Basic properties
Modulus: | \(8018\) | |
Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(630\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{4009}(451,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8018.ep
\(\chi_{8018}(41,\cdot)\) \(\chi_{8018}(91,\cdot)\) \(\chi_{8018}(127,\cdot)\) \(\chi_{8018}(165,\cdot)\) \(\chi_{8018}(413,\cdot)\) \(\chi_{8018}(451,\cdot)\) \(\chi_{8018}(507,\cdot)\) \(\chi_{8018}(603,\cdot)\) \(\chi_{8018}(629,\cdot)\) \(\chi_{8018}(705,\cdot)\) \(\chi_{8018}(725,\cdot)\) \(\chi_{8018}(775,\cdot)\) \(\chi_{8018}(793,\cdot)\) \(\chi_{8018}(851,\cdot)\) \(\chi_{8018}(1039,\cdot)\) \(\chi_{8018}(1077,\cdot)\) \(\chi_{8018}(1161,\cdot)\) \(\chi_{8018}(1173,\cdot)\) \(\chi_{8018}(1207,\cdot)\) \(\chi_{8018}(1229,\cdot)\) \(\chi_{8018}(1257,\cdot)\) \(\chi_{8018}(1269,\cdot)\) \(\chi_{8018}(1283,\cdot)\) \(\chi_{8018}(1295,\cdot)\) \(\chi_{8018}(1305,\cdot)\) \(\chi_{8018}(1397,\cdot)\) \(\chi_{8018}(1421,\cdot)\) \(\chi_{8018}(1447,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{315})$ |
Fixed field: | Number field defined by a degree 630 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((e\left(\frac{7}{18}\right),e\left(\frac{179}{210}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 8018 }(451, a) \) | \(1\) | \(1\) | \(e\left(\frac{223}{315}\right)\) | \(e\left(\frac{232}{315}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{131}{315}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{433}{630}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{323}{630}\right)\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{61}{90}\right)\) |