Basic properties
| Modulus: | \(7840\) | |
| Conductor: | \(1960\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1960}(1797,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7840.hi
\(\chi_{7840}(17,\cdot)\) \(\chi_{7840}(593,\cdot)\) \(\chi_{7840}(817,\cdot)\) \(\chi_{7840}(1137,\cdot)\) \(\chi_{7840}(1713,\cdot)\) \(\chi_{7840}(1937,\cdot)\) \(\chi_{7840}(2033,\cdot)\) \(\chi_{7840}(2257,\cdot)\) \(\chi_{7840}(2833,\cdot)\) \(\chi_{7840}(3153,\cdot)\) \(\chi_{7840}(3377,\cdot)\) \(\chi_{7840}(3953,\cdot)\) \(\chi_{7840}(4177,\cdot)\) \(\chi_{7840}(4273,\cdot)\) \(\chi_{7840}(4497,\cdot)\) \(\chi_{7840}(5073,\cdot)\) \(\chi_{7840}(5297,\cdot)\) \(\chi_{7840}(5393,\cdot)\) \(\chi_{7840}(6417,\cdot)\) \(\chi_{7840}(6513,\cdot)\) \(\chi_{7840}(6737,\cdot)\) \(\chi_{7840}(7313,\cdot)\) \(\chi_{7840}(7537,\cdot)\) \(\chi_{7840}(7633,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,4901,3137,3041)\) → \((1,-1,i,e\left(\frac{41}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 7840 }(817, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{5}{6}\right)\) |