Basic properties
| Modulus: | \(100315\) | |
| Conductor: | \(100315\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(5732\) | 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 100315.r
\(\chi_{100315}(2,\cdot)\) \(\chi_{100315}(8,\cdot)\) \(\chi_{100315}(32,\cdot)\) \(\chi_{100315}(47,\cdot)\) \(\chi_{100315}(73,\cdot)\) \(\chi_{100315}(87,\cdot)\) \(\chi_{100315}(128,\cdot)\) \(\chi_{100315}(137,\cdot)\) \(\chi_{100315}(188,\cdot)\) \(\chi_{100315}(223,\cdot)\) \(\chi_{100315}(292,\cdot)\) \(\chi_{100315}(317,\cdot)\) \(\chi_{100315}(348,\cdot)\) \(\chi_{100315}(357,\cdot)\) \(\chi_{100315}(363,\cdot)\) \(\chi_{100315}(377,\cdot)\) \(\chi_{100315}(398,\cdot)\) \(\chi_{100315}(422,\cdot)\) \(\chi_{100315}(512,\cdot)\) \(\chi_{100315}(548,\cdot)\) \(\chi_{100315}(562,\cdot)\) \(\chi_{100315}(613,\cdot)\) \(\chi_{100315}(627,\cdot)\) \(\chi_{100315}(697,\cdot)\) \(\chi_{100315}(752,\cdot)\) \(\chi_{100315}(753,\cdot)\) \(\chi_{100315}(877,\cdot)\) \(\chi_{100315}(892,\cdot)\) \(\chi_{100315}(913,\cdot)\) \(\chi_{100315}(917,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{5732})$ |
| Fixed field: | Number field defined by a degree 5732 polynomial (not computed) |
Values on generators
\((40127,40131)\) → \((-i,e\left(\frac{11}{1433}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 100315 }(753, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1723}{5732}\right)\) | \(e\left(\frac{5321}{5732}\right)\) | \(e\left(\frac{1723}{2866}\right)\) | \(e\left(\frac{328}{1433}\right)\) | \(e\left(\frac{1015}{5732}\right)\) | \(e\left(\frac{5169}{5732}\right)\) | \(e\left(\frac{2455}{2866}\right)\) | \(e\left(\frac{821}{1433}\right)\) | \(e\left(\frac{3035}{5732}\right)\) | \(e\left(\frac{3553}{5732}\right)\) |