Basic properties
| Modulus: | \(4009\) | |
| Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4009.dh
\(\chi_{4009}(526,\cdot)\) \(\chi_{4009}(656,\cdot)\) \(\chi_{4009}(737,\cdot)\) \(\chi_{4009}(773,\cdot)\) \(\chi_{4009}(789,\cdot)\) \(\chi_{4009}(984,\cdot)\) \(\chi_{4009}(1078,\cdot)\) \(\chi_{4009}(1211,\cdot)\) \(\chi_{4009}(1370,\cdot)\) \(\chi_{4009}(1617,\cdot)\) \(\chi_{4009}(1922,\cdot)\) \(\chi_{4009}(2055,\cdot)\) \(\chi_{4009}(2214,\cdot)\) \(\chi_{4009}(2461,\cdot)\) \(\chi_{4009}(2636,\cdot)\) \(\chi_{4009}(2883,\cdot)\) \(\chi_{4009}(2977,\cdot)\) \(\chi_{4009}(3110,\cdot)\) \(\chi_{4009}(3188,\cdot)\) \(\chi_{4009}(3321,\cdot)\) \(\chi_{4009}(3480,\cdot)\) \(\chi_{4009}(3727,\cdot)\) \(\chi_{4009}(3821,\cdot)\) \(\chi_{4009}(3954,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((2111,1901)\) → \((e\left(\frac{5}{18}\right),e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4009 }(526, a) \) | \(1\) | \(1\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{11}{15}\right)\) |