Basic properties
| Modulus: | \(4704\) | |
| Conductor: | \(784\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{784}(613,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4704.en
\(\chi_{4704}(25,\cdot)\) \(\chi_{4704}(121,\cdot)\) \(\chi_{4704}(457,\cdot)\) \(\chi_{4704}(697,\cdot)\) \(\chi_{4704}(793,\cdot)\) \(\chi_{4704}(1033,\cdot)\) \(\chi_{4704}(1129,\cdot)\) \(\chi_{4704}(1369,\cdot)\) \(\chi_{4704}(1465,\cdot)\) \(\chi_{4704}(1705,\cdot)\) \(\chi_{4704}(1801,\cdot)\) \(\chi_{4704}(2041,\cdot)\) \(\chi_{4704}(2377,\cdot)\) \(\chi_{4704}(2473,\cdot)\) \(\chi_{4704}(2809,\cdot)\) \(\chi_{4704}(3049,\cdot)\) \(\chi_{4704}(3145,\cdot)\) \(\chi_{4704}(3385,\cdot)\) \(\chi_{4704}(3481,\cdot)\) \(\chi_{4704}(3721,\cdot)\) \(\chi_{4704}(3817,\cdot)\) \(\chi_{4704}(4057,\cdot)\) \(\chi_{4704}(4153,\cdot)\) \(\chi_{4704}(4393,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,1765,3137,4609)\) → \((1,i,1,e\left(\frac{8}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 4704 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{37}{84}\right)\) |