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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 245.w
\(\chi_{245}(2,\cdot)\) \(\chi_{245}(23,\cdot)\) \(\chi_{245}(32,\cdot)\) \(\chi_{245}(37,\cdot)\) \(\chi_{245}(53,\cdot)\) \(\chi_{245}(58,\cdot)\) \(\chi_{245}(72,\cdot)\) \(\chi_{245}(88,\cdot)\) \(\chi_{245}(93,\cdot)\) \(\chi_{245}(102,\cdot)\) \(\chi_{245}(107,\cdot)\) \(\chi_{245}(123,\cdot)\) \(\chi_{245}(137,\cdot)\) \(\chi_{245}(142,\cdot)\) \(\chi_{245}(158,\cdot)\) \(\chi_{245}(163,\cdot)\) \(\chi_{245}(172,\cdot)\) \(\chi_{245}(193,\cdot)\) \(\chi_{245}(198,\cdot)\) \(\chi_{245}(207,\cdot)\) \(\chi_{245}(212,\cdot)\) \(\chi_{245}(228,\cdot)\) \(\chi_{245}(233,\cdot)\) \(\chi_{245}(242,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((197,101)\) → \((i,e\left(\frac{2}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 245 }(32, a) \) | \(-1\) | \(1\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{19}{21}\right)\) |