Basic properties
| Modulus: | \(289\) | |
| Conductor: | \(289\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(68\) | 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 289.h
\(\chi_{289}(4,\cdot)\) \(\chi_{289}(13,\cdot)\) \(\chi_{289}(21,\cdot)\) \(\chi_{289}(30,\cdot)\) \(\chi_{289}(47,\cdot)\) \(\chi_{289}(55,\cdot)\) \(\chi_{289}(64,\cdot)\) \(\chi_{289}(72,\cdot)\) \(\chi_{289}(81,\cdot)\) \(\chi_{289}(89,\cdot)\) \(\chi_{289}(98,\cdot)\) \(\chi_{289}(106,\cdot)\) \(\chi_{289}(115,\cdot)\) \(\chi_{289}(123,\cdot)\) \(\chi_{289}(132,\cdot)\) \(\chi_{289}(140,\cdot)\) \(\chi_{289}(149,\cdot)\) \(\chi_{289}(157,\cdot)\) \(\chi_{289}(166,\cdot)\) \(\chi_{289}(174,\cdot)\) \(\chi_{289}(183,\cdot)\) \(\chi_{289}(191,\cdot)\) \(\chi_{289}(200,\cdot)\) \(\chi_{289}(208,\cdot)\) \(\chi_{289}(217,\cdot)\) \(\chi_{289}(225,\cdot)\) \(\chi_{289}(234,\cdot)\) \(\chi_{289}(242,\cdot)\) \(\chi_{289}(259,\cdot)\) \(\chi_{289}(268,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{68})$ |
| Fixed field: | Number field defined by a degree 68 polynomial |
Values on generators
\(3\) → \(e\left(\frac{49}{68}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 289 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{34}\right)\) | \(e\left(\frac{49}{68}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{1}{68}\right)\) | \(e\left(\frac{43}{68}\right)\) | \(e\left(\frac{47}{68}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{63}{68}\right)\) | \(e\left(\frac{39}{68}\right)\) |