Basic properties
Modulus: | \(1337\) | |
Conductor: | \(1337\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(570\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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 1337.bf
\(\chi_{1337}(3,\cdot)\) \(\chi_{1337}(10,\cdot)\) \(\chi_{1337}(12,\cdot)\) \(\chi_{1337}(17,\cdot)\) \(\chi_{1337}(24,\cdot)\) \(\chi_{1337}(26,\cdot)\) \(\chi_{1337}(40,\cdot)\) \(\chi_{1337}(45,\cdot)\) \(\chi_{1337}(54,\cdot)\) \(\chi_{1337}(59,\cdot)\) \(\chi_{1337}(68,\cdot)\) \(\chi_{1337}(75,\cdot)\) \(\chi_{1337}(80,\cdot)\) \(\chi_{1337}(96,\cdot)\) \(\chi_{1337}(103,\cdot)\) \(\chi_{1337}(108,\cdot)\) \(\chi_{1337}(115,\cdot)\) \(\chi_{1337}(117,\cdot)\) \(\chi_{1337}(129,\cdot)\) \(\chi_{1337}(138,\cdot)\) \(\chi_{1337}(194,\cdot)\) \(\chi_{1337}(199,\cdot)\) \(\chi_{1337}(201,\cdot)\) \(\chi_{1337}(206,\cdot)\) \(\chi_{1337}(208,\cdot)\) \(\chi_{1337}(215,\cdot)\) \(\chi_{1337}(234,\cdot)\) \(\chi_{1337}(236,\cdot)\) \(\chi_{1337}(241,\cdot)\) \(\chi_{1337}(250,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{285})$ |
Fixed field: | Number field defined by a degree 570 polynomial (not computed) |
Values on generators
\((192,974)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{49}{95}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 1337 }(208, a) \) | \(-1\) | \(1\) | \(e\left(\frac{103}{285}\right)\) | \(e\left(\frac{379}{570}\right)\) | \(e\left(\frac{206}{285}\right)\) | \(e\left(\frac{109}{114}\right)\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{8}{95}\right)\) | \(e\left(\frac{94}{285}\right)\) | \(e\left(\frac{181}{570}\right)\) | \(e\left(\frac{10}{57}\right)\) | \(e\left(\frac{221}{570}\right)\) |