Basic properties
Modulus: | \(571\) | |
Conductor: | \(571\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(190\) | 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.n
\(\chi_{571}(7,\cdot)\) \(\chi_{571}(15,\cdot)\) \(\chi_{571}(22,\cdot)\) \(\chi_{571}(26,\cdot)\) \(\chi_{571}(27,\cdot)\) \(\chi_{571}(42,\cdot)\) \(\chi_{571}(48,\cdot)\) \(\chi_{571}(50,\cdot)\) \(\chi_{571}(68,\cdot)\) \(\chi_{571}(86,\cdot)\) \(\chi_{571}(87,\cdot)\) \(\chi_{571}(95,\cdot)\) \(\chi_{571}(111,\cdot)\) \(\chi_{571}(122,\cdot)\) \(\chi_{571}(132,\cdot)\) \(\chi_{571}(140,\cdot)\) \(\chi_{571}(156,\cdot)\) \(\chi_{571}(160,\cdot)\) \(\chi_{571}(161,\cdot)\) \(\chi_{571}(162,\cdot)\) \(\chi_{571}(166,\cdot)\) \(\chi_{571}(171,\cdot)\) \(\chi_{571}(187,\cdot)\) \(\chi_{571}(194,\cdot)\) \(\chi_{571}(217,\cdot)\) \(\chi_{571}(235,\cdot)\) \(\chi_{571}(241,\cdot)\) \(\chi_{571}(252,\cdot)\) \(\chi_{571}(254,\cdot)\) \(\chi_{571}(266,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{95})$ |
Fixed field: | Number field defined by a degree 190 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{167}{190}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 571 }(122, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{167}{190}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{87}{95}\right)\) | \(e\left(\frac{86}{95}\right)\) | \(e\left(\frac{7}{190}\right)\) | \(e\left(\frac{3}{38}\right)\) | \(e\left(\frac{72}{95}\right)\) | \(e\left(\frac{179}{190}\right)\) | \(e\left(\frac{53}{95}\right)\) |