Basic properties
| Modulus: | \(8018\) | |
| Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(45\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4009}(137,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8018.cx
\(\chi_{8018}(137,\cdot)\) \(\chi_{8018}(443,\cdot)\) \(\chi_{8018}(783,\cdot)\) \(\chi_{8018}(1707,\cdot)\) \(\chi_{8018}(1999,\cdot)\) \(\chi_{8018}(2551,\cdot)\) \(\chi_{8018}(2669,\cdot)\) \(\chi_{8018}(2733,\cdot)\) \(\chi_{8018}(3037,\cdot)\) \(\chi_{8018}(3315,\cdot)\) \(\chi_{8018}(3577,\cdot)\) \(\chi_{8018}(3721,\cdot)\) \(\chi_{8018}(3817,\cdot)\) \(\chi_{8018}(3881,\cdot)\) \(\chi_{8018}(4241,\cdot)\) \(\chi_{8018}(4357,\cdot)\) \(\chi_{8018}(4531,\cdot)\) \(\chi_{8018}(4565,\cdot)\) \(\chi_{8018}(4843,\cdot)\) \(\chi_{8018}(5003,\cdot)\) \(\chi_{8018}(5147,\cdot)\) \(\chi_{8018}(5831,\cdot)\) \(\chi_{8018}(6219,\cdot)\) \(\chi_{8018}(6773,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((2111,1901)\) → \((e\left(\frac{1}{9}\right),e\left(\frac{1}{15}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 8018 }(137, a) \) | \(1\) | \(1\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{28}{45}\right)\) |