Basic properties
Modulus: | \(1077\) | |
Conductor: | \(359\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(179\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{359}(16,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1077.e
\(\chi_{1077}(4,\cdot)\) \(\chi_{1077}(10,\cdot)\) \(\chi_{1077}(16,\cdot)\) \(\chi_{1077}(22,\cdot)\) \(\chi_{1077}(25,\cdot)\) \(\chi_{1077}(34,\cdot)\) \(\chi_{1077}(37,\cdot)\) \(\chi_{1077}(40,\cdot)\) \(\chi_{1077}(46,\cdot)\) \(\chi_{1077}(49,\cdot)\) \(\chi_{1077}(55,\cdot)\) \(\chi_{1077}(64,\cdot)\) \(\chi_{1077}(73,\cdot)\) \(\chi_{1077}(79,\cdot)\) \(\chi_{1077}(82,\cdot)\) \(\chi_{1077}(85,\cdot)\) \(\chi_{1077}(88,\cdot)\) \(\chi_{1077}(91,\cdot)\) \(\chi_{1077}(94,\cdot)\) \(\chi_{1077}(100,\cdot)\) \(\chi_{1077}(115,\cdot)\) \(\chi_{1077}(121,\cdot)\) \(\chi_{1077}(127,\cdot)\) \(\chi_{1077}(133,\cdot)\) \(\chi_{1077}(136,\cdot)\) \(\chi_{1077}(148,\cdot)\) \(\chi_{1077}(151,\cdot)\) \(\chi_{1077}(160,\cdot)\) \(\chi_{1077}(169,\cdot)\) \(\chi_{1077}(181,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{179})$ |
Fixed field: | Number field defined by a degree 179 polynomial (not computed) |
Values on generators
\((719,7)\) → \((1,e\left(\frac{91}{179}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 1077 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{113}{179}\right)\) | \(e\left(\frac{47}{179}\right)\) | \(e\left(\frac{177}{179}\right)\) | \(e\left(\frac{91}{179}\right)\) | \(e\left(\frac{160}{179}\right)\) | \(e\left(\frac{111}{179}\right)\) | \(e\left(\frac{63}{179}\right)\) | \(e\left(\frac{39}{179}\right)\) | \(e\left(\frac{25}{179}\right)\) | \(e\left(\frac{94}{179}\right)\) |