Basic properties
Modulus: | \(571\) | |
Conductor: | \(571\) | 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 571.p
\(\chi_{571}(3,\cdot)\) \(\chi_{571}(10,\cdot)\) \(\chi_{571}(12,\cdot)\) \(\chi_{571}(17,\cdot)\) \(\chi_{571}(18,\cdot)\) \(\chi_{571}(19,\cdot)\) \(\chi_{571}(28,\cdot)\) \(\chi_{571}(33,\cdot)\) \(\chi_{571}(35,\cdot)\) \(\chi_{571}(39,\cdot)\) \(\chi_{571}(40,\cdot)\) \(\chi_{571}(46,\cdot)\) \(\chi_{571}(53,\cdot)\) \(\chi_{571}(60,\cdot)\) \(\chi_{571}(63,\cdot)\) \(\chi_{571}(67,\cdot)\) \(\chi_{571}(72,\cdot)\) \(\chi_{571}(73,\cdot)\) \(\chi_{571}(74,\cdot)\) \(\chi_{571}(76,\cdot)\) \(\chi_{571}(77,\cdot)\) \(\chi_{571}(79,\cdot)\) \(\chi_{571}(88,\cdot)\) \(\chi_{571}(89,\cdot)\) \(\chi_{571}(91,\cdot)\) \(\chi_{571}(93,\cdot)\) \(\chi_{571}(101,\cdot)\) \(\chi_{571}(102,\cdot)\) \(\chi_{571}(104,\cdot)\) \(\chi_{571}(108,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{285})$ |
Fixed field: | Number field defined by a degree 570 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{253}{570}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 571 }(53, a) \) | \(-1\) | \(1\) | \(e\left(\frac{103}{114}\right)\) | \(e\left(\frac{253}{570}\right)\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{88}{285}\right)\) | \(e\left(\frac{33}{95}\right)\) | \(e\left(\frac{101}{190}\right)\) | \(e\left(\frac{27}{38}\right)\) | \(e\left(\frac{253}{285}\right)\) | \(e\left(\frac{121}{570}\right)\) | \(e\left(\frac{272}{285}\right)\) |