Basic properties
| Modulus: | \(593\) | |
| Conductor: | \(593\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(37\) | 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 593.f
\(\chi_{593}(16,\cdot)\) \(\chi_{593}(42,\cdot)\) \(\chi_{593}(60,\cdot)\) \(\chi_{593}(62,\cdot)\) \(\chi_{593}(78,\cdot)\) \(\chi_{593}(79,\cdot)\) \(\chi_{593}(92,\cdot)\) \(\chi_{593}(148,\cdot)\) \(\chi_{593}(152,\cdot)\) \(\chi_{593}(154,\cdot)\) \(\chi_{593}(162,\cdot)\) \(\chi_{593}(183,\cdot)\) \(\chi_{593}(220,\cdot)\) \(\chi_{593}(225,\cdot)\) \(\chi_{593}(232,\cdot)\) \(\chi_{593}(256,\cdot)\) \(\chi_{593}(258,\cdot)\) \(\chi_{593}(277,\cdot)\) \(\chi_{593}(281,\cdot)\) \(\chi_{593}(286,\cdot)\) \(\chi_{593}(306,\cdot)\) \(\chi_{593}(311,\cdot)\) \(\chi_{593}(345,\cdot)\) \(\chi_{593}(353,\cdot)\) \(\chi_{593}(367,\cdot)\) \(\chi_{593}(399,\cdot)\) \(\chi_{593}(425,\cdot)\) \(\chi_{593}(454,\cdot)\) \(\chi_{593}(529,\cdot)\) \(\chi_{593}(535,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{37})$ |
| Fixed field: | Number field defined by a degree 37 polynomial |
Values on generators
\(3\) → \(e\left(\frac{35}{37}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 593 }(589, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{37}\right)\) | \(e\left(\frac{35}{37}\right)\) | \(e\left(\frac{27}{37}\right)\) | \(e\left(\frac{3}{37}\right)\) | \(e\left(\frac{30}{37}\right)\) | \(e\left(\frac{26}{37}\right)\) | \(e\left(\frac{22}{37}\right)\) | \(e\left(\frac{33}{37}\right)\) | \(e\left(\frac{35}{37}\right)\) | \(e\left(\frac{11}{37}\right)\) |