Basic properties
| Modulus: | \(8018\) | |
| Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4009}(1245,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8018.dh
\(\chi_{8018}(1245,\cdot)\) \(\chi_{8018}(1799,\cdot)\) \(\chi_{8018}(2187,\cdot)\) \(\chi_{8018}(2871,\cdot)\) \(\chi_{8018}(3015,\cdot)\) \(\chi_{8018}(3175,\cdot)\) \(\chi_{8018}(3453,\cdot)\) \(\chi_{8018}(3487,\cdot)\) \(\chi_{8018}(3661,\cdot)\) \(\chi_{8018}(3777,\cdot)\) \(\chi_{8018}(4137,\cdot)\) \(\chi_{8018}(4201,\cdot)\) \(\chi_{8018}(4297,\cdot)\) \(\chi_{8018}(4441,\cdot)\) \(\chi_{8018}(4703,\cdot)\) \(\chi_{8018}(4981,\cdot)\) \(\chi_{8018}(5285,\cdot)\) \(\chi_{8018}(5349,\cdot)\) \(\chi_{8018}(5467,\cdot)\) \(\chi_{8018}(6019,\cdot)\) \(\chi_{8018}(6311,\cdot)\) \(\chi_{8018}(7235,\cdot)\) \(\chi_{8018}(7575,\cdot)\) \(\chi_{8018}(7881,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((2111,1901)\) → \((e\left(\frac{17}{18}\right),e\left(\frac{11}{30}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 8018 }(1245, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{53}{90}\right)\) |