Basic properties
Modulus: | \(571\) | |
Conductor: | \(571\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
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.m
\(\chi_{571}(2,\cdot)\) \(\chi_{571}(32,\cdot)\) \(\chi_{571}(41,\cdot)\) \(\chi_{571}(47,\cdot)\) \(\chi_{571}(58,\cdot)\) \(\chi_{571}(62,\cdot)\) \(\chi_{571}(75,\cdot)\) \(\chi_{571}(85,\cdot)\) \(\chi_{571}(107,\cdot)\) \(\chi_{571}(118,\cdot)\) \(\chi_{571}(128,\cdot)\) \(\chi_{571}(129,\cdot)\) \(\chi_{571}(135,\cdot)\) \(\chi_{571}(153,\cdot)\) \(\chi_{571}(175,\cdot)\) \(\chi_{571}(188,\cdot)\) \(\chi_{571}(195,\cdot)\) \(\chi_{571}(198,\cdot)\) \(\chi_{571}(209,\cdot)\) \(\chi_{571}(232,\cdot)\) \(\chi_{571}(243,\cdot)\) \(\chi_{571}(262,\cdot)\) \(\chi_{571}(286,\cdot)\) \(\chi_{571}(301,\cdot)\) \(\chi_{571}(313,\cdot)\) \(\chi_{571}(315,\cdot)\) \(\chi_{571}(335,\cdot)\) \(\chi_{571}(340,\cdot)\) \(\chi_{571}(351,\cdot)\) \(\chi_{571}(421,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{83}{114}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 571 }(153, a) \) | \(-1\) | \(1\) | \(e\left(\frac{91}{114}\right)\) | \(e\left(\frac{83}{114}\right)\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{14}{57}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{7}{38}\right)\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{5}{114}\right)\) | \(e\left(\frac{7}{57}\right)\) |