Basic properties
Modulus: | \(245\) | |
Conductor: | \(245\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | 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 245.x
\(\chi_{245}(3,\cdot)\) \(\chi_{245}(12,\cdot)\) \(\chi_{245}(17,\cdot)\) \(\chi_{245}(33,\cdot)\) \(\chi_{245}(38,\cdot)\) \(\chi_{245}(47,\cdot)\) \(\chi_{245}(52,\cdot)\) \(\chi_{245}(73,\cdot)\) \(\chi_{245}(82,\cdot)\) \(\chi_{245}(87,\cdot)\) \(\chi_{245}(103,\cdot)\) \(\chi_{245}(108,\cdot)\) \(\chi_{245}(122,\cdot)\) \(\chi_{245}(138,\cdot)\) \(\chi_{245}(143,\cdot)\) \(\chi_{245}(152,\cdot)\) \(\chi_{245}(157,\cdot)\) \(\chi_{245}(173,\cdot)\) \(\chi_{245}(187,\cdot)\) \(\chi_{245}(192,\cdot)\) \(\chi_{245}(208,\cdot)\) \(\chi_{245}(213,\cdot)\) \(\chi_{245}(222,\cdot)\) \(\chi_{245}(243,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((197,101)\) → \((-i,e\left(\frac{17}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 245 }(173, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{2}{21}\right)\) |