Basic properties
| Modulus: | \(141120\) | |
| Conductor: | \(35280\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{35280}(34637,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 141120.bqb
\(\chi_{141120}(113,\cdot)\) \(\chi_{141120}(4817,\cdot)\) \(\chi_{141120}(6833,\cdot)\) \(\chi_{141120}(18257,\cdot)\) \(\chi_{141120}(20273,\cdot)\) \(\chi_{141120}(24977,\cdot)\) \(\chi_{141120}(26993,\cdot)\) \(\chi_{141120}(40433,\cdot)\) \(\chi_{141120}(45137,\cdot)\) \(\chi_{141120}(47153,\cdot)\) \(\chi_{141120}(58577,\cdot)\) \(\chi_{141120}(60593,\cdot)\) \(\chi_{141120}(65297,\cdot)\) \(\chi_{141120}(67313,\cdot)\) \(\chi_{141120}(78737,\cdot)\) \(\chi_{141120}(87473,\cdot)\) \(\chi_{141120}(98897,\cdot)\) \(\chi_{141120}(100913,\cdot)\) \(\chi_{141120}(105617,\cdot)\) \(\chi_{141120}(107633,\cdot)\) \(\chi_{141120}(119057,\cdot)\) \(\chi_{141120}(121073,\cdot)\) \(\chi_{141120}(125777,\cdot)\) \(\chi_{141120}(139217,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((48511,44101,78401,112897,89281)\) → \((1,-i,e\left(\frac{5}{6}\right),i,e\left(\frac{1}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 141120 }(78737, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(-i\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{29}{42}\right)\) |