Basic properties
| Modulus: | \(1337\) | |
| Conductor: | \(1337\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(285\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1337.bc
\(\chi_{1337}(2,\cdot)\) \(\chi_{1337}(4,\cdot)\) \(\chi_{1337}(9,\cdot)\) \(\chi_{1337}(16,\cdot)\) \(\chi_{1337}(18,\cdot)\) \(\chi_{1337}(23,\cdot)\) \(\chi_{1337}(46,\cdot)\) \(\chi_{1337}(51,\cdot)\) \(\chi_{1337}(60,\cdot)\) \(\chi_{1337}(65,\cdot)\) \(\chi_{1337}(67,\cdot)\) \(\chi_{1337}(72,\cdot)\) \(\chi_{1337}(79,\cdot)\) \(\chi_{1337}(81,\cdot)\) \(\chi_{1337}(86,\cdot)\) \(\chi_{1337}(100,\cdot)\) \(\chi_{1337}(102,\cdot)\) \(\chi_{1337}(128,\cdot)\) \(\chi_{1337}(130,\cdot)\) \(\chi_{1337}(135,\cdot)\) \(\chi_{1337}(144,\cdot)\) \(\chi_{1337}(149,\cdot)\) \(\chi_{1337}(156,\cdot)\) \(\chi_{1337}(158,\cdot)\) \(\chi_{1337}(163,\cdot)\) \(\chi_{1337}(170,\cdot)\) \(\chi_{1337}(172,\cdot)\) \(\chi_{1337}(193,\cdot)\) \(\chi_{1337}(200,\cdot)\) \(\chi_{1337}(207,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{285})$ |
| Fixed field: | Number field defined by a degree 285 polynomial (not computed) |
Values on generators
\((192,974)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{89}{95}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1337 }(46, a) \) | \(1\) | \(1\) | \(e\left(\frac{158}{285}\right)\) | \(e\left(\frac{97}{285}\right)\) | \(e\left(\frac{31}{285}\right)\) | \(e\left(\frac{10}{57}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{63}{95}\right)\) | \(e\left(\frac{194}{285}\right)\) | \(e\left(\frac{208}{285}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{128}{285}\right)\) |