Basic properties
Modulus: | \(287\) | |
Conductor: | \(287\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(120\) | 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 287.bf
\(\chi_{287}(11,\cdot)\) \(\chi_{287}(30,\cdot)\) \(\chi_{287}(53,\cdot)\) \(\chi_{287}(58,\cdot)\) \(\chi_{287}(60,\cdot)\) \(\chi_{287}(65,\cdot)\) \(\chi_{287}(67,\cdot)\) \(\chi_{287}(88,\cdot)\) \(\chi_{287}(93,\cdot)\) \(\chi_{287}(95,\cdot)\) \(\chi_{287}(116,\cdot)\) \(\chi_{287}(130,\cdot)\) \(\chi_{287}(135,\cdot)\) \(\chi_{287}(142,\cdot)\) \(\chi_{287}(149,\cdot)\) \(\chi_{287}(151,\cdot)\) \(\chi_{287}(158,\cdot)\) \(\chi_{287}(170,\cdot)\) \(\chi_{287}(177,\cdot)\) \(\chi_{287}(179,\cdot)\) \(\chi_{287}(186,\cdot)\) \(\chi_{287}(193,\cdot)\) \(\chi_{287}(198,\cdot)\) \(\chi_{287}(212,\cdot)\) \(\chi_{287}(233,\cdot)\) \(\chi_{287}(235,\cdot)\) \(\chi_{287}(240,\cdot)\) \(\chi_{287}(261,\cdot)\) \(\chi_{287}(263,\cdot)\) \(\chi_{287}(268,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((206,211)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{27}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 287 }(135, a) \) | \(-1\) | \(1\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{43}{120}\right)\) | \(e\left(\frac{107}{120}\right)\) |