Basic properties
Modulus: | \(571\) | |
Conductor: | \(571\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(95\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
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.l
\(\chi_{571}(6,\cdot)\) \(\chi_{571}(20,\cdot)\) \(\chi_{571}(23,\cdot)\) \(\chi_{571}(36,\cdot)\) \(\chi_{571}(38,\cdot)\) \(\chi_{571}(49,\cdot)\) \(\chi_{571}(51,\cdot)\) \(\chi_{571}(56,\cdot)\) \(\chi_{571}(65,\cdot)\) \(\chi_{571}(105,\cdot)\) \(\chi_{571}(117,\cdot)\) \(\chi_{571}(120,\cdot)\) \(\chi_{571}(123,\cdot)\) \(\chi_{571}(125,\cdot)\) \(\chi_{571}(138,\cdot)\) \(\chi_{571}(142,\cdot)\) \(\chi_{571}(146,\cdot)\) \(\chi_{571}(148,\cdot)\) \(\chi_{571}(149,\cdot)\) \(\chi_{571}(154,\cdot)\) \(\chi_{571}(158,\cdot)\) \(\chi_{571}(163,\cdot)\) \(\chi_{571}(176,\cdot)\) \(\chi_{571}(179,\cdot)\) \(\chi_{571}(182,\cdot)\) \(\chi_{571}(186,\cdot)\) \(\chi_{571}(189,\cdot)\) \(\chi_{571}(201,\cdot)\) \(\chi_{571}(206,\cdot)\) \(\chi_{571}(208,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{95})$ |
Fixed field: | Number field defined by a degree 95 polynomial |
Values on generators
\(3\) → \(e\left(\frac{69}{95}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 571 }(51, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{19}\right)\) | \(e\left(\frac{69}{95}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{48}{95}\right)\) | \(e\left(\frac{54}{95}\right)\) | \(e\left(\frac{74}{95}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{43}{95}\right)\) | \(e\left(\frac{33}{95}\right)\) | \(e\left(\frac{62}{95}\right)\) |