Basic properties
Modulus: | \(4029\) | |
Conductor: | \(1343\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(312\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1343}(739,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4029.cv
\(\chi_{4029}(43,\cdot)\) \(\chi_{4029}(70,\cdot)\) \(\chi_{4029}(127,\cdot)\) \(\chi_{4029}(145,\cdot)\) \(\chi_{4029}(274,\cdot)\) \(\chi_{4029}(280,\cdot)\) \(\chi_{4029}(355,\cdot)\) \(\chi_{4029}(376,\cdot)\) \(\chi_{4029}(382,\cdot)\) \(\chi_{4029}(502,\cdot)\) \(\chi_{4029}(508,\cdot)\) \(\chi_{4029}(559,\cdot)\) \(\chi_{4029}(661,\cdot)\) \(\chi_{4029}(706,\cdot)\) \(\chi_{4029}(739,\cdot)\) \(\chi_{4029}(865,\cdot)\) \(\chi_{4029}(916,\cdot)\) \(\chi_{4029}(937,\cdot)\) \(\chi_{4029}(943,\cdot)\) \(\chi_{4029}(1018,\cdot)\) \(\chi_{4029}(1090,\cdot)\) \(\chi_{4029}(1141,\cdot)\) \(\chi_{4029}(1165,\cdot)\) \(\chi_{4029}(1192,\cdot)\) \(\chi_{4029}(1222,\cdot)\) \(\chi_{4029}(1267,\cdot)\) \(\chi_{4029}(1294,\cdot)\) \(\chi_{4029}(1318,\cdot)\) \(\chi_{4029}(1324,\cdot)\) \(\chi_{4029}(1396,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{312})$ |
Fixed field: | Number field defined by a degree 312 polynomial (not computed) |
Values on generators
\((2687,3556,3163)\) → \((1,e\left(\frac{5}{8}\right),e\left(\frac{61}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 4029 }(739, a) \) | \(-1\) | \(1\) | \(e\left(\frac{137}{156}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{191}{312}\right)\) | \(e\left(\frac{101}{312}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{51}{104}\right)\) | \(e\left(\frac{173}{312}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{21}{104}\right)\) | \(e\left(\frac{20}{39}\right)\) |