Basic properties
| Modulus: | \(1009\) | |
| Conductor: | \(1009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(336\) | 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 1009.bb
\(\chi_{1009}(23,\cdot)\) \(\chi_{1009}(47,\cdot)\) \(\chi_{1009}(57,\cdot)\) \(\chi_{1009}(61,\cdot)\) \(\chi_{1009}(68,\cdot)\) \(\chi_{1009}(69,\cdot)\) \(\chi_{1009}(73,\cdot)\) \(\chi_{1009}(77,\cdot)\) \(\chi_{1009}(110,\cdot)\) \(\chi_{1009}(117,\cdot)\) \(\chi_{1009}(119,\cdot)\) \(\chi_{1009}(131,\cdot)\) \(\chi_{1009}(132,\cdot)\) \(\chi_{1009}(149,\cdot)\) \(\chi_{1009}(152,\cdot)\) \(\chi_{1009}(155,\cdot)\) \(\chi_{1009}(177,\cdot)\) \(\chi_{1009}(182,\cdot)\) \(\chi_{1009}(186,\cdot)\) \(\chi_{1009}(211,\cdot)\) \(\chi_{1009}(260,\cdot)\) \(\chi_{1009}(266,\cdot)\) \(\chi_{1009}(275,\cdot)\) \(\chi_{1009}(312,\cdot)\) \(\chi_{1009}(316,\cdot)\) \(\chi_{1009}(322,\cdot)\) \(\chi_{1009}(332,\cdot)\) \(\chi_{1009}(351,\cdot)\) \(\chi_{1009}(356,\cdot)\) \(\chi_{1009}(357,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{336})$ |
| Fixed field: | Number field defined by a degree 336 polynomial (not computed) |
Values on generators
\(11\) → \(e\left(\frac{283}{336}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1009 }(986, a) \) | \(-1\) | \(1\) | \(e\left(\frac{41}{168}\right)\) | \(e\left(\frac{51}{56}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{89}{168}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{41}{56}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{283}{336}\right)\) |