Basic properties
| Modulus: | \(1077\) | |
| Conductor: | \(359\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(358\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{359}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1077.f
\(\chi_{1077}(7,\cdot)\) \(\chi_{1077}(13,\cdot)\) \(\chi_{1077}(19,\cdot)\) \(\chi_{1077}(28,\cdot)\) \(\chi_{1077}(31,\cdot)\) \(\chi_{1077}(43,\cdot)\) \(\chi_{1077}(52,\cdot)\) \(\chi_{1077}(58,\cdot)\) \(\chi_{1077}(61,\cdot)\) \(\chi_{1077}(67,\cdot)\) \(\chi_{1077}(70,\cdot)\) \(\chi_{1077}(76,\cdot)\) \(\chi_{1077}(97,\cdot)\) \(\chi_{1077}(103,\cdot)\) \(\chi_{1077}(106,\cdot)\) \(\chi_{1077}(109,\cdot)\) \(\chi_{1077}(112,\cdot)\) \(\chi_{1077}(118,\cdot)\) \(\chi_{1077}(124,\cdot)\) \(\chi_{1077}(130,\cdot)\) \(\chi_{1077}(139,\cdot)\) \(\chi_{1077}(142,\cdot)\) \(\chi_{1077}(145,\cdot)\) \(\chi_{1077}(154,\cdot)\) \(\chi_{1077}(157,\cdot)\) \(\chi_{1077}(163,\cdot)\) \(\chi_{1077}(166,\cdot)\) \(\chi_{1077}(172,\cdot)\) \(\chi_{1077}(175,\cdot)\) \(\chi_{1077}(178,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{179})$ |
| Fixed field: | Number field defined by a degree 358 polynomial (not computed) |
Values on generators
\((719,7)\) → \((1,e\left(\frac{257}{358}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 1077 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{74}{179}\right)\) | \(e\left(\frac{148}{179}\right)\) | \(e\left(\frac{127}{179}\right)\) | \(e\left(\frac{257}{358}\right)\) | \(e\left(\frac{43}{179}\right)\) | \(e\left(\frac{22}{179}\right)\) | \(e\left(\frac{27}{179}\right)\) | \(e\left(\frac{59}{358}\right)\) | \(e\left(\frac{47}{358}\right)\) | \(e\left(\frac{117}{179}\right)\) |