Basic properties
| Modulus: | \(1077\) | |
| Conductor: | \(1077\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(358\) | 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 1077.g
\(\chi_{1077}(2,\cdot)\) \(\chi_{1077}(5,\cdot)\) \(\chi_{1077}(8,\cdot)\) \(\chi_{1077}(11,\cdot)\) \(\chi_{1077}(17,\cdot)\) \(\chi_{1077}(20,\cdot)\) \(\chi_{1077}(23,\cdot)\) \(\chi_{1077}(32,\cdot)\) \(\chi_{1077}(41,\cdot)\) \(\chi_{1077}(44,\cdot)\) \(\chi_{1077}(47,\cdot)\) \(\chi_{1077}(50,\cdot)\) \(\chi_{1077}(68,\cdot)\) \(\chi_{1077}(74,\cdot)\) \(\chi_{1077}(80,\cdot)\) \(\chi_{1077}(92,\cdot)\) \(\chi_{1077}(98,\cdot)\) \(\chi_{1077}(101,\cdot)\) \(\chi_{1077}(107,\cdot)\) \(\chi_{1077}(110,\cdot)\) \(\chi_{1077}(125,\cdot)\) \(\chi_{1077}(128,\cdot)\) \(\chi_{1077}(131,\cdot)\) \(\chi_{1077}(146,\cdot)\) \(\chi_{1077}(149,\cdot)\) \(\chi_{1077}(158,\cdot)\) \(\chi_{1077}(164,\cdot)\) \(\chi_{1077}(170,\cdot)\) \(\chi_{1077}(173,\cdot)\) \(\chi_{1077}(176,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{179})$ |
| Fixed field: | Number field defined by a degree 358 polynomial (not computed) |
Values on generators
\((719,7)\) → \((-1,e\left(\frac{40}{179}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 1077 }(47, a) \) | \(-1\) | \(1\) | \(e\left(\frac{239}{358}\right)\) | \(e\left(\frac{60}{179}\right)\) | \(e\left(\frac{311}{358}\right)\) | \(e\left(\frac{40}{179}\right)\) | \(e\left(\frac{1}{358}\right)\) | \(e\left(\frac{96}{179}\right)\) | \(e\left(\frac{317}{358}\right)\) | \(e\left(\frac{145}{179}\right)\) | \(e\left(\frac{319}{358}\right)\) | \(e\left(\frac{120}{179}\right)\) |