Basic properties
Modulus: | \(980\) | |
Conductor: | \(245\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{245}(242,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 980.bv
\(\chi_{980}(37,\cdot)\) \(\chi_{980}(53,\cdot)\) \(\chi_{980}(93,\cdot)\) \(\chi_{980}(137,\cdot)\) \(\chi_{980}(193,\cdot)\) \(\chi_{980}(233,\cdot)\) \(\chi_{980}(277,\cdot)\) \(\chi_{980}(317,\cdot)\) \(\chi_{980}(333,\cdot)\) \(\chi_{980}(417,\cdot)\) \(\chi_{980}(457,\cdot)\) \(\chi_{980}(473,\cdot)\) \(\chi_{980}(513,\cdot)\) \(\chi_{980}(597,\cdot)\) \(\chi_{980}(613,\cdot)\) \(\chi_{980}(653,\cdot)\) \(\chi_{980}(697,\cdot)\) \(\chi_{980}(737,\cdot)\) \(\chi_{980}(793,\cdot)\) \(\chi_{980}(837,\cdot)\) \(\chi_{980}(877,\cdot)\) \(\chi_{980}(893,\cdot)\) \(\chi_{980}(933,\cdot)\) \(\chi_{980}(977,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((491,197,101)\) → \((1,i,e\left(\frac{11}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 980 }(977, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{2}{3}\right)\) |