Basic properties
| Modulus: | \(4009\) | |
| Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(45\) | 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.cv
\(\chi_{4009}(100,\cdot)\) \(\chi_{4009}(150,\cdot)\) \(\chi_{4009}(294,\cdot)\) \(\chi_{4009}(441,\cdot)\) \(\chi_{4009}(652,\cdot)\) \(\chi_{4009}(978,\cdot)\) \(\chi_{4009}(1366,\cdot)\) \(\chi_{4009}(1403,\cdot)\) \(\chi_{4009}(1467,\cdot)\) \(\chi_{4009}(1498,\cdot)\) \(\chi_{4009}(1678,\cdot)\) \(\chi_{4009}(1771,\cdot)\) \(\chi_{4009}(1982,\cdot)\) \(\chi_{4009}(2049,\cdot)\) \(\chi_{4009}(2247,\cdot)\) \(\chi_{4009}(2342,\cdot)\) \(\chi_{4009}(2455,\cdot)\) \(\chi_{4009}(2666,\cdot)\) \(\chi_{4009}(2893,\cdot)\) \(\chi_{4009}(2973,\cdot)\) \(\chi_{4009}(3265,\cdot)\) \(\chi_{4009}(3513,\cdot)\) \(\chi_{4009}(3608,\cdot)\) \(\chi_{4009}(3999,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((2111,1901)\) → \((e\left(\frac{8}{9}\right),e\left(\frac{4}{15}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4009 }(100, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{13}{15}\right)\) |