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 \(\chi_{4009}(89,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8018.et
\(\chi_{8018}(89,\cdot)\) \(\chi_{8018}(97,\cdot)\) \(\chi_{8018}(129,\cdot)\) \(\chi_{8018}(135,\cdot)\) \(\chi_{8018}(147,\cdot)\) \(\chi_{8018}(219,\cdot)\) \(\chi_{8018}(279,\cdot)\) \(\chi_{8018}(357,\cdot)\) \(\chi_{8018}(409,\cdot)\) \(\chi_{8018}(641,\cdot)\) \(\chi_{8018}(661,\cdot)\) \(\chi_{8018}(675,\cdot)\) \(\chi_{8018}(735,\cdot)\) \(\chi_{8018}(819,\cdot)\) \(\chi_{8018}(831,\cdot)\) \(\chi_{8018}(839,\cdot)\) \(\chi_{8018}(933,\cdot)\) \(\chi_{8018}(941,\cdot)\) \(\chi_{8018}(979,\cdot)\) \(\chi_{8018}(991,\cdot)\) \(\chi_{8018}(1097,\cdot)\) \(\chi_{8018}(1115,\cdot)\) \(\chi_{8018}(1123,\cdot)\) \(\chi_{8018}(1153,\cdot)\) \(\chi_{8018}(1363,\cdot)\) \(\chi_{8018}(1381,\cdot)\) \(\chi_{8018}(1401,\cdot)\) \(\chi_{8018}(1485,\cdot)\) \(\chi_{8018}(1495,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{315})$ |
| Fixed field: | Number field defined by a degree 630 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((e\left(\frac{5}{18}\right),e\left(\frac{33}{70}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 8018 }(89, a) \) | \(1\) | \(1\) | \(e\left(\frac{278}{315}\right)\) | \(e\left(\frac{212}{315}\right)\) | \(e\left(\frac{41}{210}\right)\) | \(e\left(\frac{241}{315}\right)\) | \(e\left(\frac{74}{105}\right)\) | \(e\left(\frac{173}{630}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{373}{630}\right)\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{41}{90}\right)\) |