Basic properties
Modulus: | \(589\) | |
Conductor: | \(589\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(45\) | 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 589.cb
\(\chi_{589}(4,\cdot)\) \(\chi_{589}(16,\cdot)\) \(\chi_{589}(35,\cdot)\) \(\chi_{589}(47,\cdot)\) \(\chi_{589}(66,\cdot)\) \(\chi_{589}(101,\cdot)\) \(\chi_{589}(157,\cdot)\) \(\chi_{589}(188,\cdot)\) \(\chi_{589}(194,\cdot)\) \(\chi_{589}(225,\cdot)\) \(\chi_{589}(233,\cdot)\) \(\chi_{589}(252,\cdot)\) \(\chi_{589}(256,\cdot)\) \(\chi_{589}(264,\cdot)\) \(\chi_{589}(283,\cdot)\) \(\chi_{589}(405,\cdot)\) \(\chi_{589}(442,\cdot)\) \(\chi_{589}(473,\cdot)\) \(\chi_{589}(481,\cdot)\) \(\chi_{589}(498,\cdot)\) \(\chi_{589}(500,\cdot)\) \(\chi_{589}(529,\cdot)\) \(\chi_{589}(560,\cdot)\) \(\chi_{589}(574,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((249,96)\) → \((e\left(\frac{8}{9}\right),e\left(\frac{3}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 589 }(252, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{7}{15}\right)\) |