Basic properties
Modulus: | \(1337\) | |
Conductor: | \(1337\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(57\) | 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.u
\(\chi_{1337}(25,\cdot)\) \(\chi_{1337}(30,\cdot)\) \(\chi_{1337}(32,\cdot)\) \(\chi_{1337}(107,\cdot)\) \(\chi_{1337}(121,\cdot)\) \(\chi_{1337}(177,\cdot)\) \(\chi_{1337}(221,\cdot)\) \(\chi_{1337}(298,\cdot)\) \(\chi_{1337}(312,\cdot)\) \(\chi_{1337}(345,\cdot)\) \(\chi_{1337}(368,\cdot)\) \(\chi_{1337}(387,\cdot)\) \(\chi_{1337}(536,\cdot)\) \(\chi_{1337}(562,\cdot)\) \(\chi_{1337}(578,\cdot)\) \(\chi_{1337}(625,\cdot)\) \(\chi_{1337}(709,\cdot)\) \(\chi_{1337}(723,\cdot)\) \(\chi_{1337}(753,\cdot)\) \(\chi_{1337}(800,\cdot)\) \(\chi_{1337}(816,\cdot)\) \(\chi_{1337}(900,\cdot)\) \(\chi_{1337}(914,\cdot)\) \(\chi_{1337}(961,\cdot)\) \(\chi_{1337}(991,\cdot)\) \(\chi_{1337}(1024,\cdot)\) \(\chi_{1337}(1080,\cdot)\) \(\chi_{1337}(1108,\cdot)\) \(\chi_{1337}(1115,\cdot)\) \(\chi_{1337}(1152,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 57 polynomial |
Values on generators
\((192,974)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{1}{19}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 1337 }(816, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{44}{57}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{35}{57}\right)\) | \(e\left(\frac{8}{57}\right)\) | \(e\left(\frac{4}{57}\right)\) |