Basic properties
Modulus: | \(1337\) | |
Conductor: | \(1337\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(114\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1337.w
\(\chi_{1337}(31,\cdot)\) \(\chi_{1337}(38,\cdot)\) \(\chi_{1337}(66,\cdot)\) \(\chi_{1337}(122,\cdot)\) \(\chi_{1337}(159,\cdot)\) \(\chi_{1337}(166,\cdot)\) \(\chi_{1337}(185,\cdot)\) \(\chi_{1337}(222,\cdot)\) \(\chi_{1337}(229,\cdot)\) \(\chi_{1337}(257,\cdot)\) \(\chi_{1337}(313,\cdot)\) \(\chi_{1337}(346,\cdot)\) \(\chi_{1337}(376,\cdot)\) \(\chi_{1337}(423,\cdot)\) \(\chi_{1337}(437,\cdot)\) \(\chi_{1337}(521,\cdot)\) \(\chi_{1337}(537,\cdot)\) \(\chi_{1337}(584,\cdot)\) \(\chi_{1337}(614,\cdot)\) \(\chi_{1337}(628,\cdot)\) \(\chi_{1337}(712,\cdot)\) \(\chi_{1337}(759,\cdot)\) \(\chi_{1337}(775,\cdot)\) \(\chi_{1337}(801,\cdot)\) \(\chi_{1337}(950,\cdot)\) \(\chi_{1337}(969,\cdot)\) \(\chi_{1337}(992,\cdot)\) \(\chi_{1337}(1025,\cdot)\) \(\chi_{1337}(1039,\cdot)\) \(\chi_{1337}(1116,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((192,974)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{35}{38}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 1337 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{57}\right)\) | \(e\left(\frac{1}{114}\right)\) | \(e\left(\frac{41}{57}\right)\) | \(e\left(\frac{101}{114}\right)\) | \(e\left(\frac{33}{38}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{1}{57}\right)\) | \(e\left(\frac{85}{114}\right)\) | \(e\left(\frac{109}{114}\right)\) | \(e\left(\frac{83}{114}\right)\) |