Basic properties
Modulus: | \(277\) | |
Conductor: | \(277\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(276\) | 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.l
\(\chi_{277}(5,\cdot)\) \(\chi_{277}(6,\cdot)\) \(\chi_{277}(11,\cdot)\) \(\chi_{277}(14,\cdot)\) \(\chi_{277}(17,\cdot)\) \(\chi_{277}(18,\cdot)\) \(\chi_{277}(20,\cdot)\) \(\chi_{277}(24,\cdot)\) \(\chi_{277}(31,\cdot)\) \(\chi_{277}(43,\cdot)\) \(\chi_{277}(44,\cdot)\) \(\chi_{277}(45,\cdot)\) \(\chi_{277}(46,\cdot)\) \(\chi_{277}(50,\cdot)\) \(\chi_{277}(53,\cdot)\) \(\chi_{277}(56,\cdot)\) \(\chi_{277}(58,\cdot)\) \(\chi_{277}(65,\cdot)\) \(\chi_{277}(68,\cdot)\) \(\chi_{277}(72,\cdot)\) \(\chi_{277}(77,\cdot)\) \(\chi_{277}(78,\cdot)\) \(\chi_{277}(80,\cdot)\) \(\chi_{277}(93,\cdot)\) \(\chi_{277}(94,\cdot)\) \(\chi_{277}(96,\cdot)\) \(\chi_{277}(97,\cdot)\) \(\chi_{277}(98,\cdot)\) \(\chi_{277}(99,\cdot)\) \(\chi_{277}(101,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{276})$ |
Fixed field: | Number field defined by a degree 276 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{77}{276}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 277 }(24, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{92}\right)\) | \(e\left(\frac{31}{69}\right)\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{77}{276}\right)\) | \(e\left(\frac{127}{276}\right)\) | \(e\left(\frac{19}{138}\right)\) | \(e\left(\frac{3}{92}\right)\) | \(e\left(\frac{62}{69}\right)\) | \(e\left(\frac{20}{69}\right)\) | \(e\left(\frac{263}{276}\right)\) |