi_{8018}(6173,\cdot)\) \(\chi_{8018}(6447,\cdot)\) \(\chi_{8018}(6515,\cdot)\) \(\chi_{8018}(6825,\cdot)\) \(\chi_{8018}(6913,\cdot)\) \(\chi_{8018}(6925,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((2111,1901)\) → \((e\left(\frac{4}{9}\right),e\left(\frac{8}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 8018 }(465, a) \) | \(1\) | \(1\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) |