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 \(\chi_{4009}(55,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8018.cw
\(\chi_{8018}(55,\cdot)\) \(\chi_{8018}(529,\cdot)\) \(\chi_{8018}(821,\cdot)\) \(\chi_{8018}(899,\cdot)\) \(\chi_{8018}(1373,\cdot)\) \(\chi_{8018}(1795,\cdot)\) \(\chi_{8018}(2087,\cdot)\) \(\chi_{8018}(2639,\cdot)\) \(\chi_{8018}(2931,\cdot)\) \(\chi_{8018}(3025,\cdot)\) \(\chi_{8018}(3353,\cdot)\) \(\chi_{8018}(3483,\cdot)\) \(\chi_{8018}(4197,\cdot)\) \(\chi_{8018}(4291,\cdot)\) \(\chi_{8018}(4697,\cdot)\) \(\chi_{8018}(5041,\cdot)\) \(\chi_{8018}(5135,\cdot)\) \(\chi_{8018}(5557,\cdot)\) \(\chi_{8018}(5963,\cdot)\) \(\chi_{8018}(6401,\cdot)\) \(\chi_{8018}(6807,\cdot)\) \(\chi_{8018}(7229,\cdot)\) \(\chi_{8018}(7245,\cdot)\) \(\chi_{8018}(7281,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((2111,1901)\) → \((e\left(\frac{5}{9}\right),e\left(\frac{2}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 8018 }(55, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{23}{45}\right)\) |