Basic properties
| Modulus: | \(2009\) | |
| Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2009.bv
\(\chi_{2009}(73,\cdot)\) \(\chi_{2009}(173,\cdot)\) \(\chi_{2009}(255,\cdot)\) \(\chi_{2009}(278,\cdot)\) \(\chi_{2009}(360,\cdot)\) \(\chi_{2009}(542,\cdot)\) \(\chi_{2009}(565,\cdot)\) \(\chi_{2009}(647,\cdot)\) \(\chi_{2009}(747,\cdot)\) \(\chi_{2009}(829,\cdot)\) \(\chi_{2009}(934,\cdot)\) \(\chi_{2009}(1034,\cdot)\) \(\chi_{2009}(1116,\cdot)\) \(\chi_{2009}(1139,\cdot)\) \(\chi_{2009}(1221,\cdot)\) \(\chi_{2009}(1321,\cdot)\) \(\chi_{2009}(1426,\cdot)\) \(\chi_{2009}(1508,\cdot)\) \(\chi_{2009}(1608,\cdot)\) \(\chi_{2009}(1690,\cdot)\) \(\chi_{2009}(1713,\cdot)\) \(\chi_{2009}(1895,\cdot)\) \(\chi_{2009}(1977,\cdot)\) \(\chi_{2009}(2000,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((493,785)\) → \((e\left(\frac{37}{42}\right),i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 2009 }(73, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{37}{84}\right)\) |