Basic properties
Modulus: | \(277\) | |
Conductor: | \(277\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(92\) | 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 277.j
\(\chi_{277}(2,\cdot)\) \(\chi_{277}(8,\cdot)\) \(\chi_{277}(15,\cdot)\) \(\chi_{277}(26,\cdot)\) \(\chi_{277}(32,\cdot)\) \(\chi_{277}(33,\cdot)\) \(\chi_{277}(37,\cdot)\) \(\chi_{277}(38,\cdot)\) \(\chi_{277}(42,\cdot)\) \(\chi_{277}(51,\cdot)\) \(\chi_{277}(54,\cdot)\) \(\chi_{277}(61,\cdot)\) \(\chi_{277}(73,\cdot)\) \(\chi_{277}(82,\cdot)\) \(\chi_{277}(104,\cdot)\) \(\chi_{277}(109,\cdot)\) \(\chi_{277}(118,\cdot)\) \(\chi_{277}(125,\cdot)\) \(\chi_{277}(128,\cdot)\) \(\chi_{277}(129,\cdot)\) \(\chi_{277}(132,\cdot)\) \(\chi_{277}(138,\cdot)\) \(\chi_{277}(139,\cdot)\) \(\chi_{277}(145,\cdot)\) \(\chi_{277}(148,\cdot)\) \(\chi_{277}(149,\cdot)\) \(\chi_{277}(152,\cdot)\) \(\chi_{277}(159,\cdot)\) \(\chi_{277}(168,\cdot)\) \(\chi_{277}(173,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{92})$ |
Fixed field: | Number field defined by a degree 92 polynomial |
Values on generators
\(5\) → \(e\left(\frac{31}{92}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 277 }(26, a) \) | \(-1\) | \(1\) | \(e\left(\frac{49}{92}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{3}{46}\right)\) | \(e\left(\frac{31}{92}\right)\) | \(e\left(\frac{81}{92}\right)\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{55}{92}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{33}{92}\right)\) |