Basic properties
Modulus: | \(571\) | |
Conductor: | \(571\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(285\) | 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.o
\(\chi_{571}(5,\cdot)\) \(\chi_{571}(9,\cdot)\) \(\chi_{571}(11,\cdot)\) \(\chi_{571}(13,\cdot)\) \(\chi_{571}(14,\cdot)\) \(\chi_{571}(21,\cdot)\) \(\chi_{571}(24,\cdot)\) \(\chi_{571}(25,\cdot)\) \(\chi_{571}(30,\cdot)\) \(\chi_{571}(34,\cdot)\) \(\chi_{571}(37,\cdot)\) \(\chi_{571}(43,\cdot)\) \(\chi_{571}(44,\cdot)\) \(\chi_{571}(45,\cdot)\) \(\chi_{571}(52,\cdot)\) \(\chi_{571}(54,\cdot)\) \(\chi_{571}(57,\cdot)\) \(\chi_{571}(61,\cdot)\) \(\chi_{571}(66,\cdot)\) \(\chi_{571}(70,\cdot)\) \(\chi_{571}(78,\cdot)\) \(\chi_{571}(80,\cdot)\) \(\chi_{571}(81,\cdot)\) \(\chi_{571}(83,\cdot)\) \(\chi_{571}(84,\cdot)\) \(\chi_{571}(92,\cdot)\) \(\chi_{571}(96,\cdot)\) \(\chi_{571}(97,\cdot)\) \(\chi_{571}(100,\cdot)\) \(\chi_{571}(115,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{285})$ |
Fixed field: | Number field defined by a degree 285 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{121}{285}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 571 }(388, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{121}{285}\right)\) | \(e\left(\frac{44}{57}\right)\) | \(e\left(\frac{47}{285}\right)\) | \(e\left(\frac{77}{95}\right)\) | \(e\left(\frac{7}{95}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{242}{285}\right)\) | \(e\left(\frac{157}{285}\right)\) | \(e\left(\frac{223}{285}\right)\) |