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.dm
\(\chi_{4009}(10,\cdot)\) \(\chi_{4009}(401,\cdot)\) \(\chi_{4009}(496,\cdot)\) \(\chi_{4009}(744,\cdot)\) \(\chi_{4009}(1036,\cdot)\) \(\chi_{4009}(1116,\cdot)\) \(\chi_{4009}(1343,\cdot)\) \(\chi_{4009}(1554,\cdot)\) \(\chi_{4009}(1667,\cdot)\) \(\chi_{4009}(1762,\cdot)\) \(\chi_{4009}(1960,\cdot)\) \(\chi_{4009}(2027,\cdot)\) \(\chi_{4009}(2238,\cdot)\) \(\chi_{4009}(2331,\cdot)\) \(\chi_{4009}(2511,\cdot)\) \(\chi_{4009}(2542,\cdot)\) \(\chi_{4009}(2606,\cdot)\) \(\chi_{4009}(2643,\cdot)\) \(\chi_{4009}(3031,\cdot)\) \(\chi_{4009}(3357,\cdot)\) \(\chi_{4009}(3568,\cdot)\) \(\chi_{4009}(3715,\cdot)\) \(\chi_{4009}(3859,\cdot)\) \(\chi_{4009}(3909,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((2111,1901)\) → \((e\left(\frac{17}{18}\right),e\left(\frac{19}{30}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4009 }(10, a) \) | \(1\) | \(1\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{14}{15}\right)\) |