Basic properties
Modulus: | \(571\) | |
Conductor: | \(571\) | 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 571.k
\(\chi_{571}(4,\cdot)\) \(\chi_{571}(16,\cdot)\) \(\chi_{571}(29,\cdot)\) \(\chi_{571}(82,\cdot)\) \(\chi_{571}(124,\cdot)\) \(\chi_{571}(143,\cdot)\) \(\chi_{571}(150,\cdot)\) \(\chi_{571}(220,\cdot)\) \(\chi_{571}(231,\cdot)\) \(\chi_{571}(236,\cdot)\) \(\chi_{571}(256,\cdot)\) \(\chi_{571}(258,\cdot)\) \(\chi_{571}(270,\cdot)\) \(\chi_{571}(285,\cdot)\) \(\chi_{571}(309,\cdot)\) \(\chi_{571}(328,\cdot)\) \(\chi_{571}(339,\cdot)\) \(\chi_{571}(362,\cdot)\) \(\chi_{571}(373,\cdot)\) \(\chi_{571}(376,\cdot)\) \(\chi_{571}(383,\cdot)\) \(\chi_{571}(396,\cdot)\) \(\chi_{571}(418,\cdot)\) \(\chi_{571}(436,\cdot)\) \(\chi_{571}(442,\cdot)\) \(\chi_{571}(443,\cdot)\) \(\chi_{571}(453,\cdot)\) \(\chi_{571}(464,\cdot)\) \(\chi_{571}(486,\cdot)\) \(\chi_{571}(496,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 57 polynomial |
Values on generators
\(3\) → \(e\left(\frac{31}{57}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 571 }(285, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{12}{19}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{5}{57}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{43}{57}\right)\) |