Basic properties
| Modulus: | \(7840\) | |
| 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 7840.ho
\(\chi_{7840}(121,\cdot)\) \(\chi_{7840}(681,\cdot)\) \(\chi_{7840}(921,\cdot)\) \(\chi_{7840}(1241,\cdot)\) \(\chi_{7840}(1481,\cdot)\) \(\chi_{7840}(1801,\cdot)\) \(\chi_{7840}(2041,\cdot)\) \(\chi_{7840}(2361,\cdot)\) \(\chi_{7840}(2601,\cdot)\) \(\chi_{7840}(3161,\cdot)\) \(\chi_{7840}(3481,\cdot)\) \(\chi_{7840}(3721,\cdot)\) \(\chi_{7840}(4041,\cdot)\) \(\chi_{7840}(4601,\cdot)\) \(\chi_{7840}(4841,\cdot)\) \(\chi_{7840}(5161,\cdot)\) \(\chi_{7840}(5401,\cdot)\) \(\chi_{7840}(5721,\cdot)\) \(\chi_{7840}(5961,\cdot)\) \(\chi_{7840}(6281,\cdot)\) \(\chi_{7840}(6521,\cdot)\) \(\chi_{7840}(7081,\cdot)\) \(\chi_{7840}(7401,\cdot)\) \(\chi_{7840}(7641,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,4901,3137,3041)\) → \((1,i,1,e\left(\frac{8}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 7840 }(3161, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{2}{3}\right)\) |