Basic properties
Modulus: | \(547\) | |
Conductor: | \(547\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(182\) | 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 547.n
\(\chi_{547}(8,\cdot)\) \(\chi_{547}(31,\cdot)\) \(\chi_{547}(55,\cdot)\) \(\chi_{547}(65,\cdot)\) \(\chi_{547}(68,\cdot)\) \(\chi_{547}(79,\cdot)\) \(\chi_{547}(80,\cdot)\) \(\chi_{547}(87,\cdot)\) \(\chi_{547}(89,\cdot)\) \(\chi_{547}(94,\cdot)\) \(\chi_{547}(98,\cdot)\) \(\chi_{547}(101,\cdot)\) \(\chi_{547}(103,\cdot)\) \(\chi_{547}(105,\cdot)\) \(\chi_{547}(125,\cdot)\) \(\chi_{547}(132,\cdot)\) \(\chi_{547}(133,\cdot)\) \(\chi_{547}(138,\cdot)\) \(\chi_{547}(148,\cdot)\) \(\chi_{547}(151,\cdot)\) \(\chi_{547}(156,\cdot)\) \(\chi_{547}(164,\cdot)\) \(\chi_{547}(173,\cdot)\) \(\chi_{547}(192,\cdot)\) \(\chi_{547}(226,\cdot)\) \(\chi_{547}(232,\cdot)\) \(\chi_{547}(236,\cdot)\) \(\chi_{547}(238,\cdot)\) \(\chi_{547}(242,\cdot)\) \(\chi_{547}(244,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{91})$ |
Fixed field: | Number field defined by a degree 182 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{69}{182}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 547 }(98, a) \) | \(-1\) | \(1\) | \(e\left(\frac{69}{182}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{69}{91}\right)\) | \(e\left(\frac{157}{182}\right)\) | \(e\left(\frac{2}{91}\right)\) | \(e\left(\frac{9}{182}\right)\) | \(e\left(\frac{25}{182}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{22}{91}\right)\) | \(e\left(\frac{7}{13}\right)\) |