Basic properties
Modulus: | \(5488\) | |
Conductor: | \(2744\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(294\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2744}(1717,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5488.co
\(\chi_{5488}(9,\cdot)\) \(\chi_{5488}(25,\cdot)\) \(\chi_{5488}(121,\cdot)\) \(\chi_{5488}(137,\cdot)\) \(\chi_{5488}(233,\cdot)\) \(\chi_{5488}(249,\cdot)\) \(\chi_{5488}(345,\cdot)\) \(\chi_{5488}(457,\cdot)\) \(\chi_{5488}(473,\cdot)\) \(\chi_{5488}(585,\cdot)\) \(\chi_{5488}(681,\cdot)\) \(\chi_{5488}(697,\cdot)\) \(\chi_{5488}(793,\cdot)\) \(\chi_{5488}(809,\cdot)\) \(\chi_{5488}(905,\cdot)\) \(\chi_{5488}(921,\cdot)\) \(\chi_{5488}(1017,\cdot)\) \(\chi_{5488}(1033,\cdot)\) \(\chi_{5488}(1129,\cdot)\) \(\chi_{5488}(1241,\cdot)\) \(\chi_{5488}(1257,\cdot)\) \(\chi_{5488}(1369,\cdot)\) \(\chi_{5488}(1465,\cdot)\) \(\chi_{5488}(1481,\cdot)\) \(\chi_{5488}(1577,\cdot)\) \(\chi_{5488}(1593,\cdot)\) \(\chi_{5488}(1689,\cdot)\) \(\chi_{5488}(1705,\cdot)\) \(\chi_{5488}(1801,\cdot)\) \(\chi_{5488}(1817,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{147})$ |
Fixed field: | Number field defined by a degree 294 polynomial (not computed) |
Values on generators
\((687,4117,689)\) → \((1,-1,e\left(\frac{97}{147}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 5488 }(345, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{294}\right)\) | \(e\left(\frac{187}{294}\right)\) | \(e\left(\frac{47}{147}\right)\) | \(e\left(\frac{221}{294}\right)\) | \(e\left(\frac{55}{98}\right)\) | \(e\left(\frac{39}{49}\right)\) | \(e\left(\frac{73}{147}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{32}{147}\right)\) | \(e\left(\frac{40}{147}\right)\) |