Basic properties
Modulus: | \(1029\) | |
Conductor: | \(1029\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(294\) | 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 1029.x
\(\chi_{1029}(5,\cdot)\) \(\chi_{1029}(17,\cdot)\) \(\chi_{1029}(26,\cdot)\) \(\chi_{1029}(38,\cdot)\) \(\chi_{1029}(47,\cdot)\) \(\chi_{1029}(59,\cdot)\) \(\chi_{1029}(89,\cdot)\) \(\chi_{1029}(101,\cdot)\) \(\chi_{1029}(110,\cdot)\) \(\chi_{1029}(122,\cdot)\) \(\chi_{1029}(131,\cdot)\) \(\chi_{1029}(143,\cdot)\) \(\chi_{1029}(152,\cdot)\) \(\chi_{1029}(164,\cdot)\) \(\chi_{1029}(173,\cdot)\) \(\chi_{1029}(185,\cdot)\) \(\chi_{1029}(194,\cdot)\) \(\chi_{1029}(206,\cdot)\) \(\chi_{1029}(236,\cdot)\) \(\chi_{1029}(248,\cdot)\) \(\chi_{1029}(257,\cdot)\) \(\chi_{1029}(269,\cdot)\) \(\chi_{1029}(278,\cdot)\) \(\chi_{1029}(290,\cdot)\) \(\chi_{1029}(299,\cdot)\) \(\chi_{1029}(311,\cdot)\) \(\chi_{1029}(320,\cdot)\) \(\chi_{1029}(332,\cdot)\) \(\chi_{1029}(341,\cdot)\) \(\chi_{1029}(353,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{147})$ |
Fixed field: | Number field defined by a degree 294 polynomial (not computed) |
Values on generators
\((344,346)\) → \((-1,e\left(\frac{235}{294}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 1029 }(311, a) \) | \(1\) | \(1\) | \(e\left(\frac{167}{294}\right)\) | \(e\left(\frac{20}{147}\right)\) | \(e\left(\frac{100}{147}\right)\) | \(e\left(\frac{69}{98}\right)\) | \(e\left(\frac{73}{294}\right)\) | \(e\left(\frac{223}{294}\right)\) | \(e\left(\frac{79}{98}\right)\) | \(e\left(\frac{40}{147}\right)\) | \(e\left(\frac{71}{147}\right)\) | \(e\left(\frac{5}{6}\right)\) |