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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 287.be
\(\chi_{287}(12,\cdot)\) \(\chi_{287}(17,\cdot)\) \(\chi_{287}(19,\cdot)\) \(\chi_{287}(24,\cdot)\) \(\chi_{287}(26,\cdot)\) \(\chi_{287}(47,\cdot)\) \(\chi_{287}(52,\cdot)\) \(\chi_{287}(54,\cdot)\) \(\chi_{287}(75,\cdot)\) \(\chi_{287}(89,\cdot)\) \(\chi_{287}(94,\cdot)\) \(\chi_{287}(101,\cdot)\) \(\chi_{287}(108,\cdot)\) \(\chi_{287}(110,\cdot)\) \(\chi_{287}(117,\cdot)\) \(\chi_{287}(129,\cdot)\) \(\chi_{287}(136,\cdot)\) \(\chi_{287}(138,\cdot)\) \(\chi_{287}(145,\cdot)\) \(\chi_{287}(152,\cdot)\) \(\chi_{287}(157,\cdot)\) \(\chi_{287}(171,\cdot)\) \(\chi_{287}(192,\cdot)\) \(\chi_{287}(194,\cdot)\) \(\chi_{287}(199,\cdot)\) \(\chi_{287}(220,\cdot)\) \(\chi_{287}(222,\cdot)\) \(\chi_{287}(227,\cdot)\) \(\chi_{287}(229,\cdot)\) \(\chi_{287}(234,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((206,211)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{11}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 287 }(110, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{71}{120}\right)\) |